MATFOR4 Ref Fortran

Reference Guide

MATFOR 4 in Fortran

2 MATFOR 4 in Fortran Reference Guide

Contents

Contents ................................................................................................................................... 2

Introduction ............................................................................................................................ 15

Typographical Conventions ...............................................................................16 Procedure Descriptions Convention ...................................................................17 MATFOR Procedure Naming Convention.........................................................19 MATFOR Parameters.........................................................................................21

Essential Functions ............................................................................................................... 23

mfArray manipulation ........................................................................................25 mfIsEmpty, mfIsLogical, mfIsReal, mfIsComplex, mfIsNumeric ..............26 mf .................................................................................................................28 mfOut ...........................................................................................................30 mfSize, msSize.............................................................................................32 mfNDims......................................................................................................34 mfShape .......................................................................................................36 mfAll, msAll ................................................................................................38 mfAny, msAny.............................................................................................40 mfLength......................................................................................................42

mfArray access ...................................................................................................43 mfMatSub, mfS............................................................................................44

Equivalency ........................................................................................................50 msAssign......................................................................................................51 msPointer .....................................................................................................52 mfEquiv........................................................................................................54

Memory Management ........................................................................................56 msReturnArray.............................................................................................57 msInitArgs, msFreeArgs ..............................................................................59

Table of Contents 3

Display................................................................................................................61 msDisplay ....................................................................................................62 msFormat .....................................................................................................64

FileIO..................................................................................................................65 mfLoad.........................................................................................................66 mfLoad.m.....................................................................................................67 mfLoadAscii ................................................................................................68 mfLoadCsv...................................................................................................70 msSave .........................................................................................................71 mfSave.m .....................................................................................................72 msSaveAscii.................................................................................................73 msSaveCsv...................................................................................................74

Data Manipulation Functions ................................................................................................ 75

Basic ...................................................................................................................76 mfMax, msMax............................................................................................77 mfMin, msMin .............................................................................................79 mfProd, msProd ...........................................................................................81 mfSort, msSort .............................................................................................83 mfSortRows, msSortRows...........................................................................85 mfSum, msSum............................................................................................87

Fast Fourier Transform.......................................................................................89 mfFFT, mfIFFT............................................................................................90 mfFFT2, mfIFFT2........................................................................................92 mfFFTShift, mfIFFTShift ............................................................................94

Cartographic Functions ......................................................................................96 msProj4, msProj4Inv....................................................................................97 msCreateGeoidData ...................................................................................102 msCreateGeoid3Data .................................................................................103 msCreateCoastlineData..............................................................................104 msCreateCoastline3Data............................................................................106


Arithmetic & Relational Operators...................................................................................... 109

Operator Precedence.........................................................................................110 Arithmetic Operators ........................................................................................112 Relational Operators.........................................................................................117

Elementary Math Functions ................................................................................................ 121

Trigonometry....................................................................................................123 mfACos, msACos ......................................................................................124 mfACosh, msACosh ..................................................................................125 mfACot, msACot .......................................................................................126 mfACoth, msACoth ...................................................................................127 mfACsc, msACsc.......................................................................................128 mfACsch, msACsch...................................................................................129 mfASec, msASec .......................................................................................130 mfASech, msASech ...................................................................................131 mfASin, msASin ........................................................................................132 mfASinh, msASinh ....................................................................................134 mfATan, msATan........................................................................................135 mfATan2, msATan2....................................................................................136 mfATanh, msATanh....................................................................................137 mfCos, msCos ............................................................................................138 mfCosh, msCosh........................................................................................139 mfCot, msCot.............................................................................................140 mfCoth, msCoth.........................................................................................141 mfCsc, msCsc ............................................................................................142 mfCsch, msCsch ........................................................................................143 mfSec, msSec.............................................................................................144 mfSech, msSech.........................................................................................145 mfSin, msSin..............................................................................................146 mfSinh, msSinh..........................................................................................147 mfTan, msTan.............................................................................................148 mfTanh, msTanh.........................................................................................149

Exponential.......................................................................................................150 mfExp, msExp............................................................................................151 mfLog, msLog............................................................................................152 mfLog10, msLog10....................................................................................153 mfLog2, msLog2........................................................................................154 mfPow2, msPow2 ......................................................................................156

Table of Contents 5

mfSqrt, msSqrt ...........................................................................................158 Complex ...........................................................................................................159

mfAbs, msAbs............................................................................................160 mfAngle, msAngle.....................................................................................161 mfComplex, msComplex ...........................................................................162 mfConj, msConj.........................................................................................163 mfImag, msImag ........................................................................................164 mfReal, msReal..........................................................................................165

Rounding and Remainder .................................................................................166 mfCeil, msCeil ...........................................................................................167 mfFix, msFix..............................................................................................169 mfFloor, msFloor .......................................................................................171 mfMod, msMod .........................................................................................173 mfRem, msRem .........................................................................................175 mfRound, msRound ...................................................................................177 mfSign, msSign..........................................................................................179

Elementary Matrix-manipulation Functions....................................................................... 181

Matrices ............................................................................................................183 mfEye, msEye ............................................................................................184 mfColon, msColon.....................................................................................185 mfLinspace, msLinspace............................................................................186 mfMagic, msMagic....................................................................................187 mfMeshgrid, msMeshgrid..........................................................................188 mfOnes, msOnes ........................................................................................190 mfRand, msRand........................................................................................191 mfRepmat, msRepmat................................................................................192 mfZeros, msZeros ......................................................................................194

Matrix Manipulation.........................................................................................195 mfDiag, msDiag.........................................................................................196 mfFind, msFind..........................................................................................198 mfLogical, msLogical ................................................................................200 mfReshape, msReshape .............................................................................201 mfTril .........................................................................................................202 mfTriu ........................................................................................................204


Matrix Functions .................................................................................................................. 207

Matrix Analysis ................................................................................................209 mfDet .........................................................................................................210 mfNorm......................................................................................................211 mfRank.......................................................................................................213 mfTrace, msTrace ......................................................................................215

Linear Equations...............................................................................................216 mfChol, msChol.........................................................................................217 mfCond ......................................................................................................219 mfInv..........................................................................................................221 mfRcond.....................................................................................................222 mfLu, msLu................................................................................................223 mfQr, msQr ................................................................................................225 mfMul ........................................................................................................227 mfRDiv, mfLDiv........................................................................................228

Eigenvalues and singular values.......................................................................229 mfEig, msEig .............................................................................................230 mfHess, msHess.........................................................................................232 mfQz, msQz ...............................................................................................234 mfSchur, msSchur......................................................................................236 mfSvd, msSvd............................................................................................238

Factorization Utilities .......................................................................................240 mfBalance, msBalance...............................................................................241

Sparse Array......................................................................................................................... 243

Sparse Array .....................................................................................................245 mfSpCreate ................................................................................................246 msSpAdd....................................................................................................247 msSpSet......................................................................................................249 mfSpGet .....................................................................................................251 mfSpGetM, mfSpGetN ..............................................................................253 mfSpGetNNZ.............................................................................................255 mfSpGetRow, mfSpGetCol........................................................................257 mfSpGetVal................................................................................................259 msSpGetIdx................................................................................................261 msSpDisplay ..............................................................................................263 msSpExport................................................................................................264 mfSpImport ................................................................................................265

Table of Contents 7

mfSpEigs....................................................................................................266 mfSpLDiv ..................................................................................................268 mfSpMul ....................................................................................................270 mfSpSize ....................................................................................................272 mfSpToFull ................................................................................................274 mfFullToSp ................................................................................................276 mfSpy, msSpy ............................................................................................278

MATFOR Visualization Routines......................................................................................... 281

Figure................................................................................................................289 mfFigure, msFigure....................................................................................290 msCloseFigure ...........................................................................................292 mfFigureCount...........................................................................................293

Window Frame .................................................................................................294 mfWindowCaption, msWindowCaption....................................................295 mfWindowSize, msWindowSize ...............................................................296 mfWindowPos, msWindowPos..................................................................297

Display..............................................................................................................298 msGDisplay................................................................................................299 msDrawNow ..............................................................................................300 msViewPause .............................................................................................301

Configuration....................................................................................................302 msSaveConfig ............................................................................................303 msLoadConfig............................................................................................304

Recording .........................................................................................................305 msRecordStart, msRecordEnd ...................................................................306 msExportImage ..........................................................................................310

Plot Creation and Control.................................................................................312 mfSubplot, msSubplot................................................................................313 msClearSubplot..........................................................................................316 msHold.......................................................................................................317 mfIsHold ....................................................................................................319

Plot Annotation and Appearance......................................................................320 mfTitle, mfXLabel, mfYLabel, mfZLabel.................................................321 mfText, msText ..........................................................................................323 mfAnnotation, msAnnotation ....................................................................324 msShading..................................................................................................326 msColorbar.................................................................................................328


msColormap...............................................................................................330 mfColormapRange, msColormapRange ....................................................333 msDrawColormap......................................................................................334 msLegendBox ............................................................................................335 msAddLegend............................................................................................337 msRemoveLegend, msRemoveAllLegend ................................................338 mfBackgroundColor, msBackgroundColor ...............................................339

Axis Control .....................................................................................................340 mfAxis, msAxis .........................................................................................341 msAxis2DMode .........................................................................................346 msAxis3DMode .........................................................................................347 msAxis2DDependency ..............................................................................348 msAxis3DDependency ..............................................................................350 mfAxis2DRange ........................................................................................352 mfAxis3DRange ........................................................................................353 msAxis2DPosition .....................................................................................354 msAxisWall................................................................................................356 msAxisGrid ................................................................................................358

Object Manipulation.........................................................................................360 msObjRotateX, msObjRotateY, msObjRotateZ ........................................361 msObjRotateWXYZ ..................................................................................363 mfObjScale, msObjScale ...........................................................................365 mfObjPosition, msObjPosition ..................................................................367 mfObjOrigin, msObjOrigin........................................................................369 mfObjOrientation, msObjOrientation ........................................................371 mfObjectModel, msObjectModel ..............................................................373

Camera Manipulation .......................................................................................375 msView ......................................................................................................376 mfCamAngle, msCamAngle......................................................................379 mfCamAzElRoll ........................................................................................380 mfCamDistance..........................................................................................381 mfCamProj, msCamProj ............................................................................382 mfCamFocal...............................................................................................383 mfCamZoom, msCamZoom ......................................................................384 mfGetCamViewParam ...............................................................................385 msSetCamViewParam................................................................................386

Linear Graphs ...................................................................................................387 mfPlot, msPlot............................................................................................388

Table of Contents 9

mfPlot3, msPlot3........................................................................................391 mfRibbon, msRibbon.................................................................................393 mfTube, msTube ........................................................................................395 mfStem, msStem ........................................................................................397 mfBar .........................................................................................................400 mfBarh .......................................................................................................403 mfBar3 .......................................................................................................405 mfBar3h .....................................................................................................407

Surface Graphs .................................................................................................409 mfSurf, msSurf...........................................................................................410 mfMesh, msMesh.......................................................................................412 mfSurfc, msSurfc .......................................................................................414 mfMeshc, msMeshc ...................................................................................416 mfPColor, msPColor ..................................................................................418 mfFastPColor, msFastPColor.....................................................................420 mfContour, msContour ..............................................................................422 mfContour3, msContour3 ..........................................................................424 mfSolidContour, msSolidContour .............................................................426 mfSolidContour3, msSolidContour3 .........................................................428 mfOutline, msOutline ................................................................................430 mfIsoSurface, msIsoSurface ......................................................................432 msGetIsoSurface ........................................................................................434

Slice Graphs .....................................................................................................435 mfSliceXYZ, msSliceXYZ........................................................................436 mfSliceIJK, msSliceIJK.............................................................................439 mfSlicePlane, msSlicePlane.......................................................................441 msGetSliceXYZ.........................................................................................444 msGetSlicePlane ........................................................................................445

Streamline Graphs ............................................................................................446 mfStreamLine2, msStreamLine2 ...............................................................447 mfStreamDashedLine2, msStreamDashedLine2 .......................................450 mfStreamRibbon2, msStreamRibbon2 ......................................................452 mfStreamTube2, msStreamTube2..............................................................454 mfStreamArrow2, msStreamArrow2 .........................................................456 mfStreamLine3, msStreamLine3 ...............................................................458 mfStreamDashedLine3, msStreamDashedLine3 .......................................461 mfStreamRibbon3, msStreamRibbon3 ......................................................463 mfStreamTube3, msStreamTube3..............................................................465


mfStreamArrow3, msStreamArrow3 .........................................................467 Triangular Surface Graphs ...............................................................................470

mfTriSurf, msTriSurf .................................................................................471 mfTriMesh, msTriMesh .............................................................................473 mfTriContour, msTriContour.....................................................................475 mfPatch, msPatch.......................................................................................478

Unstructured Grids ...........................................................................................480 mfTetSurf, msTetSurf.................................................................................481 mfTetMesh, msTetMesh.............................................................................484 mfTetContour, msTetContour ....................................................................486 mfTetIsoSurface, msTetIsoSurface ............................................................489 mfTetSliceXYZ, msTetSliceXYZ..............................................................492 mfTetSlicePlane, msTetSlicePlane.............................................................495 msGetTetIsoSurface...................................................................................498 msGetTetSliceXYZ....................................................................................499 msGetTetSlicePlane ...................................................................................500

Unstructured Streamlines .................................................................................501 mfTriStreamLine, msTriStreamLine..........................................................502 mfTriStreamDashLine, msTriStreamDashLine .........................................505 mfTriStreamRibbon, msTriStreamRibbon.................................................507 mfTriStreamTube, msTriStreamTube ........................................................509 mfTriStreamArrow, msTriStreamArrow....................................................511 mfTetStreamLine, msTetStreamLine .........................................................514 mfTetStreamDashLine, msTetStreamDashLine.........................................517 mfTetStreamRibbon, msTetStreamRibbon ................................................519 mfTetStreamTube, msTetStreamTube........................................................521 mfTetStreamArrow, msTetStreamArrow ...................................................523

Unstructured Point Set......................................................................................526 mfPoint, msPoint........................................................................................527 mfDelaunay, msDelaunay, mfGetDelaunay, msGetDelaunay ...................529 mfDelaunay3, msDelaunay3, mfGetDelaunay3, msGetDelaunay3 ..........532

Velocity Vectors...............................................................................................534 mfQuiver, msQuiver ..................................................................................535 mfQuiver3, msQuiver3 ..............................................................................537

Image ................................................................................................................540 mfImage, msImage ....................................................................................541 mfImRead ..................................................................................................543 msImWrite .................................................................................................544

Table of Contents 11

Elementary 2D/3D Objects...............................................................................545 mfCircle, msCircle.....................................................................................546 mfSquare, msSquare ..................................................................................548 mfMolecule, msMolecule ..........................................................................550 mfFastMolecule, msFastMolecule.............................................................554 mfSphere, msSphere ..................................................................................558 mfCube, msCube........................................................................................560 mfCylinder, msCylinder.............................................................................562 mfCone, msCone........................................................................................565 mfAxisMark, msAxisMark ........................................................................567

Property Setting................................................................................................569 msGSet.......................................................................................................570 msDrawMaterial ........................................................................................573 msDrawTexture..........................................................................................576 mfIsValidDraw...........................................................................................578 mfGetCurrentDraw ....................................................................................579 msRemoveDraw.........................................................................................581 msSetDrawName .......................................................................................582

Graphics Viewer Manipulation ........................................................................583 msPrintPreview..........................................................................................584 msEditorDrawList......................................................................................586 msEditorMaterial .......................................................................................587 msEditorColormap.....................................................................................588 msEditorTransform ....................................................................................589 msEditorAxis .............................................................................................590 msEditorColorbar.......................................................................................591 msEditorBackground .................................................................................592

Simple GUI.......................................................................................................593 msShowMessage........................................................................................594 mfInputString.............................................................................................595 mfInputValue..............................................................................................596 mfInputVector ............................................................................................597 mfInputMatrix............................................................................................598 mfFileDialog, mfOpenFileDialog..............................................................600 mfSaveFileDialog ......................................................................................602 mfInputYesNo............................................................................................603


Extensions of MATFOR ....................................................................................................... 605

Tecplot FileIO ..................................................................................................606 mfTecOpenFile, msTecCloseFile...............................................................607 mfTecReadTitle, mfTecWriteTitle .............................................................609 msTecReadVarName, msTecReadBlock....................................................610 mfTecReadVarCount, mfTecReadBlockCount ..........................................613 msTecWriteVarNames................................................................................614 msTecWriteIJKBlock, msTecWriteTriBlock, msTecWriteTetBlock .........615

MATLAB Interface ..........................................................................................618 mfDoMATLAB, msDoMATLAB..............................................................619 mfMATLABServer, msMATLABServer...................................................621

MATFOR GUI System........................................................................................................... 623

Initialization......................................................................................................624 msUIInitialize ............................................................................................625 msUIMainLoop..........................................................................................626

Property Setting................................................................................................627 mfUIGetPropertyString..............................................................................628 msUISetPropertyString ..............................................................................629 mfUIGetPropertyInteger ............................................................................630 msUISetPropertyInteger ............................................................................631 mfUIGetPropertyDouble............................................................................632 msUISetPropertyDouble ............................................................................633

Callback Setting................................................................................................634 msUISetOnClick ........................................................................................635 msUISetOnDoubleClick ............................................................................636 msUISetOnTabChanged ............................................................................637 msUISetOnResize ......................................................................................638 msUISetOnTextChanged ...........................................................................639 msUISetOnReturnPressed..........................................................................640 msUISetOnValueChanged .........................................................................641 msUISetOnScrollReleased.........................................................................642

UI Components.................................................................................................643 MainForm ..................................................................................................644 MenuItem...................................................................................................645 MatforWindow...........................................................................................646 TabControl .................................................................................................647 Panel...........................................................................................................649

Table of Contents 13

Button.........................................................................................................651 Label ..........................................................................................................653 RadioButton ...............................................................................................655 CheckBox...................................................................................................656 Edit.............................................................................................................658 SpinEdit......................................................................................................659 ListBox.......................................................................................................661 ComboBox .................................................................................................663 Slider ..........................................................................................................665 ScrollBar ....................................................................................................667 ProgressBar ................................................................................................669 Image..........................................................................................................671 Memo .........................................................................................................673

Index...................................................................................................................................... 675


Chapter 1 Introduction 15

C H A P T E R 1

Introduction MATFOR has two main documentations: namely the MATFOR User’s Guide, and the MATFOR Reference Guide.

MATFOR User’s Guide provides an overview on MATFOR concepts such as an

introduction to the mfArray with a focus on its structures and syntax, an introduction to using linear algebra, and a quick overview on graphical procedures.

MATFOR Reference Guide provides a detailed description of the procedures available in

MATFOR. The descriptions include information such as what modules do, procedure syntax, and input & output data types. Examples are included for most procedures. The Reference Guide is frequently updated. Please download the latest copy from the MATFOR web page.

This reference guide was written for users who have some background knowledge in programming with Fortran. For more information on Fortran, please refer to your compiler's documentation.


Typographical Conventions

Before you start using this guide, it is important to understand the terms and typographical conventions used in the documentation.

The following kinds of formatting in the text identify special information.

Formatting Convention Type of Information

Special Bold Used to emphasize the importance of a point or a title.

Emphasis and codes Represent variable expressions such as parameters, procedures and example codes.


Procedure Descriptions Convention

The descriptions of MATFOR procedures follow a fixed format. The general format is listed and described below.

Procedure Name

<Summary of procedure>

Module

<This section describes the modules to be included in order to use the procedure.>

e.g. use fml

Syntax

<This section describes most commonly used formats of the procedure. Generally, MATFOR procedures accept mfArrays as input and output arguments. If an argument type is not specified, it is an mfArray. Wherever it is convenient, other data types are supported as input arguments and are noted in this section.

For example:

call msAxis('on') supports a string data type containing 'on' as input. The input could also be an mfArray containing the string 'on'.>

Descriptions

<This section provides more detailed descriptions of the argument type and application of the procedures.>


Example

<This section usually presents a piece of code that uses the current procedure and the result of the program.>

See Also

<This section suggests a list of related procedures.>


MATFOR Procedure Naming Convention

MATFOR procedures are provided in function formats and subroutine formats. Two types of prefixes classify MATFOR procedures: procedures with an “mf” prefix, and procedures with an “ms” prefix. Standard MATFOR function format procedures have the prefix “mf”, and subroutine format procedures have the prefix “ms”. By default, MATFOR procedures use mfArrays as input and output arguments.

Procedures with an “mf” prefix

Most MATFOR procedures that return a single argument as output are prefixed with “mf”. These procedures have a function format of the form:

out = mfProcedure([mfArray, …]),

where out is the output argument and [mfArray, …] is the input argument. For example, y = mfSin(x), l = mfIsEmpty(a).

Functions that return only mfArray as the output argument will also have a corresponding subroutine of the format:

call msProcedure(mfOut(y, …), x, …),

where x and y are mfArrays. y is output, and x is input.

For example, procedure y = mfSin(x) computes sin(x) and


returns the result in mfArray y. It has a corresponding subroutine counterpart using the same input and output arguments with the format:

call msSin(mfOut(y), x)

Procedures with an “ms” prefix

Procedures prefixed with "ms" are subroutines. There are three types of subroutine formats — subroutines that do not return a value, subroutines that return a single output, and subroutines that accept multiple input and output arguments. Function mfOut is used to specify the output arguments.

The subroutines have the following general format:

call msSubroutine(mfOut([mfArray]out1,…),

[mfArray]in1,…),

where [mfArray]out1,… is the list of output arguments and [mfArray]in1,… is the list of input arguments. The input and output arguments are optional.

Examples:

call msViewPause()

call msSurf(x, y, z)

call msSubplot(2, 2, 1)

call msCos(mfOut(y), x)

call msLU(mfOut(l, u), a)

call msMeshgrid(mfOut(a, b), m, n)


MATFOR Parameters

The table below lists the MATFOR parameters provided for your convenience. Parameters mf() and MF_COL are mfArrays, while the rest of the parameters are double precision data.

Parameter Data Type Descriptions

mf() mfArray Null mfArray

MF_COL mfArray Colon ‘:’ operator

MF_I Complex(8) (0.0, 1.0)

MF_PI Real(8) π

MF_EPS Real(8) Smallest positive number.

MF_INF Real(8) Positive infinity number.

MF_NAN Real(8) Not a number.

MF_E Real(8) Natural logarithm number.

MF_REALMAX Real(8) Largest representable number.

MF_REALMIN Real(8) Smallest representable number.


Chapter 2 Essential Functions 23

C H A P T E R 2

Essential Functions This chapter introduces the essential set of MATFOR routines. The procedures are listed below:

mfArray Manipulation

mfIsEmpty Return true if mfArray is empty.

mfIsNumeric Return true if mfArray is numerical.

mfIsReal Return true if mfArray is real.

mfIsComplex Return true if mfArray is complex.

mfIsLogical Return true if mfArray is logical.

mf Convert Fortran variable to mfArray.

mfOut Specify a list of mfArrays as output of a procedure.

mfSize Return the total number of elements in an mfArray.

mfNDims Return the number of dimensions of an mfArray.

mfShape Return the number of elements in each dimension of an mfArray.

mfAll Determination of all elements.

mfAny Determination of any element.

mfLength Retrieve the number of elements of the largest extent of an mfArray.

Equivalency

msAssign Assign variable to mfArray.

msPointer Assign mfArray target to Fortran pointer.

mfEquiv Share memory storage between an mfArray and a Fortran variable.


Memory Management

msReturnArray Set status flag of mfArray to temporary.

msInitArgs Reserve mfArray for computation within procedures.

msFreeArgs Free mfArray for internal housekeeping.

Display

msDisplay Display mfArray data on a console window.

msFormat Specify displaying format of mfArray.

FileIO

mfLoad Load binary file into mfArray.

mfLoad.m Load MATFOR binary file into MATLAB workspace.

mfLoadAscii Load ASCII file into mfArray.

mfLoadCsv Load a CSV file into mfArray.

msSave Save mfArray as binary file.

msSave.m Save MATLAB matrix into a MATFOR binary file.

msSaveAscii Save mfArray as ASCII file.

msSaveCsv Save mfArray into a CSV file.


mfArray manipulation


mfIsEmpty, mfIsLogical, mfIsReal, mfIsComplex,

mfIsNumeric Return logical true or false for mfArray inquiry.

Module fml

Syntax l = mfIsEmpty(a) l = mfIsLogical(a) l = mfIsReal(a) l = mfIsComplex(a) l = mfIsNumeric(a) Descriptions Functions mfIsEmpty, mfIsLogical, mfIsReal, mfIsComplex, and mfIsNumeric are a set of mfArray inquiry functions. These functions compare mfArrays or inquire the status of an mfArray and return a logical true or false. They can be directly applied in a control if there is a statement. For example, if (mfIsEmpty(a))... h = mfIsEmpty(a) returns a logical true if mfArray a is empty, i.e. null, and logical

false otherwise.

h = mfIsLogical(a) returns a logical true if mfArray a is logical and logical false

otherwise.

h = mfIsReal(a) returns a logical true if mfArray a is real and logical false otherwise.

h = mfIsComplex(a) returns a logical true if mfArray a is complex and logical false

otherwise.

h = mfIsNumeric(a) returns a logical true if mfArray a is numeric and logical false

otherwise.

Example Code pr ogram example

use fml implicit none ty pe (mfArray):: a, b, c, d, e

! Construct an empty mfArray.


a = mf()

!Writes a output message if a is empty. if (mfIsEmpty(a)) write (*,*) 'a is empty'

! Construct three numerical mfArrays. b = 5.2 c = 5.2 d = (2, 2)

!Writes output message if b is real, b and c are equal, or d is !numeric or complex if (mfIsReal(b)) write (*,*) 'b is real' if (mfIsNumeric(c)) write (*,*) 'c is numeric' if (mfIsComplex(d)) write (*,*) 'd is complex'

! Construct a logical mfArray. e = mfMagic(3) > 5

!Writes output message if e is logical. if (mfIsLogical(e)) write (*,*) 'e is logical'

!Deallocate mfArrays. ca ll msFreeArgs(a, b, c, d, e)

e nd program example

Result a is empty b is real c is numeric d is complex e is logical

See Also


mf Convert Fortran data to mfArray.

Module fml

Syntax a = mf([b]) Descriptions Procedure mf converts Fortran data types into mfArrays. This is useful in procedure calls where MATFOR restricts the input argument to mfArray type. a = mf()

Return an empty mfArray.

a = mf(b)

Convert type real(8), complex(8), integer or character strings argument b into an mfArray and

return the resulting mfArray to argument a.


use fml im plicit none

type (mfArray) :: lt re al(8) :: A(3,3)

! Initialize A by using the random_number ! procedure provided by Fortran. ca ll random_number(A)

! Display the content of A by using MATFOR ! display() procedure. ca ll msDisplay(mf(A), 'A')

! Extract the lower triangular of A by ! using the mfTril() procedure provided by ! MATFOR. Enclose A using mf(). lt = mfTril(mf(A))

call msDisplay(lt, 'Lower Triangular of A') ca ll msFreeArgs(lt)


Result A =


0.0000 0.6669 0.3354 0.0255 0.9631 0.9153 0.3525 0.8383 0.7959 Lower Triangular of A = 0.0000 0.0000 0.0000 0.0255 0.9631 0.0000 0.3525 0.8383 0.7959

See Also


mfOut Specify a list of mfArrays as output of a function.

Module fml

Syntax mfOut(a, b, c, ...) Descriptions Procedure msOut specifies a list of mfArrays as the output of a subroutine. It differentiates the output arguments from the input arguments in a procedure call. Note that procedure mfOut encloses only mfArrays. For example, you can use function msFind to retrieve the row indices, column indices, and non-zero values of an mfArray as shown below: mfFind(mfOut(i, j, v), x)

The procedure returns three mfArrays in this usage. To get the three mfArrays i, j, and v, you

must enclose them with mfOut in your procedure call. This automatically triggers procedure

msFind to return the specified mfArrays.


use fml

implicit none

type(mfArray) :: a, i, j

! Construct a 3-by-3 random mfArray

a = mfRand(3)

! Find the element which is grater than 0.5 in mfArray a and ! output its index vector call msFind(mfOut(i, j), a > 0.5d0) call msDisplay(a, "a", i, "i", j, "j") e nd program

Result a = 0.9997 0.3917 0.6628 0.8225 0.7557 0.7853 0.4772 0.1380 0.5110 i =

1


2 2 1 2 3

j =

1 1 2 3 3 3

See Also


mfSize, msSize Return total number of elements in an mfArray.

Module fml

Syntax s = mfSize(a) b = mfSize(a, IDIM) call msSize(mfOut(m1, m2, ..., mn), a) Descriptions Procedure mfSize returns the total number of elements in an mfArray. s = mfSize(a) returns the number of elements in a.

b = mfSize(a, IDIM) returns the length of the dimension specified by scalar IDIM.

call msSize(mfOut(m1, m2, ..., mn), a) returns the lengths of the first n

dimensions of a.



type (mfArray) :: a in teger :: s

a = mfRand(4,3)

s = mfSize(a) call msDisplay(a, 'mfRand(4,3)', mf(s), 'mfSize(a)') s = mfSize(a, 1) ca ll msDisplay(mf(s), 'mfSize(a, 1)')

s = mfSize(a, 2) ca ll msDisplay(mf(s), 'mfSize(a, 2)')

ca ll msFreeArgs(a)


Result mf Rand(4,3) =


0.7620 0.6455 0.6531 0.7638 0.2717 0.7014 0.0894 0.9876 0.4027 0.3090 0.3181 0.6760 m fSize(a) =

12

m fSize(a, 1) =

4

m fSize(a, 2) =

3

See Also mfNDims, mfLength


mfNDims Return number of dimensions of an mfArray.

Module fml

Syntax r = mfNDims(a) Descriptions Procedure mfNDims returns the number of dimensions of an mfArray. Each mfArray has a minimum value of 2. (i.e. scalar, vector and matrix mfArrays have mfNDims = 2) Example Code pr ogram example


type (mfArray) :: a, b in teger :: c

! Scalar a = 3 b = mfNDims(a) ca ll msDisplay(b, 'Scalar mfArray has mfNDims')

! Vector a = (/1, 2, 3/) write(*,*) 'Vector mfArray has mfNDims =' wr ite(*,'(/,I3,/)') mfNDims(a)

! Matrix a = mfMagic(3) b = mfNDims(a) ca ll msDisplay(b, 'Matrix mfArray has mfNDims')

! Three-dimensional mfArray a = mfReshape(mfColon(1,8), (/2,2,2/)) b = mfNDims(a) ca ll msDisplay(b, 'Three-dimensional mfArray has mfNDims')

! Deallocates mfArray ca ll msFreeArgs(a, b)


Result Scalar mfArray has mfNDims = 2 Vector mfArray has mfNDims = 2 Matrix mfArray has mfNDims = 2 Three-dimensional mfArray has mfNDims = 3


See Also mfSize, mfLength


mfShape Return number of elements in each dimension of an mfArray.

Module fml

Syntax s = mfShape(x) Descriptions s = mfShape(x) • Procedure mfShape returns an integer array whose size is equal to the dimension of the

mfArray. • s is an integer vector, while argument x is an mfArray.

• Note that scalars, vectors and matrix mfArrays have a rank of 2. Example Code pr ogram example


ty pe(mfArray) :: x, s

! Scalar mfArray x = 2 s = mfShape(x) ca ll msDisplay( x, 'x', s, 'mfShape(x)')

! Vector mfArray x = (/2, 3/) s = mfShape(x) ca ll msDisplay( x, 'x', s, 'mfShape(x)')

! Matrix mfArray x = mfMagic(2) s = mfShape(x) ca ll msDisplay( x, 'x', s, 'mfShpae(x)')

! Three-dimensional mfArray x = mfRand(2, 2, 2) s = mfShape(x) ca ll msDisplay( x, 'x', s, 'mfShape(x)')

! Deallocate mfArray ca ll msFreeArgs(x, s)


Result


x =

2

S hape(x) =

1 1

x =

2 3

S hape(x) =

1 2

x =

1 3 4 2

S hape(x) =

2 2

x (:,:,1) = 0.0341 0.7507 0.8502 0.1210 x (:,:,2) = 0.2173 0.2558 0.4833 0.7332 S hape(x) =

2 2 2

See Also mfReshape


mfAll, msAll Return logical true if all elements of mfArray are nonzero.

Module fml

Syntax l = mfAll(a[, IDIM]) Descriptions Function mfAll determines if all elements of an mfArray are non-zero. l = mfAll(x)

• l is a logical mfArray, containing logical element(s).

• If x is a vector, mfAll returns a scalar containing logical 1 if all elements of x are non-zero, and logical 0 otherwise.

• If x is a matrix, mfAll is applied to each column of x, returning a row vector containing 0's or 1's.

l = mfAll(x, IDIM) operates on the dimension of x specified by IDIM.



type(mfArray) :: x, y, z lo gical :: b

x = mfMagic(3)

! Check if all elements of x are greater than 2. b = mfAll(x>2)

y = mfAll(x>2, 1)

z = mfAll(x>2, 2) call msDisplay(mf(b), 'mfAll(x > 2)', y, 'mfAll(x>2, 1)', z, 'mfAll(x>2, ') 2)

! Deallocates mfArrays ca ll msFreeArgs(x, y, z)



Result mf All(x > 2) =

0

m fAll(x, 1) =

1 0 0

m fAll(x, 2) =

0 1 0

See Also mfAny


mfAny, msAny Return logical true if any element of mfArray is nonzero.

Module fml

Syntax l = mfAny(x[, IDIM]) Descriptions Function mfAny determines if any element of an mfArray is nonzero. l = mfAny(x)

• l is a logical mfArray, containing logical elements.

• If x is a vector, mfAny returns a scalar containing logical 1 if any element of x is nonzero, and logical 0 otherwise.

• If x is a matrix, mfAny is applied to each column of x, returning a row vector containing 0's and 1's.

l = mfAny(x, IDIM) operates on the dimension of x specified by IDIM.



ty pe(mfArray) :: x, y, b

x = mfMagic(3)

! Check if any element of x is more than 5. b = mfAny(x>7) ca ll msDisplay(x, 'x', b, 'mfAny(x > 7)')

y = mfAny(x>7, 1) call msDisplay(y, 'mfAny(x>7, 1)') y = mfAny(x>7, 2) ca ll msDisplay(y, 'mfAny(x>7, 2)')

! Deallocates mfArrays ca ll msFreeArgs(x, y)


Result x =


8 1 6 3 5 7 4 9 2

m fAny(x > 7) =

1

m fAny(x>7, 1) =

1 1 0

m fAny(x>7, 2) =

1 0 1

See Also mfAll


mfLength Retrieve number of elements of the largest extent of an mfArray.

Module fml

Syntax l = mfLength(a) Descriptions Procedure mfLength returns the largest extent of an mfArray. l = mfLength(a) returns an integer scalar containing the largest extent of mfArray a. If a is

matrix, mfLength(a)returns mfMax(mfShape(a)).



type (mfArray) :: a in teger :: l

a = mfOnes(2, 5) l = mfLength(a) ca ll msDisplay(a, 'a', mf(l), 'mfLength(a)')

ca ll msFreeArgs(a)


Result a =

1 1 1 1 1 1 1 1 1 1

m fLength(a) =

5

See Also mfSize, mfNDims


mfArray access


mfMatSub, mfS Retrieve rows and columns of elements from vector or matrix mfArray.

Module fml

Syntax sub_Array = mfMatSub(A, row, column) Descriptions Procedure mfMatSub retrieves elements from an mfArray. The arguments (except the first one) specify the subscripts of the elements Notice that MATFOR also provides the abbreviated name mfS for this procedure. For example, if A is a vector mfArray, mfMatSub(A, 1.to.100.step.2)would return a vector containing the 1st, 3rd, 5th, ..., and 99th elements of A. Example Code pr ogram example


type (mfArray) :: x, y, z in teger :: i

x = reshape((/(i, i= 1, 24)/), (/2, 3, 4/)) ca ll msDisplay(x, 'x')

! Get x <= 12 y = mfS(x, x <= 12) ca ll msDisplay(y, 'mfS(x, x <= 12)')

! y = x(1:24) using 1x24 replace 2x3x4 y = mfS(x, 1.to.24) ca ll msDisplay(y, 'mfS(x, 1.to.24)')

! y = x(1:2, 1:12) using 2x12 replace 2x3x4 y = mfS(x, 1.to.2, 1.to.12) ca ll msDisplay(y, 'mfS(x, 1.to.2, 1.to.12)')

! y = x(1:2, 1:12:3) y = mfS(x, 1.to.2, 1.to.12.step.3) ca ll msDisplay(y, 'mfS(x, 1.to.2, 1.to.12.step.3)')

! y = x(24:1) y = mfS(x, MF_COL) ca ll msDisplay(y, 'mfS(x, MF_COL)')

! y = x(1, 2, 3) y = mfS(x, 1, 2, 3)


ca ll msDisplay(y, 'mfS(x, 1, 2, 3)')

! Get element using arbitrary index y = mfS(x, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/))) ca ll msDisplay(y, 'mfS(x, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/)))')

! Set element in y which <= 12 and >= 6 to 0 y = x !call msAssign(mfS(y, y <= 12 .and. y >= 6 ), 0) call msAssign(mfS(y, mfAND(y <= 12,y >= 6) ), 0) ca ll msDisplay(y, 'msAssign(mfS(y, y <= 12 .and. y >= 6), 0)')

! y(1:24) = 0 using 1x24 replace 2x3x4 y = x call msAssign(mfS(y, 1.to.24), 0) ca ll msDisplay(y, 'msAssign(mfS(y, 1.to.24), 0)')

! y(1:2, 1:12) = 0 using 1x24 replace 2x3x4 y = x call msAssign(mfS(y, 1.to.2, 1.to.12), 0) ca ll msDisplay(y, 'msAssign(mfS(y, 1.to.2, 1.to.12), 0)')

! y(1:2, 1:12:3) = 0 using 1x24 replace 2x3x4 y = x call msAssign(mfS(y, 1.to.2, 1.to.12.step.3), 0) ca ll msDisplay(y, 'msAssign(mfS(y, 1.to.2, 1.to.12.step.3), 0)')

! y(1:2, 1:3:2, 1:4:3) = reshape((/(i, i = 31, 38)/), (/2, 2, 2/)) y = x z = reshape((/(i, i = 31, 38)/), (/2, 2, 2/)) call msAssign(mfS(y, 1.to.2, 1.to.3.step.2, 1.to.4.step.3), z) call msDisplay(y, 'msAssign(mfS(y, 1.to.2, 1.to.3.step.2, 1.to.4.step.3), ') z)

! y(24:1) = .t.(/(i, i= 25, 48)/) y = x call msAssign(mfS(y, MF_COL), .t.(/(i, i= 25, 48)/)) ca ll msDisplay(y, 'msAssign(mfS(y, MF_COL), .t.(/(i, i= 25, 48)/))')

! y(1, 2, 3) = 60 y = x call msAssign(mfS(y, 1, 2, 3), 60) ca ll msDisplay(y, 'msAssign(mfS(y, 1, 2, 3), 60)')

! Set element using arbitrary index y = x z = reshape((/(i, i = 101, 112)/), (/2, 2, 3/)) call msAssign(mfS(y, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/))), z) call msDisplay(y, 'msAssign(mfS(y, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 3/))), z)') 1,

ca ll msFreeArgs(x, y)


Result x( :,:,1) =

1 3 5 2 4 6

x (:,:,2) =

7 9 11 8 10 12

x (:,:,3) =

13 15 17 14 16 18


x (:,:,4) =

19 21 23 20 22 24

m fS(x, x <= 12) =

1 2 3 4 5 6 7 8 9 10 11 12

m fS(x, 1.to.24) =

column 1 to 19 ... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

column 20 to 24 20 21 22 23 24

m fS(x, 1.to.2, 1.to.12) =

1 3 5 7 9 11 13 15 17 19 21 23 2 4 6 8 10 12 14 16 18 20 22 24

m fS(x, 1.to.2, 1.to.12.step.3) =

1 7 13 19 2 8 14 20

m fS(x, MF_COL) =

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

m fS(x, 1, 2, 3) =

15

m fS(x, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/)))(:,:,1) =

24 20


23 19

m fS(x, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/)))(:,:,2) =

6 2 5 1

m fS(x, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/)))(:,:,3) =

18 14 17 13

m sAssign(mfS(y, y <= 12 .and. y >= 6), 0)(:,:,1) =

1 3 5 2 4 0


0 0 0 0 0 0


13 15 17 14 16 18


19 21 23 20 22 24

m sAssign(mfS(y, 1.to.24), 0)(:,:,1) =

0 3 5 2 4 6

m sAssign(mfS(y, 1.to.24), 0)(:,:,2) =

7 9 11 8 10 12

m sAssign(mfS(y, 1.to.24), 0)(:,:,3) =

13 15 17 14 16 18

m sAssign(mfS(y, 1.to.24), 0)(:,:,4) =

19 21 23 20 22 24

m sAssign(mfS(y, 1.to.2, 1.to.12), 0)(:,:,1) =

0 0 0 0 0 0


0 0 0 0 0 0


0 0 0 0 0 0


0 0 0 0 0 0

m sAssign(mfS(y, 1.to.2, 1.to.12.step.3), 0)(:,:,1) =

0 3 5


0 4 6


0 9 11 0 10 12


0 15 17 0 16 18


0 21 23 0 22 24

m sAssign(mfS(y, 1.to.2, 1.to.3.step.2, 1.to.4.step.3), z)(:,:,1) =

31 3 33 32 4 34


7 9 11 8 10 12


13 15 17 14 16 18


35 21 37 36 22 38

m sAssign(mfS(y, MF_COL), .t.(/(i, i= 25, 48)/))(:,:,1) =

25 27 29 26 28 30


31 33 35 32 34 36


37 39 41 38 40 42


43 45 47 44 46 48

m sAssign(mfS(y, 1, 2, 3), 60)(:,:,1) =

1 3 5 2 4 6

m sAssign(mfS(y, 1, 2, 3), 60)(:,:,2) =

7 9 11 8 10 12

m sAssign(mfS(y, 1, 2, 3), 60)(:,:,3) =

13 60 17 14 16 18

m sAssign(mfS(y, 1, 2, 3), 60)(:,:,4) =

19 21 23


20 22 24

msAssign(mfS(y, mf((/2, 1/)), mf((/3, 1/)), mf((/4, 1, 3/))), z)(:,:,1) = 108 3 106 107 4 105




See Also


Equivalency


msAssign Assign the values of an mfArray to another.

Module fml

Syntax call msAssign(a, b) Descriptions ProceduremsAssign(a, b)assigns the values of mfArray b to mfArray a. This is equivalent to the statement a = b. Note that when you assign one mfArray to another mfArray, there is no memory copying involved. However, when you assign an mfArray to a Fortran data type, the Fortran compiler accomplishes the task by creating a temporary storage space in the stack memory. When the array size involved is large, stack overflow may occur. To avoid large data, it is advisable to use msAssign(a, F)or a = mf(F)instead of a = F. Example Code pr ogram example


type (mfArray) :: a,b re al(8) :: F(2,5)

call random_number(F) call msAssign(a, F) !Avoids stack memory copy. call msAssign(b,a) ca ll msDisplay(a, 'a',b,'b')

!Deallocate mfArray ca ll msFreeArgs(a)


Result a =

0.0000 0.3525 0.9631 0.3354 0.7959 0.0255 0.6669 0.8383 0.9153 0.8327 b =

0.0000 0.3525 0.9631 0.3354 0.7959 0.0255 0.6669 0.8383 0.9153 0.8327

See Also Shape, Size, mfSize


msPointer Assign pointer to mfArray.

Module fml

Syntax call msPointer(a, P) a : mfArray P : real(8) or complex(8) pointer Descriptions Procedure msPointer assigns a real(8) or complex(8) pointer to a target mfArray. call msPointer(a, P)

• Procedure msPointer associates pointer P and mfArray a, i.e the memory space occupied by mfArray a becomes the target of pointer P. Pointer P automatically assumes the shape of mfArray a.

Warning: Deallocating pointer P would lead to exception error. Example Code pr ogram example


type (mfArray) :: a, z real(8), pointer :: pd(:,:) co mplex(8), pointer :: pz(:,:)

a = mfOnes(3, 3) z = mfComplex(a, a)

ca ll msDisplay(a, 'a')

! pd targets a ca ll msPointer(a, pd)

! a(3, 3) has been set to 5.0. pd(3, 3) = 5.0 ca ll msDisplay(a, 'a')

ca ll msDisplay(z, 'z')

! pz targets z ca ll msPointer(z, pz)


! z(3, 3) has been set to 5.0+5.0i pz(3, 3) = cmplx(5.0, 5.0) ca ll msDisplay(z, 'z')

!Deallocate mfArray ca ll msFreeArgs(a, z)


Result a =

1 1 1 1 1 1 1 1 1

a =

1 1 1 1 1 1 1 1 5

z = 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i z = 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 1.0000 +1.0000i 5.0000 +5.0000i

See Also mfEquiv


mfEquiv Share memory storage between an mfArray and a Fortran variable.

Module fml

Syntax a = mfEquiv(T) a = mfEquiv(Z) a : mfArray T : real(8) array or scalar Z : complex(8) array or scalar Descriptions Procedure mfEquiv is provided for sharing memory storage between a Fortran variable and an mfArray. a = mfEquiv(T)

• Procedure mfEquiv returns a restricted mfArray a which shares the same memory location as Fortran variable T.

• Variable T can be 1) real(8) array or scalar or 2) complex(8) array or scalar. • Use mfEquiv when you have an existing Fortran array. The Fortran variable must not be

a temporary variable. It must be explicitly declared. The following operation is invalid: a = mfEquiv(dble(A)) ! dble(A) returns a temporary variable. Restrictions:

MATFOR enforces a few restrictions on the operations of an mfArray when it is constructed by

using procedure mfEquiv.

• Procedure msFreeArgs releases and disassociates the restricted mfArray from the Fortran variable but does not deallocate the memory space occupied by the Fortran variable.

• Operations that change the shape, data type or rank of the restricted mfArray are invalid. • The restricted mfArray cannot be used as a returned argument in procedures (functions

and subroutines). e.g. function(A, B) result (out) real (8) :: A(3,4) out = mfEquiv(A) ! This is illegal, out will be null.


• Deallocating the associated Fortran array invalids the mfArray. Example Code pr ogram example


type (mfArray) :: t real(8) :: A(3,3) in teger :: i

A = dble(ReShape( (/(i,i=1,9)/), (/3,3/)) ) t = mfEquiv(A) call msDisplay(t, 't') ca ll msDisplay(mf(A), 'A')

A = A - 1 call msDisplay(t, 't') ca ll msDisplay(mf(A), 'A')

! If you use the msFreeArgs routine on t, ! t is Deallocated, but A is still valid and usable. call msFreeArgs(t) ca ll msDisplay(mf(A), 'A')


Result t =

1 4 7 2 5 8 3 6 9

A =

1 4 7 2 5 8 3 6 9

t =

0 3 6 1 4 7 2 5 8

A =

0 3 6 1 4 7 2 5 8

A =

0 3 6 1 4 7 2 5 8

See Also msPointer


Memory Management


msReturnArray Set status flag of mfArray to temporary.

Module fml

Syntax call msReturnArray(a) Descriptions Procedure msReturnArray(a)sets the status flag of an mfArray to temporary. This procedure should be added to the end of functions that use mfArrays to return values. It ensures that temporary mfArrays created by functions or subroutines are deallocated, preventing memory leakage. For example, when you develop a function foo that returns mfArray t as below, it is recommended to add the statement call msReturnArray(t)at the end of the function: function foo(A) return (t) implicit none integer :: A type (mfArray) :: t ! program codes ------------------- ------------------- call msReturnArray(t) return end function foo

The statement sets the status property of the mfArray to temporary. MATFOR releases such

temporary mfArrays automatically.

More Details:

The mfArray is a dynamically allocated data object. It is good practice in Fortran to release

dynamically allocated memory space once you no longer need it. Due to the above principle, you

should clear all temporary mfArrays to prevent memory leakage.

A function developed for end-users in Fortran can be used in many possible ways. For example, a

user could write a = foo(x)or they may use it as an input to another function, as in b = gee(foo(x)).

In the second case, the function foo returns a temporary data object. When the returned data

object is an mfArray, it should be released from memory to prevent memory leakage. MATFOR

procedures release such temporary mfArrays automatically. By specifying the statement call msReturnArray(a, b, c, ...)at the end of your function, you set the status flag of the


mfArray to temporary. MATFOR automatically clears mfArrays once it encounters temporary

flags.


use fml implicit none external foo ty pe(mfArray) :: x, foo

x = foo(3) call msDisplay(x,'X') call msFreeArgs(x) en d program example

function foo(A) result(t) use fml implicit none integer:: A type(mfArray)::t t = mfRand(A,A) call msReturnArray(t) return e nd function

Result X = 0.2408 0.3788 0.8362 0.4143 0.7158 0.8167 0.9859 0.5995 0.3267

See Also msInitArgs, msFreeArgs


msInitArgs, msFreeArgs Set status of mfArrays in procedure development.

Module fml

Syntax call msInitArgs(a, b, ...) call msFreeArgs(a, b, ...) Descriptions Procedures msInitArgs and msFreeArgs are used in procedure development to set the status flags of mfArrays. Procedure msInitArgs stops temporary mfArrays from being released by MATFOR. Procedure msFreeArgs reverses the 'lock' action performed by procedure msInitArgs, so that temporary mfArrays are automatically released by MATFOR. For example, when developing a subroutine foo that accepts mfArrays a, b, and c, as below, it is recommended to enclose the program code with call msInitArgs(a, b, c), and call msFreeArgs(a, b, c): Subroutine foo(a, b, c) implicit none type (mfArray) :: a, b, c call msInitArgs(a, b, c) ! program codes ------------------- ------------------- call msFreeArgs(a, b, c) return end Subroutine foo

More Details:

The mfArray is a dynamically allocated data object. It is good practice in Fortran to release

dynamically allocated memory space once you no longer need it. Due to the above principle,

MATFOR automatically releases all temporary mfArrays once they are passed into MATFOR

procedures. A temporary mfArray is created when you use a function without assigning its output

to a variable. For example, in the statement

call bar(foo(x)),

foo(x) returns a temporary mfArray used as input to the subroutine bar(). Such temporary

mfArrays have their status flag sets to temporary if the function developer added the statement

below at the end of the function:


call msReturnArray(a)

MATFOR automatically clears mfArrays with temporary flag 'on' in MATFOR procedures. To

prevent temporary mfArrays from being released in subroutine code, the procedure

msInitArgs()is used to stop MATFOR from releasing the specified mfArrays.

msFreeArgs()is added at the end of the subroutine to enable the memory clearing action of

MATFOR.

In conclusion, use the procedure pair msInitArgs()and msFreeArgs()to enclose program

code in your subroutine.


use fml implicit none external foo type(mfArray) :: x, foo x = foo(3) call RandSum(x,foo(3),foo(3)) call msDisplay(x,'X') call msFreeArgs(x) en d program example

subroutine RandSum(a,b,c) use fml implicit none type(mfArray)::a,b,c call msInitArgs(a,b,c) a = a + b + c call msFreeArgs(b,c) en d subroutine

function foo(A) result(t) use fml implicit none integer:: A type(mfArray)::t t = mfRand(A,A) call msReturnArray(t) return e nd function

Result X = 1.7950 1.5861 1.9579 0.9590 1.2635 1.8789 2.0209 1.4347 2.0302

See Also msRelease, msReturnArray


Display


msDisplay Display mfArray data.

Module fml

Syntax call msDisplay(x[, name]) call msDisplay(x, name[, x1 , name1, ...]) Descriptions ProceduremsDisplay shows the content of mfArrays on a console window. call msDisplay(x) call msDisplay(x, name)

• Displays the content of mfArray x. • Argument name is a character string specifying the accompanying output message. E.g.

call msDisplay(x, 'x')prints 'x =' on the console window followed by the content of mfArray x. When argument name is not specified, msDisplay prints the caption

'ans =' followed by the content of mfArray.

• You can specify the number of display digits by using procedure msFormat. call msDisplay(x, name) call msDisplay(x, name, x1, name1,...) • Display the content of the specified mfArrays with captions specified by the

corresponding name strings. When multiple mfArrays are displayed, the arguments must be specified in pairs, i.e., one mfArray accompanied by one name string. For example, call msDisplay(x, 'x', y, 'y', z, 'z').

• The number of mfArrays displayed in a single procedure call is limited to thirty-two. Example Code pr ogram example


type (mfArray) :: x in teger :: i

x = (/(i, i=1, 5)/)

call msDisplay(x, 'x') ca ll msFreeArgs(x)


Result


x =

1 2 3 4 5

See Also msFormat, msGDisplay


msFormat Specify displaying format of mfArray.

Module fml

Syntax call msFormat(mode) Descriptions Procedure msFormat specifies display format of mfArray. call msFormat("long")

Return 8 - byte precision with procedure mfDisplay

call msFormat("short")

Return 4 - byte precision with procedure mfDisplay.



ty pe(mfArray) :: x, y

x = 2.02 y = mfCos(x)

call msFormat("short") ca ll msDisplay(y, "y (short format)")

call msFormat("long") ca ll msDisplay(y, "y (long format)")

e nd program

Result y (short format) = -0.4342 y (long format) = -0.434248328937034

See Also msDisplay


FileIO


mfLoad Load binary file into mfArray.

Module fml

Syntax x = mfLoad(filename) Descriptions Procedure mfLoad reads data from a binary file, created by procedure msSave, into an mfArray. x = mfLoad(filename)

• Argument filename is a Fortran string containing the name of the binary file. For example, x = mfLoad("y.mfb").

• The MATFOR binary file uses ".mfb" as a file extension. Example Code pr ogram example



x = Reshape((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

call msSave('x.mfb', x) y = mfLoad('x.mfb') call msDisplay(x, 'x', y, 'y') ca ll msFreeArgs(x, y)


Result x =

1 3 5 2 4 6

y =

1 3 5 2 4 6

See Also msSave, msSaveAscii, mfLoadAscii


mfLoad.m Load MATFOR binary file into MATLAB workspace.

Module mfLoad.dll

Syntax x = mfLoad(filename) Descriptions Function mfLoad retrieves data from a MATFOR *.mfb binary file into a MATLAB matrix x. x = mfLoad(filename)

• Argument filename is a string containing the name of the source binary file. A .mfb extension is assumed if one is not specified.

• You can use this function to load data saved using mfSave in MATFOR or mfSave in MATLAB.

Note that to use this function, ensure that the files mfLoad.m and mfLoad.dll are in your MATLAB working directory. The two files are installed in your MATFOR directory <MATFOR4>/tools/matlab when MATFOR is installed. Example See Also msSave, mfLoad, mfSave.m


mfLoadAscii Load an ASCII file into mfArray.

Module fml

Syntax x = mfLoadAscii(filename) Descriptions Procedure mfLoadAscii reads in data from an ASCII file into an mfArray. x = mfLoadAscii(filename)

• The ASCII file must be in 2-D matrix format with m rows and n columns corresponding to an m x n matrix mfArray.

• Argument filename is a string containing the filename of the ASCII file. For example, x = mfLoadAscii("y.txt").

You can produce an ASCII file for loading by using procedure msSaveAscii. Example Code pr ogram example



x = RESHAPE((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

call msSaveAscii('x.txt', x) y = mfLoadAscii('x.txt') call msDisplay(x, 'x', y, 'y') ca ll msFreeArgs(x, y)


Result x =

1 3 5 2 4 6

y =

1 3 5


2 4 6

See Also msSave, mfLoad, msSaveAscii


mfLoadCsv Load a CSV file into mfArray.

Module fml

Syntax x = mfLoadCsv(filename) Descriptions Procedure mfLoadCsv reads in data from a CSV file into an mfArray. x = mfLoadCsv(filename)

• A CSV file is a common text file that contains comma-delimited values. • The CSV file must be in 2-D matrix format with m rows and n columns corresponding to

an m x n matrix mfArray.

• Argument filename is a string containing the filename of the CSV file. For example, x = mfLoadCsv("y.csv").

You can produce a CSV file for loading by using procedure msSaveCsv. Example To be referred to mfLoadAscii See Also msSaveCsv


msSave Save mfArray into a MATFOR binary file.

Module fml

Syntax call msSave(filename, x) Descriptions Procedure msSave writes data contained in an mfArray to a binary file with extension .mfb. call msSave(filename, x)

• Argument filename is a Fortran string containing the name of the target binary file. For example, call msSave("x.mfb",x).

• Argument x is the name of the mfArray to be saved. Example Code pr ogram example



x = RESHAPE((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

call msSave('x.mfb', x) y = mfLoad('x.mfb') call msDisplay(x, 'x', y, 'y') ca ll msFreeArgs(x, y)


Result x =

1 3 5 2 4 6

y =

1 3 5 2 4 6

See Also mfLoad, msSaveAscii, mfLoadAscii


mfSave.m Save MATLAB matrix into a MATFOR binary file.

Module mfSave.dll

Syntax mfSave(filename, x) Descriptions Procedure mfSave(filename, x)saves data contained in a MATLAB matrix x as MATFOR *.mfb binary file format. • Argument filename is a string containing the name of the target binary file. An

extension of .mfb is assumed if one is not specified.

• The data saved by using this function can be reloaded into the MATLAB workspace using function mfLoad or retrieved in Fortran using procedure mfLoad. This facilitates

exchange of data between Fortran and MATLAB environments. Note that to use this function, ensure that the files mfSave.m and mfSave.dll are in your MATLAB working directory. The two files are installed in your MATFOR directory <MATFOR4>/tools/matlab when MATFOR is installed. Example See Also msSave, mfLoad, mfLoad.m


msSaveAscii Save mfArray into an ASCII file.

Module fml

Syntax call msSaveAscii(filename, x) Descriptions Procedure msSaveAscii writes data contained in an mfArray to an ASCII file with the extension the user specified. call msSaveAscii(filename, x)

• The data is written in a 2-D matrix format, with m rows and n columns, corresponding to an m-by-n matrix mfArray.

• Argument filename is a string containing the name of the target binary file. For example, msSaveAscii("x.dat", x).

• Argument x is the name of the mfArray to be saved. Example To be referred to mfLoadAscii See Also msSave, mfLoad, mfLoadAscii


msSaveCsv Save mfArray into a CSV file.

Module fml

Syntax call msSaveCsv(filename, x) Descriptions Procedure msSaveCsv writes data contained in an mfArray to a CSV file with the extension the user specified. call msSaveCsv(filename, x)

• A CSV file is a common text file that contains comma-delimited values. • The data is written in a 2-D matrix format, with m rows and n columns, corresponding to

an m-by-n matrix mfArray.

• Argument filename is a string containing the name of the target CSV file. For example, msSaveCsv("x.csv", x).

• Argument x is the name of the mfArray to be saved. Example To be referred to mfLoadAscii See Also mfLoadCsv

Chapter 3 Data Manipulation Functions 75

C H A P T E R 3

Data Manipulation Functions This chapter introduces a set of data manipulation functions.


Basic


mfMax, msMax Find the maximum value along different dimensions of an mfArray.

Module fml

Syntax a = mfMax(x[, mf(), IDIM]) a = mfMax(x, y) call msMax(mfOut(a, i), x[, mf(), IDIM]) Descriptions a = mfMax(x) • For vectors, mfMax returns the largest element in x. • For matrices, mfMax returns a row vector containing the maximum element from each

dimension. y = mfMax(x, mf(), IDIM)

• operates along the dimension of x specified by scalar IDIM. a = mfMax(x, y)

• returns an array the same size as x and y with the larger corresponding elements from x or y chosen. Either one can be a scalar.

For complex input x, mfMax returns the largest absolute value. Example Code pr ogram example


type(mfArray) :: x, c, y in teger(4) :: i

x = Reshape((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

y = Reshape((/3,5,4,6,2,1/), (/2, 3/)) ! y is 3 4 2 ! 5 6 1

i = mfMax(mf((/ 1, 2, 3 /))) ca ll msDisplay(mf(i), 'mfMax(mf((/ 1, 2, 3 /)))')


c = mfMax(x, MF_NULL, 1) call msDisplay(x, 'x', y, 'y', c,'mfMax(x, MF_NULL, 1)') c = mfMax(x, MF_NULL, 2) call msDisplay(x, 'x', y, 'y', c,'mfMax(x, MF_NULL, 2)') c = mfMax(x, y) ca ll msDisplay(c, 'mfMax(x, y)')

ca ll msFreeArgs(x, c, y)


Result mf Max(mf((/ 1, 2, 3 /))) =

3

x =

1 3 5 2 4 6

y =

3 4 2 5 6 1

m fMax(x, MF_NULL, 1) =

2 4 6

x =

1 3 5 2 4 6

y =

3 4 2 5 6 1

m fMax(x, MF_NULL, 2) =

5 6

m fMax(x, y) =

3 4 5 5 6 6

See Also mfMin


mfMin, msMin Find the minimum value along different dimensions of an mfArray.

Module fml

Syntax a = mfMin(x[, mf(), IDIM]) a = mfMin(x, y) call msMin(mfOut(a, i), x[, mf(), IDIM]) Descriptions a = mfMin(x) • For vectors, mfMin returns the largest element in x. • For matrices, mfMin returns a row vector containing the Minimum elements from each

dimension. a = mfMin(x, mf(), IDIM)

• operates along the dimension of x specified by scalar IDIM. a = mfMin(x, y)

• returns an array the same size as x and y with the smaller corresponding elements from x or y chosen. Either one can be a scalar.

For complex input x, mfMin returns the smallest absolute value. Example Code pr ogram example


type(mfArray) :: x, c, y in teger(4) :: i

x = Reshape((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6 y = Reshape((/3,5,4,6,2,1/), (/2, 3/)) ! y is 3 4 2 ! 5 6 1

i = mfMin(mf((/ 1, 2, 3 /))) ca ll msDisplay(mf(i), 'mfMin(mf((/ 1, 2, 3 /)))')

c = mfMin(x, MF_NULL, 1)


call msDisplay(x, 'x', y, 'y', c, 'mfMin(x, MF_NULL, 1)') c = mfMin(x, MF_NULL, 2) call msDisplay(c, 'mfMin(x, MF_NULL, 2)') c = mfMin(x, y) ca ll msDisplay(c, 'mfMin(x,y) ')

ca ll msFreeArgs(x, c, y)


Result mf Min(mf((/ 1, 2, 3 /))) =

1

x =

1 3 5 2 4 6

y =

3 4 2 5 6 1

m fMin(x, MF_NULL, 1) =

1 3 5

m fMin(x, MF_NULL, 2) =

1 2

m fMin(x,y) =

1 3 2 2 4 1

See Also mfMax


mfProd, msProd Find the product of mfArray elements.

Module fml

Syntax a = mfProd(x[, IDIM]) Descriptions a = mfProd(x) • For matrices, mfProd(x) returns a row vector containing the product of each column of

mfArray x.

• For N-dimensional arrays, mfProd(x) operates on the first non-singleton dimension. a = mfProd(x, IDIM)

• Argument IDIM is an integer(4) scalar specifying the dimension that procedure mfProd(x) works along.



type(mfArray) :: x, y, c in teger(4) :: i

x = (/1, 2, 3/) y = Reshape((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

i = mfProd(x) ! returns 6 call msDisplay(x, 'x', mf(i), 'mfProd(x)') c = mfProd(y, 1) ! returns 2 12 30 ca ll msDisplay(y, 'y', c, 'mfProd(y, 1)')

ca ll msFreeArgs(x, y, c)


Result x =

1 2 3

m fProd(x) =


6

y =

1 3 5 2 4 6

m fProd(y, 1) =

2 12 30

See Also mfSum


mfSort, msSort Sort elements of mfArray in ascending order.

Module fml

Syntax y = mfSort(x,[, IDIM]) call msSort(mfOut(y, i), x) Descriptions y = mfSort(x), y = mfSort(x, IDIM) • The procedure returns to y an mfArray containing the elements of mfArray x sorted in

ascending order along different dimensions.

• For vector x, the elements are sorted in ascending order. • For matrix x, the elements in each column of x are sorted in ascending order accordingly.

In effect, the procedure returns an mfArray y assuming the shape of x, with the elements

in each column sorted in ascending order.

• For n-dimensional x, the elements are sorted along the first non-singleton dimension of x.

• Argument IDIM is an integer specifying the dimension to be sorted along. By default, IDIM = 1, corresponding to sorting along the column.

• When x is complex, the function returns mfArray y containing sorted elements of mfAbs(x). Complex matches are further sorted according to mfAtan2(mfImag(x), mfReal(x)).

call msSort(mfOut(y, i), x)

• This format returns an additional index mfArray i, containing the indices of elements in x, corresponding to the sorted elements in y.

For example, x = 8 1 6 3 5 7 4 9 2 call msSort(mfOut(y, i), x) returns mfArray y and i containing,

y = 3 1 2


4 5 6 8 9 7 i = 2 1 3 3 2 1 1 3 2

• For two values of the same magnitude, their original order is preserved. Example Code pr ogram example


ty pe(mfArray) :: x, a

x = RESHAPE((/3,5,4,6,2,1/), (/2, 3/)) ! x is 3 4 2 ! 5 6 1

a = mfSort(x) call msDisplay(x, 'x', a, 'mfSort(x)') a = mfSort(x,2) call msDisplay(x, 'x', a, 'mfSort(x,2)') ca ll msFreeArgs(x, a)


Result x =

3 4 2 5 6 1

m fSort(x) =

3 4 1 5 6 2

x =

3 4 2 5 6 1

m fSort(x,2) =

2 3 4 1 5 6

See Also mfSortRows


mfSortRows, msSortRows Sort rows of mfArray in ascending order.

Module fml

Syntax y = mfSortRows(x[, col]) call msSortRows(mfOut(y, i), x) Descriptions y = mfSortRows(x), y = mfSortRows(x, col) • The procedure returns mfArray y containing the rows of matrix mfArray x sorted in

ascending order as a group.

• If x contains strings, the function performs a dictionary sort. • When x is complex, the rows are sorted according to mfAbs(x). Complex matches are

further sorted according to mfAtan2(mfImag(x), mfReal(x)).

• If argument col is specified, the rows are sorted according to the columns specified in vector mfArray col.

For example, x = 8 1 6 3 5 7 4 9 2 col = 3 y = mfSortRows(x, col) returns, y = 4 9 2 8 1 6 3 5 7 call msSortRows(mfOut(y,i), x)

• This format returns an additional index mfArray i, which contains the row indices after the corresponding rows have been swapped.

Example Code


pr ogram example


ty pe(mfArray) :: x, y, i

x = mfMagic(5) !y = mfSortRows(x) call msSortRows(mfOut(y, i), x) call msDisplay(x, 'x', y, 'Sort rows according to first column') call msDisplay(i, 'Corresponding index') ca ll msFreeArgs(x, y, i)


Result x =

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

S ort rows according to first column =

4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 17 24 1 8 15 23 5 7 14 16

C orresponding index =

2 3 4 5 1

See Also mfSort


mfSum, msSum Find the sum of mfArray elements.

Module fml

Syntax a = mfSum(x[, IDIM]) Descriptions a = mfSum(x), a = mfSum(x, IDIM) a = mfSum(x)

For vectors, the procedure returns the sum of the elements of x. For matrices, a is a row vector

with the sum over each column. For N-dimensional arrays, a operates along the first non-singleton

dimension.

a = mfSum(X, IDIM)sums along the dimension IDIM.

Example The following example uses the mfSum function. Code pr ogram example


type(mfArray) :: x, y, c in teger(4) :: I

x = (/1, 2, 3/) y = RESHAPE((/1, 2, 3, 4, 5, 6/), (/2, 3/)) ! x is 1 3 5 ! 2 4 6

i = mfSum(x) ! returns 6 call msDisplay(x, 'x', mf(i), 'mfSum(x)') c = mfSum(y, 1) ! returns 3 7 11 call msDisplay(y, 'y', c, 'mfSum(y, 1)') ca ll msFreeArgs(x, y, c)


Result x =

1 2 3

m fSum(x) =

6


y =

1 3 5 2 4 6

m fSum(y, 1) =

3 7 11

See Also mfProd


Fast Fourier Transform


mfFFT, mfIFFT Compute the discrete Fourier transform and the inverse discrete Fourier transform.

Module fml

Syntax y = mfFFT(x) y = mfFFT(x[, n]) y = mfFFT(x[, mf(), dim]) The syntax is the same between _mfFFT and _mfIFFT. Descriptions Procedure mfFFT computes the discrete Fourier transform of mfArray x using fast Fourier transform algorithm. y = mfFFT(x)

• This procedure returns y, the discrete Fourier transform of mfArray x. • If x is a matrix, the operation is applied in each column of x. y = mfFFT(x[, n])

• This procedure returns the discrete Fourier transform of mfArray x given the length n. • The length of x is adjusted according to n; either to be truncated or to be padded with

zeros. y = mfFFT(x[, n, dim])

• This procedure returns the discrete Fourier transform of mfArray x given the length n and the dimension dim.

• Argument dim is an integer(4) scalar specifying the dimension that procedure mfFFT works along. If dim = 1, the operation is applied along x dimension. If dim = 2, the operation is applied along y dimension and etc.

• If n is not specified, a null value mf() will be used by default. Example Code Pr ogram fft

use fml use fgl im plicit none


integer(4), parameter :: n = 1000, tmax = 10 ty pe(mfArray) :: t, f, x1, x2, y1, y2

t = mfLinspace( 0, tmax, n ) f = mfLinspace( 0, n/tmax, n )

x1 = mfCos( t * 2d0 * MF_PI ) + mfSin( t * 2d0 * MF_PI * 1.746d0 + t ) + 0.2d0 * mfRand(1,n) y1 = mfFFT(x1)

! remove the freq above 1.2 y2 = y1 ca ll msAssign( mfS( y2, (tmax * 6 / 5).to.n ), 0 )

! do reverse x2 = mfIFFT( y2 ) x2 = mfReal( x2 )

call msSubplot( 3, 1, 1 ) call msTitle('orig') ca ll msPlot( t, x1)

call msSubplot( 3, 1, 2 ) call msTitle('FFT') call msPlot( f, mfAbs(y1) ) ca ll msAxis( 0, 10, 0, 0 )

call msSubplot( 3, 1, 3 ) call msTitle('low pass with cutoff freq = 1.5') ca ll msPlot( t, x2 )

ca ll msViewPause()

e nd Program fft

See Also mfFFT2, mfIFFT2, mfFFTShift


mfFFT2, mfIFFT2 Compute the two-dimensional discrete Fourier transform and the two-dimensional inverse discrete Fourier transform.

Module fml

Syntax y = mfFFT2(x) y = mfFFT2(x[, m, n]) The syntax is the same between _mfFFT2 and _mfIFFT2. Descriptions Procedure mfFFT computes the two-dimensional inverse discrete Fourier transform of mfArray x using fast Fourier transform algorithm. y = mfFFT(x)

• This procedure returns y, the two-dimensional discrete Fourier transform of mfArray x. y = mfFFT2(x[, m, n]) • This procedure returns the two-dimensional discrete Fourier transform of mfArray x

given m and n to be the length of row and column.

• The shape of x is adjusted according to m and n; either to be truncated or to be padded with zeros.

Example Code Pr ogram fft2

use fml us e fgl

im plicit none

ty pe(mfArray) :: im, imf

! ****************************************************************** ! load data ! ******************************************************************

im = mfImRead( mf('ancad.bmp') ) im = mfS( im, MF_COL, MF_COL, 1)-128.0d0

! ****************************************************************** ! FFT2 ! ******************************************************************

imf = mfFFT2(im)


im f = mfFFTShift(imf)

! ****************************************************************** ! Draw ! ******************************************************************

call msSubplot(1,2,1) call msFastPColor(im) call msColormap('gray') ca ll msAxis('equal')

call msSubplot(1,2,2) call msFastPColor(mfAbs(imf)) call msColormap('gray') call msColormapRange(0,50000) ca ll msAxis('equal')

ca ll msViewPause()

e nd Program fft2

See Also mfFFT, mfIFFT, mfFFTShift


mfFFTShift, mfIFFTShift Shift zero frequency components of discrete Fourier transform and inverse discrete Fourier transform to the center of the matrix.

Module fml

Syntax y = mfFFTShift(x) y = mfFFTShift(x[, dim]) The syntax is the same between _mfFFTShift and _mfIFFTShift. _mfIFFTShift undoes what was done with _mfFFTShift. Descriptions Procedure mfFFTShift moves the zero frequency components along the dimension to the center of the mfArray. y = mfFFTShift(x)

• This procedure shifts the zero frequency components to the middle of the mfArray. • mfArray x is the output of fast Fourier transform. • If x is a vector, the procedure swaps the left-half space with the right-half space. If x is a

matrix, the procedure swaps the left-half space with the right-half space, then the top-half space with the bottom-half space.

For one dimension x

For multiple dimensions x

y = mfFFT(x[, dim])

• This procedure shifts the zero frequency components to the middle of the mfArray along


the dimension specified. For dim = 1, the operation is applied along x dimension. For dim = 2, the operation is applied along y dimension and so on.

Example To be referred to mfFFT2 See Also mfFFT, mfFFT2


Cartographic Functions


msProj4, msProj4Inv Perform cartographic projection and its inverse operation.

Module fgl

Syntax call msProj4(mfOut(x,y), proj_name, lon_0, u, v[, options]) call msProj4Inv(mfOut(u,v),proj_name, lon_0, x, y[, options] ) Descriptions Procedure msProj4 performs cartographic projection by converting geographic longitude and latitude coordinates into Cartesian coordinates in the form of mfArray x and y. • proj_name is the selection of cartographic projection. For example, use "robin" for

Robinson projection, and "lcc" for Lambert Conformal Conic projection. Available project

names are listed in the table below.

• Argument lon_0 sets the central meridian for the projection. The normal geographic range for longitude is from 180W to 180E.

• mfArrays u and v are the respective geographic longitude and latitude coordinates. • mfArrays x, y, are the Cartesian coordinates output from the projection. • Argument options give additional information to be passed to the proj4 engine. It is in

the form of string.

Cylindrical Projections

proj_name Projection

merc Mercator Projection

tmerc Transverse Mercator Projection

cc Central Cylindrical Projection

tcc Transverse Central Cylindrical Projection

mill Miller Projection

cea Lambert Cylindrical Equal Area Projection

gall G � �all Stereographic Projection

tcea Transverse Cylindrical Equal Area Projection

eqc Transverse Cylindrical Equal Area Projection

cass Cassini Projection

Pseudocylindrical Projections


sinu Sinusoidal Projection


moll Mollweide Projection

robin Robinson Projection

eck1 Eckert I Projection

eck2 Eckert II Projection

eck3 Eckert III Projection

eck4 Eckert IV Projection

eck5 Eckert V Projection

eck6 Eckert VI Projection

aatano �Hatano Asymmetrical Equal Area Projection

loxim Loximuthal Projection

mbtfpp � �McBryde Thomas Flat Polar Parabolic Projection

mbtfpq � �McBryde Thomas Flat Polar Quartic Projection

mbtfps � �McBryde Thomas Flat Polar Sinusoidal Projection

putp2 �Putnins P Projection

putp5 Putnins P Projection

qua_aut Quartic Authalic Projection

wink1 Winkel I Projection

boggs Boggs Eumorphic Projection

collg Collignon Projection

denoy Denoyer Semi Elliptical Projection

crast Craster Parabolic Projection

Conic Projections


lcc Lambert Conformal Conic Projection

eqdc Equidistant Conic Projection

aea Albers Equal Area Projection

leac Lambert Equal Area Projection

poly � �Polyconic American Projection

rpoly Rectangular Polyconic Projection

bonne Bonne Projection

Azimuthal Projections


stere Stereographic Projection

gnom Gnomonic Projection

ortho Orthographic Projection

airy Airy Projection

laea Lambert Azimuthal Equal Area Projection


aeqd Azimuthal Equidistant Projection

hammer Hammer Projection

wag7 Wagner VII Projection

aitoff Aito Projection

wintri Winkel Tripel Projection

Miscellaneous Projections


august August Epicycloidal Projection

bacon Bacon Globular Projection

nicol Nicolosi Globular Projection

apian Apian Globular I Projection

ortel Ortelius Oval Projection

vandg � �Van der Grinten I Projection

vandg2 Van der Grinten II Projection

vandg3 Van der Grinten III Projection

vandg4 Van der Grinten IV Projection

lagrng Lagrange Projection

Complete details including technical usage and execution of program proj4 can be referred to http://proj.maptools.org/ Example Code pr ogram example

use fgl use fml im plicit none

integer(4), parameter :: N1 = 36, N2 = 18 in teger(4), parameter :: LON_0 = 120

type(mfArray) :: x, y, z, u, v, tu, tv type(mfArray) :: h ty pe(mfArray) :: pathX,pathY,wave,roX,roY,h2

call msFigure('Robin') z = mfZeros( N2+1, N1+1 ) !Create geographic mesh call msCreateGeoidData( mfOut( u, v, tu, tv ), & LON_0-180, LON_0+180, -90, 90 ,N1,N2) ! robin map projection call msProj4( mfOut(x, y), 'robin', LON_0, u, v ) !Draw geographic mesh h = mfSurf(x, y, z) ca ll DrawImgMap(h)


!Draw two path call msHold('on') pathX = .t.(mfLinspace(-60,300,30).vc.mfLinspace(-60,300,30)) pathY = .t.(mfLinspace(5,35,30).vc.mfLinspace(-35,5,30)) wave = mfCos(pathY)*3d0 pathY = pathY + wave call msProj4( mfOut(rox, roy), 'robin', LON_0, pathX, pathY ) call msPlot(rox,roy,'ro-') ca ll msHold('off')

call msView( '2' ) call msAxis('equal') call msAxis('clipping', 'on') ca ll msAxisWall('off')

call msFigure('3D Earth') call msCreateGeoid3Data( mfOut( x, y, z, tu, tv), -180, 180, -90, 90 ) h = mfSurf(x, y, z) call DrawImgMap(h) call Draw3DPath(pathX, pathY) ca ll msAxis('equal')

! Pause program execution ca ll msViewPause()

! Deallocate mfArray call msFreeArgs( x, y, z, u, v, tu, tv ) ca ll msFreeArgs( h,pathX,pathY,wave,roX,roY,h2 )

co ntains

subroutine DrawImgMap(h) type(mfArray), intent(in) :: h call msDrawTexture(h, mf('map'), mf('earth.png'), & mf('coord_s'), tu, mf('coord_t'), tv )

call msDrawMaterial(h, mf('surf'), & mf('smooth'), mf('on'), & mf('colormap'), mf('off'), & mf('ambient'), mf(0), & mf('diffuse'), mf(25), &

mf('specular'), mf(85) )

call msDrawMaterial(h, mf('edge'), & mf('trans'), mf(80), & mf('smooth'), mf('on'), & mf('colormap'), mf('off'), & mf('color'), mf( (/1,1,1/) ) ) en d subroutine DrawImgMap

subroutine Draw3DPath( pathX, pathY) implicit none type(mfArray), intent(in) :: pathX, pathY type(mfArray) ::x, y, z, c, r, th, phi,h

r = 1.1d0 th = pathX * MF_PI / 180 phi = pathY * MF_PI / 180

x = r * mfCos( th ) * mfCos( phi ) y = r * mfSin( th ) * mfCos( phi ) z = r * mfSin( phi ) c = x*y-z

!Draw path call msHold('on') h = mfPlot3(x,y,z,c) call msDrawMaterial(h,mf('edge'),mf('line_width'),mf(3)) call msHold('off')

call msFreeArgs(x, y, z, r, th, phi,h) end subroutine Draw3DPath



Result

See Also


msCreateGeoidData 2-D geoid data.

Module fgl

Syntax call msCreateGeoidData(mfOut(x,y), lon0, lon1, lat0, lat1[, nlon, nlat ] ); call msCreateGeoidData(mfOut(x, y, tu, tv), lon0, lon1, lat0, lat1[, nlon, nlat ] ); Descriptions Procedure msCreateGeoidData creates the geoid data for 2-D mesh plots. • Arguments lon0 and lon1 specify the geographic longitude range. The normal

geographic longitude ranges from -180 to +180.

• Arguments lat0 and lat1 specify the geographic latitude range. The normal geographic latitude ranges from -90 to +90.

• nlon and nlat represent respective number of meridians and number of parallels to be

plotted. By default, nlon=36, nlat=18.

• The output variables x , y, tu, tv are matrix mfArray in the shape of (nlon+1) by (nlat+1).

Example To be referred to msProj4 See Also msProj4


msCreateGeoid3Data 3-D geoid data.

Module fgl

Syntax call msCreateGeoid3Data(mfOut(x,y,z), lon0, lon1, lat0, lat1[, nlon, nlat ] ); call msCreateGeoid3Data(mfOut(x, y, z, tu, tv), lon0, lon1, lat0, lat1[, nlon, nlat ] ); Descriptions Procedure msCreateGeoid3Data creates the geoid data for 3-D mesh plots. • Arguments lon0 and lon1 specify the geographic range for longitude. The normal

geographic longitude ranges from -180 to +180.

• Arguments lat0 and lat1 specify the geographic range for latitude. The normal geographic latitude ranges from -90 to +90.

• nlon and nlat represent respective number of meridians and number of parallels to be

plotted. By default, nlon=36, nlat=18.

• The output variables x , y, z, tu, tv are matrix mfArray in the shape of (nlon+1) by (nlat+1).

Example To be referred to msProj4 See Also msProj4


msCreateCoastlineData 2-D coastline data.

Module fgl

Syntax call msCreateCoastlineData(mfOut(x,y)[, lon0, lon1, lat0, lat1]) Descriptions Procedure msCreateCoastlineData creates coastline data for 2-D plots. • This procedure returns mfArray x and y. You may use procedure msPlot to draw the

coastline.

• Arguments lon0 and lon1, lat0 and lat1 specify the geographic ranges for longitude and latitude respectively.

You can set geoid label on the axis object using procedure msAxis('geoid_label', 'on'). Example Code pr ogram example

use fml us e fgl

im plicit none

ty pe (mfArray) :: x, y

!Create 2D coastline data ca ll msCreateCoastlineData( mfOut(x,y), -180, 180, -90, 90 )

!plot 2D linear graph call msPlot( x, y) call msTitle('2D Coastline') ca ll msAxis('geoid_label', 'off')

ca ll msViewPause()


Result


See Also msCreateCoastline3Data


msCreateCoastline3Data 3-D coastline data.

Module fgl

Syntax call msCreateCoastline3Data(mfOut(x,y,z)[, lon0, lon1, lat0, lat1]) Descriptions Procedure msCreateCoastline3Data creates coastline data for 3-D plots. • This procedure returns mfArray x y and z. You may use procedure msPlot3 to draw

the coastline.

• Arguments lon0 and lon1, lat0 and lat1 specify the geographic ranges for longitude and latitude respectively.


use fml us e fgl

im plicit none

ty pe (mfArray) :: x, y, z

!Create 3D coastline data ca ll msCreateCoastline3Data( mfOut(x, y, z), -180, 180, -90, 90 )

!plot 3D linear graph call msPlot3( x, y, z ) call msColormapRange(-1d0,1d0) ca ll msTitle('3D Coastline')

ca ll msViewPause()


Result


See Also msCreateCoastlineData


Chapter 4 Arithmetic & Relational Operators 109

C H A P T E R 4

Arithmetic & Relational

Operators This chapter describes the operators and functions available for matrix and array manipulation.

Operator Precedence

Arithmetic Operators

Relational Operators


Operator Precedence

The table below lists the MATFOR operator precedence. Operators having the same symbol as Fortran operators also share the same precedence level. All MATFOR-defined operators occupy the lowest precedence level.

Note that operators having the same precedence level are evaluated from left to right.

Operators Descriptions Precedence

.h. mfArray complex transpose Highest

.t. mfArray transpose

** mfArray power

* mfArray multiplication

/ mfArray right division

+ mfArray addition or unary plus

- mfArray subtraction or unary minus

>= mfArray greater than or equal to comparison

> mfArray greater than comparison

<= mfArray less than or equal to

< mfArray less than comparison

/= mfArray inequality comparison

== mfArray equality comparison

.hc. Horizontal concatenation


.vc. Vertical concatenation Lowest


Arithmetic Operators Arithmetic operators mean symbols of addition, subtraction, multiplication and division.

Module use fml

or

use mod_ops

Syntax type (mfArray) :: x, y, z

integer :: n

z = x + y

z = + x

z = x – y

z = - x

z = x*y

z = x/y

z = x**y

z = x**n

z = mfMul(x, y)

z = mfLDiv(x, y)

z = mfRDiv(x, y)

z = .t.x

z = .h.x

Descriptions

Arithmetic operators provided by MATFOR include both array

and matrix operators. Array operators operate

element-by-element on the mfArrays while matrix operators

operate on whole mfArrays.

The following lists the operators available with a brief


description of their operation.

+ Array addition or unary plus

x + y adds mfArrays x and y. Unless one is scalar, the two

mfArrays must be the same size. A scalar can be added to mfArrays of any size.


- Array subtraction or unary minus

x – y subtracts mfArray y from x. Unless one is scalar, the

two mfArrays must be the same size. A scalar can subtract and be subtracted from mfArrays of any size.

* Array multiplication

x * y returns element-by-element the multiplication of mfArrays x and y. Unless one is scalar, the two mfArrays

must be the same size. A scalar can be multiplied with an mfArray of any size.

mfMul Matrix multiplication

mfMul(x, y) returns the matrix product of mfArrays x and y, where x is an m-by-p matrix and y is a p-by-n

matrix. The product of the matrix multiplication is an m-by-n mfArray.

mfRDiv Matrix right division

mfRDiv(x, y) returns an mfArray approximately equal to x*mfInv(y). The result is the same as .t.( mfLDiv((.t.y), (.t.x))).

mfLDiv Matrix left division

mfLDiv(y, x) returns an mfArray approximately equal to mfInv(y)*x. Depending on the structure of y,

MATFOR overloads several methods for solving the simultaneous linear equation.

** Array power


x**y returns an mfArray containing elements of x(i,j) raised to the power of corresponding elements of y(i,j).

Unless one is scalar, the two mfArrays must be the same size.

x**n, where n is a Fortran scalar, returns an mfArray containing the elemens of x raised to the power of n.


.t., mfTranspose Array transpose

.t.x returns an mfArray containing the transpose of mfArray x. In a transpose operation, ai,j and aj,i are

interchanged.

Complex elements are not conjugated.

You can also use the msTranspose procedure to

perform the same operation.

c = .t. a

c = mfTranspose(a)

call msTranspose(mfOut(c), a)

.h., mfCTranspose Complex conjugate transpose

.h.x returns an mfArray containing the complex conjugate transpose of mfArray x. If x is real, this operation returns the same result as .t.x.

When performing linear algebra operations on complex matrices, it is almost always the complex conjugate transpose (also called the Hermitian transpose) that is needed.

You can also use the mfCTranspose procedure to

perform the same operation.

c = .h. a

c = mfCTranspose(a)

call msCTranspose(mfOut(c), a)

See Also




Module use mod_ops

Syntax type (mfArray) :: x, y, z

z = x == y

z = x >= y

z = x > y

z = x <= y

z = x < y

z = x /= y

Descriptions

The relational operators ==, >=, >, <=, and /=, perform element-by-element

comparisons between two mfArrays.

The returned logical mfArray records the result of the comparison. Each element records a logical true(1) if the relationship is true, and logical false(0)

otherwise.

Note that unless one is scalar, the two mfArrays x and y must be the same size. The

scalar will be expanded into an mfArray the same size as the other mfArray.

== mfArray equality comparison


x == y checks if each element of x equals the corresponding element of y. The operator tests both real and imaginary parts of the elements.

When you use the equality (= =) operator in an if statement, use the all function to enclose it. The all function ensures that the equality

condition is satisfied by all elements of the returned mfArray.

>= mfArray greater than or equal to comparison

x >= y checks if each element of x is more than or equal to the corresponding element of y. The function returns 1 if the relation is true

and 0 otherwise. The operator only compares the real part of the elements.


> mfArray greater than comparison

x > y checks if each element of x is greater than the corresponding element of y. The function returns 1 if the relation is true and 0

otherwise. The operator only compares the real part of the elements.

<= mfArray less than or equal to comparison

x <= y checks if each element of x is less than or equal to the corresponding element of y. The function returns 1 if the relation is true

and 0 otherwise. The operator only compares the real part of the elements.

< mfArray less than comparison

x < y checks if each element of x is less than the corresponding element of y. The function returns 1 if the relation is true and 0 otherwise. The

operator only compares the real part of the elements.

/= mfArray inequality comparison

x /= y checks if each element of x is different from the corresponding element of y. The operator tests both real and imaginary parts of the

elements.

See Also

Arithmetic Operators, Any, All


Chapter 5 Elementary Math Functions 121

C H A P T E R 5

Elementary Math Functions

This chapter introduces a set of elementary math functions including trigonometric, exponential, complex, rounding and remainder. The functions are listed below:

Trigonometric

mfACos Inverse cosine function

mfACosh Inverse hyperbolic cosine function

mfACot Inverse cotangent function

mfACoth Inverse hyperbolic cotangent function

mfACsc Inverse cosecant function

mfACsch Inverse hyperbolic cosecant function

mfASec Inverse secant function.

mfASech Inverse hyperbolic secant function.

mfASin Inverse sine function.

mfASinh Inverse hyperbolic sine function.

mfATan Inverse tangent function.

mfATan2 Four quadrant arctangent function

mfATanh Inverse hyperbolic tangent function

mfCos Cosine function

mfCosh Hyperbolic cosine function

mfCot Cotangent function

mfCoth Hyperbolic cotangent function

mfCsc Cosecant function

mfCsch Hyperbolic cosecant function

mfSec Secant function

mfSech Hyperbolic secant function


mfSin Sine function

mfSinh Hyperbolic sine function

mfTan Tangent function

mfTanh Hyperbolic tangent function

Exponential

mfExp Exponential function

mfLog Natural logarithm

mfLog10 Common logarithm (base 10)

mfLog2 Base 2 Logarithmic and floating point dissection

mfPow2 Base 2 power and floating point number scaling

mfSqrt Square Root function

Complex

mfAbs Absolute of real and complex value

mfAngle Phase angle of complex

mfComplex Convert input number to complex

mfConj Conjugate of complex

mfImag Imaginary part of complex

mfReal Real part of complex

Rounding and Remainder

mfCeil Round towards positive infinity

mfFix Round towards zero

mfFloor Round towards minus infinity

mfMod Modulus (signed remainder after division)

mfRem Remainder after division

mfRound Round towards nearest integer

mfSign Signum function


Trigonometry


mfACos, msACos Request inverse cosine function.

Module fml

Syntax y = mfACos(x) Descriptions Procedure mfACos(x) returns the arccosine of the mfArray x, in radians, where cos-1(x) = -i*log[x + i*(1-x2)1/2] The function domain and range includes real and complex data. For |x| <= 1, the function result is real and lies between 0 and π. For |x| >1, the function returns a complex value. Example Code pr ogram example



x = 2.02d0 y = mfACos(x)

call msDisplay(x, 'x', y, 'mfACos(x)') ca ll msFreeArgs(x, y)


Result x = 2.0200 mfACos(x) = 0.0000 +1.3284i

See Also mfACosh, mfCos


mfACosh, msACosh Request inverse hyperbolic cosine function.

Module fml

Syntax y = mfACosh(x) Descriptions Procedure mfACosh(x) returns element-by-element the inverse hyperbolic cosine of the mfArray x, in radians, where cosh-1(x) = log[x + (x2-1)1/2] The function domain and range include real and complex data. Example Code pr ogram example



x = (2, -2) y = mfACosh(x)

call msDisplay(x, 'x', y, 'mfACosh(x)') ca ll msFreeArgs(x, y)


Result x = 2.0000 -2.0000i mfACosh(x) = 1.7343 -0.8165i

See Also mfCos, mfCosh


mfACot, msACot Request inverse cotangent function.

Module fml

Syntax y = mfACot(x) Descriptions Procedure mfACot(x) returns element-by-element the arccotangent of the mfArray x, in radians, where cot-1(x) = tan-1(1/x) The function domain and range include real and complex data. Example Code pr ogram example



x = (-5, -5) y = mfACot(x)

call msDisplay(x, 'x', y, 'mfACot(x)') ca ll msFreeArgs(x, y)


Result x = -5.0000 -5.0000i mfACot(x) = - 0.1007 +0.0993i

See Also mfACoth, mfCot, mfCoth


mfACoth, msACoth Request inverse hyperbolic cotangent function.

Module fml

Syntax y = mfACoth(x) Descriptions Procedure mfACoth(x) returns element-by-element the inverse hyperbolic cotangent of the mfArray x in radians, where coth-1(x) = tanh-1(1/x) The function domain and range include real and complex data. For |x| <= 1, the function result is complex or infinity. Example Code pr ogram example



x = 0.5d0 y = mfACoth(x)

call msDisplay(x, 'x', y, 'mfACoth(x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfACoth(x) = 0.5493 -1.5708i

See Also mfACot, mfCot, mfCoth


mfACsc, msACsc Request inverse cosecant function.

Module fml

Syntax y = mfACsc(x) Descriptions Procedure mfACsc(x) returns element-by-element the inverse cosecant of the mfArray x in radians, where csc-1(x) = sin-1(1/x) The function domain and range include real and complex data. For |x| < 1, the function result is complex or NaN. Example Code pr ogram example



x = 3.0d0 y = mfACsc(x)

call msDisplay(x, 'x', y, 'mfACsc(x)') ca ll msFreeArgs(x, y)


Result x =

3

mfACsc(x) = 0.3398

See Also mfACsch, mfCsc, mfCsch


mfACsch, msACsch Request inverse hyperbolic cosecant function.

Module fml

Syntax y = mfACsch(x) Descriptions Procedure mfACsch(x) returns element-by-element the inverse hyperbolic cosecant of the mfArray x in radians, where csch-1(x) = sinh-1(1/x) The function domain and range include real and complex data. For x = 0, the function result is infinity. Example Code pr ogram example



x = 0.5d0 y = mfACsch(x)

call msDisplay(x, 'x', y, 'mfACsch(x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfACsch(x) = 1.4436

See Also mfACsc, mfCsc, mfCsch


mfASec, msASec Request inverse secant function.

Module fml

Syntax y = mfASec(x) Descriptions Procedure mfASec(x) returns element-by-element the inverse secant of the mfArray x in radians, where sec-1(x) = cos-1(1/x) The function domain and range include real and complex data. For |x| < 1, the function result is complex or NaN. Example Code pr ogram example



x = 0.1d0 y = mfASec(x)

call msDisplay(x, 'x', y, 'mfASec(x)') ca ll msFreeArgs(x, y)


Result x = 0.1000 mfASec(x) = 0.0000 +2.9932i

See Also mfASech, mfSec, mfSech


mfASech, msASech Request inverse hyperbolic secant function.

Module fml

Syntax y = mfASech(x) Descriptions Procedure mfASech(x) returns element-by-element the inverse hyperbolic secant of the mfArray x in radians, where sech-1(x) = cosh-1(1/x) The function domain and range include real and complex data. Example Code pr ogram example



x = 0.1d0 y = mfASech(x)

call msDisplay(x, 'x', y, 'mfASech(x)') ca ll msFreeArgs(x, y)


Result x = 0.1000 mfASech(x) = 2.9932

See Also mfASec, mfSec, mfSech


mfASin, msASin Request inverse sine function.

Module fml

Syntax y = mfASin(x) Descriptions Procedure mfASin(x) returns element-by-element the arcsine of the mfArray x in radians, where sin-1(x) = -i*log[i*x+(1-x2)1/2] The function domain and range include real and complex data. For real |x| < 1, the function result is real and lies in the range [-π/2, π/2]. For real |x| >1, the function returns a complex value. Example Code pr ogram example



x = 0.5d0 y = mfASin(x)

call msDisplay(x, 'x', y, 'mfASin(x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfASin(x) = 0.5236

See Also mfASinh, mfSin, mfSinh



mfASinh, msASinh Request inverse hyperbolic sine function.

Module fml

Syntax y = mfASinh(x) Descriptions Procedure mfASinh(x) returns element-by-element the inverse hyperbolic sine of the mfArray x in radians, where sinh-1(x) = log[x +(x2+1)1/2]. The function domain and range include real and complex data. Example Code pr ogram example



x = (2.d0, -2.d0) y = mfASinh(x)

call msDisplay(x, 'x', y, 'mfASinh(x)') ca ll msFreeArgs(x, y)


Result x = 2.0000 -2.0000i mfASinh(x) = 1.7343 -0.7542i

See Also mfASin, mfSin, mfSinh


mfATan, msATan Request inverse tangent function.

Module fml

Syntax y = mfATan(x) Descriptions Procedure mfATan(x) returns element-by-element the inverse tangent of the mfArray x in radians, where tan-1(x) = (i/2)* log((i+x)/(i-x)) The function domain and range include real and complex data. For real x, the result lies in the range [-π/2, π/2]. Example Code pr ogram example



x = 0.154d0 y = mfATan(x)

call msDisplay(x, 'x', y, 'mfATan(x)') ca ll msFreeArgs(x, y)


Result x = 0.1540 mfATan(x) = 0.1528

See Also mfATan2, mfATanh, mfTan, mfTanh


mfATan2, msATan2 Request four quadrant arctangent function.

Module fml

Syntax z = mfATan2(y, x) Descriptions Procedure mfATan2(y, x) returns an mfArray z containing element-by-element the principal value of the complex number defined by mfArrays y and x, where y is the imaginary part and x is the real part. For x approaching 0, the function result is approximately mfATan(y/x). However, in contrast to mfATan(y/x), which is limited to the range -π/2 <= mfATan(y/x) <= π/2, the function result lies in the range of -mfATan2(y,x) in the four quadrants. Example Code pr ogram example



x = 0.5d0 y = mfATan2(x, x)

call msDisplay(x, 'x', y, 'mfATan2(x, x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfATan2(x, x) = 0.7854

See Also mfATan, mfATanh, mfTan, mfTanh


mfATanh, msATanh Request inverse hyperbolic tangent function.

Module fml

Syntax y = mfATanh(x) Descriptions Procedure mfATanh(x) returns element-by-element the inverse hyperbolic tangent of the mfArray x in radians, where tan-1(x) = (1/2)* log((1+x)/(1-x)) The function domain and range include real and complex data. Example Code pr ogram example



x = 1.5782d0 y = mfATanh(x)

call msDisplay(x, 'x', y, 'mfATanh(x)') ca ll msFreeArgs(x, y)


Result x = 1.5782 mfATanh(x) = 0.7475 -1.5708i

See Also mfATan, mfATan2, mfTan, mfTanh


mfCos, msCos Request cosine function.

Module fml

Syntax y = mfCos(x) Descriptions Procedure mfCos(x) returns element-by-element the circular cosine of mfArray x, where x is in radians. The function domain and range include real and complex data. Example Code pr ogram example



x = (3.14d0, -3.14d0) y = mfCos(x)

call msDisplay(x, 'x', y, 'mfCos(x)') ca ll msFreeArgs(x, y)


Result x = 3.1400 -3.1400i mfCos(x) = - 11.5736 +0.0184i

See Also mfACos, mfACosh, mfCosh


mfCosh, msCosh Request hyperbolic cosine function.

Module fml

Syntax y = mfCosh(x) Descriptions Procedure mfCosh(x) returns element-by-element the hyperbolic cosine of mfArray x, where x is in radians. The function domain and range include real and complex data. Example Code pr ogram example



x = 0.1d0 y = mfCosh(x)

call msDisplay(x, 'x', y, 'mfCosh(x)') ca ll msFreeArgs(x, y)


Result x = 0.1000 mfCosh(x) = 1.0050

See Also mfACos, mfACosh, mfCos


mfCot, msCot Request cotangent function.

Module fml

Syntax y = mfCot(x) Descriptions Procedure mfCot(x) returns element-by-element the cotangent of mfArray x in radians where mfCot(x) = 1/mfTan(x) The function domain and range include real and complex data. Example Code pr ogram example



x = 0.7d0 y = mfCot(x)

call msDisplay(x, 'x', y, 'mfCot(x)') ca ll msFreeArgs(x, y)


Result x = 0.7000 mfCot(x) = 1.1872

See Also mfCoth, mfACot, mfACoth


mfCoth, msCoth Request hyperbolic cotangent function.

Module fml

Syntax y = mfCoth(x) Descriptions Procedure mfCoth(x) returns element-by-element the hyperbolic cotangent of the mfArray x in radians, where mfCoth(x) = 1/mfTanh(x) The function domain and range include real and complex data. Example Code pr ogram example



x = 0.5d0 y = mfCoth(x)

call msDisplay(x, 'x', y, 'mfCoth(x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfCoth(x) = 2.1640

See Also mfCot, mfACot, mfACoth


mfCsc, msCsc Request cosecant function.

Module fml

Syntax y = mfCsc(x) Descriptions Procedure mfCsc(x) returns the element-by-element cosecant of mfArray x, where mfCsc(x) = 1/mfSin(x) The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example



x = 2.0d0 y = mfCsc(x)

call msDisplay(x, 'x', y, 'mfCsc(x)') ca ll msFreeArgs(x, y)


Result x =

2

mfCsc(x) = 1.0998

See Also mfCsch, mfACsc, mfACsch


mfCsch, msCsch Request hyperbolic cosecant function.

Module fml

Syntax y = mfCsch(x) Descriptions Procedure mfCsch(x) returns element-by-element the hyperbolic cosecant of mfArray x, where mfCsch(x) = 1/mfSinh(x) The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example



x = 0.5d0 y = mfCsch(x)

call msDisplay(x, 'x', y, 'mfCsch(x)') ca ll msFreeArgs(x, y)


Result x = 0.5000 mfCsch(x) = 1.9190

See Also mfCsc, mfACsc, mfACsch


mfSec, msSec Request secant function.

Module fml

Syntax y = mfSec(x) Descriptions Procedure mfSec(x) returns element-by-element the secant of mfArray x, where mfSec(x) = 1/mfCos(x) The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example



x = MF_PI y = mfSec(x)

call msDisplay(x, 'x', y, 'mfSec(x)') ca ll msFreeArgs(x, y)


Result x = 3.1416 m fSec(x) =

-1

See Also mfSech, mfASec, mfASech


mfSech, msSech Request hyperbolic secant function.

Module fml

Syntax y = mfSech(x) Descriptions Procedure mfSech(x) returns element-by-element the hyperbolic secant of mfArray x, where mfSech(x) = 1/mfCosh(x) The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example



x = (-1, 4) y = mfSech(x)

call msDisplay(x, 'x', y, 'mfSech(x)') ca ll msFreeArgs(x, y)


Result x = -1.0000 +4.0000i mfSech(x) = - 0.5578 -0.4918i

See Also mfSec, mfASec, mfASech


mfSin, msSin Request sine function.

Module fml

Syntax y = mfSin(x) Descriptions Procedure mfSin(x) returns element-by-element the circular sine of mfArray x. The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example

use mod_ess use mod_elfun im plicit none


x = 0.5236d0 y = mfSin(x)

call msDisplay(x, 'x', y, 'mfSin(x)') ca ll msFreeArgs(x, y)


Result x = 0.5236 mfSin(x) = 0.5000

See Also mfSinh, mfASin, mfASinh


mfSinh, msSinh Request hyperbolic sine function.

Module fml

Syntax y = mfSinh(x) Descriptions Procedure mfSinh(x) returns element-by-element the hyperbolic sine of mfArray x, where x is in radians. The function domain and range include real and complex data. Example Code pr ogram example



x = 3 y = mfSinh(x)

call msDisplay(x, 'x', y, 'mfSinh(x)') ca ll msFreeArgs(x, y)


Result x =

3

mfSinh(x) = 10.0179

See Also mfSin, mfASin, mfASinh


mfTan, msTan Request tangent function.

Module fml

Syntax y = mfTan(x) Descriptions Procedure mfTan(x) returns element-by-element the tangent of mfArray x. The function domain and range include real and complex data. All angles are in radians. mfTan(x) = mfSin(x)/mfCos(x). Example Code pr ogram example



x = 1.0d0 y = mfTan(x)

call msDisplay(x, 'x', y, 'mfTan(x)') ca ll msFreeArgs(x, y)


Result x =

1

mfTan(x) = 1.5574

See Also mfTanh, mfATan, mfATanh


mfTanh, msTanh Request hyperbolic tangent function.

Module fml

Syntax y = mfTanh(x) Descriptions Procedure mfTanh(x) returns element-by-element the hyperbolic tangent of mfArray x, where mfTanh(x) = mfSinh(x)/mfCosh(x) The function domain and range include real and complex data. All angles are in radians. Example Code pr ogram example



x = 1 y = mfTanh(x)

call msDisplay(x, 'x', y, 'mfTanh(x)') ca ll msFreeArgs(x, y)


Result x =

1

mfTanh(x) = 0.7616

See Also mfTan, mfATan, mfATanh


Exponential


mfExp, msExp Request exponential function.

Module fml

Syntax y = mfExp(x) Descriptions Procedure mfExp(x) returns element-by-element the exponential of mfArray x. The function domain and range include real and complex data. Example Code pr ogram example



x = (2.d0, 3.d0) y = mfExp(x)

call msDisplay(x, 'x', y, 'mfExp(x)') ca ll msFreeArgs(x, y)


Result x = 2.0000 +3.0000i mfExp(x) = - 7.3151 +1.0427i

See Also mfLog, mfLog10


mfLog, msLog Request natural logarithm.

Module fml

Syntax y = mfLog(x) Descriptions Procedure mfLog(x) returns element-by-element the natural logarithm of mfArray x. The function domain and range include real and complex data. Example Code pr ogram example



x = MF_E y = mfLog(x)

call msDisplay(x, 'x', y, 'mfLog(x)') ca ll msFreeArgs(x, y)


Result x = 2.7183 m fLog(x) =

1

See Also mfExp, mfLog10, mfLog2


mfLog10, msLog10 Request common logarithm (base 10).

Module fml

Syntax y = mfLog10(x) Descriptions Procedure mfLog10(x) returns element-by-element the base 10 logarithm of mfArray x. The function domain and range include real and complex data. Example Code pr ogram example



x = 5.d0 y = mfLog10(x)

call msDisplay(x, 'x', y, 'mfLog10(x)') ca ll msFreeArgs(x, y)


Result x =

5

mfLog10(x) = 0.6990

See Also mfExp, mfLog, mfLog2


mfLog2, msLog2 Base 2 logarithm and floating-point dissection.

Module fml

Syntax y = mfLog2(x) call msLog2(mfOut(f, e), x) Descriptions Procedure msLog2 computes base 2 logarithm or extract mantissa and exponent of a floating-point number. y = mfLog2(x) returns the elemental base 2 logarithm of mfArray x.

call msLog2(mfOut(f,e),x) dissects each element of mfArray x into the binary

floating-point format consisting of a mantissa, mfArray f, and an exponent, mfArray e, where x

= f*2e for real x. mfArray f contains real values lying in the range of 0.5 <= mfAbs(f) < 1. For

elements of x = 0, the corresponding elements of f and e are equal to zero.

Example The example below evaluates the mfLog2 of mfArray x. Code pr ogram example


ty pe (mfArray) :: x, y, f, e

! MF_PI is MATFOR intrinsic parameter for pi.

x = (/MF_PI, 2* MF_PI, 3* MF_PI/) y = mfLog2(x)

call msLog2(mfout(f, e), x) call msDisplay(y, 'mfLog2(x)' ) call msDisplay(f, 'the mantissa', e, 'the exponent') ca ll msFreeArgs(x, y, f, e)


Result mfLog2(x) = 1.6515 2.6515 3.2365 the mantissa =


0.7854 0.7854 0.5890 t he exponent =

2 3 4

See Also mfLog, mfPow2, mfLog10


mfPow2, msPow2 Base 2 power and floating point number scaling.

Module fml

Syntax y = mfPow2(x) y = mfPow2(f,e) Descriptions Procedure mfPow2 computes base 2 power or floating point number scaling. y = mfPow2(x) returns an mfArray y with elements computed from two raised to the power of

each element of mfArray x, i.e., y = 2x.

y = mfPow2(f, e) returns the mfArray y containing elements computed from y = f*2e. The

result is equivalent to scaling each element of f by exponent e or adding each element of e to the

corresponding floating-point exponent of e.

Example The example below evaluates the mfPow2 of mfArray x, a 1-by-10 vector. Code pr ogram example


ty pe(mfArray) :: x, y, z, f, e

! Initialize the mfArrays x = 3 f = (/1.0, 0.5, -0.75/) e = (/2, 3, 5/)

! Compute base 2 power y = 2**x y = mfPow2(x)

! Perform floating point scaling z = f*(2**e) z = mfPow2(f, e)

! Display the values call msDisplay(x, 'x', y, 'mfPow2(x)') ca ll msDisplay(f, 'f', e, 'e', z, 'mfPow2(f, e)')

! Deallocate mfArrays ca ll msFreeArgs(x, y, z, f, e)


Result


x =

3

m fPow2(x) =

8

f = 1.0000 0.5000 -0.7500 e =

2 3 5

m fPow2(f, e) =

4 4 -24

See Also mfLog2, mfExp


mfSqrt, msSqrt Square root function.

Module fml

Syntax y = mfSqrt(x) Descriptions Procedure mfSqrt(x) returns element-by-element the square root of mfArray x. The procedure domain includes real and complex data. For negative and complex elements of x, complex results are returned. Example The example below evaluates mfSqrt(-4). Code pr ogram example


ty pe (mfArray):: x, y

x = -4 y = mfSqrt(x)

call msDisplay(x, 'x', y, 'mfSqrt(x)') ca ll msFreeArgs(x, y)


Result x =

- 4

mfSqrt(x) = 0.0000 +2.0000i

See Also mfExp, mfLog, mfLog2, mfLog10


Complex


mfAbs, msAbs Absolute value of real and complex numbers.

Module fml

Syntax y = mfAbs(x) Descriptions Procedure mfAbs(x) returns element-by-element the absolute of mfArray x. For real x, mfAbs(x) returns |x|. For complex z = x + iy, mfAbs(z) returns the magnitude of the complex computed as sqrt(x2+y2). Example The example below evaluates the absolute value of complex number (2, -2) Code pr ogram example



x = (2, -2) y = mfAbs(x)

call msDisplay(x, 'x', y,'mfAbs(x)') ca ll msFreeArgs(x, y)


Result x = 2.0000 -2.0000i mfAbs(x) = 2.8284

See Also mfAngle, mfSign


mfAngle, msAngle Phase angle of complex numbers.

Module fml

Syntax p = mfAngle(z) Descriptions Procedure mfAngle(z) returns an mfArray p containing the element-by-element phase angle of complex mfArray z. Example The example below evaluates the phase angle of complex mfArray z over a range of value. Code pr ogram example


ty pe(mfArray) :: theta, z, x, y

x = mfColon(0, 5, 10) y = mfColon(-2, 5, 8) z = mfComplex(x, y) th eta = mfAngle(z)

call msDisplay(z, 'z', theta, 'mfAngle(z)') ca ll msFreeArgs(theta, z, x, y)


Result z =

co lumn 1 to 3

0.0000 -2.0000i 5.0000 +3.0000i 10.0000 +8.0000i mfAngle(z) = -1.5708 0.5404 0.6747

See Also mfAbs


mfComplex, msComplex Convert input numbers into complex numbers.

Module fml

Syntax z = mfComplex(x, y) z = mfComplex(x) Descriptions Procedure mfComplex(x, y) returns a complex mfArray whose real part is specified by the elements of mfArray x and imaginary part is specified by elements of mfArray y i.e. z = x + yi. z = mfComplex(x) returns a complex mfArray whose real part is specified by the elements of

mfArray x and imaginary part is zero i.e. z = x + 0i.

Example The example below constructs a complex mfArray z from two real mfArrays x and y. Code pr ogram example


ty pe (mfArray) :: z, x, y

x = (/-5, 7, 0/) y = (/ 3, 1, 2/) z = mfComplex(x, y)

call msDisplay(x, 'x', y, 'y', z, 'mfComplex(x, y)') ca ll msFreeArgs(x, y, z)


Result x =

- 5 7 0

y =

3 1 2

mfComplex(x, y) = - 5.0000 +3.0000i 7.0000 +1.0000i 0.0000 +2.0000i

See Also mfImag, mfReal


mfConj, msConj Returns conjugate of complex numbers.

Module fml

Syntax c = mfConj(z) Descriptions Procedure mfConj(z) returns an mfArray containing the element-by-element conjugate of complex mfArray z. Example The example below evaluates the conjugate of complex mfArray z. Code pr ogram example


ty pe (mfArray) :: c, z

z = (-2, 2) c = mfConj(z)

call msDisplay(z, 'z', c, 'mfConj(z)') ca ll msFreeArgs(c, z)


Result z = -2.0000 +2.0000i mfConj(z) = - 2.0000 -2.0000i

See Also mfImag, mfReal


mfImag, msImag Returns imaginary part of complex numbers.

Module fml

Syntax y = mfImag(z) Descriptions Procedure mfImag(z) returns element-by-element the imaginary part of complex mfArray z. Example The example below gets the imaginary part of complex mfArray z. Code pr ogram example



x = (2, -2) y = mfImag(x)

call msDisplay(x, 'x', y, 'mfImag(x)') ca ll msFreeArgs(x, y)


Result x = 2.0000 -2.0000i m fImag(x) =

-2

See Also mfReal, mfConj


mfReal, msReal Returns real part of complex numbers.

Module fml

Syntax x = mfReal(z) Descriptions Procedure mfReal(z) returns element-by-element the real part of complex mfArray z. Example The example below gets the real part of complex mfArray z. Code pr ogram example


ty pe (mfArray) :: z, x

z = (-2, 2) x = mfReal(z)

call msDisplay(z, 'z', x, 'mfReal(z)' ) ca ll msFreeArgs(z, x)


Result z = -2.0000 +2.0000i m fReal(z) =

-2

See Also mfImag, mfConj


Rounding and Remainder


mfCeil, msCeil Round mfArray elements toward positive infinity.

Module fml

Syntax y = mfCeil(x) Descriptions Procedure mfCeil(x) returns an mfArray containing the elements of mfArray x rounded to the nearest integer toward positive infinity. The real and imaginary parts of a complex number are rounded independently. Example The example below performs the mfCeil operation on mfArray x. Code pr ogram example


ty pe (mfArray) :: x, y, u, v

x = (/-1.6, 2.3/) u = (3.2, 2.2) y = mfCeil(x) v = mfCeil(u)

call msDisplay(x, 'x', y, 'mfCeil(x)') call msDisplay(u, 'u', v, 'mfCeil(u)') ca ll msFreeArgs(x, y, u, v)


Result x = -1.6000 2.3000 m fCeil(x) =

- 1 3

u = 3.2000 +2.2000i mfCeil(u) =


4.0000 +3.0000i

See Also mfFix, mfFloor, mfRound


mfFix, msFix Round mfArray elements toward zero.

Module fml

Syntax y = mfFix(x) Descriptions Procedure mfFix(x) returns an mfArray containing the elements of mfArray x rounded to the nearest integer toward zero. The real and imaginary parts of a complex number are rounded independently. Example The example below performs the mfFix operation on mfArray x. Code pr ogram example



x = (/-1.6, 2.3/) y = mfFix(x) u = dcmplx(3.2, 2.2) v = mfFix(u)

call msDisplay(x, 'x', y, 'mfFix(x)') call msDisplay(u, 'u', v, 'mfFix(u)') ca ll msFreeArgs(x, y, u, v)


Result x = -1.6000 2.3000 m fFix(x) =

- 1 2

u = 3.2000 +2.2000i mfFix(u) =


3.0000 +2.0000i

See Also mfCeil, mfFloor, mfRound


mfFloor, msFloor Round mfArray elements toward minus infinity.

Module fml

Syntax y = mfFloor(x) Descriptions Procedure mfFloor(x) returns an mfArray containing the elements of mfArray x rounded to the nearest integer toward negative infinity. The real and imaginary parts of a complex number are rounded independently. Example The example below performs the mfFloor operation on mfArray x. Code pr ogram example



x = (/-1.6, 2.3/) u = (3.2, 2.2) y = mfFloor(x) v = mfFloor(u)

call msDisplay(x, 'x', y, 'mfFloor(x)') call msDisplay(u, 'u', v, 'mfFloor(u)') ca ll msFreeArgs(x, y, u, v)


Result x = -1.6000 2.3000 m fFloor(x) =

- 2 2

u = 3.2000 +2.2000i mfFloor(u) =


3.0000 +2.0000i

See Also mfCeil, mfFix, mfRound


mfMod, msMod Returns modulus (signed remainder after division).

Module fml

Syntax m = mfMod(x, y) Descriptions Procedure mfMod(x, y) returns an mfArray containing element-by-element the signed remainder of x, y division. The procedure uses the following algorithm: y ≠0, mfMod(x, y) = x - y*mfFloor(x/y) y = 0, mfMod(x, y) = x. Note that : • The shape of the input arguments x and y must conform. • mfMod(x, y) always differs from x by a multiple of y.

• mfMod(x, y) has the same sign as y while mfRem(x,y) has the same sign as x.

• mfMod(x, y) and mfRem(x, y) are equal if x and y are of the same sign. They differ if

the sign of x and y are different.

Limitations: Arguments x and y should be integers. Due to the inexact representation of floating-point numbers on a computer, real (or complex) inputs may lead to unexpected results. Example The example below finds the modulus of x and y. Code pr ogram example


ty pe (mfArray) :: x, y, m

x = (/-5, 7, -15/) y = (/2, -3, -4/) m = mfMod(x, y)

call msDisplay(x, 'x', y, 'y', m, 'mfMod(x,y)') ca ll msFreeArgs(x, y, m)



Result x =

-5 7 -15

y =

2 -3 -4

m fMod(x,y) =

1 -2 -3

See Also mfRem


mfRem, msRem Returns remainder after division.

Module fml

Syntax r = mfRem(x, y) Descriptions Procedure mfRem(x, y) returns an mfArray containing the element-by-element remainder of x/y division. The result lies between 0 and mfSign(x)*mfAbs(y). The input x and y are either scalars or conformable arrays. Note that : • mfRem(x,y) = x - y*mfFix(x/y) for y ≠0

• mfFix(x,y) is the integer of the quotient x/y.

• If y is zero, mfRem returns MF_NAN. Limitations: Arguments x and y should be integers. Due to the inexact representation of floating-point numbers on a computer, real (or complex) inputs may lead to unexpected results. Example The example below finds the remainder of x/y. Code pr ogram example


ty pe (mfArray) :: x, y, r

x = (/-5, 7, -15/) y = (/2, -3, -4/)

r = mfRem(x,y) call msDisplay(x, 'x', y, 'y', r, 'mfRem(x,y)') ca ll msFreeArgs(x, y, r)


Result x =

-5 7 -15

y =

2 -3 -4


m fRem(x,y) =

-1 1 -3

See Also mfMod


mfRound, msRound Round towards nearest integer.

Module fml

Syntax y = mfRound(x) call msRound(mfOut(y), x) Descriptions Procedure mfRound(x) rounds the elements of mfArray x to the nearest integer. The real and imaginary parts of a complex number are rounded independently. Example The example below performs the round operation on mfArray x. Code pr ogram example



x = (/-1.6, 2.3/) u = (3.2, 2.2)

y = mfRound(x) v = mfRound(u)

call msDisplay(x, 'x', y, 'mfRound(x)') call msDisplay(u, 'u', v, 'mfRound(u)') ca ll msFreeArgs(x, y, u, v)


Result x = -1.6000 2.3000 m fRound(x) =

- 2 2

u = 3.2000 +2.2000i m fRound(u) =


3.0000 +2.0000i

See Also mfCeil, mfFix, mfFloor


mfSign, msSign Signum function.

Module fml

Syntax y = mfSign(x) Descriptions Procedure mfSign(x) returns an mfArray y containing the element-by-element information on the sign of each element in mfArray x. Note that : For elements x >0, corresponding element of y = 1. For elements x = 0, corresponding element of y = 0. For elements x < 0, corresponding element of y = -1. For nonzero elements of complex x, mfSign(x) = x/mfAbs(x). Example The example below finds the sign of elements of mfArray x. Code pr ogram example



x = (/-5, 7, 0/) y = mfSign(x)

ca ll msDisplay(x, 'x', y, 'mfSign(x)')



Result x =

- 5 7 0

m fSign(x) =

-1 1 0

See Also mfAbs


Chapter 7 Matrix Functions 181

C H A P T E R 6

Elementary Matrix-manipulation Functions

This chapter describes the elementary matrix-manipulation functions. Please see below

Matrices

mfEye Identity matrix

mfLinSpace Constructs linearly spaced vectors.

mfMagic Constructs magic matrix.

msMeshgrid Constructs grids for two matrices.

mfRepmat Replicate and tile an array.

mfOnes Arrays containing ones.

mfRand Arrays containing random numbers.

mfZeros Arrays containing zeros.

Matrix Manipulation

mfDiag Diagonal matrices and diagonals of a matrix.

mfFind Find indices and values of nonzero elements.

mfReshape Change shape of an array.

mfTril Returns lower triangular of an mfArray.

mfTriu Returns upper triangular of an mfArray.

mfLogical Converts numerical values to logical.



Matrices


mfEye, msEye Construct an identity matrix.

Module fml

Syntax a = mfEye(m[, n]) Descriptions Procedure mfEye generates an identity matrix. a = mfEye(m) returns an m-by-m identity matrix for scalar m. If mfArray m contains

information about the shape of an array, mfEye returns mfArray whose shape is specified by m.

For example, a = mfEye(mfShape(b)).

a = mfEye(m, n) returns an m-by-n identity matrix.



ty pe (mfArray) :: a,b

b = mfRand(3,3) a = mfEye(mfShape(b))

call msDisplay(a, 'mfEye(3,3)') ca ll msFreeArgs(a,b)


Result mf Eye(3,3) =

1 0 0 0 1 0 0 0 1

See Also mfOnes, mfZeros


mfColon, msColon Construct a vector mfArray consisting of a ramp of data.

Module fml

Syntax x = mfColon(start[, step][, end]) Descriptions Function mfColon constructs a regularly spaced vector mfArray. The input arguments, start, step and end can be integers or real. For complex inputs, imaginary parts are ignored. x = mfColon(a, b, c)

• Vector mfArray x is constructed with elements [a, a+b, ..., a+b*m, ...,c] where m = mfFix((c-a)/b).

• The procedure returns empty when b>0, a>c, or when b<0, a<c. x = mfColon(a, c)

• Vector mfArray x is constructed with elements [a, a+1, ...,c]. • It returns empty if a>c. Example The following example constructs an mfArray x by using mfColon. Code pr ogram example


ty pe (mfArray) :: x

x = mfColon(1d0, 0.5d0, 2d0) ca ll msDisplay (x, 'x')

ca ll msFreeArgs(x)


Result x = 1.0000 1.5000 2.0000

See Also


mfLinspace, msLinspace Construct a linearly spaced vector.

Module fml

Syntax a = mfLinSpace(l, u) a = mfLinSpace(l, u, n) Descriptions Procedure mfLinSpace generates linearly spaced row vectors. a = mfLinSpace(l, u) returns a row vector mfArray with 100 linearly and equally spaced

points between l and u, where l is the initial value and u is the final value.

a = mfLinSpace(l, u, n) generates n linearly and equally spaced points between l and u.



ty pe (mfArray) :: a

a = mfLinspace(3, 4, 5)

call msDisplay(a, 'mfLinspace(3, 4, 5)') ca ll msFreeArgs(a)


Result mfLinspace(3, 4, 5) = 3.0000 3.2500 3.5000 3.7500 4.0000

See Also mfColon, mfMeshgrid


mfMagic, msMagic Construct a magic square.

Module fml

Syntax a = mfMagic(m) Descriptions Procedure mfMagic creates a magic square mfArray. A magic square is a special matrix with equal row, column and diagonal sums. a = mfMagic(m) generates an m-by-m magic matrix constructed from the integers 1 through m2. This procedure produces valid magic squares for all m > 0, except for m = 2.



ty pe (mfArray) :: a, rsum, csum

a = mfMagic(3) rsum = mfSum(a, 2) cs um = mfSum(a, 1)

call msDisplay(a, 'mfMagic(3)', rsum, 'row sum', csum, 'column sum') ca ll msFreeArgs(a, rsum, csum)


Result mf Magic(3) =

8 1 6 3 5 7 4 9 2

r ow sum =

15 15 15

c olumn sum =

15 15 15

See Also mfZeros, mfOnes


mfMeshgrid, msMeshgrid Generate x and y matrices for three-dimensional plots.

Module fml

Syntax call msMeshgrid(mfOut(a, b), m) call msMeshgrid(mfOut(a, b), m, n) call msMeshgrid(mfOut(a, b, c), m, n, k) Descriptions Procedure msMeshgrid generates grids from two matrices to make three-dimensional plots. • call msMeshgrid(mfOut(a, b), m, n) transforms the domain specified by vectors

m and n into matrix mfArrays a and b. The rows of output matrix a are copies of vector m

and the columns of output matrix b are copies of vector n.

• call msMeshgrid(mfOut(a, b), m) is an abbreviation for call

msMeshgrid(mfOut(a, b), m, n).

• call msMeshgrid(mfOut(a, b, c), m, n, k) returns three-dimensional arrays

that can be used to evaluate functions of three variables and make three-dimensional

volumetric plots.



ty pe (mfArray) :: x, y, a, b

! Generate vectors a and b using the colon function. a = mfColon(-1d0, 0.5d0, 1d0) b = mfColon(-1.5d0, 0.3d0, 1.5d0)

! Use the meshgrid procedure to transform the domain ! specified by vectors a and b into a two-dimensional function domain. ca ll msMeshgrid(mfOut(x, y), a, b)

! Display the generated matrices. ca ll msDisplay(x, 'x', y, 'y')

! Release the memory occupied by the mfArrays at the ! end of the program.


ca ll msFreeArgs(x, y, a, b)


Result x = -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 -1.0000 -0.5000 0.0000 0.5000 1.0000 y = -1.5000 -1.5000 -1.5000 -1.5000 -1.5000 -1.2000 -1.2000 -1.2000 -1.2000 -1.2000 -0.9000 -0.9000 -0.9000 -0.9000 -0.9000 -0.6000 -0.6000 -0.6000 -0.6000 -0.6000 -0.3000 -0.3000 -0.3000 -0.3000 -0.3000 0.0000 0.0000 0.0000 0.0000 0.0000 0.3000 0.3000 0.3000 0.3000 0.3000 0.6000 0.6000 0.6000 0.6000 0.6000 0.9000 0.9000 0.9000 0.9000 0.9000 1.2000 1.2000 1.2000 1.2000 1.2000 1.5000 1.5000 1.5000 1.5000 1.5000

See Also mfLinSpace, mfColon


mfOnes, msOnes Construct a matrix of ones.

Module fml

Syntax a = mfOnes(m) a = mfOnes(m, n) a = mfOnes(m, n[, d3, ..., d7]) Descriptions Procedure mfOnes generates a matrix containing ones. a = mfOnes(m) returns an m-by-m matrix of ones.

a = mfOnes(m, n) returns an m-by-n matrix of ones.

a = mfOnes(m, n, d3, ..., d7) returns an m-by-n-by-d3-by-...-by-d7 array of ones.




a = mfOnes(3, 2)

call msDisplay(a, 'mfOnes(3, 2)') ca ll msFreeArgs(a)


Result mf Ones(3, 2) =

1 1 1 1 1 1

See Also mfZeros, mfEye


mfRand, msRand Generate mfArrays with uniformly distributed random number entries.

Module fml

Syntax a = mfRand(m) a = mfRand(m, n) a = mfRand(m, n[, d3, ..., d7]) Descriptions Procedure mfRand randomly generates an mfArray. a = mfRand(m) returns an m-by-m matrix with random entries chosen from a uniform

distribution on the interval (0, 1).

a = mfRand(m, n) generates an m-by-n matrix with random entries chosen from a uniform

distribution on the interval (0, 1).

a = mfRand(m, n, d3, ..., d7) generates a m-by-n-by-d3-by-...-by-d7 matrix with

random entries chosen from a uniform distribution on the interval (0,1).




a = mfRand(3, 2)

call msDisplay(a, 'mfRand(3, 2)') ca ll msFreeArgs(a)


Result mfRand(3, 2) = 0.5497 0.0012 0.5496 0.6887 0.4378 0.6035

See Also mfZeros, mfOnes, mfMagic


mfRepmat, msRepmat Replicate and tile an array.

Module fml

Syntax x = mfRepmat(a, m, n) x = mfRepmat(a, p) call msRepmat(mfOut(x), a, m, n) call msRepmat(mfOut(x), a, p) Descriptions Procedure mfRepmat generates mfArray matrices by replicating copies of an array into a larger block array. x = mfRepmat(a, m, n) and call msRepmat(mfOut(x), a, m, n) generate an

mfArray x consisting of m-by-n tiling of vector mfArray a copies.

x = mfRepmat(a, p) and call msRepmat(mfOut(x), a, p) generate an mfArray

x containing p block copies of mfArray a. Vector p contains information about the number of

mfArray x blocks in each dimension. The information is in the form of [m, n], or

[m, n, d3, ..., d7].




! Create a 3-by-2 mfArray consisting of ones. a = mfRepmat(mf(1), mf((/3, 2/))) ! This is similar to mfOnes(3,2) but is much faster. ca ll msDisplay (a, ' mfRepmat(mf(1), mf((/3,2/)))')

! Create 3-by-2 block copies of mfMagic(3) a = mfRepmat(mfMagic(2), mf((/3,2/))) ca ll msDisplay (a, 'mfRepmat(mfMagic(2), (/3,2/))')

! Deallocate mfArrays. ca ll msFreeArgs(a)


Result


mf Repmat(mf(1), mf((/3,2/))) =

1 1 1 1 1 1

m fRepmat(mfMagic(2), (/3,2/)) =

1 3 1 3 4 2 4 2 1 3 1 3 4 2 4 2 1 3 1 3 4 2 4 2

See Also mfMeshgrid


mfZeros, msZeros Generate matrices with all zeros.

Module fml

Syntax a = mfZeros(m) a = mfZeros(m, n) a = mfZeros(m, n[, d3, ..., d7]) Descriptions Procedure mfZeros generates the mfArrays of zeros. It is used to allocate memory for mfArrays. a = mfZeros(m) returns an m-by-m mfArray of zeros.

a = mfZeros(m, n) returns an m-by-n mfArray of zeros.

a = mfZeros(m, n, d3, ..., d7) returns an m-by-n-by-d3-by-...-by-d7 array of zeros.




a = mfZeros(2, 2)

call msDisplay(a, 'mfZeros(2, 2)') ca ll msFreeArgs(a)


Result mf Zeros(2, 2) =

0 0 0 0

See Also mfOnes, mfEye


Matrix Manipulation


mfDiag, msDiag Request diagonals of a matrix.

Module fml

Syntax d = mfDiag(a[, k]) a = mfDiag(d[, k]) Descriptions Procedure mfDiag(a) returns a vector mfArray d containing the elements extracted from the main diagonal of matrix mfArray a. a = mfDiag(d) returns a diagonal matrix mfArray a, with its main diagonal composed of

member elements of vector d.

d = mfDiag(a, k) returns a vector mfArray d, containing the elements extracted from the kth

diagonal of matrix mfArray a.

a = mfDiag(d, k) returns a diagonal matrix a of order mfLength(d) + mfAbs(k) whose kth

diagonal is composed of elements from vector mfArray d. k = 0 represents the main diagonal, k >

0 is above the main diagonal, and k < 0 is below the main diagonal.



ty pe (mfArray) :: a, d, b

! Construct an mfArray using the magic function. a = mfMagic(3)

! Extract the 1st diagonal of mfArray a. d = mfDiag(a, 1)

! Construct an mfArray b, whose main diagonal is ! composed of d. b = mfDiag(d)

! Display the resulting mfArrays. call msDisplay(a, 'mfMagic(3)', d, 'k = 1 diagonal') ca ll msDisplay(b, 'mfDiag(d)')

! Release the memory occupied by mfArrays a ,b, and d. ca ll msFreeArgs(a, b, d)

end program example



8 1 6 3 5 7 4 9 2

k = 1 diagonal =

1 7

m fDiag(d) =

1 0 0 7

See Also mfTriu, mfTril


mfFind, msFind Find indices of nonzero elements.

Module fml

Syntax y = mfFind(x) call msFind(mfOut(i, j), x) call msFind(mfOut(i, j, v), x) Descriptions Procedure mfFind generates indices of nonzero elements. y = mfFind(x) returns an mfArray y containing long column indices of nonzero entries in

mfArray x. If none are found, mfFind returns an empty matrix.

call msFind(mfOut(i, j), x) returns two mfArrays i and j containing the row and

column indices of nonzero entries in matrix mfArray x.

call msFind(mfOut(i, j, v), x) returns three mfArrays i, j, and v containing the

row indices, column indices, and nonzero entries of matrix mfArray x respectively.

Example The example below retrieves the indices of non-zero elements of a matrix mfArray. Code pr ogram example


ty pe (mfArray) :: a, i, j

a = mfMagic(3) > 7 ca ll msFind(mfOut(i,j), a)

call msDisplay(a, 'a', i, 'i', j, 'j') ca ll msFreeArgs(a, i, j)


Result a =

1 0 0 0 0 0 0 1 0


i =

1 3

j =

1 2

See Also mfColon, relational_operators


mfLogical, msLogical Convert numeric values to logical values.

Module fml

Syntax l = mfLogical(x) Descriptions Procedure mfLogical(x) returns a logical mfArray. An element of mfArray l is assigned logical "true" if the corresponding element in mfArray x is nonzero, otherwise it is assigned "false". Note: Most arithmetic operations remove the logical characteristic from an array. For example, adding zero to a logical array. Example Code pr ogram example


ty pe (mfArray) :: b, x, y, z

x = mfEye(3) b = mfLogical(x) y = (/1,2,3/) .vc. (/4,5,6/) .vc. (/7,8,9/) z = mfS(y, b)

ca ll msDisplay(y, 'y', z, 'z')

ca ll msFreeArgs(b, x, y, z)


Result y =

1 2 3 4 5 6 7 8 9

z =

1 5 9

See Also mfZeros, mfOnes, mfMagic


mfReshape, msReshape Change size of an mfArray.

Module fml

Syntax y = mfReshape(x, m, n) a = mfReshape(b, m[, n, d3,...,d7]) Descriptions Procedure mfReshape reshapes arrays. y = mfReshape(x, m, n) returns the m-by-n matrix mfArray y whose elements are taken

column-wise from mfArray x. An error occurs if x does not have m*n entries.

a = mfReshape(b, m, n, d3, ..., d7) returns the m-by-n-by-d3-...-d7 array mfArray

a whose elements are taken column-wise from mfArray b. An error occurs if b does not have

m*n*d3*...*d7 entries.



ty pe(mfArray):: x, y

x = (/1, 2, 3, 4, 5, 6/) y = mfReshape(x, (/3, 2/)) ca ll msDisplay(x, 'x', y, 'mfReshape(x, (/3, 2/))')



Result x =

1 2 3 4 5 6

m fReshape(x, (/3, 2/)) =

1 4 2 5 3 6

See Also mfSize


mfTril Return the lower triangular part of a matrix.

Module fml

Syntax l = mfTril(a[, k]) Descriptions Procedure mfTril returns the lower triangular part of a matrix. l = mfTril(a) returns an mfArray l containing the elements on and below the main diagonal

of mfArray a.

l = mfTril(a, k) returns an mfArray l containing the elements on and below the kth

diagonal of mfArray a. k = 0 is the main diagonal, k > 0 is above the main diagonal, and k < 0 is

below the main diagonal.



ty pe (mfArray) :: a, l, l1


! Get the lower triangular of mfArray a from the main ! diagonal downwards. l = mfTril(a)

! Get the lower triangular a from the 1sdiagonal downwards. l1 = mfTril(a, 1)

! Display the resulting mfArrays. call msDisplay(a, 'mfmagic(3)', l, 'lower triangular') ca ll msDisplay(l1, 'lower triangular from k = 1')

! Release the memory occupied by mfArrays a, l, and l1. ca ll msFreeargs(a, l, l1)


Result mf magic(3) =

8 1 6 3 5 7


4 9 2

l ower triangular =

8 0 0 3 5 0 4 9 2

l ower triangular from k = 1 =

8 1 0 3 5 7 4 9 2

See Also mfTriu, mfDiag


mfTriu Return the upper triangular part of a matrix.

Module fml

Syntax u = mfTriu(a[, k]) Descriptions Procedure mfTriu returns the upper triangular part of a matrix. u = mfTriu(a) returns an mfArray u containing the elements on and above the main diagonal

of mfArray a.

u = mfTriu(a, k) returns an mfArray u containing the elements on and above the kth

diagonal of mfArray a. k = 0 is the main diagonal, k > 0 is above the main diagonal, and k < 0 is

below the main diagonal.



ty pe (mfArray) :: a, u, u1


! Extract the upper triangular of mfArray a from the main ! diagonal upwards. u = mfTriu(a)

! Extract the upper triangular a from the 1sdiagonal upwards. u1 = mfTriu(a, 1)

! Display the resulting mfArrays. call msDisplay(a, 'mfMagic(3)', u, 'upper triangular') ca ll msDisplay(u1, 'upper triangular from k = 1')

! Release the memory occupied by mfArrays a, u, and u1. ca ll msFreeArgs(a, u, u1)



8 1 6 3 5 7


4 9 2

u pper triangular =

8 1 6 0 5 7 0 0 2

u pper triangular from k = 1 =

0 1 6 0 0 7 0 0 0

See Also mfTril, mfDiag



C H A P T E R 7

Matrix Functions

This chapter introduces a set of matrix functions for solving linear algebra problems, please see below:

Matrix Analysis

mfDet

mfNorm

mfRank

mfTrace

Linear Equations

mfChol

mfCond

mfInv

mfRcond

mfLu

mfQr


Eigenvalues and singular values

mfEig

mfHess

mfQz

mfSchur

mfSvd

Factorization Utilities

mfBalance

Fast Fourier Transform

mfFFT

mfIFFT

mfFFT2

mfIFFT2

mfFFTShift

mfIFFTShift


Matrix Analysis


mfDet Find the determinant of a matrix.

Module fml

Syntax d = mfDet(x) Descriptions Procedure mfDet(x) returns a scalar mfArray containing the determinant of square matrix mfArray x. For matrices of modest order with small integer entries, the procedure can be used as a test for matrix singularity. Example The following example uses the mfDet procedure to compute the determinant of a non-singular square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, d

! Construct a 3-by-3 mfArray x using vertical concatenation. x = (/1.0d0, 2.0d0, 3.0d0/) .vc. & (/7.0d0, 8.0d0, 9.0d0/) .vc. & (/1.0d0, 2.0d0, 4.0d0/)

! Compute determinant of mfArray x d = mfDet(x)

! Display value of x and determinant of x ca ll msDisplay(x, 'x', d, 'mfDet(x)')

! Deallocate mfArrays x and d ca ll msFreeArgs(x, d)


Result x =

1 2 3 7 8 9 1 2 4

m fDet(x) =

-6

See Also mfCond, mfInv, mfLu


mfNorm Calculate the matrix or vector norm.

Module fml

Syntax n = mfNorm(x[, p]) Descriptions n = mfNorm(x), n = mfNorm(x, p) Procedure mfNorm generates the norm value differently for matrices and vectors. For matrices: • mfNorm(x) returns a scalar mfArray containing the largest singular value of mfArray x.

• mfNorm(x, p) returns a different kind of norm, depending on the value of p.

• mfNorm(x, 1) returns the largest column sum of x.

• mfNorm(x, 2) is equivalent to mfNorm(x). It returns the largest singular value of

mfArray x.

• mfNorm(x, MF_INF) returns the largest row sum of x, which is also the infinity norm of

x.

• mfNorm(x, "fro") returns the Frobenius norm.

For vectors: • mfNorm(v, 1) returns a scalar mfArray equal to the sum of elements in mfArray v.

• mfNorm(v) is the same as mfNorm(v, 2)and returns the value of

mfSum(mfAbs(v).^2)^(1/2).

Example The following example uses the mfNorm procedure to compute the norm of a non-singular square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, n



! Compute norm of mfArray x n = mfNorm(x)

! Display value of x and norm n of x ca ll msDisplay(x, 'x', n, 'norm')

! Deallocate mfArrays x and n ca ll msFreeArgs(x, n)


Result x =

1 2 3 7 8 9 1 2 4

norm = 15.0130

See Also mfCond


mfRank Return the rank of a matrix.

Module fml

Syntax r = mfRank(x[, tol]) Descriptions For matrices, procedure mfRank(x) is used as an estimation for the number of linearly independent rows and columns of a matrix x. mfRank(x), mfRank(x[, tol])

• Procedure mfRank(x) returns a scalar mfArray containing the number of independent rows or columns of a matrix x.

• Procedure mfRank(x) uses the default tol = mfMax(mfSize(x)) * mfNorm(x) * MF_EPS.

• Procedure mfRank(x, tol) returns the singular values of matrix x that are larger than tol.

Example The following example uses the mfRank procedure to compute the rank of a square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, r

! Construct a 3-by-3 mfArray x using vertical ! concatenation. x = (/1.0d0, 2.0d0, 3.0d0/) .vc. & (/7.0d0, 8.0d0, 9.0d0/) .vc. & (/2.0d0, 4.0d0, 6.0d0/)

! Compute the rank of mfArray x r = mfRank(x)

! Display value of x and the rank r of x ca ll msDisplay(x, 'x', r, 'mfRank(x)')

! Deallocate mfArrays x and r ca ll msFreeArgs(x, r)



Result x =

1 2 3 7 8 9 2 4 6

m fRank(x) =

2

See Also mfSize


mfTrace, msTrace Return the sum of diagonal elements.

Module fml

Syntax s = mfTrace(x) Descriptions For matrices, procedure mfTrace(x) returns the sum of diagonal elements of mfArray x, which is equivalent to the sum of eigenvalues of mfArray x. Example The following example uses the mfTrace procedure to compute the sum of the diagonal elements of the square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, s

! Construct a 3-by-3 mfArray x using vertical ! concatenation. x = (/10.0d0, 0.0d0, 6.0d0/) .vc. & (/0.0d0, -3.0d0, 9.0d0/) .vc. & (/0.0d0, 2.0d0, 4.0d0/)

! Compute the trace of mfArray x s = mfTrace(x)

! Display value of x and trace s of x ca ll msDisplay(x, 'x', s, 'mfTrace(x)')

! Deallocate mfArrays x and s ca ll msFreeArgs(x, s)


Result x =

10 0 6 0 -3 9 0 2 4

m fTrace(x) =

11

See Also


Linear Equations


mfChol, msChol Cholesky factorization.

Module fml

Syntax r = mfChol(x) call msChol(mfOut(r, p), x) Descriptions Procedure mfChol(x) uses only the diagonal and upper triangle of x. r = mfChol(x)

For matrices, if mfArray x is positively definite, then procedure mfChol(x) returns an upper

triangular mfArray r so that .h.r * r = x. If x is not a positive definite mfArray, an error occurs.

call msChol(mfOut(r, p), x)

Error is prevented from occurring when call msChol(mfOut(r, p), x) is used. If x is

positively definite, p is 0 and r is the same as above. Otherwise, p is a positively scalar mfArray

and r is an upper triangular mfArray such that: .h.r * r = mfGet(x, mfColon(1, p-1), mfColon(1,

p-1))

Example The following example uses the mfChol procedure to derive the Cholesky factorization of a non-positive square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, r ,p


! Compute mfChol of mfArray x ca ll msChol(mfout(r, p), x)

! Display value of x, r and p ca ll msDisplay(x, 'x', r, 'r', p, 'p')

! Deallocate mfArrays x and r and p ca ll msFreeArgs(x, r, p)

end program example


Result x =

10 2 6 6 3 9 3 2 4

r = 3.1623 0.6325 0.0000 1.6125 p =

3

See Also mfLu


mfCond Return condition number of a matrix.

Module fml

Syntax c = mfCond(x[, p]) Descriptions For matrices, procedure mfCond returns the p-norm condition number of x. c = mfCond(x) , c = mfCond(x, p)

• Procedure mfCond(x) returns the 2-norm condition number. It is also the ratio of the largest singular value of x to the smallest. A large condition number indicates a nearly singular mfArray x.

• Specifying argument p returns a p-norm condition number of x, which is equal to mfNorm(x, p) * mfNorm(mfInv(x), p), where p is 1, 2, MF_INF or "fro".

p = 1 The mfCond returns the 1-norm condition number. p = 2 The mfCond returns the 2-norm condition number. p = "fro" Return the Frobenius norm condition number. p = MF_INF Return the Infinity norm condition number. Example The following example uses the mfCond procedure to compute the condition number with respect to inversion in the 2-norm of a square matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, c


! Compute the condition number with respect to inversion ! of mfArray x c = mfCond(x)

! Display value of x and c of x ca ll msDisplay(x, 'x', c, 'mfCond(x)')

! Deallocate mfArrays x and c


ca ll msFreeArgs(x, c)


Result x =

10 8 6 5 15 5 6 7 8

mfCond(x) = 8.2853

See Also mfNorm


mfInv Return matrix inverse.

Module fml

Syntax out = mfInv(in) Descriptions For matrices, procedure mfInv(x) returns the inverse of mfArray x. y = mfInv(x)

Procedure mfInv is applicable only for square matrices. A warning message will be printed when x is badly scaled or nearly singular. Example The following example uses the mfInv procedure to compute the inverse of a matrix mfArray x. Code pr ogram example

use fml

implicit none

type(mfArray) :: A, InvA, I

A = (/5.0, 1.0, 2.0, 2.0, 10.0, 3.0 , 3.0, 2.0, 5.0/)

A = mfReshape(A, (/3, 3/))

InvA = mfInv(A) call msDisplay(A, "A", InvA, "InvA")

call msFreeArgs(A,InvA)

e nd program

Result x =

5 2 3 1 10 2 2 3 5

y = 0.2635 -0.0060 -0.1557 -0.0060 0.1138 -0.0419 -0.1018 -0.0659 0.2874

See Also mfCond


mfRcond LINPACK reciprocal condition estimator.

Module fml

Syntax c = mfRcond(x) Descriptions For matrices, procedure mfRcond(x) uses the LAPACK condition estimator to get an estimate for the reciprocal of the condition of x in the 1-norm. c = mfRcond(x) returns a value near 1.0 when matrix x is well conditioned and returns a value

near 0.0 when x is badly conditioned.

Example The following example uses the mfRcond procedure to compute the reciprocal of the condition of x in the 1-norm of a square matrix mfArray x. Code pr ogram example

use fml

implicit none

type(mfArray) :: A, C

A = (/5.0, 1.0, 2.0, 2.0, 10.0, 3.0 , 3.0, 2.0, 5.0/)

A = mfReshape(A, (/3, 3/))

C = mfRcond(A) call msDisplay(A, "A", C, "Condition")

call msFreeArgs(A,C)

e nd program

Result A =

5 2 3 1 10 2 2 3 5

Condition = 0.1374

See Also mfCond, mfNorm


mfLu, msLu Perform LU matrix factorization.

Module fml

Syntax out = mfLu(in) call msLu(mfout(l, u), x) call msLu(mfout(l, u, p), x) Descriptions Procedure mfLu(x) returns the LU decomposition of a square mfArray x. call msLu(mfout(l, u), x)

When used, the procedure mfLu(x) returns mfArray u containing the upper triangular matrix,

and mfArray l containing product of the lower triangular matrix and permutation array, so that

x = l*u

call msLu(mfout(l, u, p), x)

When used, the procedure returns an upper triangular mfArray u, lower triangular mfArray l,

and permutation mfArray p, such that p*x = l*u.

When y = mfLu(x) is used, the procedure returns the one output from LINPACK'S ZGEFA

routine.

Example The following example uses the mfLu procedure to compute the LU decomposition of matrix mfArray x. Code pr ogram example


ty pe(mfArray) :: x, l, u, p


! Compute lu decomposition of mfArray x ca ll msLu(mfout(l, u, p), x)

! Display value of x, l, u and p


call msDisplay(x, 'x', l, 'l' ,u, 'u', p, 'p') ca ll msDisplay(mfNorm(mfMul(p,x)-mfMul(l,u)),'Error')

! Deallocate mfArrays x, l , u, p ca ll msFreeArgs(x, l, u, p)


Result x =

1 2 3 7 8 9 1 2 4

l = 1.0000 0.0000 0.0000 0.1429 1.0000 0.0000 0.1429 1.0000 1.0000 u = 7.0000 8.0000 9.0000 0.0000 0.8571 1.7143 0.0000 0.0000 1.0000 p =

0 1 0 1 0 0 0 0 1

E rror =

0

See Also mfQr


mfQr, msQr Perform orthogonal-triangular decomposition.

Module fml

Syntax out = mfQr(in1[, 0]) call msQr(mfOut(q, r), a[, 0]) call msQr(mfOut(q, r, e), a[, 0]) Descriptions Procedure mfQr returns the orthogonal-triangular decomposition of a matrix. call msQr(mfOut(q, r), a)

• This procedure returns an upper triangular mfArray r of the same shape as a and a unitary mfArray matrix q, such that a = q*r.

call msQr(mfOut(q, r), a, 0)

• This procedure performs an "economy size" decomposition. If a is an m-by-n mfArray with

m > n, only the first n columns of q will be computed. call msQr(mfOut(q, r, e), a)

• This procedure returns an upper triangular mfArray r, a unitary mfArray q, and a permutation matrix mfArray e, such that a*e = q*r.

call msQr(mfOut(q, r, e), a, 0)

• This procedure performs an "economy size" decomposition, returning a permutation vector e, such that q*r = mfGet(a, MF_COL, e). The column permutation e is chosen so that mfAbs(mfDiag(r)) is decreasing.

Example The following example uses the mfQr procedure to compute the orthogonal-triangular decomposition of matrix mfArray x. Code pr ogram example



ty pe(mfArray) :: q, r, a, e

! Construct a 3-by-3 mfArray a using vertical ! concatenation. a = (/1.0d0, 2.0d0, 3.0d0/) .vc. & (/7.0d0, 8.0d0, 9.0d0/) .vc. & (/1.0d0, 2.0d0, 4.0d0/)

! Compute qr decomposition of mfArray a ca ll msQr(mfOut(q, r, e), a)

! Display value of a, q, r and e call msDisplay(a, 'a', q, 'q' ,r, 'r', e, 'e') ca ll msDisplay(mfNorm(mfMul(a,e)-mfMul(q,r)),'Error')

! Deallocate mfArrays a, q, r, e ca ll msFreeArgs(q, r, a, e)


Result a =

1 2 3 7 8 9 1 2 4

q = -0.2914 0.4491 -0.8447 -0.8742 -0.4836 0.0445 -0.3885 0.7513 0.5335 r = -10.2956 -6.7990 -8.3531 0.0000 -2.1849 -1.4681 0.0000 0.0000 -0.2667 e =

0 1 0 0 0 1 1 0 0 Error = 1.0e-14 * 0.4378

See Also mfLu


mfMul Return matrix product of two mfArrays.

Module fml

Syntax z = mfMul(x, y) Descriptions Function mfMul(x, y) returns the matrix product of mfArrays x and y, where x is an m-by-p matrix and y is a p-by-n matrix. The product of the matrix multiplication is an m-by-n mfArray. Example Code pr ogram example


ty pe(mfArray) :: x, y, z

x = mfMagic(3) y = mfInv(x) z = mfMul(x,y) ca ll msDisplay(x, 'x', y, 'Inv',z,'Eye')

ca ll msFreeArgs(x, y, z)


Result x =

8 1 6 3 5 7 4 9 2

Inv = 0.1472 -0.1444 0.0639 -0.0611 0.0222 0.1056 -0.0194 0.1889 -0.1028 Eye = 1.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 1.0000

See Also Arithmetic Operators


mfRDiv, mfLDiv Matrix left division and right division operators.

Module fml

Syntax x = mfLDiv(a, b) x = mfRDiv(b, a) Descriptions Function mfLDiv and mfRDiv are normally used in solving systems of linear equations represented by (xa=b). x = mfLDiv(a, b) is an approximation of mfMul(mfInv(a), b).

x = mfRDiv(b, a) is an approximation of mfMul(b, mfInv(a)).

The two functions are related by mfLDiv(a, b) = mfTranspose(mfRDiv ((mfTranspose(b)),(mfTranspose(a))))

Depending on the structure of the coefficient matrix a, MATFOR uses different algorithms to

solve the simultaneous linear equations mfLDiv(a, b) and mfRDiv(b, a). Figure 2.2

provides an overview of the different methods used for solving the linear equation, depending on

the structure of matrix a.

Figure 2.2 Algorithms applicable for each type of matrix a. If a is an n-by-n square matrix, and b is an n-by-p matrix, then mfLDiv(a, b) is solved by using Gaussian elimination. MATFOR performs a structural test on matrix a to select the optimal factorization method. Non-symmetry and non-positive definite systems are detected almost immediately, hence this does not take much of the computation time. If a is an m-by-n rectangle matrix, and b is an m-by-p matrix, for m /= n, MATFOR uses the least squares method for solving the under-determined or over-determined system. There are two approaches to solving a least squares problem - QR and normal equations method. MATFOR uses the normal equations method as it requires half the arithmetic when m<n and much less storage space compared to the QR method. Note that MATFOR uses LAPACK for solving Linear Algebra equations. Example Please refer to MATFOR in Fortran User's Guide Example 3_3. See Also Arithmetic Operators


Eigenvalues and singular values


mfEig, msEig Calculate eigenvalues and eigenvectors.

Module fml

Syntax e = mfEig(a[, flag]) e = mfEig(a, b[, flag]) call msEig(mfOut(v, d), a[, flag]) call msEig(mfOut(v, d), a, b[, flag]) Descriptions Procedure mfEig computes the eigenvalues and eigenvectors of a matrix mfArray a. e = mfEig(a), e = mfEig(a, flag)

• This procedure returns a vector e containing the eigenvalues of square mfArray a. • Argument flag can be a string containing 'nobalance', so that the procedure can perform

the computation with balancing switched off. This usually produces more accurate results for specific problems.

call msEig(mfOut(v, d), a), call msEig(mfOut(v, d), a, flag) • This procedure returns a diagonal matrix d of eigenvalues, and a full matrix mfArray v

whose columns are the corresponding eigenvectors such that a*v = v*d. e = mfEig(a, b), e = mfEig(a, b, flag)

• This procedure returns a vector containing the generalized eigenvalues of square matrix mfArrays a and b.

• The procedure specifies the algorithm used to compute eigenvalues and eigenvectors through the argument flag, which is specified in More Detail below.

call msEig(mfOut(v, d), a, b), call msEig(mfOut(v, d), a, b, flag)

• This procedure returns a diagonal matrix mfArray d of generalized eigenvalues and a full matrix mfArray v whose columns are the corresponding eigenvectors so that a*v = b*v*d.

• The procedure specifies the algorithm used to compute eigenvalues and eigenvectors through the argument flag, which is specified in More Detail below.

More Detail

Argument flag can be:

• "chol" This is the default for symmetric (Hermitian) a and symmetric (Hermitian) positive


definite b. The generalized eigenvalues of a and b are computed using the Cholesky

factorization of b.

• "qz" This uses the mfQz algorithm to compute eigenvlaues for nonsymmetrical

(non-Hermitian) a and b.

Example The following example uses the mfEig procedure to compute the eigenvalues and eigenvectors of a square matrix mfArray a. Code pr ogram example


ty pe(mfArray) :: v, d, a

! Construct a 3-by-3 mfArray a using vertical concatenation. a = (/5.0d0, 4.0d0, 3.0d0/) .vc. & (/2.0d0, 4.0d0, 6.0d0/) .vc. & (/10.0d0, 15.0d0, 25.0d0/)

! Compute eigenvalues and eigenvectors of mfArray a ca ll msEig(mfout(v, d), a)

! Display value of a, v and d ca ll msDisplay(a, 'a', v, 'v' ,d, 'd')

! Deallocate mfArrays a, v, d ca ll msFreeArgs(a, v, d)


Result a =

5 4 3 2 4 6 10 15 25

v = -0.1512 -0.9354 0.5446 -0.2317 0.2120 -0.7954 -0.9610 0.2830 0.2660 d = 30.1904 0.0000 0.0000 0.0000 3.1857 0.0000 0.0000 0.0000 0.6238

See Also mfBalance, mfHess, mfQz, mfSchur


mfHess, msHess Produce Hessenberg form of a matrix.

Module fml

Syntax h = mfHess(a) call msHess(mfOut(p, h), a) Descriptions Procedure mfHess returns the Hessenberg form of an mfArray. h = mfHess(a)

This procedure returns an mfArray h with zeros below the first sub diagonal and has the same

eigenvalues as a. If the original mfArray a is symmetric or Hermitian, h will be tridiagonal.

call msHess(mfOut(p, h), a)

This procedure produces an unitary matrix p and a Hessenberg matrix h so that a = p*h*.h.p

and .h.p*p results in the identity matrix.

Example The following example uses the mfHess procedure to compute the Hessenberg form of a square matrix mfArray a. Code pr ogram example


ty pe(mfArray) :: a, p, h

! Construct a 3-by-3 mfArray a using vertical concatenation. a = (/5.0d0, 4.0d0, 3.0d0/) .vc. & (/9.0d0, 8.0d0, 7.0d0/) .vc. & (/5.0d0, 1.0d0, 2.0d0/)

! Compute the Hessenberg form of mfArray a ca ll msHess(mfout(p, h), a)

! Display value of a, p and h ca ll msDisplay(a, 'a', p, 'p' , h, 'h')

! Deallocate mfArrays a, p, h ca ll msFreeArgs(a, p, h)


Result


a =

5 4 3 9 8 7 5 1 2

p = 1.0000 0.0000 0.0000 0.0000 -0.8742 -0.4856 0.0000 -0.4856 0.8742 h = 5.0000 -4.9536 0.6799 -10.2956 9.9811 -2.5660 0.0000 3.4340 0.0189

See Also


mfQz, msQz Perform QZ factorization for generalized eigenvalues.

Module fml

Syntax aa = mfQz(a, b[, flag]) call msQz(mfOut(aa[, bb, q, z, v]), a, b[, flag]) Descriptions Procedure mfQz performs QZ factorization for generalized eigenvalues of square mfArrays. call msQz(mfOut(aa, bb, q, z, v), a, b)

This procedure returns upper triangular mfArrays aa and bb, the left and right transformed

mfArrays q and z, and the generalized eigenvector mfArray v, such that q*a*z = aa, and

q*b*z = bb.

call msQz(mfOut(aa, bb, q, z, v), a, b[, flag])

This procedure depends on the value of flag:

• "complex" produces a possibly complex decomposition with a triangular aa. This is the default option.

• "real" produces a real decomposition with a quasitriangular aa, containing 1-by-1 and 2-by-2 blocks on its diagonal.

Example The following example uses the mfQz procedure to compute the QZ factorization of square matrices in mfArray a and b. Code pr ogram example


ty pe(mfArray) :: aa, bb, q, z, v, a, b

! Construct a 3-by-3 mfArray a and b using vertical ! concatenation. a = (/4.0d0, 2.0d0, 3.0d0/) .vc. & (/7.0d0, 8.0d0, 9.0d0/) .vc. & (/5.0d0, 2.0d0, 4.0d0/)

b = (/3.0d0, 5.0d0, 7.0d0/) .vc. & (/2.0d0, 1.0d0, 1.0d0/) .vc. & (/3.0d0, 2.0d0, 5.0d0/)


! Compute qz factorization of mfArray a and b ca ll msQz(mfOut(aa, bb, q, z, v ), a, b)

! Display values of aa, bb, q, z and v ca ll msDisplay(aa, 'aa', bb, 'bb' ,q, 'q', z, 'z', v, 'v')

! Deallocate mfArrays a, b, aa, bb, q, z, v ca ll msFreeArgs(a, b, aa, bb, q, z, v)


Result aa =

co lumn 1 to 3

6.3661 +0.0000i -9.8642 +0.0000i 10.4110 +0.0000i 0.0000 +0.0000i -1.4632 +0.0000i 4.2403 +0.0000i 0.0000 +0.0000i 0.0000 +0.0000i 1.2882 +0.0000i bb = 2.3112 +0.0000i -6.1276 +0.0000i 6.0482 +0.0000i 0.0000 +0.0000i 4.3735 +0.0000i -4.9870 +0.0000i 0.0000 +0.0000i 0.0000 +0.0000i 1.8797 +0.0000i q = -0.4555 +0.0000i -0.7072 +0.0000i -0.5407 +0.0000i 0.6410 +0.0000i -0.6820 +0.0000i 0.3521 +0.0000i -0.6178 +0.0000i -0.1862 +0.0000i 0.7640 +0.0000i z = -0.9116 +0.0000i 0.4095 +0.0000i 0.0353 +0.0000i -0.1805 +0.0000i -0.3219 +0.0000i -0.9294 +0.0000i 0.3693 +0.0000i 0.8536 +0.0000i -0.3674 +0.0000i v = -1.0000 +0.0000i -0.7564 +0.0000i 0.0489 +0.0000i -0.1980 +0.0000i -0.4240 +0.0000i -1.0000 +0.0000i 0.4051 +0.0000i 1.0000 +0.0000i 0.8466 +0.0000i

See Also mfEig


mfSchur, msSchur Perform Schur decomposition.

Module fml

Syntax qt = mfSchur(a[, flag]) call msSchur(mfOut(u, qt), a) Descriptions Procedure mfSchur performs the Schur decomposition on a square matrix mfArray. qt = mfSchur(a), qt = mfSchur(a, flag)

• This procedure returns a quasitriangular Schur mfArray matrix qt. If a is complex, mfSchur returns the complex Schur form in matrix qt. The complex Schur form is an upper triangular matrix containing the eigenvalues of a on the diagonal.

• This procedure returns a Schur matrix qt in one of two forms for real matrix a, depending on the value of flag.

• If flag is "complex", qt is triangular. If a has complex eigenvalues, qt is complex. If flag is "real", qt has real eigenvalues on the diagonal. Complex eigenvalues are located in 2-by-2 blocks on the diagonal. By default, flag is "real".

call msSchur(mfOut(u, qt), a)

• This procedure returns a unitary matrix u and a quasitriangular Schur matrix mfArray qt such that a = u*qt*.h.u and .h.u*u is an identity matrix given by mfEye(Shape(u)).

Example The following example uses the mfSchur procedure to compute the Schur decomposition of a square matrix mfArray a. Code pr ogram example


ty pe(mfArray) :: u, qt, a



! Compute the Schur decomposition of mfArray a ca ll msSchur(mfOut(u, qt), a)

! Displays values of a, u and qt ca ll msDisplay(a, 'a', u, 'u' , qt, 'qt')

! Deallocate mfArrays a, u, qt ca ll msFreeArgs(a, u, qt)


Result a =

3 4 3 2 1 4 6 2 2

u = 0.6118 0.7878 -0.0707 0.4634 -0.4295 -0.7751 0.6410 -0.4415 0.6279 qt = 9.1729 1.2110 -0.5957 0.0000 -1.5865 -1.4934 0.0000 2.4025 -1.5865

See Also


mfSvd, msSvd Perform singular value decomposition.

Module fml

Syntax s = mfSvd(a) call msSvd(mfOut(u, s, v), a[, 0]) Descriptions Procedure mfSvd performs singular value decomposition on matrix mfArray a. s = mfSvd(a) returns an mfArray vector containing singular values.

call msSvd(mfOut(u, s, v), a) returns two unitary matrices u and v, and a diagonal

matrix s such that a = u*s*.h.v . Diagonal matrix s has the same shape as a and contains

nonnegative elements in decreasing order.

call msSvd(mfOut(u, s, v), a, 0) returns the "economy size" decomposition. If a is

m-by-n and m > n, then only the first n columns of u are computed. s is n-by-n.

Example The following example uses the mfSvd procedure to compute the singular value decomposition of a square matrix mfArray a. Code pr ogram example


ty pe(mfArray) :: a, u, s, v


! Compute singular value decomposition of mfArray a ca ll msSvd(mfOut(u, s, v), a)

! Display value of a, u, s and v ca ll msDisplay(a, 'a', u, 'u' ,s, 's', v, 'v')

! Deallocate mfArrays a, u, s, v ca ll msFreeArgs(a, u, s, v)



Result a =

10 20 30 7 8 9 5 15 25

u = -0.7568 -0.1344 -0.6397 -0.2688 -0.8280 0.4921 -0.5958 0.5444 0.5905 s = 49.4333 0.0000 0.0000 0.0000 5.0350 0.0000 0.0000 0.0000 0.0000 v = -0.2514 -0.8776 0.4082 -0.5305 -0.2279 -0.8165 -0.8095 0.4219 0.4082

See Also


Factorization Utilities


mfBalance, msBalance Perform diagonal scaling to improve eigenvalue accuracy.

Module fml

Syntax b = mfBalance(a) call msBalance(mfOut(t, b), a) Descriptions For matrices, procedure mfBalance performs diagonal scaling to improve the eigenvalue accuracy. b = mfBalance(a) returns the balanced matrix mfArray b.

call msBalance(mfOut(t, b), a) returns a similarity transformation t, such that

b = mfLDiv(t, a*t) has, as closely as possible, approximately equal row and column norms.

Example The following example uses the mfBalance procedure to find the balanced matrix mfArray b of the original mfArray a. Code pr ogram example


ty pe(mfArray) :: a, b

! Construct a 3-by-3 mfArray a using vertical concatenation. a = (/100.0d0, 200.0d0, 300.0d0/) .vc. & (/4.0d0, 5.0d0, 6.0d0 /) .vc. & (/7.0d0, 8.0d0, 9.0d0 /)

! Compute the balanced matrix b of mfArray a b = mfBalance(a)

! Display values of a and b ca ll msDisplay(a, 'a', b, 'mfBalance(a)')

! Deallocate mfArrays a and b ca ll msFreeArgs(a, b)


Result a =

100 200 300


4 5 6 7 8 9

mfBalance(a) = 100.0000 25.0000 37.5000 32.0000 5.0000 6.0000 56.0000 8.0000 9.0000

See Also mfEig

Chapter 8 Sparse Array 243

C H A P T E R 8

Sparse Array

A Sparse Array is an array in which most of its entries are zeros and only very few entries are in practice used. This is particularly in use for large scale simulations. MATFOR mfSparse is a Sparse Array defined by MATFOR that can be used for Sparse Array creation, manipulations and solution to linear system.

This chapter describes the Sparse functions available, as listed below:

msSpAdd Add one or multiple real entries to the sparse array.

msSpSet Set one or multiple entries in the sparse array.

mfSpGet Get a specific element from a sparse array.

mfSpGetM Get number of row, number of column from a sparse array

mfSpGetNNZ Get number of nonzero elements of a sparse array.

mfSpGetRow Get row indices, column indices of nonzero elements in a sparse array.

mfSpGetVal Get values of nonzero elements in a sparse array.

msSpGetIdx Get row indices, column indices and values of nonzero elements in a sparse array.

msSpDisplay Display sparse array data.

msSpExport Export sparse array data.

mfSpImport Export sparse array data.

mfSpEigs Find the eigenvalues and eigenvectors of a sparse array.

mfSpLDiv Solve a sparse array system of linear equations.

mfSpMul Multiply a sparse array onto an mfArray.

mfSpSize Return total number of elements in a sparse array.


mfSpToFull Convert a sparse array into a full array.

mfFullToSp Convert a full array into a sparse array.

mfSpy Draw patterns of a sparse array.


Sparse Array


mfSpCreate Create a sparse matrix.

Module spml

Syntax spA = mfSpCreate(m, n) Descriptions Procedure spA = mfSpCreate(m, n) creates an m-by-n matrix with sparse internal representation. Argument m is a m x 1 matrix that represents the number of column and n is a 1 x n matrix that represents the number of row. Example To be referred to mfSpy See Also mfSpy


msSpAdd Add one or multiple real entries to the sparse array.

Module spml

Syntax call msSpAdd(spA, row, col, value) call msSpAdd(spA, rindex, cindex, values) Descriptions Procedure msSpAdd adds one or multiple real entries to the sparse array. call msSpAdd(spA, row, col, value)

• Add a real entry into the sparse array. call msSpAdd(spA, rindex, cindex, values) • Add real entries into the sparse array. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(4), cindex(4) real(8) :: values(4)

type(mfSparse) :: sp

rindex = (/1, 2, 2, 3/) cindex = (/3, 1, 3, 2/)

values = (/-1.5, -0.5, 0.5, 1.5/)

! Add multi elements. call msSpAdd(sp, rindex, cindex, values)

call msSpDisplay(sp, "oringal sparse array sp")

! Add single element sp(1, 1) = -2 call msSpAdd(sp, 1, 1, -2.0d0) ! Add single element sp(3, 2) = 2 call msSpAdd(sp, 3, 2, 2.0d0) call msSpDisplay(sp, "modified sp") e nd program

Result oringal sparse array sp =


oringal sparse array sp(1,3) = -1.500000e+000 ; oringal sparse array sp(2,1) = -5.000000e-001 ; oringal sparse array sp(2,3) = 5.000000e-001 ; o ringal sparse array sp(3,2) = 1.500000e+000 ;

mo dified sp =

modified sp(1,1) = -2.000000e+000 ; modified sp(1,3) = -1.500000e+000 ; modified sp(2,1) = -5.000000e-001 ; modified sp(2,3) = 5.000000e-001 ; modified sp(3,2) = 3.500000e+000 ;

See Also msSpSet


msSpSet Set one or multiple entries in the sparse array.

Module spml

Syntax call msSpSet(spA, row, col, value) call msSpSet(spA, rindex, cindex, values) Descriptions Procedure msSpSet sets one or multiple entries in the sparse array. call msSpSet(spA, row, col, value)

• Set a real entry into the sparse array. call msSpSet(spA, rindex, cindex, values) • Set real entries into the sparse array. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(4), cindex(4), mr(3), mc(3) real(8) :: values(4), mv(3)

type(mfSparse) :: a

! Create sparse array a. rindex = (/1, 2, 3, 3/) cindex = (/1, 3, 2, 3/) values = (/9, 8, 7, 6/) call msSpAdd(a, rindex, cindex, values)

call msSpDisplay(a, "oringal sparse array a")

! Set single element a(1, 1) = -9 call msSpSet(a, 1, 1, -9.0d0)

call msSpDisplay(a, "modified a")

! Set multi elements. mr = (/2, 3, 3/) mc = (/3, 2, 3/) mv = (/-8, -7, -6/) call msSpSet(a, mr, mc, mv)

call msSpDisplay(a, "modified a")



Result or ingal sparse array a =

oringal sparse array a(1,1) = 9.000000e+000 ; oringal sparse array a(2,3) = 8.000000e+000 ; oringal sparse array a(3,2) = 7.000000e+000 ; o ringal sparse array a(3,3) = 6.000000e+000 ;

mo dified a =

modified a(1,1) = -9.000000e+000 ; modified a(2,3) = 8.000000e+000 ; modified a(3,2) = 7.000000e+000 ; m odified a(3,3) = 6.000000e+000 ;

mo dified a =

modified a(1,1) = -9.000000e+000 ; modified a(2,3) = -8.000000e+000 ; modified a(3,2) = -7.000000e+000 ; modified a(3,3) = -6.000000e+000 ;

See Also msSpAdd


mfSpGet Get a specific element from a sparse array.

Module spml

Syntax value = mfSpGet(spA, rowIdx, colIdx) Descriptions Procedure msSpGet gets a specific element from a sparse array. The return type is a real number. value = mfSpGet(spA, rowIdx, colIdx)

• Get a specific element given row and column indices from a sparse array. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: RowIdx(5), ColIdx(5) real(8) :: Values(5) integer(4) :: m, n, nnz real(8) :: value

type(mfSparse) :: sp,sp2

! Create a sparse matrix RowIdx = (/1, 2, 2, 3, 3/) ColIdx = (/3, 1, 2, 3, 4/) Values = (/-1.5, -0.9, 0.7, 1.8, 2.3/) call msSpAdd(sp, RowIdx, ColIdx, Values)

call msSpDisplay(sp, "sp")

! Get number of row of sparse matrix m = mfSpGetM(sp)

write(*,*) "m = ", m

! Get number of column of sparse matrix n = mfSpGetN(sp)

write(*,*) "n = ", n

! Get number of nonzero elements of sparse matrix nnz = mfSpGetNNZ(sp)

write(*,*) "nnz = ", nnz

! Get value of sp(2, 1) value = mfSpGet(sp, 2, 1) write(*,*) "sp(2, 1) = ", value


e nd program

Result sp =

sp(1,3) = -1.500000e+000 ; sp(2,1) = -9.000000e-001 ; sp(2,2) = 7.000000e-001 ; sp(3,3) = 1.800000e+000 ; s p(3,4) = 2.300000e+000 ;

m = 3 n = 4 nnz = 5 sp(2, 1) = -0.899999976158142

See Also mfSpGetRow, mfSpGetCol, mfSpGetVal, msSpGetIdx


mfSpGetM, mfSpGetN Get number of row, number of column from a sparse array.

Module spml

Syntax m = mfSpGetM(spA) n = mfSpGetN(spA) Descriptions Procedure msSpGetM gets respective number of row and column of a sparse array. The return type is a real number. m = mfSpGetM(spA)

• Get number of row of mfSparse spA. n = mfSpGetN(spA)

• Get number of column of mfSparse spA. Example To be referred to mfSpGet Code Pr ogram Main

use fml use spml

implicit none

integer(4) :: RowIdx(5), ColIdx(5) real(8) :: values(5) type(mfArray) :: m integer(4) :: n


! Create a sparse matrix RowIdx = (/1, 1, 3, 4, 5/) ColIdx = (/1, 3, 1, 2, 3/) values = (/5.1, 1.2, 4.3, 2.4, 7.5/) call msSpAdd(sp, RowIdx, ColIdx, values)

call msSPDisplay(sp, 'sp')

! Get number of row of sp m = mfSpGetM(sp)

call msDisplay(m, 'm')

! Get number of column of sp n = mfSpGetN(sp)

write(*,'(1x,A3,/,/,I3)') 'n =', n


e nd Program Main

Result sp =

sp(1,1) = 5.100000e+000 ; sp(1,3) = 1.200000e+000 ; sp(3,1) = 4.300000e+000 ; sp(4,2) = 2.400000e+000 ; s p(5,3) = 7.500000e+000 ;

m =

5

n =

3



mfSpGetNNZ Get number of nonzero elements of a sparse array.

Module spml

Syntax nnz = mfSpGetNNZ(spA) Descriptions Procedure msSpGetNNZ gets number of nonzero elements of a sparse array. The return type is a real number. nnz = mfSpGetNNZ(spA)

• Get number of nonzero elements of mfSparse spA. Example To be referred to mfSpGet Code Pr ogram Main

use fml use spml

implicit none

integer(4) :: RowIdx(5), ColIdx(5) real(8) :: values(5) integer(4) :: nnz



call msSPDisplay(sp, 'sp')

! Get number of nonzero elements of sp nnz = mfSpGetNNZ(sp)

write(*,*) 'nnz =', nnz

e nd Program Main

Result sp =



nnz = 5



mfSpGetRow, mfSpGetCol Get row indices, column indices of nonzero elements in a sparse array.

Module spml

Syntax RowIdx = mfSpGetRow(spA) ColIdx = mfSpGetCol(spA) Descriptions Procedure msSpGetRow and msSpGetCol get row indices and column indices of a sparse array. The return type is an mfArray. RowIdx = mfSpGetRow(spA)

• Get row indices of nonzero elements in a sparse array. ColIdx = mfSpGetCol(spA)

• Get column indices of nonzero elements in a sparse array. Example Code pr ogram example

use fml use spml

implicit none

type(mfArray) :: RowIdx, ColIdx, Values


! Create a sparse matrix call msSpAdd(sp, 1, 4, 53.0d0) call msSpAdd(sp, 2, 3, 27.0d0) call msSpAdd(sp, 3, 2, 16.0d0) call msSpAdd(sp, 4, 5, 91.0d0) call msSpAdd(sp, 5, 1, 14.0d0)


! Get row indices of nonzero elements in given sparse matrix RowIdx = mfSpGetRow(sp) call msDisplay(RowIdx, "Row indices of nonzero elements in sp")

! Get column indices of nonzero elements in given sparse matrix ColIdx = mfSpGetCol(sp) call msDisplay(ColIdx, "Column indices of nonzero elements in sp")

! Get nonzero values in given sparse matrix Values = mfSpGetVal(sp) call msDisplay(Values, "Nonzero values in sp")


e nd program

Result sp =


R ow indices of nonzero elements in sp =

1 2 3 4 5

C olumn indices of nonzero elements in sp =

4 3 2 5 1

N onzero values in sp =

53 27 16 91 14

See Also Get, GetM, GetN, GetNNZ


mfSpGetVal Get values of nonzero elements in a sparse array.

Module spml

Syntax Values = mfSpGetVal(spA) call msSpGetVal(mfOut(RowIdx, ColIdx, Values), spA) Descriptions Procedure msSpGetVal gets values of nonzero elements from a sparse array. The return type is an mfArray. ValIdx = mfSpGetVal(spA)

• Get nonzero values of a sparse array. Example To be referred to mfSpGetRow Code pr ogram example

use fml use spml

implicit none

integer(4) :: RowIdx(5), ColIdx(5) real(8) :: values(5) type(mfArray) :: NonZeroVal




! Get nonzero values in sp NonZeroVal = mfSpGetVal(sp) call msDisplay(NonZeroVal,'NonZero Values') e nd program example

Result sp =

sp(1,1) = 5.100000e+000 ; sp(1,3) = 1.200000e+000 ; sp(3,1) = 4.300000e+000 ; sp(4,2) = 2.400000e+000 ;


s p(5,3) = 7.500000e+000 ;

NonZero Values = 5.1000 1.2000 4.3000 2.4000 7.5000

See Also mfSpGet, mfSpGetM, mfSpGetN, mfSpGetNNZ


msSpGetIdx Get row indices, column indices and values of nonzero elements in a sparse array.

Module spml

Syntax call msSpGetIdx(mfOut(RowIdx, ColIdx, Values), spA) Descriptions Procedure msSpGetIdx gets row indices, column indices, and values of nonzero elements in a sparse array at the same time. The return values are type mfArray. call msSpGetIdx(mfOut(RowIdx, ColIdx, Values), spA)

• Get row indices, column indices, and values of nonzero elements in a sparse array all at once.


use fml use spml

implicit none

integer(4) :: RowIdx(5), ColIdx(5) real(8) :: values(5) type(mfArray) :: growidx, gcolidx, gval


! Create a sparse matrix RowIdx = (/1, 1, 3, 4, 5/) ColIdx = (/1, 3, 1, 2, 3/) Values = (/5.1, 1.2, 4.3, 2.4, 7.5/) call msSpAdd(sp, RowIdx, ColIdx, Values)


! Get row/column indices and values of nonzero elements in sp call msSpGetIdx(mfOut(growidx, gcolidx, gval), sp) call msDisplay(growidx, 'nonzero elements row index') call msDisplay(gcolidx, 'nonzero elements column index') call msDisplay(gval, 'nonzero elements values') e nd program example

Result sp =

sp(1,1) = 5.100000e+000 ; sp(1,3) = 1.200000e+000 ; sp(3,1) = 4.300000e+000 ; sp(4,2) = 2.400000e+000 ;


s p(5,3) = 7.500000e+000 ;

n onzero elements row index =

1 1 3 4 5

n onzero elements column index =

1 3 1 2 3

nonzero elements values = 5.1000 1.2000 4.3000 2.4000 7.5000

See Also mfSpGet, mfSpGetM, mfSpGetN, mfSpGetNNZ


msSpDisplay Display sparse array data.

Module spml

Syntax call msSpDisplay(spA) call msSpDisplay(spA, name) call msSpDisplay(spA1, name1, spA2, name2[, spA3, name3]) Descriptions Procedure msSpDisplay shows the entries of a sparse array under MS-DOS console window. mfSpDisplay(x) displays the entries of mfSparse spA, with the caption 'ans ='.


use fml use spml

implicit none


type(mfSparse) :: a

rindex = (/1, 1, 1, 2, 2, 2/) cindex = (/1, 2, 3, 1, 2, 3/) values = (/1, 2, 3, 4, 5, 6/)

call msSpAdd(a, rindex, cindex, values)

call msSpDisplay(a, "a")


Result a =

a(1,1) = 1.000000e+000 ; a(1,2) = 2.000000e+000 ; a(1,3) = 3.000000e+000 ; a(2,1) = 4.000000e+000 ; a(2,2) = 5.000000e+000 ; a(2,3) = 6.000000e+000 ;

See Also mfDisplay


msSpExport Export sparse array data.

Module spml

Syntax call msSpExport(sp, filename) Descriptions Procedure msSpExport exports sparse array data to a file. Example Code pr ogram example

use fml use spml

implicit none


type(mfSparse) :: a

rindex = (/1, 1, 2, 2/) cindex = (/1, 2, 1, 2/) values = (/1, 2, 3, 4/)


! Export sparse array a to a.txt

call msSpExport(a, "a.txt")


See Also mfSpImport


mfSpImport Import sparse array data.

Module spml

Syntax spA = mfSpImport(filename); Descriptions Procedure msSpImport imports sparse array data from a file. Example Code pr ogram example

use fml use spml

implicit none


type(mfSparse) :: a, b

rindex = (/1, 1, 2, 2/) cindex = (/1, 2, 1, 2/) values = (/1, 2, 3, 4/)


! Export sparse array a to a.txt.

call msSpExport(a, "a.txt")

! Import sparse array b from a.txt.

b = mfSpImport("a.txt")

! Display sparse b.

call msSpDisplay(b, "b")


Result b =

b(1,1) = 1.000000e+000 ; b(1,2) = 2.000000e+000 ; b(2,1) = 3.000000e+000 ; b(2,2) = 4.000000e+000 ;

See Also msSpExport


mfSpEigs Find the eigenvalues and eigenvectors of a sparse array.

Module spml

Syntax eig = mfSpEigs(spA[, N, opt ]) call msSpEigs(mfOut(val, vec), spA[, N, opt]) Descriptions Procedure msSpEigs computes the eigenvalues and eigenvectors of a sparse array. eig = mfSpEigs(spA, N, opt)

• This procedure returns a vector eig containing the eigenvalues of mfSparse spA. • Argument N is the number of eigenvalues based on the option given in opt. • Argument opt can be: LM: the N largest eigenvalues of mfSparse spA. SM: the N smallest eigenvalues of mfSparse spA. call msSpEigs(mfOut(val, vec), spA, N, opt) • This procedure returns a vector of eigenvalues val, and a full matrix mfArray vec

whose columns are the corresponding eigenvectors, spA*vec = val*vec. Note: MATFOR uses ARPACK for computing eigen problems, but it uses mfEig(mfSpToFull(spA))when NCV - N < 2such that NCV is the number of column in spA. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(7), cindex(7) real(8) :: values(7) type(mfArray) :: value, vector

type(mfSparse) :: a

rindex = (/1, 2, 3, 3, 4, 4, 5/) cindex = (/5, 2, 1, 3, 1, 3, 4/) values = (/19, 21, 44, 32, 88, 64, 90/) call msSpAdd(a, rindex, cindex, values)



! Evaluate eigenvalue and eigenvector of sparse array a.

call msSpEigs(mfOut(value, vector), a)

! Display eigenvalue and eigenvector.

call msDisplay(value, "value", vector, "vector")


Result a =

a(1,5) = 1.900000e+001 ; a(2,2) = 2.100000e+001 ; a(3,1) = 4.400000e+001 ; a(3,3) = 3.200000e+001 ; a(4,1) = 8.800000e+001 ; a(4,3) = 6.400000e+001 ; a (5,4) = 9.000000e+001 ;

value = 66.2673 +0.0000i -17.1337 +44.4662i -17.1337 -44.4662i 0.0000 +0.0000i 2 1.0000 +0.0000i

v ector =

co lumn 1 to 4 ...

0.2161 +0.0000i 0.1167 +0.3028i 0.1167 -0.3028i 0.0000 +0.0000i 0.0000 +0.0000i 0.0000 +0.0000i 0.0000 +0.0000i 1.0000 +0.0000i 0.2775 +0.0000i 0.0775 -0.2011i 0.0775 +0.2011i 0.0000 +0.0000i 0.5550 +0.0000i 0.1550 -0.4021i 0.1550 +0.4021i 0.0000 +0.0000i 0.7538 +0.0000i -0.8139 +0.0000i -0.8139 +0.0000i 0.0000 +0.0000i co lumn 5 to 5

0.5882 +0.0000i 0.0000 +0.0000i -0.8087 +0.0000i 0.0000 +0.0000i 0.0000 +0.0000i

See Also mfEig


mfSpLDiv Solve a sparse array system of linear equations.

Module spml

Syntax X = mfSpLDiv(spA, b) call msSpLDiv(mfOut(X), spA, b) Descriptions Procedure msSSpLDiv is normally used in solving an mfSprse array system of linear equations represented by Ax = b. Note: MATFOR uses SPOOLES for solving sparse Linear Algebra equations. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(4), cindex(4) real(8) :: values(4) type(mfArray) :: x, b

type(mfSparse) :: A

! Create sparse array A. rindex = (/1, 1, 2, 2/) cindex = (/1, 2 ,1 ,2/) values = (/1, 2, 3, 2/) call msSpAdd(A, rindex, cindex, values)

call msSpDisplay(A, "A")

! Create mfArray b. b = (/3.0, 5.0/)

b = mfReshape(b, (/2, 1/))

! Evaluate mfArray x that satisfies Ax = b. x = mfSpLDiv(A, b)

call msDisplay(b, "b", x, "x")


Result A =

A(1,1) = 1.000000e+000 ; A(1,2) = 2.000000e+000 ;


A(2,1) = 3.000000e+000 ; A (2,2) = 2.000000e+000 ;

b =

3 5

x =

1 1

See Also mfLDiv


mfSpMul Multiply a sparse array onto an mfArray.

Module spml

Syntax c = mfSpMul(spA, B) call msSpMul(mfOut(c), spA, B) Descriptions Procedure mfSpMul returns the matrix product of mfSparse spA and mfArray B, where spA is an m-by-p matrix and B is a p-by-n matrix. The product of the matrix multiplication is an m-by-n mfArray. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(3), cindex(3) real(8) :: values(3) type(mfArray) :: y, m

type(mfSparse) :: x

! Create sparse array x. rindex = (/1, 2, 3/) cindex = (/1, 2, 1/) values = (/1, 2, 3/) call msSpAdd(x, rindex, cindex, values)

call msSpDisplay(x, "x")

! Create mfArray y.

y = mfOnes(2, 4)

! Evaluate mfArray m that satisfies x * y = m. m = mfSpMul(x, y)

call msDisplay(y, "y", m, "m")


Result x =

x(1,1) = 1.000000e+000 ; x(2,2) = 2.000000e+000 ; x (3,1) = 3.000000e+000 ;

y =


1 1 1 1 1 1 1 1

m =

1 1 1 1 2 2 2 2 3 3 3 3

See Also mfMul


mfSpSize Return total number of elements in a sparse array.

Module spml

Syntax n = mfSpSize(spA) m = mfSpSize(spA, IDIM) call msSpSize(mfOut(nRow, nCol), spA) Descriptions Procedure mfSpSize returns the total number of elements in a sparse array. n = mfSpSize(spA) returns the number of elements in mfSparse spA.

m = mfSpSize(spA, IDIM) returns the length of the dimension specified by the scalar

IDIM.

call msSpSize(mfOut(nRow, nCol), spA) returns the lengths of row and column

dimensions of mfSparse spA.


use spml use fml

implicit none

integer(4) :: k, m, n integer(4) :: rindex(3), cindex(3) real(8) :: values(3)

type(mfSparse) :: a

! Create sparse array a. rindex = (/1, 3, 2/) cindex = (/2, 2, 5/) values = (/3, 5, 6/) call msSpAdd(a, rindex, cindex, values)


! Compute number elements in a. k = mfSpSize(a)

call msDisplay(mf(k), "mfSpSize(a)")

! Compute number of row in a. m = mfSpSize(a, 1) call msDisplay(mf(m), "mfSpSize(a, 1)")


! Compute number of column in a. n = mfSpSize(a, 2)

call msDisplay(mf(n), "mfSpSize(a, 2)")

e nd program

Result a =

a(1,2) = 3.000000e+000 ; a(2,5) = 6.000000e+000 ; a (3,2) = 5.000000e+000 ;

m fSpSize(a) =

15

m fSpSize(a, 1) =

3

m fSpSize(a, 2) =

5

See Also mfSize


mfSpToFull Convert a sparse array into a full array.

Module spml

Syntax A = mfSpToFull(spA) call msSpToFull(mfOut(A), spA) Descriptions Procedure msSpToFull converts an mfSparse spA to a full mfArray A. If spA is a full matrix, it will remain unchanged. Example Code pr ogram example

use fml use spml

implicit none

integer(4) :: rindex(5), cindex(5) real(8) :: values(5) type(mfArray) :: FULL

type(mfSparse) :: SP

! Create sparse array SP. rindex = (/1, 1, 2, 3, 3/) cindex = (/1, 3, 2, 1, 3/) values = (/3, 2, 7, 5, 4/) call msSpAdd(SP, rindex, cindex, values)

call msSpDisplay(SP, "SP")

! Convert sparse array SP into mfArray FULL. FULL = mfSpToFull(SP) call msDisplay(FULL, "FULL") e nd program example

Result SP =

SP(1,1) = 3.000000e+000 ; SP(1,3) = 2.000000e+000 ; SP(2,2) = 7.000000e+000 ; SP(3,1) = 5.000000e+000 ; S P(3,3) = 4.000000e+000 ;

F ULL =

3 0 2 0 7 0


5 0 4

See Also mfFullToSp


mfFullToSp Convert a full array into a sparse array.

Module spml

Syntax spA = mfFullToSp(A) call msFullToSp(mfOut(spA), A) Descriptions Procedure msFullToSp converts a full mfArray A to an mfSparse spA. If A is a sparse matrix, it will remain unchanged. Example Code pr ogram example

use spml use fml

implicit none

type(mfArray) :: full


! Create mfArray. full = mfRand(2, 3)

call msAssign(mfS(full,MF_COL,2),0d0)

! Convert mfArray to sparse array.

sp = mfFullToSp(full)

! Display mfArray.

call msDisplay(full, "full")

! Display sparse array.



Result full = 0.5742 0.0000 0.9509 0.9433 0.0000 0.9647 sp =

sp(1,1) = 5.741892e-001 ; sp(1,3) = 9.508580e-001 ; sp(2,1) = 9.432698e-001 ;


sp(2,3) = 9.646586e-001 ;

See Also mfSpToFull


mfSpy, msSpy Draw pattern of a sparse array.

Module spml

Syntax h = mfSpy(sp) call msSpy(sp) Descriptions Procedure mfSpy shows the sparsity pattern of the given sparse array sp, in which the nonzero elements are plotted. Example The example plots a 100 by 100 sparse array. Code pr ogram example

use fml use fgl use spml implicit none

integer(4) :: i,j,c real(8) :: values type(mfSparse) :: a

values = 10d0 a = mfSpCreate(100,100)

do i=1,100 call msSpSet(a,i,i,values)

end do

j=1 do i=10,70 call msSpSet(a,j,i,values) call msSpSet(a,i,j,values) j=j+1;

end do

c = j; do j=71,100 call msSpSet(a,c,j,values) call msSpSet(a,j,c,values)

end do

!Show Graph of Sparse array a call msSpy(a); call msAxis('equal'); call msColormap('spy'); call msColorbar('on'); call msViewPause();



Result

See Also mfSpToFull


Chapter 9 Visualization Routines 281

C H A P T E R 9

MATFOR Visualization Routines

Windows Frame and Figure Figure

msFigure Create figure in Graphics Viewer. msCloseFigure Close figure in Graphics Viewer. mfFigureCount Number of figures in graphics viewer. Window Frame

mfWindowCaption Graphics Viewer title. mfWindowSize Graphics Viewer frame size. mfWindowPos Graphics Viewer frame position. Display

msGDisplay Display mfArray data on a MATFOR Data

Viewer. msDrawNow Draw all pending graphs in current figure. msViewPause Pause program execution. Configuration msSaveConfig Save display configuration. msLoadConfig Load pre-saved display configuration. Recording


mfRecordStart/

mfRecordEnd

Record animation as AVI file or MATFOR mfa file.

mfExportImage Save figure graph as picture file. Subplot Plot Creation and Control

mfSubplot Create subplot in active figure. msClearSubplot Remove all draws in specified subplot. msHold Hold previous graph on plot space. mfIsHold Return status of plot space. Plot Annotation and Appearance

mfTitle Graph title. mfXLabel X-axis label. mfYLabel Y-axis label. mfZLabel Z-axis label. mfText 2-D text annotation mfAnnotation 3-D text annotation msShading Shading methodology of surface object. msColorbar Display color scale. msColormap Colormap type. mfColormapRange Range of colormap. mfBackgroundColor Background color of plot space. Axis Control

mfAxis Manipulate axis object. mfAxis2DMode Switch display mode to 2D mode. mfAxis3DMode Switch display mode to 3D mode. mfAxis2DDependency Set axis dependency of 2D display mode. mfAxis3DDependency Set axis dependency of 3D display mode. mfAxis2DRange Set the axis range of 2D display mode. mfAxis3DRange Set the axis range of 3D display mode. msAxis2DPosition Set axis position in the plot window.


msAxisWall Manipulate the axis wall object. msAxisGrid Display grid lines. Object & Camera

Object Manipulation

msObjRotateX Rotate draw object in degrees about the x-axis

using the right hand rule. msObjRotateY Rotate draw object in degrees about the y-axis

using the right hand rule. msObjRotateZ Rotate draw object in degrees about the z-axis

using the right hand rule. msObjRotateWXYZ Rotate draw object in degrees about an arbitrary

axis. mfObjScale Scale of draw object. mfObjPosition Position of draw object in world coordinates. mfObjOrigin Origin of draw object. mfObjOrientation Return WXYZ orientation of draw object. Camera Manipulation

mfCamAngle Set the camera view angle. mfCamAzElRoll Set the camera view direction. mfCamDistance Set the camera distance. mfCamProj Set the camera projection mode. mfCamFocal Set the camera focal point. mfCamZoom Zoom the displaying object in or out. mfGetCamViewParam Retrieve camera configuration values of an

object. msSetCamViewParam Set camera configuration values for the display

object. msView Viewpoint specification. Graphics Linear Graphs


mfPlot 2-D linear graphs. mfPlot3 3-D linear graphs. mfRibbon 3-D ribbons. mfTube 3-D tubes. mfStem 2-D stem graphs. mfBar 2-D vertical bars. mfBarh 2-D horizontal bars. mfBar3 3-D vertical bars. mfBar3h 3-D horizontal bars. Surface Graphs mfSurf Surface plot. mfMesh Mesh plot. mfSurfc Combined plot of surface and contour3. mfMeshc Combined plot of mesh and contour3. mfPColor

mfFastPColor Pseudocolor plot of a matrix. mfContour 2-D contour. mfContour3 3-D contour. mfSolidContour 2-D solid contour. mfSolidContour3 3-D solid contour. mfOutline Wireframe outline corners. mfIsoSurface 3-D plot isovalue surface from volume data.

mfGetIsoSurface

3-D iso-value surface plots from volumetric data.

Slice Graphs mfSliceXYZ Display orthogonal slice-planes through

volumetric data. mfSliceIJK Display orthogonal slice-planes along i, j or k

indices. mfSlicePlane Display orthogonal slice-planes along arbitrary

direction. mfGetSliceXYZ Retreive orthogonal slice-plane(s) through

volumetric data.


mfGetSliceIJK Retrieve orthogonal slice-plane(s) along i, j or k indices.

mfGetSlicePlane Retrieve orthogonal slice-plane(s) along arbitrary direction.

Streamline Graphs mfStreamLine2 Streamlines from 2-D vector data. mfStreamDashedLine2 Stream of dashed lines from 2-D vector data. mfStreamRibbon2 Stream of ribbons from 2-D vector data. mfStreamArrow2 Stream of arrows from 2-D vector data. mfStreamTube2 Stream of tubes from 2-D vector data. mfStreamLine3 Streamlines from 3-D vector data. mfStreamDashedLine3 Stream of dashed lines from 3-D vector data. mfStreamRibbon3 Stream of ribbons from 3-D vector data. mfStreamTube3 Stream of tubes from 3-D vector data. mfStreamArrow3 Stream of arrows from 3-D vector data. Triangular Surface Graphs mfTriSurf Polygonal surface plot. mfTriMesh Polygonal mesh plot. mfTriContour Contour on polygonal plot. mfPatch Add patch on 2-D or 3-D coordinates. Unstructured Grids mfTetSurf Polyhedral surface plot. mfTetMesh Polyhedral mesh plot. mfTetContour Contour on polyhedral plot. mfTetIsoSurface Poyhedral isosurface plot.

mfTetSliceXYZ Orthogonal slice-planes through volumetric data.


mfTetSlicePlane

Orthogonal slice-planes along an arbitrary direction.

msGetTetIsoSurface

3-D iso-value surface plots from polyhedral data.

msGetTetSliceXYZ

Orthogonal slice-planes through polyhedral data.

msGetTetSlicePlane Orthogonal slice-planes along an arbitrary direction.

Unstructured Streamlines mfTriStreamLine Create streamlines from two-dimensional

unstructured mesh data. mfTriStreamDashedLine Create stream dashed-lines from

two-dimensional unstructured mesh data. mfTriStreamRibbon Create stream ribbons from two-dimensional

unstructured mesh data. mfTriStreamTube Create stream tubes from two-dimensional

unstructured mesh data. mfTriStreamArrow Create stream arrows from two-dimensional

unstructured mesh data. mfTetStreamLine Create streamlines from three-dimensional

unstructured mesh data. mfTetStreamDashedLine Create stream dashed-lines from

three-dimensional unstructured mesh data. mfTetStreamRibbon Create stream ribbons from three-dimensional

unstructured mesh data. mfTetStreamTube Create stream tubes from three-dimensional

unstructured mesh data. mfTetStreamArrow Create stream arrows from three-dimensional

unstructured mesh data. Unstructured Point Set mfPoint Display input points in 3-D space. mfDelaunay Display 2-D Delaunay triangulation of input

points.


mfDelaunay3 Display 3-D Delaunay triangulation of input points.

mfGetDelaunay Retreive 2-D Delaunay triangulation of input points.

mfGetDelaunay3 Retreive 3-D Delaunay triangulation of input points.

Velocity Vectors mfQuiver 2-D velocity vectors. mfQuiver3 3-D velocity vectors. Image Image Display image file. mfImRead Read in image file. mfImWrite Write to image file.

2-D&3-D Objects mfCircle Draw a circle mfSquare Draw a square. mfMolecule Draw stick and ball model of molecules. mfSphere Draw a sphere. mfCube Draw a cube. mfCylinder Draw a cylinder. mfCone Draw a cone. mfAxisMark 3-directional mark on arbitrary point. Property Setting msGSet Set property of specified graph. msDrawMaterial Set draw object's transparency reflectance,

ambient reflectance, diffuse reflectance and specular reflectance.

msDrawTexture Texture mapping.


mfIsValidDraw Check validity of draw object. mfGetCurrentDraw Return handle of current draw object. msRemoveDraw Remove draw object from plot space. msSetDrawName Name of draw object. Graphics Viewer Manipulation mfPrintPreview Pop up print preview dialog box. mfEditorDrawList Pop up draw-list editor. mfEditorMaterial Pop up material editor. mfEditorColormap Pop up colormap editor. mfEditorTransform Pop up transformation editor. mfEditorAxis Pop up axis editor. mfEditorColorbar Pop up colorbar editor. mfEditorBackground Pop up background editor. Simple GUI msShowMessage Pop up message dialog box. mfInputString Pop up string insertion dialog box. mfInputValue Pop up value insertion dialog box. mfInputVector Pop up vector insertion dialog box. mfInputMatrix Pop up matrix insertion dialog box. mfFileDialog Pop up file open dialog box. mfInputYesNo Pop up yes-no query dialog box.


Figure


mfFigure, msFigure Create figure in Graphics Viewer.

Module fgl

Syntax call msFigure(figure_id) call msFigure(figure_name) call msFigure(figure_id, figure_name) id = mfFigure() Descriptions Procedure mfFigure creates a new figure with ID specified by argument figure_id and with name specified by argument figure_name. The ID and name of the figure is displayed on the figure tab. call msFigure()

• If argument figure_id is not provided, it creates a new figure with an automatically selected figure ID.

id = mfFigure(...)

• If the procedure is used in function format, it will return the figure ID once the figure is created.



type (mfArray) :: x, y1, y2, y3 in teger :: num

x = mfLinspace(-MF_PI, MF_PI, 100) y1 = mfSin(x) y2 = mfCos(x) y3 = mfLinspace(-1, 1, 100)

! Create figure 1 and plot x, y1 call msFigure(1) call msPlot(x, y1) ca ll msAxis(mf((/-MF_PI, MF_PI, -1.0d0, 1.0d0/)))

! Returns number of figures num = mfFigureCount()


call msDisplay(mf(num), 'mfFigureCount()') ca ll msViewPause()

! Create figure 2 and plot x, y2 call msFigure(2) call msPlot(x, y2, 'r') ca ll msAxis(mf((/-MF_PI, MF_PI, -1.0d0, 1.0d0/)))

! Returns number of figures num = mfFigureCount() call msDisplay(mf(num), 'mfFigureCount()') ca ll msViewPause()

! Create figure 3 and plot x, y3 call msFigure(3) call msPlot(x, y3, 'g') ca ll msAxis(mf((/-MF_PI, MF_PI, -1.0d0, 1.0d0/)))


! Close figure 2 ca ll msCloseFigure(2)


ca ll msFreeArgs(x, y1, y2, y3)


See Also mfCloseFigure, mfFigureCount


msCloseFigure Close figure in Graphics Viewer.

Module fgl

Syntax call msCloseFigure(figure_id) Descriptions Procedure msCloseFigure closes the target figure specified by argument figure_id. Example To be referred to mfFigure See Also mfFigure, mfFigureCount


mfFigureCount Number of figures in Graphics Viewer.

Module fgl

Syntax num = mfFigureCount() Descriptions Procedure mfFigureCount returns the number of figures that are in the Graphics Viewer. Example To be referred to mfFigure See Also mfFigure, msCloseFigure


Window Frame


mfWindowCaption, msWindowCaption Graphics Viewer title.

Module fgl

Syntax title = mfWindowCaption() call msWindowCaption(title) Descriptions Procedure mfWindowCaption sets the caption on the top window panel of the Graphics Viewer. title = mfWindowCaption()

• It can also be used as an inquiry procedure if given no argument. call msWindowCaption(title)

• Argument title can be a string or an mfArray containing a string. Example Code pr ogram example



x = mfLinspace(0, 2*MF_PI, 101) y = mfSin(x)

call msPlot(x, y) ca ll msWindowCaption('Example Change WindowCaption to 2D Plot')

ca ll msViewPause()



See Also mfWindowSize, mfWindowPos


mfWindowSize, msWindowSize Graphics Viewer frame size.

Module fgl

Syntax size = mfWindowSize() call msWindowSize(width, height) call msWindowSize(size) Descriptions Procedure mfWindowSize sets the frame size of the Graphics Viewer. call msWindowSize(width, height)

• Arguments width and height can be integer scalars or mfArrays containing integer scalars.

msWindowSize(size)

• Argument size is a 1x2 mfArray. size = mfWindowSize()

• It can be used as an inquiry function for the frame size if no argument is specified. The return argument size is a double vector in the format [width, height].





call msPlot(x, y) call msWindowSize(600, 600) ca ll msViewPause()



See Also


mfWindowPos, msWindowPos Graphics Viewer frame position.

Module fgl

Syntax pos = mfWindowPos() call msWindowPos(x, y) call msWindowPos(pos) Descriptions Procedure mfWindowPos sets the frame position of the Graphics Viewer. call msWindowPos(x, y)

• Arguments x and y can be integer scalars or mfArrays containing integer scalars. call msWindowPos(pos)

• Argument pos is a 1x2 mfArray. pos = mfWindowPos()

• It can be used as an inquiry function for the frame position if no argument is specified. The return argument pos is a integer vector in the format [x, y].





call msPlot(x, y) call msWindowPos(220, 0) ca ll msViewPause()



See Also mfWindowSize


Display


msGDisplay Display mfArray data on a MATFOR Data Viewer.

Module fgl

Syntax call msGDisplay(x) call msGDisplay(x, "name"[, x1, "name1", ...]) Descriptions Procedure msGDisplay displays your mfArray data on a Data Viewer. You can output single or multiple mfArray data to the Data Viewer. call msGDisplay(x), call msGDisplay(x , "name")

• Display data of mfArray x on Data Viewer. • Character string "name" specifies the label on the spreadsheet tab displaying data of x. call msGDisplay(x, "name", x1, "name1", ...)

• Display multiple datasets x, x1, ...), on the Data Viewer, labeled with "name", "name1", ... respectively. The arguments must be specified in pairs.



type (mfArray):: x, y, z in teger :: i

x = (/(i, i=1, 10)/) y = (/(i, i=-10, -1)/) z = mfComplex(x,y)

! Next, display the data of X, Y and Z on a MATFOR Data ! Viewer. ca ll msGDisplay(x, 'x', y, 'y', z, 'z')

! Pause program to display Data Viewer ca ll msViewPause

! Deallocate mfArrays ca ll msFreeArgs(x, y, z)


See Also msDisplay


msDrawNow Draw all pending graphs.

Module fgl

Syntax call msDrawNow() Descriptions Procedure msDrawNow draws all pending graphics on the current Figure. The procedure is used mainly for animation, it does not pause program execution. As a result, the Figure is displayed, updated, and flushed almost immediately. Animation results when msDrawNow is used within a do loop in which the graphics object is continuously being updated. Example Code pr ogram example


type (mfArray) :: x, y, h in teger :: i

x = mfLinspace(-MF_PI, MF_PI, 50) y = mfSin(x)

! Create an initial copy of the graph to be animated. ! This is recommended as you can obtain the current ! graphics handle and use erase mode for the animation. h = mfPlot(x, y) ca ll msAxis(mf((/-MF_PI, MF_PI, -1d0, 1d0/)))

! Use a Do Loop to animate the sin(x) curve. Note, ! msGSet continuously updates the specified data and ! sleep slows down the program execution. do i = 1, 100 y = mfSin(x+0.1d0*i) call msGSet(h, 'ydata', y) call msDrawNow() en d do

! Pause the program to continue displaying the ! Graphics Viewer after the Do Loop ends. ca ll msViewPause()

! Deallocate mfArrays ca ll msFreeArgs(x, y, h)


See Also msViewPause


msViewPause Pause program execution.

Module fgl

Syntax call msViewPause() Descriptions Procedure msViewPause pauses program execution for graphical display. Use this procedure wherever you wish to pause a program to visualize your data. To continue your program execution, you can click on the "Continue" button located at the top right corner of the Graphics Viewer. You must add at least one line of call msViewPause() after each set of graphical creation routines. If the procedure were left out, you would only see a flash as the Graphics Viewer is opened and closed almost immediately by the program. Example To be referred to msDrawNow See Also


Configuration


msSaveConfig Save display configuration.

Module fgl

Syntax call msSaveConfig(filename, config) Descriptions Procedure msSaveConfig saves the display configuration into a MATFOR defined configuration file (*.mfcg) with the filename given. Argument config is a string that can be "all", "axis", "background", "colorbar" or "colormap". Example See Also msLoadConfig


msLoadConfig Load pre-saved display configuration.

Module fgl

Syntax call msLoadConfig(filename, config) Descriptions Procedure msLoadConfig loads the pre-saved configuration file (*.mfcg) with the specified configuration type. Argument config is a string that can be "all", "axis", "background", "colorbar", "colormap" or "material". Example Code pr ogram example

use fml use fgl implicit none

type(mfArray) :: x,y,z,h

!Create Surface Data to draw

call msCreateSurfData(mfOut(x,y,z),1,30,30)

call msFigure('Save Config') !Load Previous saved setting(Colorbar,Axis...)

call msLoadConfig('graphic.mfcg','all')

call msSurf(x,y,z) call msAxis3DDependency('xyz_depend',2,1) call msAxis('xtick_format','%-3.1e') call msXLabel('First Axis') call msYLabel('Second Axis')

call msZLabel('Third Axis')

call msViewPause()

!Save Current setting before program exit !If user change property like axis wall color will be saved

call msSaveConfig('graphic.mfcg','all')


See Also msSaveConfig


Recording


msRecordStart, msRecordEnd Record animation as an avi file or multiple bitmap files.

Module fgl

Syntax call msRecordStart(filename[, property1, value1, ...]) call msRecordEnd() Descriptions Procedures msRecordStart and msRecordEnd are built-in MATFOR procedures for recording visualized data as avi animation files. call msRecordStart(filename, property1, value1, property2, value2, property3, value3)

• Records the animations as avi files. • Argument filename can take the following values.


• The optional arguments property1,property2 and property3 and the

corresponding arguments value1,value2 and value3 can take the following values.

Property Meaning

Value Meaning

“*.avi” Example: “filename.avi”.

Record the current animation in an avi file.

Avi or video recording uses frame capturing method to capture the animation playing on the current Graphics Viewer. The recorder automatically detects the type of video compression utilities available in your system and presents a drop-list for you to choose.

“*.mfa” Example: “filename.mfa”.

Record the current animation as an mfa file. The mfa file format is a MATFOR-specific record of all data used for generating the current animation on the Graphics Viewer. You can playback the animation by using MATFOR mfPlayer at a later time.

Using mfPlayer, you can perform graphical manipulations on the animation, such as zoom in/out, rotation, colormap adjustment, etc.

“*.bmp” Example: “filename.bmp”.

Save each frame of the animation into a bitmap file. The name of each bitmap file is set to be the input file name followed by four digits starting from 0000 counting up. In the example, the names of the first two bitmap files would be “filename0000.bmp” and “filename0001.bmp”.

“*.tif” Example: “filename.tif”.

Save each frame of the animation into a TIFF file. The naming method of the saved files is similar to saving as bitmap files.


“framerate” Specify the number of frames captured per second. The argument applies only when the animation file is saved in avi format. By default, MATFOR records avi file at 15 frames per second. The recommended range is 5 to 30 frames per second. The higher the frame rate, the faster the frames are looped through. Likewise, smaller frame rate slows down the animation.

“width” Specify the width of the captured figure frame. The argument

applies only when the animation is saved in avi format or bmp format. Without specifying the argument, the captured figure frame will have the exact same width as the displaying figure frame.

“height” Specify the height of the captured figure frame. The argument

applies only when the animation is saved in avi format or bmp format. Without specifying the argument, the captured figure frame will have the exact same height as the displaying figure frame.

call msRecordEnd() • Stop the recording. The general syntax of the recording procedures is as follows: call msRecordStart('animation.avi')

or

call msRecordStart('animation.bmp')

------- <animation codes>

call msRecordEnd()



type(mfArray) :: a, b, c, x, y, z, indxi, indxj, h in teger :: i

a = mfLinspace(-3, 7, 51)


b = mfLinspace(-2, 8, 51) ca ll msMeshgrid(mfout(x, y), a, b)

! Next, initialize indxi and indxj using Meshgrid. ! Compute z using indxi and indxj. ! Note, a 'd0' is added to the integers, to ensure ! double precision. MATFOR uses only double precision ! data. c = mfColon(1, 51) call msMeshgrid(mfout(indxi, indxj), c) z = 3d0*mfSin((indxi+1)/10d0)*mfCos((indxj+1)/10d0) & + 2d0*mfSin((indxi+indxj)/10d0)

! Plot a mesh grid using mfArray x, y and z for the grid ! intersections. h = mfMesh(x, y, z)

! Start record of an animation using avi file format ! Records scarf.avi in the Debug directory ca ll msRecordStart('scarf.avi')

! Animate the mesh using a do loop. do i = 1, 10 z = 3d0*mfSin((indxi+i+1)/10d0)*mfCos((indxj+1-i)/10d0) & + 2d0*mfSin((indxi+indxj+i)/10d0)

! Update z call msGSet(h, 'zdata', z) ! Update Graphics Viewer call msDrawNow() en d do

! end video record ca ll msRecordEnd()

! Pause to display the graph. ca ll msViewPause()

! Deallocate mfArray ca ll msFreeArgs(a, b, c, x, y, z, indxi, indxj)


See Also msGSet, mfFigure


msExportImage Save figure graph as picture file.

Module fgl

Syntax call msExportImage(filename[, width, height]) Descriptions Procedure msExportImage saves the graph(s) in the current figure as a picture file. You can choose the picture format by specifying the extension in argument filename. For example, "filename.bmp" would save it as a bitmap file. The supported formats are: BMP, JPEG, TIFF, PS and PNG. Example Code pr ogram example


type(mfArray) :: a, b, c, x, y, z, indxi, indxj, h integer :: i,j ch aracter*4 FileNameID

a = mfLinspace(-3, 7, 51) b = mfLinspace(-2, 8, 51) ca ll msMeshgrid(mfout(x, y), a, b)

c = mfColon(1, 51) call msMeshgrid(mfout(indxi, indxj), c) z = 3d0*mfSin((indxi+1)/10d0)*mfCos((indxj+1)/10d0) & + 2d0*mfSin((indxi+indxj)/10d0)

! Plot a mesh grid using mfArray x, y and z for the grid ! intersections. h = mfMesh(x, y, z)

! Animate the mesh using a do loop. do i = 1, 10 write(FileNameID,'(I4)')i do j=1,4 if(FileNameID(j:j).eq.' ')FileNameID(j:j)='0' end do z = 3d0*mfSin((indxi+i+1)/10d0)*mfCos((indxj+1-i)/10d0) & + 2d0*mfSin((indxi+indxj+i)/10d0)

! Update z call msGSet(h, 'zdata', z) ! Update Graphics Viewer call msDrawNow() ! Export Visualization Result to JPG file.


call msExportImage('exImg'//FileNameID//'.jpg',640,480) en d do

! Pause to display the graph. call msViewPause() ! Deallocate mfArray ca ll msFreeArgs(a, b, c, x, y, z, indxi, indxj)


See Also


Plot Creation and Control


mfSubplot, msSubplot Create subplots in an active figure.

Module fgl

Syntax call msSubplot(m, n, p) call msSubplot(formatString, p) Descriptions Procedure mfSubplot divides the plot space of Graphics Viewer into m-by-n rectangular subplot spaces, as specified by the m, n arguments. Each subplot space is numbered column-wise so that a subplot space at position (2, 1) is numbered 2 and (2, 2) is numbered 4. The current subplot is set to the subplot number, given p. Any subsequent operations will be performed on the current subplot.

(1, 1)

subplot 1

(1, 2)

subplot 3

(2, 1)

subplot 2

(2, 2)

subplot 4

A more powerful subplot division can be specified using mfSubplot(formatString, p). formatString is a string of subplot format specified using numbers, commas, and open/closed braces ([,]) that represents column width/row height ratios. For example, mfSubplot('4,6[5,5]', 1) divides the plot space into left and right subplots with width ratio of 4:6. The right subplot is then divided into top and bottom subplots with height ratio of 5:5. The current subplot is set to subplot 1.

subplot 2 subplot 1

subplot 3

To select another subplot within the same layout, a null string can be used for formatString argument. For example, mfSubplot(" ", 2) will set the current subplot to subplot 2. mfSubplot("3, 3, 4", 2) creates three subplots under plot space with width ration of 3:3:4. And the current subplot is set to subplot 2.

subplot 1 subplot 2 subplot 3


Example Code program example use fml use fgl implicit none type(mfArray) :: x, y1, y2,h(4)

integer i

x = mfLinspace(0, 2*MF_PI, 101) y1 = mfSin(x)

y2 = mfASin(y1)

! Divide the plotting space into 1 on left 2 on right sub-plot spaces, ! and specify the subplot space 1 or left sub-plot as current. call msSubplot("4, 6[4, 6[5, 5]]", 1) ! Plot and label the graph. h(1) = mfPlot(x, y1) !call msPlot(x, y1) call msTitle("1: Graph of sin(x)")

call msXLabel("Angle in Radians, x")

! Next, specify subplot space p=2, or the right-top subplot ! space as current. call msSubplot("", 2) ! Again, plot and label the graph. !call msPlot(y1, y2, "r") h(2) = mfPlot(y1, y2, "r") call msTitle("2: Graph of Arcsine(x)")

call msXLabel("sin(x)")

! Finally, specify subplot space p=3, or the right-bottom subplot ! space as current. call msSubplot("", 3) ! Again, plot and label the graph. h(3) = mfPlot(x, y1+y2, "g") call msTitle("3: Difference Plot")

call msXLabel("sin(x)")

call msSubplot("", 4) h(4) = mfPlot(x, y1-y2, "y") call msTitle("4: Subplot 4") ! Pause the program to display the graphs.

call msViewPause()

!Animation do i=1,100 y1 = mfSin(x+i*1d-1) y2 = mfASin(y1) call msGSet(h(1),'ydata',y1) call msGSet(h(2),'ydata',y2) call msGSet(h(3),'ydata',y1+y2) call msGSet(h(4),'ydata',y1-y2) call msDrawNow()

end do

!Remove 3rd Subplot ID call msShowMessage("Remove 3rd Subplot ID") call msSubplot("",3) call msClearSubplot()

call msViewPause()

!Free Memory resource call msFreeArgs(x, y1, y2)


do i=1,4 call msFreeArgs(h(i))

end do


Result

See Also msClearSubplot


msClearSubplot Remove all drawings from specified subplot.

Module fgl

Syntax call msClearSubplot() Descriptions Procedure msClearSubplot removes all drawings from the current subplot. Example To be referred to msSubplot See Also mfSubplot


msHold Hold previous graph on plot space.

Module fgl

Syntax call msHold(mode) Descriptions Procedure msHold holds the current graph in plot space so that it would not be overwritten by the next graph creation. Subsequent graphs are drawn one after another in the plot space. Argument mode is a string containing "on" or "off". Example Code pr ogram example


ty pe(mfArray) :: x, y1, y2, a

x = mfLinspace(0, 2*MF_PI, 100) y1 = mfSin(x) y2 = mfCos(x)

! Plot y1 = mfSin(x) call msPlot(x, y1) ca ll msAxis(mf((/0d0, 2*MF_PI, -1d0, 1d0/)))

! Hold the figure for plotting ca ll msHold('on')

! Plot y2 = mfCos(x) to the same figure ca ll msPlot(x, y2, 'r')

call msHold('off') ! Pause the figure for viewing ca ll msViewPause()

! Deallocates the mfArrays call msFreeArgs(x, y1, y2) e nd program example

Result


See Also mfIsHold


mfIsHold Return status of plot space.

Module fgl

Syntax status = mfIsHold() Descriptions Procedure mfIsHold returns the status of the current plot space. The output is an mfArray containing logical data. Returns true if the plot space is on hold, false otherwise. Example To be referred to msHold See Also msHold


Plot Annotation and Appearance


mfTitle, mfXLabel, mfYLabel, mfZLabel Label the axis objects.

Module fgl

Syntax title = mfTitle() xlabel = mfXLabel() ylabel = mfYLabel() zlabel = mfZLabel() call msTitle(title[, color][, font_size]) call msXLabel(xlabel) call msYLabel(ylabel) call msZLabel(zlabel) Descriptions Procedures mfTitle, mfXLabel, mfYLabel and mfZLabel annotate a graph with title, x-axis label, y-axis label and z-axis label respectively. By default, x-axis is labeled as "X Axis", y-axis is labeled as "Y Axis" and z-axis label is labeled as "Z Axis". You can also annotate the graph through Axis Setting ->Axis ->Label on the Graphics Viewer. title = mfTitle() xlabel = mfXLabel() ylabel = mfYLabel() zlabel = mfZLabel()

They can also be used as inquiry procedures to retrieve the title and labels that are set by users.

call msTitle(title, color, font_size)

• Set the rgb color code and the font size of the title by specifying arguments color and font_size. The rgb color code is specified as [r, g, b] where 0 < r, g, b < 1.



integer i ty pe(mfArray) :: x, y, ht(5)



! Plot the x, y curve using msPlot. ca ll msPlot(x, y, 'rx-')

! Annotate the graph with title, x-axis label and y-axis label. call msTitle('Graph of sin(x)') call msXLabel('x in radians') ca ll msYLabel('sin(x)')

! Add 2d Text annotation ht(1) = mfText(mf('Left Bottom corner'),mf((/0d0,0.02d0/)), & mf((/1,0,0/)),mf(5)) call msGSet(ht(1),'just','left') ht(2) = mfText(mf('Left Top corner'),mf((/0d0,1d0/)), & mf((/1,1,0/)),mf(5)) call msGSet(ht(2),'just','left') ht(3) = mfText(mf('Right Top corner'),mf((/1d0,1d0/)), & mf((/0,1,0/)),mf(5)) call msGSet(ht(3),'just','right') ht(4) = mfText(mf('Right Bottom corner'),mf((/1d0,0.02d0/)), & mf((/0,1,1/)),mf(5)) call msGSet(ht(4),'just','right') ht(5) = mfText(mf('Center'),mf((/0.5d0,0.5d0/)), & mf((/1,1,1/)),mf(4)) ca ll msGSet(ht(5),'just','center')

! Pause program execution. ca ll msViewpause

! Deallocate mfArray call msFreeArgs(x, y) do i=1,5 call msFreeArgs(ht(i)) en d do


Result

See Also mfCaption


mfText, msText 2-D text annotation on the location specified in the subplot window.

Module fgl

Syntax handle = mfText(text[, loc][, color][, font_size]) Descriptions Procedure mfText places two-dimensional text on the current subplot. call msText(text, loc, color, font_size)

• Argument text can be a string or an mfArray containing a string. • Argument loc is a 1-by-2 vector in the format [m, n]. Each element contains a value

ranging from 0 to 1. Specifying m as 0 would place the text annotation at the left-most position of the subplot window, and specifying n as 0 would place the text annotation at the bottom of the subplot window. For example, the vector [0, 0] would place the text

annotation on the bottom-left corner of the subplot, and vector [0.5, 0.5] would place the text annotation in the center of the plot space.

• You can set the color and the font size through arguments color and font_size.

Argument color contains the rgb color code which is specified as [r, g, b] where 0 < r, g,

b < 1. h = mfText(...)

• Handle h retrieves a handle to the text annotation created by mfText(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the text annotation through handle h with procedure msGSet. The properties available are: 1. text 2. location 3. color 4. font_size 5. just Example To be referred to mfTitle See Also mfAnnotation


mfAnnotation, msAnnotation 3-D text annotation on the location specified in the axes.

Module fgl

Syntax handle = mfAnnotation(text[, loc][, color][, font_size]) Descriptions Procedure mfAnnotation places a three-dimensional text annotation in the axes. call msAnnotation(text, loc, color, font_size)

• Argument text can be a string or an mfArray containing a string. • Argument loc is a 1-by-3 vector in the format [m, n, p] where m, n, p are the actual

coordinate of the text annotation on the axes. h = mfAnnotation(...) • Handle h retrieves a handle to the text annotation created by mfAnnotation(...). • Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the

current graphics object. You can specify properties of the text annotation through handle h with procedure msGSet. The properties available are: 1. text 2. location 3. color 4. font_size 5. offset (2x1 array) Example Code pr ogram example


type(mfArray) :: m, x, y, z, cm, zz ty pe(mfArray) :: maxid,maxz, minid, minz, LocMax, LocMin, ha

m = mfLinspace(-3, 3, 30) call msMeshGrid(mfOut(x, y), m) z = mfSin(x) * mfCos(y) / ( x*(x-0.5d0) + (y+0.5d0)*y + 1)

! Find Max Z-value and it's Coordinate zz = mfReshape(z,900,1) call msMax(mfOut(maxz,maxid),zz,MF_NULL,1) Lo cMax = mfS(x,maxid).vc.mfS(y,maxid).vc.maxz


!Find Min Z-value and it's Coordinate call msMin(mfOut(minz,minid),zz,MF_NULL,1) Lo cMin = mfS(x,minid).vc.mfS(y,minid).vc.minz

call msSurf(x, y, z) call msAxis(-3.0d0, 3.0d0, -3.0d0, 3.0d0, -0.4d0, 0.6d0) !Draw Maximum text annotation call msAnnotation(mf('Maximum'), LocMax,mf((/0,0,1/)),mf(7)) !Draw Minimum text annotation ha = mfAnnotation(mf('Minimum'), LocMin,mf((/1,0,0/)),mf(5)) !Change offset of Minimum text annotation ca ll msGSet(ha,'offset',mf(-15d0).vc.mf(-10d0))

ca ll msViewPause()

call msFreeArgs(m, x, y, z, zz) ca ll msFreeArgs(maxid,maxz, minid, minz, LocMax, LocMin, ha)


Result

See Also mfText


msShading Shading methodology of surface object.

Module fgl

Syntax call msShading(mode) call msShading(handle, mode) Descriptions Procedure msShading sets the shading mode for all drawings in the plot space. call msShading(mode)

• Specify shading type for procedures mfSurf and mfMesh. The options available are listed in the table below.

Value Meaning

“mesh” Set the surface object to a surface composed of quadrilateral outlines. The color of point is adjusted to reflect the z-height of the corresponding point.

“flat” Set the surface object to a surface composed of colored quadrilaterals with uniform color.

“facet” Same as “flat” but with mesh outlines.

“interp” Apply interpolated shading to the surface plot, thus producing a surface that presents a smooth color variation across the surface.



type (mfArray) :: a, x, y, z, h


a = mfLinspace(-3, 3, 30) call msMeshGrid( mfOut(x, y), a) z = mfSin(x) * mfCos(y) / ( x*(x-0.5d0) + (y+0.5d0)*y + 1)

call msSubplot(2, 2, 1) call msSurf(x, y, z) call msShading('facet') call msTitle('facet') ca ll msCamZoom(1.2d0)

call msSubplot(2, 2, 2) call msSurf(x, y, z) call msShading('flat') call msTitle('flat') ca ll msCamZoom(1.2d0)

call msSubplot(2, 2, 3) call msSurf(x, y, z) call msShading('interp') call msTitle('interp') ca ll msCamZoom(1.2d0)

call msSubplot(2, 2, 4) h = mfSurf(x, y, z) call msTitle('mesh') call msCamZoom(1.2d0) !pass handle to msShading subroutine call msShading(h,mf('mesh')) ca ll msViewPause()

ca ll msFreeArgs(a, x, y, z, h)


Result

See Also msDrawMaterial


msColorbar Display color scale.

Module fgl

Syntax call msColorbar(mode) call msColorbar(property, value) Descriptions Procedure msColorbar controls the colorbar through specification of argument mode. A colorbar displays the current color map and acts as a color scale showing the relationship between graphics data and color. In the case of a surface object, it shows the relationship between color and height of the surface object. You can also select the colorbar setting from the menu and toolbar functions of the Graphics Viewer. call msColorbar(mode) call msColorbar(property, value)

Argument mode can be:

mode Meaning

“on” Display a colorbar on the Graphics Viewer.

“off” Hide the colorbar.

“vert” Display a vertical colorbar.

“horz” Display a horizontal colorbar.

Argument property can be:

Property Meaning

“label_count” Number of labels displayed on the colorbar.

“label_color” Color of the colorbar labels. Corresponding argument value is

a 1-by-3 mfArray contains the rgb codes.


“title” Title of the colorbar.



ty pe(mfArray) :: m, x, y, z, h, bakcolor,color1,color2

m = mfLinspace(-3, 3, 30) call msMeshGrid(mfOut(x, y), m) z = mfSin(x) * mfCos(y) / ( x*(x-0.5d0) + (y+0.5d0)*y + 1)

call msSurf(x, y, z) ca ll msAxis(-3.0d0, 3.0d0, -3.0d0, 3.0d0, -0.4d0, 0.6d0)

!Show Colorbar call msColorbar('on') call msColorbar(mf('label_count'),mf(12)) call msColorbar(mf('label_color'),mf((/1,0,0/))) ca ll msColorbar(mf('title'),mf('Field 1'))

!Save background color bakcolor = mfBackgroundColor() !Get two color variable color1 = mfS(bakcolor,2.to.4) color2 = mfS(bakcolor,5.to.7) !Change background color's blue channel to decrease 0.3d0 call msAssign(mfS(color1,3),mfS(color1,3)-0.3d0) !Change background color ca ll msBackgroundColor(color1,color2);

ca ll msViewPause()

call msFreeArgs(m, x, y, z, bakcolor,color1,color2) e nd program example

Result

See Also


msColormap Colormap type.

Module fgl

Syntax call msColormap(type) call msColormap(colormap) call msColormap(colormap_file) call msColormap(property, value) Descriptions Procedure msColormap specifies the colormap type used for drawing surface objects. call msColormap(type)

• Argument type specifies the type of colormap used. The argument can be an mfArray containing a string specifying the type of colormap or a character string. MATFOR provides the following types of colormapping:

Value Meaning

“jet” Range from blue to red, and pass through the colors cyan, yellow, and orange.(default)

“gray” Return a linear grayscale colormap.

“hot” Vary smoothly from black, through shades of red, orange, and

yellow, to white.

“cool” Vary smoothly from cyan to magenta.

“copper” Vary smoothly from black to bright copper.

“hsv” Vary the hue component of the hue-saturation-value color model.

“spring” Consist of colors that are shades of magenta and yellow.

“summer” Consist of colors that are shades of green and yellow.


“autumn” Vary smoothly from red, through orange, to yellow.

“winter” Consist of colors that are shades of blue and green.

call msColormap(colormap)

• Allows users to customize the colormap through the argument colormap which is an m-by-3 matrix consisting of m sets of rgb color code. The rgb color code is specified as [r, g, b], where 0 < r, g, b < 1.

call msColormap(colormap_file)

• Allows users to load pre-saved colormap files. The pre-saved colormap file can be created, added, imported and exported using the colormap setting dialog box. For example, create a colormap "mycolor", add to the warehouse or export as mycolor.mfcm. Then, call msColormap('mycolor.mfcm')

call msColormap(property, value)

• Allows users to specify properties of the colormap. MATFOR provides the following properties of colormapping:

Property Values

‘kind’ ‘linear’, ‘step1’, ‘step2’.

‘undef’ ‘Clamp’, ‘no_drawing’, color (1 by 3 mfArray ) .

‘range’ min_max (1 by 2 mfArray).



type(mfArray) :: x, u, v, z, h ty pe(mfArray) :: mcolor,mv

x = mfLinspace(-3, 3, 25) call msMeshgrid(mfout(u, v), x) z = 3*((1-u)**2)*mfExp(-(u**2)-((v+1)**2)) & - (10*(u/5-(u**3)-(v**5))*mfExp(-(u**2)-(v**2))) & - mfExp(-(u+1)**2-v**2)/3


call msSubPlot(2, 2, 1) call mstitle('Spring') h = mfSurf(u, v, z) call msColorMap('spring') call msColormapRange(-5d0,5d0); ca ll msCamZoom(1.2d0)

call msSubPlot(2, 2, 2) call mstitle('Summer') h = mfSurf(u, v, z) call msColorMap('summer') ! Specify the range between -4 and 5 call msDrawColormap(h, mf('range'), mf((/-4d0, 5d0/))) ! Color undefined area to white call msDrawColormap(h, mf('undef'), mf((/1,1,1/))) ca ll msCamZoom(1.2d0)

call msSubPlot(2, 2, 3) call mstitle('Colormap File') h = mfSurf(u, v, z) call msColorMap('mycolor.mfcm') ca ll msCamZoom(1.2d0)

call msSubPlot(2, 2, 4) call mstitle('Customize') h = mfSurf(u, v, z) mv = .T.mfLinSpace(1, 0, 64) mcolor = mv.hc.mv.hc.mv call msColorMap(mcolor) ca ll msCamZoom(1.2d0)

ca ll msViewPause()

ca ll msFreeArgs(x, u, v, z)


Result

See Also msDrawColormap, msColormapRange


mfColormapRange, msColormapRange Range of color map.

Module fgl

Syntax range = mfColormapRange() call msColormapRange(min, max) call msColormapRange([min, max]) call msColormapRange("auto") Descriptions Procedure mfColormapRange sets the range of color map. call msColormapRange(min, max), call msColormapRange([min, max])

• Arguments min and max specify the minimum and maximum of the range. • The range can also be input as a vector containing the min and max of the range. range = mfColormapRange()

• It can also be used as an inquiry procedure to retrieve the color map range in the format of [min, max]if no argument is specified.

Example To be referred to msColormap. See Also msColormap, msDrawColormap


msDrawColormap Change colormap properties.

Module fgl

Syntax call msDrawColormap(h, colormap) call msDrawColormap(h, type) call msDrawColormap(h, colormap_file) call msDrawColormap(h, property, value) Descriptions Procedure msDrawColormap changes the properties of colormap given the object handler h. Please refer to msColormapfor argument specification. Example To be referred to msColormap See Also msColormap, msColormapRange


msLegendBox Display legend box in the plot window

Module fgl

Syntax call msLegendBox(mode) call msLegendBox(property, value[, property2, value2,...]) Descriptions Procedure msLegendBox displays legend box in current plot window. call msLegendBox(mode)

• Argument mode is a string containing 'on' or 'off'. Legend off removes the legend box from the plot window.

call msLegendBox(property, value[, property2, value2,...])

• Arguments property and value can be:

Property Meaning

“title” An mfArray containing a string specifies the title of the legend box.

“width” An mfArray containing a real number specifies the width of the legend box.

“height” An mfArray containing a real number specifies the height of the legend box.

“pos_x” An mfArray containing a real number ranges from 0 to 1. Specifying value as 0 would place the legend box at the right-most position of the plot window.

“pos_y” An mfArray containing a real number ranges from 0 to 1. Specifying value as 0 would place the legend box at the top of the plot window.




type(mfArray) :: x, y1, y2 type(mfArray) :: h1,h2,h3

x = mfColon(0, 0.25, 50) y1 = x*mfSin(x)

y2 = mfSin(x)

! Plot the graphs

h1 = mfPlot(x, y1, 'b-')

call msHold('on'); h2 = mfPlot(x, y2, 'r-') h3 = mfPlot(x,y2-y1,'g-')

call msHold('off')

call msTitle('Three Plot') call msLegendBox('on') call msLegendBox('title','My Legend') call msLegendBox(mf('pos_x'),mf(0.6)) call msLegendBox(mf('pos_y'),mf(0.6)) call msLegendBox(mf('width'),mf(0.2))

call msLegendBox(mf('height'),mf(0.2))

call msAddLegend(h1,mf('Plot 1 blue')) call msAddLegend(h2,mf('Plot 2 red'))

call msAddLegend(h3,mf('Plot 3 green'))

! Pause the program for drawing

call msViewPause()

call msRemoveLegend(h2) call msViewPause() e nd program example

Result

See Also mfAddLegend, mfRemoveLegend


msAddLegend Add legend to the legend box.

Module fgl

Syntax call msAddLegend(h, label [, h2, label2, ...] ) Descriptions Procedure mfAddLegend associates given handle with the label. Example To be referred to msLegendBox See Also msRemoveLegend, msLegendBox


msRemoveLegend, msRemoveAllLegend Remove legends from the legend box.

Module fgl

Syntax call msRemoveLegend(h [,h2, ...] ) call msRemoveAllLegend() Descriptions Procedures mfRemoveLegend and mfRemoveAllLegend remove the specified or all legends from the legend box in the plot window. Example To be referred to msLegendBox See Also msAddLegend, msLegendBox


mfBackgroundColor, msBackgroundColor Background color of plot space.

Module fgl

Syntax call msBackgroundColor(r, g, b) call msBackgroundColor(color) call msBackgroundColor(color1, color2) colorCode = mfBackgroundColor() Descriptions Procedure mfBackgroundColor sets the background color of the plot space. call msBackgroundColor(r, g, b)

• Arguments r, g, b contain a real number within the range 0 to 1 specifying the rgb code of the background color. For example, call msBackgroundColor(1, 1, 1) sets

the background color to white. call msBackgroundColor(color)

• Argument color is a 1-by-3 mfArray containing the rgb color codes where 0 < r, g, b < 1. For example, call msBackgroundColor(mfV(1, 0, 1)).

call msBackgroundColor(color1, color2)

• This procedure creates an easy gradient for the background using two colors. Argument color1 and color2 are 1-by-3 mfArrays containing the rgb color where 0 < r, g, b < 1. For example, call msBackgroundColor(mfV(0.5, 0.5, 0.5), mfV(1,0,1)).

colorCode = mfBackgroundColor()

• This procedure retrieves the color code of the current plot space in the format of [r, g, b], where 0 < r, g, b < 1.

Example To be referred to msColorbar See Also


Axis Control


mfAxis, msAxis Manipulate the axis object.

Module fgl

Syntax xyzrange = mfAxis() call msAxis(xyzrange) call msAxis(x_min, x_max, y_min, y_max[, z_min, z_max]) call msAxis(mode) call msAxis(property, value) Descriptions Procedure mfAxis sets the properties of the x-axis, y-axis and z-axis, such as the range, mode and color. It can also be used as an inquiry function for the range of the axes. xyzrange = mfAxis()

• Retrieves the range of the axis objects. The output argument xyzrange is a vector in the format [x_min, x_max, y_min, y_max, z_min, z_max].

call msAxis(xyzrange) call msAxis(x_min, x_max, y_min, y_max) call msAxis(x_min, x_max, y_min, y_max, z_min, z_max)

• Sets the ranges of the axis objects. The input data can be provided in two ways: through a vector xyzrange in which the ranges of the axes objects are specified or in the

element-by-element way.

• Argument xyzrange is a vector in the format [x_min, x_max, y_min, y_max, z_min, z_max].

• Arguments x_min,x_max,y_min,y_max,z_min,z_max specify the displaying ranges of the x-axis, y-axis and z-axis.

call msAxis(mode) call msAxis(property, value)

• Sets the mode and property of the axis objects. Argument mode can be:

mode Meaning

“on” Display the tick marks, labeling and background of the current axis object.


“off” Remove the tick marks, labeling and background of the current axis object.

“Normal” Restore the current axis object to its full size and remove any restrictions on scaling.

“equal” Use the same aspect ratio for each axis of the axis object. In other words, tick marks of equal increments have the same size on all axes.

“Auto” Set axes scaling to automatic mode. MATFOR sets the limits, minimum and maximum of each axis based on the extents of the graphs plotted. It is the default setting.

Argument property can be:

property Meaning

“axis_color” Color of all three axes. The corresponding argument value is an mfArray containing a string that specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the

rgb codes.

"xaxis_color" Color of the x-axis. The corresponding argument value is an mfArray containing a string that specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the

rgb codes.

"yaxis_color" Color of the y-axis. The corresponding argument value is an mfArray containing a string that specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the

rgb codes.

“zaxis_color” Color of the z-axis. The corresponding argument value is an mfArray containing a string that specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the

rgb codes.

“xtick_custom” Customized tick label for x-axis. The corresponding arguments are a vector containing locations of the tick


marks and a string containing labels of the tick marks.

“ytick_custom” Customized tick label for y-axis. The corresponding arguments are a vector containing locations of the tick marks and a string containing labels of the tick marks.

“ztick_custom” Customized tick label for z-axis. The corresponding arguments are a vector containing locations of the tick marks and a string containing labels of the tick marks.

“xtick_format” Tick format of x-axis. The corresponding argument value is a printf style format string*.

“ytick_format” Tick format of y-axis. The corresponding argument value is a printf style format string*.

“zxtick_format” Tick format of z-axis. The corresponding argument value is a printf style format string*.

“xtick_space” Interval between tick marks of the x-axis.

“ytick_space” Interval between tick marks of the y-axis.

“ztick_space” Interval between tick marks of the z-axis.

“xtick_anchor” Where one tick marks is placed and, other tick marks are placed relative to this point.

“ytick_anchor” Where one tick marks is placed and, other tick marks are placed relative to this point.

“ztick_anchor” Where one tick marks is placed and, other tick marks are placed relative to this point.

“clipping” Sets the cropping mode “on” or “off”. Graphs are

cropped if it exceeds the min value and/or max value of the particular axis setting.

“tight” Sets the axes boundary to fit in axes range and sets yzx ratio to 1.

“geoid_label” Display geoid labels on current axis object. The


corresponding argument is “on” or “off”.

* printf Format String: Code Format %c character %d signed integers %i signed integers %e scientific notation, with a lowercase "e" %E scientific notation, with a uppercase "E" %f floating point %g use %e or %f, whichever is shorter %G use %E or %f, whichever is shorter Example Code pr ogram example


type (mfArray) :: a, b, c, x, y, z, indxi, indxj type (mfArray) :: range a = mfLinspace(-7, 7, 51) b = mfLinspace(-2, 3, 51) c = mfColon(1, 51) call msMeshgrid(mfout(x, y), a, b) call msMeshgrid(mfout(indxi, indxj), c) z = 1*mfSin((indxi+1)/10)*mfCos((indxj+1)/10) & + 2*mfSin((indxi+indxj)/10)

call msSubplot(1,2,1) call msSurf(x, y, z) !Switch display mode to 2D mode call msAxis2DMode() call msAxis2DRange(-7, 5, -2, 3) !Set Axis clipping on call msAxis('clipping', 'on') !Set axis dependency of 2D display mode call msAxis2DDependency('xy_tight',3.5d0) call msAxis('xtick_format','%-3.1e') ca ll msAxis('ytick_format','%4.3g')

range = mfAxis2DRange() ca ll msDisplay(range,'2D Axis range')

call msSubplot(1,2,2) call msSurf(x, y, z) !Set Axis range call msAxis(-7, 5, -2, 3, -5, 5) !Set Axis clipping off call msAxis('clipping', 'off') !Switch display mode to 3D mode call msAxis3DMode()


!Set axis dependency of 3D display mode call msAxis3DDependency('xyz_depend',1d0,0.5d0) call msAxis('xtick_format','%-3.1e') call msAxis('ytick_format','%4.3g') call msAxis("ztick_custom",mfLinspace(-5,5,5), & "B0|B1|Z0|T0|T1") range = mfAxis3DRange() call msDisplay(range,'3D Axis range') ca ll msViewPause()

ca ll msFreeArgs(a, b, c, x, y, z, indxi, indxj)


Result

See Also


msAxis2DMode Switch display mode to 2D mode.

Module fgl

Syntax call msAxis2DMode() Descriptions Procedure msAxis2DMode switches display mode to 2D mode. This procedure will only take effect when calling after the last graphic function. Example To be referred to mfAxis See Also msAxis3DMode, msAxis2DDependency, msAxis3DDependency


msAxis3DMode Switch display mode to 3D mode.

Module fgl

Syntax call msAxis3DMode() Descriptions Procedure msAxis3DMode switches display mode to 3D mode. This procedure will only take effect when calling after the last graphic function. Example To be referred to mfAxis See Also msAxis2DMode, msAxis2DDependency, msAxis3DDependency


msAxis2DDependency Set axis dependency of 2D display mode.

Module fgl

Syntax call msAxis2DDependency(mode) call msAxis2DDependency(mode, y2xratio) Descriptions Procedure msAxis2DDependency sets axis dependency of 2D display mode. call mfAxis2DDependency(mode, y2xratio)

• Argument mode can take the following values.

Value Meaning

“indep” In this mode, the units of x-axis and y-axis

are independent. The graph will be

normalized to fit the whole area of the

display window.

“xy_depend” In this mode, the units of x-axis and y-axis

are dependent to each other. If the ratio

y2xratio is equal to 1, the graph has the

same unit length.

y2xratio determines the display ratio

between y-axis unit and x-axis unit. For

example, if y2xratio = 2, the display

length of vector (0,1) is 2-times long of

the vector (1,0) in the display window.

“xy_tight” See xy_depend.

Sets the axis limits to the range of the

axis.

• Argument y2xratio determines the display ratio of units in y-axis and x-axis in

"xy_depend" mode. It has no effect in "indep" mode. The default vaule is 1.0.


Example To be referred to mfAxis See Also msAxis3DMode, msAxis2DDependency


msAxis3DDependency Set axis dependency of 3D display mode.

Module fgl

Syntax call msAxis3DDependency(mode) call msAxis3DDependency(mode, y2xratio, z2xratio) Descriptions Procedure msAxis3DDependency sets axis dependency of 3D display mode. call mfAxis3DDependency(mode, y2xratio, z2xratio)

• Argument mode can take the following values.

Value Meaning

“indep” In this mode, the units of x-axis, y-axis and

z-axis are independent. The display size of the

graph in x-, y- and z-dimension will be

normalized by the ratio y2xratio and z2xratio.

For example, if y2xratio=2, z2xratio=3, the

bounding box of the graph will be the size of

1x2x3 in the display window.


In this mode, the units of x-axis, y-axis and

z-axis are dependent to each other. if the ratio

y2xratio and z2xratio are both equal to 1, the

graph has the same unit length in all

three-axes.

y2xratio determines the display ratio between

y-axis unit and x-axis unit. For example, if

y2xratio = 2, the display length of vector (0,1)

is 2-times long of the vector (1,0) in the

display window.

“xyz_depend”

z2xratio determines the display ratio between

z-axis unit and x-axis unit. For example, if

z2xratio = 2, the display length of vector

(0,0,1) is 2-times long of the vector (1,0,0)

in the display window.

“xy_depend” In this mode, the units of x-axis, y-axis are

dependent to each other but and the unit of

z-axis is independent to x-axis and y-axis. It

is a mixed mode. The unit behavior between

x-axis and y-axis are like “xyz_depend” mode

and The unit behavior between z-axis and x-axis

are like “indep” mode.

• Argument y2xratio determines the display size ratio between y-dimension and

x-dimension in "indep" mode. Argument y2xratio also determines the display ratio of units in y-axis and x-axis in "xyz_depend" and "xy_depend" modes. The default

vaule is 1.0.

• Argument z2xratio determines the display size ratio between z-dimension and x-dimension in "indep" and "xyz_depend" modes. The default vaule is 1.0.

Example To be referred to mfAxis See Also msAxis2DMode, msAxis3DMode, msAxis2DDependency


mfAxis2DRange Set the axis range of 2D display mode.

Module fgl

Syntax xyrange = mfAxis2DRange() call msAxis2DRange(xyrange) call msAxis2DRange(x_min, x_max, y_min, y_max) Descriptions Procedure mfAxis2DRange set the axis range of 2D display mode. xyrange = mfAxis2DRange()

• Retrieves the ranges of the axis objects. The output argument xyrange is a vector in the format [x_min, x_max, y_min, y_max].

call mfAxis2DRange(xyrange) call mfAxis2DRange(x_min, x_max, y_min, y_max)

• Set the ranges of the axis objects. The input data can be provided in two ways: through a vector xyzrange in which the ranges of the axes objects are specified, or in the


• Argument xyrange is a vector in the format [x_min, x_max, y_min, y_max]. • Arguments x_min,x_max,y_min,y_max specify the displaying ranges of the x-axis

and y-axis.

• You can specify x_min,x_max,y_min,y_max by MF_AUTO_RANGE as a special parameter to let visualization to automatically determine the data range bound for you.

Example To be referred to mfAxis See Also msAxis, msAxis3DRange


mfAxis3DRange Set the axis range of 3D display mode.

Module fgl

Syntax xyzrange = mfAxis3DRange() call msAxis3DRange(xyzrange) call msAxis3DRange(x_min, x_max, y_min, y_max, z_min, z_max) Descriptions Procedure mfAxis3DRange set the axis range of 3D display mode. xyzrange = mfAxis3DRange()

• Retrieves the ranges of the axis objects. The output argument xyzrange is a vector in the format [x_min, x_max, y_min, y_max, z_min, z_max].

call mfAxis3DRange(xyzrange) call mfAxis3DRange(x_min, x_max, y_min, y_max, z_min, z_max)

• Set the ranges of the axis objects. The input data can be provided in two ways: through a vector xyzrange in which the ranges of the axes objects are specified, or in the


• Argument xyrange is a vector in the format [x_min, x_max, y_min, y_max, z_min, z_max].

• Arguments x_min,x_max,y_min,y_max,z_min,z_max specify the displaying ranges of x-axis, y-axis, z-axis.

• You can specify x_min,x_max,y_min,y_max,z_min,z_max by MF_AUTO_RANGE as a special parameter to let vizulization to automatically determine

the data range bound for you. Example To be referred to mfAxis See Also msAxis, msAxis2DRange


msAxis2DPosition Set axis position in the plot window

Module fgl

Syntax call msAxis2DPosition(pos_x1, pos_x2, pos_y1, pos_y2) Descriptions Procedure msAxis2DPosition sets the axis box position on current plot window. call msAxis2DPosition(pos_x1, pos_x2, pos_y1, pos_y2)

• Argument pos_x1, pos_x2, pos_y1, pos_y2 are four real numbers ranging from 0 to 1. They represent the coordinates of the axis box on current plot window. For example, specifying x1=0, y1=0 would place the axis box at the very left bottom corner of the plot window.

• Argument pos_x1 indicates the distance along x-coordinate from the left bottom corner

of the plot window to the left bottom corner of the axis box.

• Argument pos_x2 indicates the distance along x-coordinate from the left bottom corner of the plot window to the right bottom corner of the axis box.

• Argument pos_y1 indicates the distance along y-coordinate from the left bottom corner of the plot window to the left bottom corner of the axis box.

• Argument pos_y2 indicates the distance along y-coordinate from the left bottom corner of the plot window to the left top corner of the axis box.



!call msSubplot(1,2,1) !Draw red circle call msCircle(mf((/0, 0, 0/)), mf(0.5), mf((/1, 0, 0/))) call msAxis("equal") !Draw first 2D Plot at right-bottom corner ca ll msAxis2DPosition( mf((/0.1, 0.7, 0.1, 0.7/)) )

!call msSubplot(1,2,2) !Draw green circle


!call msCircle(mf((/0, 0, 0/)), mf(0.5), mf((/0, 1, 0/))) !call msAxis("equal") !Draw second 2D Plot at top side !c all msAxis2DPosition( mf((/0.2, 1.0, 0.5, 1.0/)) )

! Pause the program for display ca ll msViewPause()


Result

See Also mfAxis


msAxisWall Manipulate the axis wall object.

Module fgl

Syntax call msAxisWall(mode) call msAxisWall(property, value) Descriptions Procedure msAxisWall sets the color of the three axis-wall objects and switches them on or off. The axis-wall object represents the three axis planes. call msAxisWall(mode)

• Switches the three axis-planes on or off. Argument mode is either "on" or "off". call msAxisWall(property, value)

• Sets the color of the axis-wall object. Argument property can be a string specified as "color" and argument value contains the rgb color code which is specified as [r, g, b]

where 0 < r, g, b < 1. Example Code pr ogram example


ty pe(mfArray) :: u, v, x, z


call msSurf(u, v, z) call msAxisWall('color', mf((/1, 1, 0/))) ca ll msViewPause()

ca ll msFreeArgs(u, v, x, z)


Result


See Also


msAxisGrid Display grid lines.

Module fgl

Syntax call msAxisGrid(axis, mode) call msAxisGrid(property, value) Descriptions Procedure msAxisGrid sets the properties of the axis grid objects, such as the width, color and pattern. call msAxisGrid(axis, mode)

• Switch an axis on or off. Argument axis can be "xaxis", "yaxis" or "zaxis" which corresponds to the three axes respectively. Argument mode is either "on or "off".

call msAxisGrid(property, value)

• Sets a property of the axis grid objects. Argument property can be:

property Meaning

“width” Line width. Corresponding argument value is a scalar integer

value.

“color” Line color. Corresponding argument value can be an mfArray containing a string specifies the color, e.g. “y”, or a 1-by-3

mfArray contains the rgb codes.

“pattern” Line pattern. Corresponding argument value can be an mfArray containing the string that is specified as “solid", "dashed", "dotted" or "dashdot".




ty pe(mfArray) :: u, v, x, z


call msSurf(u, v, z) call msAxisGrid('width', mf(2)) call msAxisGrid('color', mf((/1, 0, 0/))) call msAxisGrid('pattern', 'dashed') ca ll msViewPause()

ca ll msFreeArgs(u, v, x, z)


Result

See Also


Object Manipulation


msObjRotateX, msObjRotateY, msObjRotateZ Rotate the draw object in degrees about the x-axis, y-axis and z-axis using the right hand rule.

Module fgl

Syntax call msObjRotateX(handle, angle) call msObjRotateY(handle, angle) call msObjRotateZ(handle, angle) Descriptions Procedures msObjRotateX, msObjRotateY and msObjRotateZ rotate the draw object that is associated with argument handle in degrees about the x-, y-, z-axes respectively using the right hand rule. The axes are the draw object's axes. If you want to rotate about the world x-, y- and z-axes, use msObjRotateWXYZ(handle, angle, 1, 0, 0),msObjRotateWXYZ(handle, angle, 0, 1, 0) and msObjRotateWXYZ(handle, angle, 0, 0, 1). Example Code pr ogram example


ty pe (mfArray) :: center, cubesize, color, h, h2, color2

center = (/0, 0, 0/) cubesize = (/0.2, 0.3, 0.4/) color = (/0, 1, 0/) co lor2 = (/1, 0, 0/)

call msSubplot(1,2,1) h = mfCube(center, cubesize, color) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) call msSubplot(1,2,2) h2 = mfCube(center, cubesize, color2) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) ca ll msViewPause()

call msSubplot(1,2,1) call msObjRotateX(h, 30) call msSubplot(1,2,2) call msObjRotateWXYZ(h2, 30, 1, 0, 0) ca ll msViewPause()

call msSubplot(1,2,1)


call msObjRotateY(h, 30) call msSubplot(1,2,2) call msObjRotateWXYZ(h2, 20, 0, 1, 0) ca ll msViewPause()

call msSubplot(1,2,1) call msObjRotateZ(h, 30) call msSubplot(1,2,2) call msObjRotateWXYZ(h2, 20, 0, 0, 1) ca ll msViewPause()

ca ll msFreeArgs(center, cubesize, h)


Result

See Also


msObjRotateWXYZ Rotate the draw object in degrees about an arbitrary axis.

Module fgl

Syntax call msObjRotateWXYZ(h, angle, x, y, z) Descriptions Procedure msObjRotateWXYZ rotates the draw object about an arbitrary axis specified by arguments x, y and z. In other words, (x, y, z) specifies the axis the object will rotate along. To rotate along each individual axis, please use msObjRotateX, msObjRotateY and msObjRotateZ. Example Code pr ogram example


ty pe (mfArray) :: center, cubesize, color, h

center = (/0, 0, 0/) cubesize = (/0.2, 0.3, 0.4/) co lor = (/1, 0, 0/)

h = mfCube(center, cubesize, color) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) call msViewPause() call msObjRotateWXYZ(h, 30, 1, 1, 1) call msHold('off') ca ll msViewPause()

ca ll msFreeArgs(center, cubesize, h)


Result


See Also msObjRotateX


mfObjScale, msObjScale Return or modify the draw object scale.

Module fgl

Syntax scale = mfObjScale(handle) call msObjScale(handle, scale) call msObjScale(handle, x, y, z) Descriptions Procedure msObjScale resets the scale independently on the x-, y- and z-axes. A scale of zero is illegal and will be replaced with one. scale = mfObjScale(handle)

It can also be used as an inquiry procedure to retrieve the scale of the draw object if only the

handle associated with the draw object is given.





h = mfCube(center, cubesize, color) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) call msViewPause() call msObjScale(h, 1.5d0, 1.5d0, 1.5d0) call msDisplay(mfObjScale(h),'Scale') ca ll msViewPause()

ca ll msFreeArgs(center, cubesize, color, h)


Result


See Also


mfObjPosition, msObjPosition Return or modify position of the draw object in world coordinates.

Module fgl

Syntax position = mfObjPosition(handle) call msObjPosition(handle, [x, y, z]) Descriptions Procedure mfObjPosition sets the position of the draw object that is associated with argument handle to world coordinates specified in argument [x, y, z]. position = mfObjPosition(handle)

It can also be used as an inquiry procedure to retrieve the position of the draw object if only the






h = mfCube(center, cubesize, color) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) call msViewPause() call msObjPosition(h, 0.1d0, 0.1d0, 0.1d0) call msDisplay(mfObjPosition(h),'Position') ca ll msViewPause()



Result


See Also


mfObjOrigin, msObjOrigin Return or modify origin of the draw object.

Module fgl

Syntax origin = mfObjOrigin(handle) call msObjOrigin(handle, [x, y, z]) Descriptions Procedure mfObjOrigin sets the origin of the draw object. All rotations performed on the draw object pivot around the origin. Note that the origin is relative to the position of the object; whenever the object moves, the origin moves along with it so that they maintain a constant relationship relative to each other. origin = mfObjOrigin(handle)

It can also be used as an inquiry procedure to retrieve the origin of the draw object if only the





center = (/0, 0, 0/) cubesize = (/0.2, 0.3, 0.4/) co lor = (/0.75, 0.0, 0.75/)

h = mfCube(center, cubesize, color) call msAxis('equal') ca ll msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0)

! Set origin (0.0d0, 0.15d0, 0.0d0) call msObjOrigin(h, 0.0d0, 0.15d0, 0.0d0) call msDisplay(mfObjOrigin(h),'Origin') ca ll msViewPause()

call msObjRotateX(h, 30) call msViewPause() call msObjRotateY(h, 30) call msViewPause() call msObjRotateZ(h, 10) ca ll msViewPause()




Result

See Also


mfObjOrientation, msObjOrientation Return or modify WXYZ orientation of the draw object.

Module fgl

Syntax orientation = mfObjOrientation(handle) call msObjOrientation(handle, [x, y, z]) Descriptions Procedure mfObjOrientation sets the WXYZ orientation of the draw object as a vector of x, y and z rotation. The order in which these rotations are performed is Rotate z, Rotate x and then Rotate y. orientation = mfObjOrientation(handle)

It can also be used as an inquiry procedure to retrieve the orientation of the draw object if only the





center = (/0, 0, 0/) cubesize = (/0.2, 0.3, 0.4/) co lor = (/0.0, 0.75, 0.75/)

h = mfCube(center, cubesize, color) call msAxis('equal') call msAxis(-0.3d0, 0.3d0, -0.4d0, 0.4d0, -0.5d0, 0.5d0) call msViewPause() call msObjOrientation(h, 15, 15, 15) call msDisplay(mfObjOrientation(h),'Orientation') ca ll msViewPause()



Result


See Also


mfObjectModel, msObjectModel Import a 3-D object.

Module fgl

Syntax h = mfObjectModel( filename[, loc][, scale][, orientation] ) call msObjectModel( filename[, loc][, scale][, orientation] ) Descriptions Procedure mfObjectModel loads a 3-D object into an mfArray. call msObjectModel( filename ) call msObjectModel( filename, loc, scale, orientation )

• Argument filename is a string containing the filename of the object file. MATFOR supports file formats with extension .obj, .stl and .3ds.

• Argument loc is a 1-by-3 vector in the format [m, n, p] where m, n, p are the actual coordinate of the object on the axes.

• Argument scale sets the scale for the draw object. • Argument orientation is a 1-by-3 vector that specifies the angle-rotation along x, y

and z dimensions. You can retrieve properties of the object through handle h with procedure mfObjPosition, mfObjScale and mfObjOrientation. Example Code pr ogram example


type(mfArray)::x,y,z,h

call msFigure('Satellite') call msSubplot(1,2,1) !Read the Satellite object h = mfObjectModel( 'Satellite.obj', mf((/0, 0, 0/)), mf(0.002)) call msDrawMaterial(h, mf('surf'), mf('ambient'), & mf(0), mf('diffuse'), mf(100))

call msDrawMaterial(h, mf('edge'), mf('trans'), mf(90))

call msAxis('equal') call msAxis(-1, 1, -1, 1, -1, 1)


call msSubplot(1,2,2) !Read the Satellite object h = mfObjectModel( 'Satellite.obj', mf((/0, 0, 0/)), mf(0.002)) call msDrawMaterial(h, mf('surf'), mf('ambient'), & mf(0), mf('diffuse'), mf(100))

call msDrawMaterial(h, mf('edge'), mf('trans'), mf(90))

call msAxis('equal') call msAxis(-1, 1, -1, 1, -1, 1) !Rotate the Satellite object call msObjRotateX(h,30) call msObjRotateY(h,30)

call msObjRotateZ(h,10)

call msViewPause()


Result

See Also mfObjPosition, mfObjScale, and mfOrientation


Camera Manipulation


msView Viewpoint specification.

Module fgl

Syntax call msView(az, el) call msView(az, el, roll) call msView(mode) Descriptions Procedure msView specifies the orientation of an axis object. The orientation of the axis object is determined by the azimuth az and elevation el of the viewing angle from a viewpoint. Argument roll determines the upward direction of the camera.

-Y

X

Z

Camera

azimuth

elevation

roll

Argument mode can be "2", "3", "home", "top", "bottom", "front", "back", "left" or "right". Example


Code pr ogram example


ty pe(mfArray) :: x, y, z, a

z = mfLinspace(0, 10*MF_PI, 315) x = mfExp(-z/20)*mfCos(z) y = mfExp(-z/20)*mfSin(z)

!Plot a 3-D line graph using mfPlot3() routine and title it. call msFigure('View') call msSubplot(1,2,1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) ca ll msView('3')

call msSubplot(1,2,2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msView('2') ca ll msAxis2DDependency('xy_tight',1)

call msFigure('CamAngle') call msSubplot(1, 2, 1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') call msCamAngle(50d0) ca ll msDisplay(mfCamAngle(),'Modify Angle')

call msSubplot(1, 2, 2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') ca ll msDisplay(mfCamAngle(),'Original Angle')

call msFigure('AzElRoll') call msSubplot(1, 2, 1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') ca ll msCamAzElRoll(30d0,20d0,10d0)

ca ll msDisplay(mfCamAzElRoll(),'Modify AzElRoll')

call msSubplot(1, 2, 2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') ca ll msDisplay(mfCamAzElRoll(),'Original AzElRoll')

call msFigure('Distance') call msSubplot(1, 2, 1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') call msCamDistance(6d0) ca ll msDisplay(mfCamDistance(),'Modify Distance')

call msSubplot(1, 2, 2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') ca ll msDisplay(mfCamDistance(),'Original Distance')

call msFigure('Focal')


call msSubplot(1, 2, 1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') call msCamFocal(mf((/4d0,5d0,6d0/))) ca ll msDisplay(mfCamFocal(),'Modify Focal')

call msSubplot(1, 2, 2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamProj('perspective') ca ll msDisplay(mfCamFocal(),'Original Focal')

call msFigure('Zoom') call msSubplot(1, 2, 1) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msCamZoom(1.5d0) ca ll msDisplay(mfCamZoom(),'Modify Zoom')

call msSubplot(1, 2, 2) call msPlot3(x, y, z) call msAxis(mf((/-1, 1, -1, 1, 0, 32/))) call msDisplay(mfCamZoom(),'Original Zoom') !Pauses the program to display graph. ca ll msViewPause()

!Deallocate mfArray ca ll msFreeArgs(x, y, z)


Result

See Also


mfCamAngle, msCamAngle Set the camera view angle.

Module fgl

Syntax angle = mfCamAngle() call msCamAngle(angle) Descriptions Procedure mfCamAngle sets the camera view angle, which is the angular height of the camera view measured in degrees. The default angle is 10 degrees. This procedure has no effect when used in parallel projection mode. angle = mfCamFieldAngle()

• It can also be used an inquiry function to retrieve the view angle of the camera. Example To be referred to msView See Also msCamProj, msCamDistance, msCamZoom


mfCamAzElRoll Set the camera view direction.

Module fgl

Syntax vdir = mfCamAzElRoll() call msCamAzElRoll(az, el) call msCamAzElRoll(az, el, roll) call msCamAzElRoll([az, el]) Descriptions Procedure msCamAzElRoll specifies the view direction of a camera object.

-Y

X

Z

Camera

azimuth

elevation

roll

The view direction of a camera object is determined by the azimuth az, elevation el, and roll roll of the viewing angle from a viewpoint. Example To be referred to msView See Also mfView


mfCamDistance Set the camera distance.

Module fgl

Syntax dist = mfCamDistance() call msCamDistance(dist) Descriptions Procedure msCamDistance sets the distance between the camera and the focal point. This procedure has no effect when used in parallel projection mode. dist = mfCamFieldAngle()

• It can also be used an inquiry function to retrieve the distance between the camera and the focal point.

Example To be referred to msView See Also msCamProj, msCamAngle, msCamZoom, msCamFocal


mfCamProj, msCamProj Set the camera projection mode.

Module fgl

Syntax mode = mfCamProj() call msCamProj(mode) Descriptions Procedure msCamProj sets the camera projection mode to be either perspective or parallel projection. Argument mode can be "orthographic" or "perspective". mode = mfCamProj()

• It can also be used an inquiry function to retrieve the camera projection mode. The output argument is a logical mfArray whose value is true if the projection mode is orthographic, false otherwise.

Example To be referred to msView See Also msView, msCamAzElRoll, msCamZoom, msCamAngle, msCamDistance


mfCamFocal Set the camera focal point.

Module fgl

Syntax fp = mfCamFocal() call msCamFocal(fp) Descriptions Procedure msCamFocal sets the camera focal point using a 3x1 vector fp. fp = mfCamFocal()

• It can also be used an inquiry function to retrieve the camera focal point. Example To be referred to msView See Also msView, msCamAzElRoll


mfCamZoom, msCamZoom Zoom in on or out of the displayed object.

Module fgl

Syntax zf = mfCamZoom() call msCamZoom(zf) Descriptions Procedure msCamZoom zooms in on or out of the displayed object. • In perspective mode, it decreases the view angle by the specified zoom factor zf. • In parallel mode, it decreases the parallel scale by the specified zoom factor zf. A value greater than 1 is a zoom-in, whereas a value less than 1 is a zoom-out. Example To be referred to msView See Also msCamProj, msAngle, msCamDistance


mfGetCamViewParam Retrieve camera configuration values of an object.

Module fgl

Syntax h = mfGetCamViewParam(mode) call msGetCamViewParam(mfOut(h),mode) Descriptions Procedure mfGetCamViewParam returns various camera configuration values of an object. Argument mode is a string. For return values specification details, please refer to msSetCamViewParam. Example Code pr ogram example


type(mfArray):: x,y,z,h

!Create Surface Data to draw

call msCreateSurfData(mfOut(x,y,z),1,30,30)

call msFigure("Get Camera") call msSurf(x,y,z) !Change first Camera angle call msCamAzElRoll(mf((/30.0,20.0,10.0/))) !Get first Camera's view direction

h = mfGetCamViewParam('view_dir')

call msFigure('Set Camera') call msSurf(x,y,z) !Set second Camera's view direction

call msSetCamViewParam(mf('view_dir'),h)

call msViewPause()


See Also mfSetCamViewParam


msSetCamViewParam Set camera configuration values for the display object.

Module fgl

Syntax call msSetCamViewParam(mode,value) Descriptions Procedure msSetCamViewParam sets various camera configuration values of the display object. Argument mode and value are specified as the following:

mode value

“all” A 1-by-9 mfArray contains all values of camera configuration. The sequence of the output values goes vertically down this table.

“view_dir” A 1-by-3 mfArray contains the view direction of a camera object which is determined by the azimuth, elevation and roll of the viewing angle from a viewpoint.

“focal” A 1-by-3 mfArray contains the camera focal point.

“zoom” A 1-by-1 mfArray contains the room values of the display object.

“distance” A 1-by-1 mfArray contains the distance between the camera and the focal point.

“angle” A 1-by-1 mfArray contains the angular height of the camera view measured in degrees.

Example See Also mfGetCamViewParam


Linear Graphs


mfPlot, msPlot Plot two-dimensional linear graphs.

Module fgl

Syntax handle = mfPlot(y[, linespec]) handle = mfPlot(x, y[, linespec]) handle = mfPlot(x1, y1, linespec1, x2, y2, linespec2, ...) call msPlot(y) call msPlot(y, linespec) Descriptions Procedure mfPlot generates two-dimensional line graphs. call msPlot(y) call msPlot(y, linespec)

• Plot elements of vector y against their indices. If y is a matrix, multiple lines are plotted from each column of y.

• Argument linespec contains special characters that specify line color and marker type of the graph. For example, "yo", specifies a graph drawn from yellow-colored, circular markers. linespec can be an mfArray containing the special characters or a character

string. Refer to linespec for a list of special characters applicable for line specifications.

Linespec

The table below lists the linespec characters.

Character Line color Character Marker Type Character Line Type

y yellow . point - solid

m magenta o circle : dotted

c cyan x x-mark -. dashdot

r red + plus -- dashed

g green s square


b blue d diamond

w white v triangle down

k black ^ triangle up

[h1, h2, h3, ...] = mfPlot(...) h = mfPlot(...)

• Handles h1, h2, h3, ... retrieve the respective handles to the plot objects created by mfPlot(...).

• If only one handle h is given, the procedure returns the handles in a vector mfArray. • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the plot object through handle h with procedure msGSet. Properties available are: 1. linespec 2. symbol_scale: The size of the legend. By default, legend size is 1, a half is 0.5. Example Code pr ogram example


ty pe(mfArray) :: x, y1, y2, h

x = mfColon(0, 0.25d0, 50) y1 = x*mfSin(x) y2 = mfSin(x)

! Plot the graphs call msPlot(x, y1, 'b-', x, y2, 'r-') call msHold('on') h = mfPlot(x,y2-y1,'g-') ca ll msHold('off')

! Pause the program for drawing ca ll msViewPause()

ca ll msGSet(h,'linespec','g+')


! Deallocates mfArrays ca ll msFreeArgs(x, y1, y2, h)

end program example


Result

See Also mfPlot3


mfPlot3, msPlot3 Plot three-dimensional linear graphs.

Module fgl

Syntax handle = mfPlot3(x, y, z[, c]) handle = mfPlot3(xyz[, c]) call msPlot3(x, y, z) call msPlot3(x, y, z, c) Descriptions Procedure mfPlot3 draws three-dimensional linear graphs. call msPlot3(x, y, z) call msPlot3(x, y, z, c)

• If arguments x, y and z are vectors, mfPlot3 draws a line whose x-, y-, and z- coordinates are elements of arguments x, y and z respectively.

• If arguments x, y and z are matrices, mfPlot3 draws multiple lines from the columns of x, y and z matrices.

• Shape of each argument must be conformed. • Complex data is not supported. • Argument c contains the corresponding scalar values of the coordinates x, y and z. By

default, c = z. call msPlot3(xyz) call msPlot3(xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfPlot3(...)

• Handle h retrieves a handle to the three-dimensional linear graph objects created by mfPlot3(...).

• Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the current graphics object.

You can specify properties of the graphics objects through handle h with procedure msGSet. The property available is:


1. xyz : Vertex vectors. Example Code pr ogram example


ty pe (mfArray) :: x, y, z, h

z = mfLinspace(0, 10*MF_PI, 101) x = mfCos(z) y = mfExp(-z/20)*mfSin(z)

ca ll msAxis(mf((/-1, 1, -1, 1, 0, 32/)))

! Plot the three-dimensional graph h = mfPlot3(x, y, z)

! Specify the viewpoint ca ll msView(60,30)

! Pause program for graphics display ca ll msViewPause()

!Change Vertex vectors x = mfSin(z) call msGSet(h,'xyz',(.t.x).hc.(.t.y).hc.(.t.z)) ca ll msViewPause()

! Deallocate memory ca ll msFreeArgs(x, y, z, h)


Result

See Also mfViewPause, mfAxis, mfSubplot, mfView, mfSurf, mfMesh


mfRibbon, msRibbon Plot three-dimensional ribbons.

Module fgl

Syntax handle = mfRibbon(x, y, z[, c]) handle = mfRibbon(xyz[, c]) call msRibbon(x, y, z[, c]) call msRibbon(xyz[, c]) Descriptions Procedure mfRibbon draws three-dimensional ribbons. call msRibbon(x, y, z) call msRibbon(x, y, z, c)

• If arguments x, y and z are vectors, mfRibbon draws a ribbon whose x-, y-, and z-coordinates are elements of the respective arguments.

• If arguments x, y and z are matrices, mfRibbon draws multiple ribbons from the columns of the argument matrices.


default, c = z. call msRibbon(xyz) call msRibbon(xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfRibbon(...)

• Handle h retrieves a handle to the three-dimensional ribbon objects created by mfRibbon(...).

• Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the current graphics object.

You can specify properties of the graphics objects through handle h with procedure msGSet. The properties available are: 1. sizefactor: The width of the ribbon object. By default, sizefactor is 1.


2. xyz: Vertex vectors. Example Code pr ogram example


ty pe (mfArray) :: x, y, z, h, c, h2

z = mfLinspace(0, 10*MF_PI, 100) x = z*mfSin(z) y = z*mfCos(z) call msSubplot(1,2,1) call msRibbon(x, y, z) ca ll msAxis(-32, 32, -32, 32, 0, 34)

call msSubplot(1,2,2) h =mfTube(x, y, z, z) ca ll msAxis(-32, 32, -32, 32, 0, 34)

x = z*mfCos(z) y = z*mfSin(z) c = mfCos(z)

call msGSet(h,'sizefactor',2d0) call msGSet(h,'xyz',(.t.x).hc.(.t.y).hc.(.t.z)) ca ll msGSet(h,'cdata',.t.c)

ca ll msViewPause()

ca ll msFreeArgs(x, y, z, h, c)


Result

See Also


mfTube, msTube Plot three-dimensional tubes.

Module fgl

Syntax handle = mfTube(x, y, z[, c]) handle = mfTube(xyz[, c]) call msTube(x, y, z[, c]) call msTube(xyz[, c]) Descriptions Procedure mfTube draws three-dimensional tubes. call msTube(x, y, z) call msTube(x, y, z, c)

• If arguments x, y and z are vectors, mfTube draws a tube whose x-, y-, and z- coordinates are elements of the respective arguments.

• If arguments x, y and z are matrices, mfTube draws multiple tubes from the columns of the argument matrices.


default, c = z. call msTube(xyz) call msTube(xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTube(...)

• Handle h retrieves a handle to the three-dimensional tube objects created by mfTube(...).


You can specify properties of the graphics objects through handle h with procedure msGSet. The properties available are:


1. sizefactor: The diameter of the tube objects. By default, size factor is 1. 2. xyz: Vertex vectors. Example To be referred to mfRibbon See Also mfRibbon


mfStem, msStem Plot two-dimensional stem graphs.

Module fgl

Syntax handle = mfStem(y[, linespec]) handle = mfStem(x, y[, linespec]) handle = mfStem(x1, y1, linespec1, x2, y2, linespec2, ...) call msStem(y) call msStem(y, linespec) Descriptions Procedure mfStem generates two-dimensional stem graphs. call msStem(y) call msStem(y, linespec)

• Plot elements of vector y against their indices. If y is a matrix, multiple lines are plotted from each column of y.

• Argument linespec contains special characters that specify line colors and marker types of the graph. For example, "yo", specifies a graph drawn from yellow-colored, circular markers. linespec can be an mfArray containing the special characters or a

character string. Refer to linespec for a list of special characters applicable for line specifications.

Linespec

The table below lists the linespec characters.

Character Line color Character Marker Type Character Line Type

y yellow . point - solid

m magenta o circle : dotted

c cyan x x-mark -. dashdot


r red + plus -- dashed

g green s square

b blue d diamond

w white v triangle down

k black ^ triangle up

[h1, h2, h3, ...] = mfStem(...) h = mfStem(...)

• Handles h1, h2, h3, ... retrieve respective handles to the plot objects created by mfStem(...).

• If only one handle h is given, the procedure returns the handle in a vector mfArray. • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of

current graphics object. You can specify properties of the plot object through handle h with procedure msGSet. The property available is: 1. linespec 2. symbol_scale: The size of the legend. By default, legend size is 1, a half is 0.5. Example Code pr ogram example


ty pe(mfArray) :: x, y1, y2, h

x = mfColon(0, 0.2d0, 10) y1 = x*mfSin(x) y2 = mfSin(x)

! Plot the Stem call msStem(x, y1, 'bo-', x, y2, 'r') call msHold('on') h = mfStem(x,y2-y1,'g') ca ll msHold('off')


! Deallocates mfArrays ca ll msFreeArgs(x, y1, y2, h)

end program example


Result

See Also mfPlot


mfBar Plot two-dimensional vertical bars.

Module fgl

Syntax handle = mfBar(x,y) handle = mfBar(y) handle = mfBar(x,y[, width]) handle = mfBar(...[, color]) handle = mfBar(...[,'group']) handle = mfBar(...[,'stack']) call msBar(y) call msBar(x,y) call msBar(y, color) Descriptions Procedure mfBar plots vertical bars in two-dimensional space. call msBar(y) call msBar(y, color)

• Plot elements of vector y against their indices. If y is a matrix, multiple bars are plotted from each raw of y.

• Argument color contains special characters that specify bar colors. For example, 'r', specifies a graph drawn from red-colored. The Color table below contains a list of special characters applicable for color specifications.

Color Character y m c r g b w k

Line

color yellow magenta cyan red green blue white black

You can specify colors of the plot object through handle h with procedure msColorbar or msDrawMaterial. call msBar(x,y)

• Plot elements of vector y specified at x. If y is a matrix, multiple bars are plotted from


each raw of y. Each element in vector x specifies the location for the corresponding raw in y.

h = mfBar(...)

• The procedure returns the handle h in a vector mfArray. • Argument width sets the bar width that ranges from 0 to 1. For example, width = 1 sets

bars in the same group touching one another.

• Argument 'group' groups and displays elements in each raw of y side by side. This is set by default for the display.

• Argument 'stack' displays elements in each raw of y in one bar. Example Code Pr ogram bar

use fml us e fgl

im plicit none

ty pe(mfArray) :: d1, d2, d3, d4

d1 = mfColon(1,20) * mfSqrt( mfColon(20,-1,1) ) d2 = mfMagic(5) d3 = mfCreateSurfData( 1, 5, 5 )

call msFigure('bar') ca ll msBar(d1, 1)

call msFigure('bar') ca ll msBar(d2)

call msFigure('barh') ca ll msBarh( d2, 'stack' )

call msFigure('barh') ca ll msBarh( mfColon(10,5,30), d2 )

call msFigure('bar3') ca ll msBar3( d2 )

call msFigure('bar3') ca ll msBar3( d3 )

call msFigure('bar3') call msBar3( d2, 'group' ) ca ll msAxis3DDependency('xy_depend', 1, 10)

call msFigure('bar3h') call msBar3h( d2, 'stack' ) call msAxis3DDependency('xz_depend', 10, 1) ca ll msAxis( 0, 0, 0, 0, 0, 6 )

ca ll msViewPause

e nd Program bar

Result


See Also mfBarh, mfBar3


mfBarh Plot two-dimensional horizontal bars.

Module fgl

Syntax handle = mfBarh(x,y) handle = mfBarh(y) handle = mfBarh(x,y[, width]) handle = mfBarh(...[, color]) handle = mfBarh(...[,'group']) handle = mfBarh(...[,'stack']) call msBarh(y) call msBarh(x,y) call msBarh(y, color) Descriptions Procedure mfBarh plots horizontal bars in two-dimensional space. call msBarh(y) call msBarh(y, color)




Line


You can specify colors of the plot object through handle h with procedure msColorbar or procedure msDrawMaterial. call msBarh(x,y)




h = mfBarh(...)



• Argument 'group' groups and displays elements in each raw of y side by side. This is set by default for the display.

• Argument 'stack' displays elements in each raw of y in one bar. Example To be referred to mfBar See Also mfBar, mfBar3h


mfBar3 Plot three-dimensional vertical bars.

Module fgl

Syntax handle = mfBar3(x,y) handle = mfBar3(y) handle = mfBar3(x,y[, width]) handle = mfBar3(...[, color]) handle = mfBar3(...[,'detach']) handle = mfBar3(...[,'group']) handle = mfBar3(...[,'stack']) call msBar3(y) call msBar3(x,y) call msBar3(y, color) Descriptions Procedure mfBar3 plots vertical bars in three-dimensional space. call msBar3(y) call msBar3(y, color)




Line


You can specify colors of the plot object through handle h with procedure msColorbar or procedure msDrawMaterial . call msBar3(x,y)




h = mfBar3(...)



• Argument 'detach' displays elements of y separately. This is set by default for the display.

• Argument 'group' groups and displays elements in each raw of y side by side. • Argument 'stack' displays elements in each raw of y in one bar. Example To be referred to mfBar See Also mfBarh, mfBar


mfBar3h Plot three-dimensional horizontal bars.

Module fgl

Syntax handle = mfBar3h(x,y) handle = mfBar3h(y) handle = mfBar3h(x,y[, width]) handle = mfBar3h(...[, color]) handle = mfBar3h(...[,'detach']) handle = mfBar3h(...[,'group']) handle = mfBar3h(...[,'stack']) call msBar3h(y) call msBar3h(x,y) call msBar3h(y, color) Descriptions Procedure mfBar3h plots horizontal bars in three-dimensional space. call msBar3h(y) call msBar3h(y, color)




Line


You can specify colors of the plot objects through handle h with procedure msColorbar or procedure msDrawMaterial. call msBar3h(x,y)




h = mfBar3h(...)



• Argument 'detach' displays elements of y separately. This is set by default for the display.

• Argument 'group' groups and displays elements in each raw of y side by side. • Argument 'stack' displays elements in each raw of y in one bar. Example To be referred to mfBar See Also mfBar3, mfBarh


Surface Graphs


mfSurf, msSurf Create surface plots.

Module fgl

Syntax handle = mfSurf(z[, c]) handle = mfSurf(x, y, z[, c]) call msSurf(x, y, z[, c]) call msSurf(z[, c]) Descriptions Procedure mfSurf creates three-dimensional graphs composed of colored quadrilateral surfaces. You can choose amongst several shading options including mesh, flat, faceted, and interpolated. The options can be set using procedure mfShading or through the menu and toolbar functions of the Graphics Viewer. Note that mesh surfaces can also be plotted using procedure mfMesh. call msSurf(x, y, z) call msSurf(x, y, z, c)

• Plot surface objects from arguments x, y and z. The arguments x, y and z contain the respective coordinates of the surface object's grid intersections.

• x, y and z are matrices, hence the size of x and y should be conformed to that of z. The

grid intersections are given by (x(i,j), y(i,j), z(i,j)).

• By default, the color of the surface is proportional to the z coordinates of the surface object. Specifying argument c overrides the default color scale.

• By default, mfSurf draws surfaces with faceted shading. call msSurf(z) call msSurf(z, c)

• Creates a three-dimensional surface from the m-by-n matrix z. Arguments x and y are set to the default msMeshgrid(mfOut(x,y), mfColon(1,n), mfColon(1,m)).Argument z is a single-valued matrix defined over a rectangular grid formed by x and y.

h = mfSurf(...)

• Handle h retrieves a handle to the surface object created by mfSurf(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the


current graphics object. You can specify the properties of surface objects through handle h with procedure msGSet. Example Code pr ogram example


ty pe(mfArray) :: a, b, c, x, y, z, indxi, indxj

a = mfLinspace(-3, 7, 51) b = mfLinspace(-2, 8, 51) c = mfColon(1, 51) call msMeshgrid(mfout(x, y), a, b) call msMeshgrid(mfout(indxi, indxj), c) z = 3*mfSin((indxi+1)/10)*mfCos((indxj+1)/10) & + 2*mfSin((indxi+indxj)/10)

! Plot a surf using mfArray x, y and z ca ll msSurf(x, y, z)

! Pause to display the graph ca ll msViewPause()



Result

See Also mfViewPause, mfAxis, mfSubplot, mfView, mfMesh, mfPlot3


mfMesh, msMesh Create mesh plots.

Module fgl

Syntax handle = mfMesh(z[, c]) handle = mfMesh(x, y, z[, c]) call msMesh(z[, c]) call msMesh(x, y, z[, c]) Descriptions Procedure mfMesh plots a three-dimensional mesh surface consisting of criss-crossed lines that looks like a net draped over the surface defined by your data. call msMesh(x, y, z) call msMesh(x, y, z, c)

• Plot surface objects from arguments x,y and z. The arguments x,y and z contain the respective coordinates of the surface object's grid intersections.

• x,y and z are matrices, hence their shapes should conform. The grid intersections are given

by (x(i,j), y(i,j), z(i,j)).

• By default, the color of the wire-frame grid is proportional to the z coordinates of the surface object. Specifying argument c overrides the default color scale.

call msMesh(z) call msMesh(z, c)

• Creates a three-dimensional surface from the m-by-n matrix z. Arguments x and y are set to the default msMeshgrid(mfOut(x,y), mfColon(1,n), mfColon(1,m)). Argument z is a single-valued matrix defined over a rectangular grid formed by x and y.

h = mfMesh(...)

• Handle h retrieves a handle to the mesh surface object created by mfMesh(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the surface objects through handle h with procedure procedure msGSet.





a = mfLinspace(-3, 7, 51) b = mfLinspace(-2, 8, 51) c = mfColon(1, 51) call msMeshgrid(mfout(x, y), a, b) call msMeshgrid(mfout(indxi, indxj), c) z = 3*mfSin((indxi+1)/10)*mfCos((indxj+1)/10) & + 2*mfSin((indxi+indxj)/10)

! Plot a mesh grid using mfArray x, y and z for the grid ! intersections. ca ll msMesh(x, y, z)




Result

See Also mfViewPause, mfAxis, mfSubplot, mfView, mfSurf, mfPlot3


mfSurfc, msSurfc Create plots combined of surface and contour3.

Module fgl

Syntax handle = mfSurfc(z[, c]) handle = mfSurfc(x, y, z[, c]) call msSurfc(mfOut(h1, h2), z[, c]) call msSurfc(mfOut(h1, h2), x, y, z[, c]) Descriptions Procedure mfSurfc draws a contour below the surface object. call msSurfc(z) draws a contour below the surface object created by mfSurf(z).

call msSurfc(x, y, z) draws a contour below the surface object created by mfSurf(x, y, z).

call msSurfc(mfOut(h1, h2), ...)

• Handles h1 and h2 retrieve the handles to the surface object and contour object created by mfSurfc(...)respectively.

• If only one handle h is given, the procedure returns two handles in a vector mfArray. mfS(h,1) represents the mesh object and mfS(h,2) represents the contour object.

• Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the contour graphics object.

You can specify properties of the surface object through handle h with procedure msGSet. For properties, see the description on mfSurf. Example Code pr ogram example



a = mfLinspace(-3, 7, 51) b = mfLinspace(-2, 8, 51) c = mfColon(1, 51) call msMeshgrid(mfout(x, y), a, b)


call msMeshgrid(mfout(indxi, indxj), c) z = 3*mfSin((indxi+1)/10)*mfCos((indxj+1)/10) & + 2*mfSin((indxi+indxj)/10)

! Plot a surf using mfArray x, y and z and Plot Contour below the surf ca ll msSurfc(x, y, z)




Result

See Also mfSurf


mfMeshc, msMeshc Create plots combined of mesh and contour3.

Module fgl

Syntax handle = mfMeshc(z[, c]) handle = msMeshc(x, y, z[, c]) call msMeshc(mfOut(h1, h2), z[, c]) call msMeshc(mfOut(h1, h2), x, y, z[, c]) Descriptions Procedure mfMeshc draws a contour below the meshed surface object. call msMeshc(z) draws a contour below the meshed surface object created by

mfSurf(z).

call msMeshc(x, y, z) draws a contour below the meshed surface object created by

mfSurf(x, y, z).

call msSurfc(mfOut(h1, h2), ...)

• Handles h1 and h2 retrieve the handles to the meshed surface object and contour object created by mfMeshc(...) respectively.

• If only one handle h is given, the procedure returns two handles in a vector mfArray. mfS(h,1) represents the mesh object and mfS(h,2) represents the contour object.

• Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the contour graphics object.

You can specify properties of the surface object through handle h with procedure msGSet. Example Code pr ogram example



a = mfLinspace(-3, 7, 51) b = mfLinspace(-2, 8, 51) c = mfColon(1, 51) call msMeshgrid(mfout(x, y), a, b)


call msMeshgrid(mfout(indxi, indxj), c) z = 3*mfSin((indxi+1)/10)*mfCos((indxj+1)/10) & + 2*mfSin((indxi+indxj)/10)

! Plot a mesh grid using mfArray x, y and z for the grid ! intersections and Plot Contour below the mesh ca ll msMeshc(x, y, z)




Result

See Also mfMesh


mfPColor, msPColor Create pseudocolor plots.

Module fgl

Syntax handle = mfPColor(c) handle = mfPColor(x,y,c) call msPColor(c) call msPColor(x, y, c) Descriptions Procedure mfPColor produces a pseudocolor plot of matrix mfArray c by mapping the elements of c to the current colormap. This procedure is equivalent to a top-view of mfSurf. call msPColor(c)

• The procedure displays matrix mfArray c as a checker-board plot with elements of c specifying each cell of the plot, mapped to the index of the current colormap.

• The smallest and largest elements of matrix c correspond to the minimum and maximum indices of the colormap.

• By default, the shading is "faceted", with each cell containing a constant color. Each element of matrix c specifies the color of a rectangular patch in the image.

call msPColor(x, y, c)

• Draws the checker-board plot on the grid defined by arguments x and y. The arguments x and y can be vectors or matrices.

h = mfPColor(...)

• Handle h retrieves a handle to the pseudocolor plot object created by mfPColor(...).


You can specify properties of the pseudocolor plot object through handle h with procedure msGSet. Example


Code pr ogram example


ty pe(mfArray) :: theta, phi, x, y, z

theta = mfLinspace(-MF_PI, MF_PI, 31) phi = .t. theta /4 x = mfMul(mfSin(phi), mfCos(theta)) y = mfMul(mfSin(phi), mfSin(theta)) z = mfMul(mfSin(phi), mfOnes(1,31))

! Plot the surface object using X, Y and Z call msSubplot(1,2,1) call msPColor(x, y, z) call msAxis('equal') ca ll msCamZoom(0.8d0)

call msSubplot(1,2,2) call msFastPColor(x,mf((/5d0,10d0,5d0,10d0/))) call msAxis('equal') ca ll msCamZoom(0.8d0)


! Deallocate mfArray ca ll msFreeArgs(x, y, z)


Result

See Also mfSurf


mfFastPColor, msFastPColor Create pseudocolor plots.

Module fgl

Syntax handle = mfFastPColor(c) handle = mfFastPColor(c, extent) call msFastPColor(c) call msFastPColor(c, extent) Descriptions Procedure mfFastPColor produces a pseudocolor plot of matrix mfArray c by mapping the elements of c to current colormap. This procedure is equivalent to a top-view of mfSurf. call msFastPColor(c)

• The procedure displays matrix mfArray c as a checker-board plot with elements of c specifying each cell of the plot, mapped to the index of the current colormap.

• The smallest and largest elements of matrix c correspond to the minimum and maximum indices of the colormap.

call msFastPColor(x, y, c)

• The procedure draws a checker-board plot using extent (a 1 by 4 vector defined by [Xmin, Xmax, Ymin, Ymax]), where each element of extend represents the boundary of matrix c.

(Xmin, Ymax) (Xmax, Ymax)

(Xmin, Ymin) (Xmax, Ymin) h = mfFastPColor(...)


• Handle h retrieves a handle to the pseudocolor plot object created by mfFastPColor(...).


You can specify properties of the pseudocolor plot object through handle h with procedure msGSet. Example To be referred to mfPColor See Also mfPColor, mfSurf


mfContour, msContour Plot two-dimensional line contours.

Module fgl

Syntax handle = mfContour(c) handle = mfContour(x, y, c) call msContour(c) call msContour(x, y, c) Descriptions Procedure mfContour plots constant value lines in two-dimensional space. handle = mfContour(x, y, c)

• Generate two-dimensional contour lines of matrix c. The values plotted are selected automatically.

• Argument c is assumed to contain data representing the scalar values. • Arguments x and y specify the corresponding coordinates of the scalar values. • Similar to mfSurf and mfMesh,the colors of the contour lines are selected based on the

current colormap. call msContour(c)

• The scalar value c is assumed to be defined over a geometrically rectangular grid where x = mfColon(1, n) and y = mfColon(1, m).

h = mfContour(...)

• Handle h retrieves a handle to the contour object created by mfContour(...). • Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the

current graphics object. You can specify properties of the contour object through handle h with procedure msGSet. See mfContour3 for available properties. Example Code pr ogram example

use fml


use fgl im plicit none

ty pe(mfArray) :: a, x, y, z

a = mfLinspace(-MF_PI, MF_PI, 50) call msMeshgrid(mfout(x, y) ,a) z = (1/mfCosh(x))*mfCos(y+MF_PI/2)

! Draw a 2-D contour plot call msContour(z) call msAxis('equal') ca ll msCamZoom(0.8d0)

! Pause the program to display the graphics ca ll msViewPause()

! Deallocate mfArrays ca ll msFreeArgs(a, x, y, z)


Result

See Also mfSolidContour, mfContour3


mfContour3, msContour3 Plot three-dimensional line contours.

Module fgl

Syntax handle = mfContour3(z[, c]) handle = mfContour3(x, y, z[, c]) call msContour3(z, c) call msContour3(x, y, z, c) Descriptions Procedure mfContour3 plots constant value lines of matrix z in three-dimensional space. The values plotted are selected automatically. call msContour3(z, c) call msContour3(x, y, z, c)

• This procedure is similar to mfContour. The contour lines are presented in three-dimensional perspective reflecting their scalar values. The values plotted are selected automatically.

h = mfContour3(...)

• Handle h retrieves a handle to the three-dimensional contour object created by mfContour3(...).


You can specify properties of the three-dimensional contour object through handle h with procedure msGSet. The properties available are: 1. iso: iso-values, a vector containing an iso-value set. Setting this property will replace the default set of contour lines. 2. autolevel: given the number of levels, it will automatically generate iso-value sets. 3. label: "on" or "off" Example Code


pr ogram example


ty pe(mfArray) :: a, x, y, z, h


! Draw a 3-D contour plot h = mfContour3(z) !Set Contour's label On ca ll msGSet(h,'label','on')


! Deallocate mfArrays ca ll msFreeArgs(a, x, y, z, h)


Result

See Also mfContour, mfSolidContour, mfSolidContour3, mfTriContour


mfSolidContour, msSolidContour Plot two-dimensional solid contours.

Module fgl

Syntax handle = mfSolidContour(c) handle = mfSolidContour(x, y, c) call msSolidContour(c) call msSolidContour(x, y, c) Descriptions Procedure mfSolidContour colors areas that are in between constant value lines in two-dimensional space. handle = mfSolidContour(x, y, c)

• The values plotted are selected automatically. • Argument c is assumed to contain data representing the scalar values. • Arguments x and y specify the corresponding x-, y- coordinates of the scalar values. • Similar to mfSurf and mfMesh, the surface colors are selected based on the current

colormap. call msSolidContour(c)

• The scalar value c is assumed to be defined over a geometrically rectangular grid where x = mfColon(1, n) and y = mfColon(1, m).

h = mfSolidContour(...)

• Handle h retrieves a handle to the contour object created by mfSolidContour(...).


You can specify properties of the contour object through handle h with procedure msGSet. The properties available are: 1. iso: iso-values, a vector containing an iso-value set. Setting this property will replace the default set of contour lines. 2. autolevel: given the number of levels, it will automatically generate iso-value sets. 3. label: "on" or "off"4. clipping: "on" or "off"




ty pe(mfArray) :: a, x, y, z


! Draw a 2-D solidcontour call msSolidContour(z) call msAxis('equal') ca ll msCamZoom(0.8d0)


! Deallocate mfArrays ca ll msFreeArgs(a, x, y, z)


Result

See Also


mfSolidContour3, msSolidContour3 Plot three-dimensional solid contours.

Module fgl

Syntax handle = mfSolidContour3(z[, c]) handle = mfSolidContour3(x, y, z[, c]) call msSolidContour3(z, c) call msSolidContour3(x, y, z, c) Descriptions Procedure mfSolidContour3 colors areas that are in between the constant value lines in three-dimensional space. call msSolidContour3(x, y, z, c) call msSolidContour3(z, c)

• This procedure is similar to mfSolidContour. The areas are presented in three-dimensional perspective reflecting their scalar values specified in argument c.

h = mfSolidContour3(...)

• Handle h retrieves a handle to the three-dimensional contour object created by mfSolidContour3(...).


You can specify properties of the three-dimensional contour object through handle h with procedure msGSet. The properties available are: 1. iso: iso-values, a vector containing an iso-value set. 2. autolevel: given the number of levels, it will automatically generate iso-value sets. 3. label: "on" or "off". 4. clipping: "on" or "off": setting clipping "on" will erase the excess iso-value specified. By default, clipping is set to "off". Example Code


pr ogram example


ty pe(mfArray) :: a, x, y, z, iso, h1, h2


! Draw a 3-D solidcontour call msSubplot(1,2,1) h1 = mfSolidContour3(z) ca ll msGSet(h1,'label','on')

call msSubplot(1,2,2) h2 = mfSolidContour3(z) call msGSet(h2,'label','on') iso = mfLinspace(-0.6d0,0.6d0,8) call msGSet(h2,'iso',iso) ca ll msGSet(h2,'clipping','on')


! Deallocate mfArrays ca ll msFreeArgs(a, x, y, z, iso, h1, h2)


Result

See Also mfContour, mfContour3, mfSolidContour, mfSolidContour, mfTriContour


mfOutline, msOutline Create wireframe outline boundaries.

Module fgl

Syntax handle = mfOutline(x, y, z) handle = mfOutline(z) Descriptions Procedure mfOutline generates a wireframe outline boundary for a given data set. Arguments x,y and z specify the corresponding coordinates of the points in the data set. handle = mfOutline(...)

• Handle h retrieves a handle to the outline object created by mfOutline(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the outline object through handle h with procedure msGSet. Example Code pr ogram example


ty pe(mfArray) :: a, x, y, z, h1, h2

a = mfLinspace(-MF_PI, MF_PI, 35) call msMeshgrid(mfOut(x, y) ,a) z = (1/mfCosh(x))*mfCos(y+MF_PI/2)

! Draw a 3-D surface h1 = mfSurf(x,y,z)

call msHold('on') h2 = mfOutline(x,y,z) ca ll msHold('off')

!Change material of surface and outline call msDrawMaterial(h1,mf('edge'),mf('visible'),mf('off')) call msDrawMaterial(h1,mf('surf'),mf('colormap'),mf('off'), & mf('diffuse'),mf(20),mf('specular'),mf(90),mf('ambient'),mf(0)) call msDrawMaterial(h2,mf('edge'),mf('color'),mf((/1,0,0/))) ! Pause the program to display the graphics ca ll msViewPause()


! Deallocate mfArrays ca ll msFreeArgs(a, x, y, z, h1, h2)


Result

See Also


mfIsoSurface, msIsoSurface Create three-dimensional iso-value surface plots from volumetric data.

Module fgl

Syntax handle = mfIsoSurface(c, isovalue) handle = mfIsoSurface(x, y, z, c, isovalue) call msIsoSurface(c, isovalue) call msIsoSurface(x, y, z, c, isovalue) Descriptions Procedure mfIsoSurface creates 3-D graphs composed of isosurface data from the volumetric data c at the isosurface value specified in argument isovalue. call msIsoSurface(c, isovalue)

• The coordinates for volume c are of a geometrically rectangular grid where x = mfColon(1, n) and y = mfColon(1, m) and z = mfColon(1, p).

call msIsoSurface(x, y, z, c, isovalue)

• The arguments x,y and z define the coordinates for the volume c. h = mfIsoSurface(...)

• Handle h retrieves a handle to the isosurface object created by mfIsoSurface(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the isosurface object through handle h with procedure msGSet. The properties available are: 1. iso: iso-values, a vector containing an iso-value set. Example Code pr ogram example



type(mfArray) :: x, y, z, v, v2, a, b, c, h type(mfArray) :: g_tri,g_x,g_y,g_z,g_c a = mfLinspace(-2, 2.2d0, 21) b = mfLinspace(-2, 2.25d0, 17) c = mfLinspace(-1.5d0, 1.6d0, 31) call msMeshgrid(mfout(y, x, z), b, a, c) v = 2*mfCos(x**2)*mfExp(-(y**2)-(z**2))

call msSubplot(1,2,1) ! Plot IsoSurface and Set Transparency to 70 h = mfIsoSurface(x, y, z, v, mf((/1.0, 0.6, 0.3/))) ca ll msDrawMaterial(h, mf('surf'), mf('trans'), mf(70))

! Set Colorbar ca ll msColorbar('on')

call msSubplot(1,2,2) !Get IsoSurface data and draw it. call msGetIsoSurface(mfOut(g_tri,g_x,g_y,g_z,g_c),& x, y, z, v, mf(0.4d0)) v2 = 2*mfSin(g_x**2)*mfExp(-(g_y**2)-(g_z**2)) h = mfTriSurf(g_tri,g_x,g_y,g_z,v2)

call msDrawMaterial(h, mf('edge'),mf('visible'),mf('off')) call msDrawMaterial(h,mf('surf'),mf('smooth'),mf('on'),& mf('ambient'),mf(0),& mf('diffuse'),mf(100),& mf('specular'),mf(0)) ca ll msColorbar('on')


! Deallocate mfArrays call msFreeArgs(x, y, z, v, a, b, c, h) call msFreeArgs(g_tri,g_x,g_y,g_z,g_c,v2) e nd program example

Result

See Also msViewPause, mfAxis, mfSubplot, mfView, mfMesh, mfSurf


msGetIsoSurface Retrieve three-dimensional iso-value surface plots from volumetric data.

Module fgl

Syntax call msGetIsoSurface(mfOut(tri,x,y,z,c),c, iso) call msGetIsoSurface(mfOut(tri,x,y,z,c),x, y, z, c, iso) Descriptions Procedure mfGetIsoSurface retrieves 3-D graphs composed of isosurface data from the volumetric data c. It returns the triangular mesh tri and the vertex vectors of isourface. For details on the input arguments, please refer to the description of procedure mfIsoSurface. Example To be referred to mfIsoSurface See Also mfIsoSurface


Slice Graphs


mfSliceXYZ, msSliceXYZ Display orthogonal slice-planes through volumetric data.

Module fgl

Syntax handle = mfSliceXYZ([x, y, z,] c, Sx, Sy, Sz) call msSliceXYZ([x, y, z,] c, Sx, Sy, Sz) Descriptions Procedure mfSliceXYZ displays orthogonal slice-planes of a specified set of volumetric data. The information on the slice-planes can be retrieved using procedure msGetSliceXYZ. call msSliceXYZ(x, y, z, c, Sx, Sy, Sz)

• Displays orthogonal slice-planes along the x-, y- and z- directions specified by points in vector mfArrays Sx, Sy and Sz.

• Substitute mf() for any of the direction vectors Sx, Sy or Sz that you are not drawing any slice along. E.g. call msSliceXYZ(x, y, z, v, Sx, mf(), Sz) draws slices along the x-axis as specified by Sx and along the z-axis as specified by Sz.

• The arguments x, y and z define the corresponding coordinates of scalar values mfArray c,where c is an m-by-n-by-p three-dimensional array.

• The arguments x, y and z must be of the same shape as c and be monotonic and three-dimensional plaid as if produced by procedure mfMeshgrid.

• The color at each point is determined by three-dimensional interpolation of the elements of volume c, mapped onto the current colormap.

call msSliceXYZ(c, Sx, Sy, Sz)

• Assumes x is composed of mfColon(1, n) vectors, y is composed of mfColon(1, m) vectors, and z is composed of mfColon(1, p) vectors.

h = mfSliceXYZ(...)

• Handle h retrieves a handle to the volumetric slice object created by mfSliceXYZ(...).


You can specify properties of the volumetric slice objects through handle h with procedure


msGSet. The properties available are: 1. slicex: specifies the slice-planes along the x direction. 2. slicey: specifies the slice-planes along the y direction. 3. slicez: specifies the slice-planes along the z direction. Example Code pr ogram example


type(mfArray) :: nx, ny, nz, x, y, z, c ty pe(mfArray) :: stri,sx,sy,sz,sc

nx = mfLinspace(-2, 2.2d0, 21) ny = mfLinspace(-2, 2.25d0, 17) nz = mfLinspace(-1.5d0, 1.6d0, 31) call msMeshgrid(mfout(y, x, z), ny, nx, nz) c = 2*mfCos(x**2)*mfExp(-(y**2)-(z**2))

ca ll msSliceXYZ(x, y, z, c, mf((/-1.0d0, 1.0d0/)), mf(0), mf())

call msHold('on') call msGetSliceXYZ(mfOut(stri,sx,sy,sz,sc), & x, y, z, c, mf(),mf(),mf(-.75d0)) call msTriContour(stri,sx,sy,sz,sc) call msHold('off') ca ll msViewPause()

call msFreeArgs(nx, ny, nz, x, y, z, c) call msFreeArgs(stri,sx,sy,sz,sc) e nd program example

Result


See Also mfSliceIJK, mfSlicePlane, mfGetSliceXYZ


mfSliceIJK, msSliceIJK Display orthogonal slice-planes along the i, j or k indices.

Module fgl

Syntax handle = mfSliceIJK(x, y, z, c, Si, Sj, Sk) handle = mfSliceIJK(c, Si, Sj, Sk) call msSliceIJK(x, y, z, c, Si, Sj, Sk) call mfSliceIJK(c, Si, Sj, Sk) Descriptions Procedure mfSliceIJK displays slice-planes along i, j and k which are index of x, index of y and index of z respectively. call msSliceIJK(x, y, z, c, Si, Sj, Sk)

• Displays slice-planes along arbitrary indices specified by mfArrays Si,Sj and Sk. • Use mf() to substitute any of the index vectors Si,Sj or Sk if you are not drawing any

slice along the respective index. For example, call msSliceIJK(x, y, z, c, Si, mf(), Sk) draws slices along indices of x as specified by Si and z as specified by Sk.

• Arguments x, y and z define the corresponding coordinates of volumetric data c, where c is an m-by-n-by-p three-dimensional array.

• Arguments x, y and z must be of the same shape as c and be monotonic and three-dimensional plaid as if produced by procedure mfMeshgrid.

h = mfSliceIJK(c, Sx, Sy, Sz)

• Handle h retrieves a handle to the slice objects created by mfSliceIJK(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the slice objects through handle h with procedure msGSet. The properties available are: 1. slicei: specifies indices of x. 2. slicej: specifies indices of y. 3. slicek: specifies indices of z. Example


Code pr ogram Example


ty pe(mfArray) :: nu, nv, nw, u, v, w, x, y, z, c, h

nu = mfLinspace(0, 1.5d0*MF_PI, 20) nv = mfLinspace(0, 2*MF_PI, 20) nw = mfLinspace(0, 1, 20) call msMeshGrid( mfOut(u, v, w), nu, nv, nw ) x = ( 1 + 0.6d0 * mfCos(v) ) * mfCos(u) y = ( 1 + 0.6d0 * mfCos(v) ) * mfSin(u) z = w c = 1 - ( x ** 2 + y ** 2 + z ** 2)

h = mfSliceIJK(x, y, z, c, mf((/4, 8, 12, 16/)), & mf((/4, 8, 12, 16/)), mf((/8, 16/))) call msAxis('equal') !call msCamZoom(1.5d0) ca ll msViewPause()

ca ll msFreeArgs(nu, nv, u, v, x, y, z, c, h)


Result

See Also


mfSlicePlane, msSlicePlane Display orthogonal slice-planes along arbitrary directions.

Module fgl

Syntax handle = mfSlicePlane(x, y, z, c, plane) handle = mfSlicePlane(c, plane) call msSlicePlane(x, y, z, c, plane) call msSlicePlane(c, plane) Descriptions Procedure mfSlice displays orthogonal slice-planes of a specified set of volumetric data along an arbitrary direction. The information on the slice-planes can be retrieved by using procedure msGetSlicePlane. call msSlicePlane(x, y, z, c, plane)

• Displays orthogonal slice-planes along the direction specified by plane. • The arguments x, y and z are structured grid data which define the corresponding

coordinates of scalar values specified in argument c, where c is an m-by-n-by-p

three-dimensional array.

• Argument plane is a vector of size 4 representing the coefficients of the sliced plane equation, i.e. [a, b, c, d], where ax + by + cz + d = 0.


• The color at each point is determined by three-dimensional interpolation onto the elements of volume c, mapped to the current colormap.

call msSlicePlane(c, plane)

• Assumes x is composed of mfColon(1, n) vectors, y is composed of mfColon(1, m) vectors, and z is composed of mfColon(1, p) vectors.

h = mfSlicePlane(...)

• Handle h retrieves a handle to the volumetric slice objects created by mfSlicePlane(...).



You can specify properties of the volumetric slice objects through handle h with procedure msGSet. The property available is: 1. plane Example Code pr ogram example


type(mfArray) :: nx, ny, nz, x, y, z, c ty pe(mfArray) :: stri,sx,sy,sz,sc


ca ll msSlicePlane(x, y, z, c, mf((/1, 0, -1, 0/)))

call msHold('on') call msGetSlicePlane(mfOut(stri,sx,sy,sz,sc), & x, y, z, c, mf((/1, 1, 0, 0/))) call msTriContour(stri,sx,sy,sz,sc) ca ll msHold('off')

ca ll msViewPause()

call msFreeArgs(nx, ny, nz, x, y, z, c) e nd program example

Result


See Also mfSlice, mfGetSlicePlane


msGetSliceXYZ Retrieve orthogonal slice-planes through volumetric data.

Module fgl

Syntax call msGetSliceXYZ(mfOut(tri,x,y,z,c), [x, y, z, ]c, Sx, Sy, Sz) Descriptions Procedure mfGetSliceXYZ retrieves orthogonal slice-planes of a specified set of volumetric data. It returns the triangular mesh tri and the vertex vectors of the sliced-planes defined in the n-by-3 matrix xyz. For details on the input arguments, refer to the description of procedure mfSliceXYZ. Example To be referred to mfSliceXYZ See Also mfSliceXYZ


msGetSlicePlane Retrieve orthogonal slice-planes along an arbitrary direction.

Module fgl

Syntax call msGetSlicePlane(mfOut(tri,x,y,z,c), [x, y, z,] c, planes) Descriptions Procedure mfGetSlicePlane retrieves orthogonal slice-planes of a specified set of volumetric data along an arbitrary direction. It returns the triangular mesh tri and the vertex vectors of the sliced-planes defined in the n-by-3 matrix xyz. call msGetSlicePlane(mfOut(tri,x,y,z,c), x, y, z, c, planes)

• Retrieve the triangular mesh tri. With tri and the coordinates xyz, you may use mfTriSurf to plot the triangular surface.

• The arguments x, y and z are structured grid data which define the corresponding coordinates of scalar values specified in argument c, where c is an m-by-n-by-p




For details on the input arguments, refer to the description of procedure mfSlicePlane. Example To be referred to mfSlicePlane See Also mfSlicePlane


Streamline Graphs


mfStreamLine2, msStreamLine2 Create stream lines from two-dimensional vector data.

Module fgl

Syntax handle = mfStreamLine2(x, y, u, v, Sx, Sy) handle = mfStreamLine2(u, v, Sx, Sy) call msStreamLine2(x, y, u, v, Sx, Sy) call msStreamLine2(u, v, Sx, Sy) Descriptions Procedure mfStreamLine2 creates stream lines from two-dimensional vector components u and v . call msStreamLine2(x, y, u, v, Sx, Sy)

• Arguments u and v are two-dimensional orthogonal vector components corresponding to the x- and y-directions respectively.

• Arguments x and y define the coordinates for u and v and must be monotonic and two-dimensional plaid (as if produced by mfMeshgrid).

• Arguments Sx and Sy define the starting positions of the stream lines. call msStreamLine2(u, v, Sx, Sy)

• Arguments x and y are derived from mfMeshgrid(mfOut(x, y), mfColon(1, n), mfColon(1, m)), where n and m are dimensions of u.

h = mfStreamLine2(...)

• Handle h retrieves a handle to the stream lines created by mfStreamLine2(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the stream lines through handle h with procedure msGSet. The properties available are: 1. start: an n-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream lines. 3. steplength: step length of the stream lines; the smaller the steplength is, the smoother the stream lines are. By default, MATFOR uses sizefactor=1 and steplength=0.5.


Example Code program Example use fml use fgl implicit none type(mfArray) :: x, y, v, u, sx, sy type(mfArray) :: h, px, py

px = mfLinspace( -2, 2, 20 ) py = mfLinspace( -2, 2, 20 )

call msMeshgrid( mfOut( x, y), px, py)

u = mfSin( 2 * x * y ) v = mfCos( 2 * x - y )

sx = mfLinspace( -2, 2, 10 ) sy = mfLinspace( 0, 0, 10 )

call msSubplot(2,2,1) call msTitle("Stream Line") call msColormapRange(-2.d0,2.d0) h = mfStreamLine2(x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 )

call msSubplot(2,2,2) call msTitle("Stream Dashed Line") call msColormapRange(-2.d0,2.d0) h = mfStreamDashedLine2(x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 ) call msDrawMaterial(h,mf('surf'),mf('colormap'), & mf('off'),mf('color'),mf((/0,0,0/)))

call msSubplot(2,2,3) call msTitle("Stream Ribbon") call msColormapRange(-2.d0,2.d0) h = mfStreamRibbon2(x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.02d0 )

call msSubplot(2,2,4) call msTitle("Stream Tube") call msColormapRange(-2.d0,2.d0) h = mfStreamTube2(x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0 ) call msDrawMaterial(h,mf('surf'),mf('ambient'),mf(0), & mf('diffuse'),mf(100),mf('specular'),mf(0))

call msViewPause() call msFreeArgs(x, y, v, u, h, px, py, sx, sy) e nd program Example

Result


See Also mfQuiver


mfStreamDashedLine2, msStreamDashedLine2 Create stream dashed-lines from two-dimensional vector data.

Module fgl

Syntax handle = mfStreamDashedLine2(x, y, u, v, Sx, Sy) handle = mfStreamDashedLine2(u, v, Sx, Sy) call msStreamDashedLine2(x, y, u, v, Sx, Sy) call msStreamDashedLine2(u, v, Sx, Sy) Descriptions Procedure mfStreamDashedLine2 creates stream dashed-lines from two-dimensional vector components u and v . call msStreamDashedLine2(x, y, u, v, Sx, Sy)



• Arguments Sx and Sy define the starting positions of the stream dashed-lines. call msStreamDashedLine2(u, v, Sx, Sy)


h = mfStreamDashedLine2(...)

• Handle h retrieves a handle to the stream dashed-lines created by mfStreamDashedLine2(...).


You can specify properties of the stream dashed-lines through handle h with procedure msGSet. The properties available are: 1. start: an n-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream dashed-lines. 3. steplength: step length of the stream dashed-lines; the smaller the steplength is, the smoother the stream dashed-lines are.


By default, MATFOR uses sizefactor=1 and steplength=0.5. Example To be referred to mfStreamLine2 See Also mfQuiver


mfStreamRibbon2, msStreamRibbon2 Create stream ribbons from two-dimensional vector data.

Module fgl

Syntax handle = mfStreamRibbon2(x, y, u, v, Sx, Sy) handle = mfStreamRibbon2(u, v, Sx, Sy) call msStreamRibbon2(x, y, u, v, Sx, Sy) call msStreamRibbon2(u, v, Sx, Sy) Descriptions Procedure mfStreamRibbon2 creates stream ribbons from two-dimensional vector components u and v . call msStreamRibbon2(x, y, u, v, Sx, Sy)



• Arguments Sx and Sy define the starting positions of the stream ribbons. call msStreamRibbon2(u, v, Sx, Sy)


h = mfStreamRibbon2(...)

• Handle h retrieves a handle to the stream ribbons created by mfStreamRibbon2(...).


You can specify properties of the stream ribbons through handle h with procedure msGSet. The properties available are: 1. start: an n-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream ribbons. 3. steplength: step length of the stream ribbons; the smaller the steplength is, the smoother the stream ribbons are. By default, MATFOR uses sizefactor=1 and steplength=0.5.


Example To be referred to mfStreamLine2 See Also mfQuiver


mfStreamTube2, msStreamTube2 Create stream tubes from two-dimensional vector data.

Module fgl

Syntax handle = mfStreamTube2(x, y, u, v, Sx, Sy) handle = mfStreamTube2(u, v, Sx, Sy) call msStreamTube2(x, y, u, v, Sx, Sy) call msStreamTube2(u, v, Sx, Sy) Descriptions Procedure mfStreamTube2 creates stream tubes from two-dimensional vector components u and v . call msStreamTube2(x, y, u, v, Sx, Sy)



• Arguments Sx and Sy define the starting positions of the stream tubes. call msStreamTube2(u, v, Sx, Sy)


h = mfStreamTube2(...)

• Handle h retrieves a handle to the stream tubes created by mfStreamTube2(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the stream tubes through handle h with procedure msGSet. The properties available are: 1. start: an n-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream tubes. 3. steplength: step length of the stream tubes. By default, sizefactor=1 and steplength=0.5.


Example To be referred to mfStreamLine2 See Also mfQuiver


mfStreamArrow2, msStreamArrow2 Create stream arrows from two-dimensional vector data.

Module fgl

Syntax handle = mfStreamArrow2(x, y, u, v, Sx, Sy) handle = mfStreamArrow2(u, v, Sx, Sy) call msStreamArrow2(x, y, u, v, Sx, Sy) call msStreamArrow2(u, v, Sx, Sy) Descriptions Procedure mfStreamArrow2 creates stream arrows from two-dimensional vector components u and v . call msStreamArrow2(x, y, u, v, Sx, Sy)



• Arguments Sx and Sy define the starting positions of the stream arrows. call msStreamArrow2(u, v, Sx, Sy)


h = mfStreamArrow2(...)

• Handle h retrieves a handle to the stream arrows created by mfStreamArrow2(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the stream arrows through handle h with procedure msGSet. The properties available are: 1. start: an n-by-2 matrix containing starting points coordinates. 2. arrowsize: thickness of the stream arrows. 3. arrowstep: step length of the stream arrows; the smaller the steplength is, the smoother the stream arrows are. By default, MATFOR uses arrowsize=1 and arrowstep=0.5.


Example Code program Example use fml use fgl implicit none type(mfArray) :: x, y, v, u, sx, sy type(mfArray) :: h, px, py

px = mfLinspace( -2, 2, 20 ) py = mfLinspace( -2, 2, 20 )

call msMeshgrid( mfOut( x, y ), px, py )

u = mfSin( 2 * x * y ) v = mfCos( 2 * x - y )

sx = mfLinspace( -1, 1, 10 ) sy = mfLinspace( 0, 0, 10 )

call msTitle("Stream Arrow") call msColormapRange(-2d0,2d0) h = mfStreamArrow2(x, y, u, v, sx, sy) call msGSet( h, "arrowsize", 0.15d0 )

call msGSet( h, "arrowstep", 0.25d0 )

call msHold("on")

h = mfStreamTube2(x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0)

call msDrawMaterial(h,"surf","trans",70d0)

call msViewPause() call msFreeArgs(x, y, v, u, h, px, py, sx, sy) e nd program Example

Result

See Also mfQuiver


mfStreamLine, msStreamLine, mfStreamLine3,

msStreamLine3 Create stream lines from three-dimensional vector data.

Module fgl

Syntax handle = mfStreamLine(x, y, z, u, v, w, Sx, Sy, Sz) handle = mfStreamLine(u, v, w, Sx, Sy, Sz) call msStreamLine(x, y, z, u, v, w, Sx, Sy, Sz) call msStreamLine(u, v, w, Sx, Sy, Sz) Descriptions Procedure mfStreamLine creates stream lines from three-dimensional vector components u, v and w. call msStreamLine(x, y, z, u, v, w, Sx, Sy, Sz)

• Arguments u, v and w are three-dimensional orthogonal vector components corresponding to the x-, y- and z- directions respectively.

• Arguments x, y and z define the coordinates for u, v and w and must be monotonic and three-dimensional plaid (as if produced by mfMeshgrid).

• Arguments Sx, Sy and Sz define the starting positions of the stream lines. call msStreamLine(u, v, w, Sx, Sy, Sz)

• Arguments x, y and z are derived from mfMeshgrid(mfOut(x, y, z), mfColon(1, n), mfColon(1, m), mfColon(1, p)), where n, m and p are dimensions of u.

h = mfStreamLine(...)

• Handle h retrieves a handle to the stream lines created by mfStreamLine(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the stream lines through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream lines.


3. steplength: step length of the stream lines. By default, sizefactor=1 and steplength=0.5. Example Code program Example use fml use fgl implicit none type(mfArray) :: x, y, z, v, u, w, sx, sy, sz type(mfArray) :: h, px, py, pz

px = mfLinspace( -2, 2, 20 ) py = mfLinspace( -2, 2, 20 ) pz = mfLinspace( -2, 2, 20 )

call msMeshgrid( mfOut( x, y, z ), px, py, pz )

u = mfSin( 2 * x * y * z ) v = mfCos( 2 * x - y ) w = mfCos( x + y - z )

sx = mfLinspace( -2, 2, 10 ) sy = mfLinspace( 0, 0, 10 ) sz = mfLinspace( 0, 0, 10 )

call msSubplot(2,2,1) call msTitle("Stream Line") call msColormapRange(-2.d0,2.d0) h = mfStreamLine(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 )

call msSubplot(2,2,2) call msTitle("Stream Dashed Line") call msColormapRange(-2.d0,2.d0) h = mfStreamDashedLine(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 ) call msDrawMaterial(h,mf('surf'),mf('colormap'), & mf('off'),mf('color'),mf((/0,0,0/)))

call msSubplot(2,2,3) call msTitle("Stream Ribbon") call msColormapRange(-2.d0,2.d0) h = mfStreamRibbon(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.02d0 )

call msSubplot(2,2,4) call msTitle("Stream Tube") call msColormapRange(-2.d0,2.d0) h = mfStreamTube(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0 ) call msDrawMaterial(h,mf('surf'),mf('ambient'),mf(0), & mf('diffuse'),mf(100),mf('specular'),mf(0))

call msViewPause() call msFreeArgs(x, y, z, v, u, w, h, px, py, pz,sx, sy, sz) e nd program Example

Result


See Also mfQuiver, mfQuiver3


mfStreamDashedLine, msStreamDashedLine,

mfStreamDashedLine3, msStreamDashedLine3 Create stream dashed-lines from three-dimensional vector data.

Module fgl

Syntax handle = mfStreamDashedLine(x, y, z, u, v, w, Sx, Sy, Sz) handle = mfStreamDashedLine(u, v, w, Sx, Sy, Sz) call msStreamDashedLine(x, y, z, u, v, w, Sx, Sy, Sz) call msStreamDashedLine(u, v, w, Sx, Sy, Sz) Descriptions Procedure mfStreamDashedLine creates stream dashed-lines from three-dimensional vector components u, v and w. call msStreamDashedLine(x, y, z, u, v, w, Sx, Sy, Sz)

• Arguments u, v and w are three-dimensional orthogonal vector components corresponding to the x-, y- and z- direction respectively.


• Arguments Sx, Sy and Sz define the starting positions of the stream dashed-lines. call msStreamDashedLine(u, v, w, Sx, Sy, Sz)


h = mfStreamDashedLine(...)

• Handle h retrieves a handle to the stream dashed-lines created by mfStreamDashedLine(...).


You can specify properties of the stream dashed-lines through handle h with procedure msGSet.


The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream dashed-lines. 3. steplength: step length of the stream dashed-lines. By default, sizefactor=1and steplength=0.5. Example To be referred to msStreamLine See Also


mfStreamRibbon, msStreamRibbon, mfStreamRibbon3,

msStreamRibbon3 Create stream ribbons from three-dimensional vector data.

Module fgl

Syntax handle = mfStreamRibbon(x, y, z, u, v, w, Sx, Sy, Sz) handle = mfStreamRibbon(u, v, w, Sx, Sy, Sz) call msStreamRibbon(x, y, z, u, v, w, Sx, Sy, Sz) call msStreamRibbon(u, v, w, Sx, Sy, Sz) Descriptions Procedure mfStreamRibbon creates stream ribbons from three-dimensional vector components u, v and w. call msStreamRibbon(x, y, z, u, v, w, Sx, Sy, Sz)



• Arguments Sx, Sy and Sz define the starting positions of the stream ribbons. call msStreamRibbon(u, v, w, Sx, Sy, Sz)


h = mfStreamRibbon(...)

• Handle h retrieves a handle to the stream ribbons created by mfStreamRibbon(...).

• Alternatively, you use procedure h = mfGetCurrentDraw() to retrieve the handle of the current graphics object.

You can specify properties of the stream ribbons through handle h with procedure msGSet. The properties available are:


1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream ribbons. 3. steplength: step length of the stream ribbons. By default, sizefactor=1and steplength=0.5. Example To be referred to msStreamLine See Also


mfStreamTube, msStreamTube, mfStreamTube3,

msStreamTube3 Create stream tubes from three-dimensional vector data.

Module fgl

Syntax handle = mfStreamTube(x, y, z, u, v, w, Sx, Sy, Sz) handle = mfStreamTube(u, v, w, Sx, Sy, Sz) call msStreamTube(x, y, z, u, v, w, Sx, Sy, Sz) call msStreamTube(u, v, w, Sx, Sy, Sz) Descriptions Procedure mfStreamTube creates stream tubes from three-dimensional vector components u, v and w. call msStreamTube(x, y, z, u, v, w, Sx, Sy, Sz)



• Arguments Sx, Sy and Sz define the starting positions of the stream tubes. call msStreamTube(u, v, w, Sx, Sy, Sz)


h = mfStreamTube(...)

• Handle h retrieves a handle to the stream tubes created by mfStreamTube(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the stream tubes through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates.


2. sizefactor: thickness of the stream tubes. 3. steplength: step length of the stream tubes. By default, sizefactor=1and steplength=0.5. Example To be referred to msStreamLine See Also


mfStreamArrow, msStreamArrow, mfStreamArrow3,

msStreamArrow3 Create stream arrows from three-dimensional vector data.

Module fgl

Syntax handle = mfStreamArrow(x, y, z, u, v, w, Sx, Sy, Sz) handle = mfStreamArrow(u, v, w, Sx, Sy, Sz) call msStreamArrow(x, y, z, u, v, w, Sx, Sy, Sz) call msStreamArrow(u, v, w, Sx, Sy, Sz) Descriptions Procedure mfStreamArrow creates stream arrows from three-dimensional vector components u, v and w. call msStreamArrow(x, y, z, u, v, w, Sx, Sy, Sz)



• Arguments Sx, Sy and Sz define the starting positions of the stream arrows. call msStreamArrow(u, v, w, Sx, Sy, Sz)


h = mfStreamArrow(...)

• Handle h retrieves a handle to the stream arrows created by mfStreamArrow(...). • Alternatively, you use procedure h = mfGetCurrentDraw() to retrieve the handle of

the current graphics object. You can specify properties of the stream arrows through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates.


2. arrowsize: thickness of the stream arrows. 3. arrowstep: step length of the stream arrows. By default, arrowsize=1and arrowstep=0.5. Example Code program Example use fml use fgl implicit none type(mfArray) :: x, y, z, v, u, w, sx, sy, sz type(mfArray) :: h, px, py, pz

px = mfLinspace( -2, 2, 20 ) py = mfLinspace( -2, 2, 20 ) pz = mfLinspace( -2, 2, 20 )

call msMeshgrid( mfOut( x, y, z ), px, py, pz )



call msTitle("Stream Arrow") call msColormapRange(-2d0,2d0) h = mfStreamArrow(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "arrowsize", 0.15d0 )


call msHold("on")

h = mfStreamTube(x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0)


call msViewPause() call msFreeArgs(x, y, z, v, u, w, h, px, py, pz,sx, sy, sz) e nd program Example

Result

See Also



Triangular Surface Graphs


mfTriSurf, msTriSurf Create polygonal surface plots.

Module fgl

Syntax handle = mfTriSurf(tri, x, y, z[, c]) handle = mfTriSurf(tri, xyz[, c]) call msTriSurf(tri, x, y, z[, c]) call msTriSurf(tri, xyz[, c]) Descriptions Procedure mfTriSurf displays polygons defined by a face matrix. The polygons must be convex polygons. call msTriSurf(tri, x, y, z) call msTriSurf(tri, x, y, z, c)

• Display the polygons defined by an m-by-n face matrix tri as a surface object, where m is the number of polygons to be drawn and n is the number of edges of each polygon. For example, a 4-by-3 face matrix tri draws a surface object of 4 triangles, while a 3-by-4 face matrix tri draws a surface object of 3 quadrilaterals.

• Each row of face matrix tri contains indices to x,y and z vertex vectors that define a single polygonal face.

• As with procedure mfSurf, the color scale is assumed to be proportional to the surface height specified by vertex z.

• Argument c overrides the default color specification and defines the new edge color. • The shapes of the four mfArrays x,y,z and c should be conformed. • Note that you can use mfSurf to plot the polygons and switch the shading mode using

the toolbar function shading mode. call msTriSurf(tri, xyz) call msTriSurf(tri, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTriSurf(...)

• Handle h retrieves a handle to the polygonal surface object created by mfTriSurf(...).

• Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the


current graphics object. You can specify properties of the polygonal surface object through handle h with procedure msGSet. The properties available are: 1. tri 2. xyz Example Code pr ogram example


ty pe (mfArray) :: tri, x, y, z, c

x = mfRand(400,1) y = mfRand(400,1) z = 1 - ((x-0.5d0)**2 + (y-0.5d0)**2) c = mfSin(z) * mfCos(z) tr i = mfGetDelaunay(x, y)

call msTitle('msTriSurf') call msTriSurf(tri, x, y, z) ca ll msViewPause()

ca ll msFreeArgs(tri, x, y, z, c)


Result

See Also mfTriMesh


mfTriMesh, msTriMesh Create polygonal mesh plots.

Module fgl

Syntax handle = mfTriMesh(tri, x, y, z[, c]) handle = mfTriMesh(tri, xyz[, c]) call msTriMesh(tri, x, y, z[, c]) call msTriMesh(tri, xyz[, c]) Descriptions Procedure mfTriMesh displays polygons in a mesh defined by a face matrix. The polygons must be convex polygons. call msTriMesh(tri, x, y, z) call msTriMesh(tri, x, y, z, c)

• Display the polygons defined by an m-by-n face matrix tri as a meshed surface object, where m is the number of polygons to be drawn and n is the number of edges of each polygon. For example, a 4-by-3 face matrix tri draws a surface object of 4 triangles, while a 3-by-4 face matrix tri draws a surface object of 3 quadrilaterals.

• Each row of face matrix tri contains indices to x,y and z vertex vectors that define a single polygonal face.

• As with the procedure mfSurf, the color scale is assumed to be proportional to the surface height specified by vertex z.

• Argument c overrides the default color specification and defines the new edge color. • The shapes of the four mfArrays x,y,z and c should be conformed. • Note that you can use mfMesh to plot the polygons and switch the shading mode using

the toolbar function shading mode. call msTriMesh(tri, xyz) call msTriMesh(tri, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTriMesh(...)

• Handle h retrieves a handle to the polygonal meshed surface object created by mfTriMesh.

• Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the


current graphics object. You can specify properties of the polygonal meshed surface object through handle h with procedure msGSet. The properties available are: 1. tri 2. xyz Example Code pr ogram example


ty pe (mfArray) :: tri, x, y, z, c

x = mfRand(400,1) y = mfRand(400,1) z = 1 - ((x-0.5d0)**2 + (y-0.5d0)**2) c = mfSin(z) * mfCos(z) tr i = mfGetDelaunay(x, y)

call msTitle('msTriMesh') call msTriMesh(tri, x, y, z) ca ll msViewPause()

ca ll msFreeArgs(tri, x, y, z, c)


Result

See Also mfTriSurf


mfTriContour, msTriContour Create contours on polygonal plots.

Module fgl

Syntax handle = mfTriContour(tri, x, y, z[, c]) handle = mfTriContour(tri, xyz[, c]) call msTriContour(tri, x, y, z[, c]) call msTriContour(tri, xyz[, c]) Descriptions Procedure mfTriSurface plots contour lines of matrix z on the polygons defined by a face matrix. The polygons must be convex polygons. call msTriContour(tri, x, y, z) call msTriContour(tri, x, y, z, c)

• Generate contour lines on the polygons for selected scalar values. The values plotted are selected automatically.

• As with procedures mfTriSurf and mfTriMesh, the polygons are defined by an m-by-n face matrix tri. Each row of face matrix tri contains indices to x, y and z

vertex vectors that define a single polygonal face.

• As with the Surface Graphs procedures, the color scale is assumed to be proportional to the surface height specified by vertex z.

• Argument c overrides the default edge color specification, and defines the new edge color.

• The shapes of the four mfArrays x, y, z and c should be conformed. call msTriContour(tri, xyz) call msTriContour(tri, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTriContour(...)

• Handle h retrieves a handle to the contour line objects created by mfTriContour(...).


You can specify properties of the contour line objects through handle h with procedure


msGSet. The properties available are: 1. tri 2. xyz 3. iso: iso-values, a vector containing iso-value set. Setting this property will replace default set of contour lines. 4. autolevel: given number of levels, it will generate the iso-value set automatically. 5. clipping: "on" or "off"6. Label: "on" or "off" Example Code pr ogram example


ty pe (mfArray) :: tri, x, y, z, c,h

x = mfRand(400, 1) y = mfRand(400, 1) z = 1 - ((x-0.5d0)**2 + (y-0.5d0)**2) c = mfSin(z) * mfCos(z) tr i = mfGetDelaunay(x, y)

call msSubplot(1,2,1) call msTriContour(tri, x, y, z, c) ca ll msTitle('TriContour')

call msSubplot(1,2,2) h=mfTriContour(tri, x, y, z, c) call msGSet(h,'label','on') call msGSet(h,'iso',mf((/0.46d0,0.47d0,0.48d0,0.49d0/))) call msGSet(h,'clipping','on') ca ll msTitle('TriContour with clipping')

ca ll msViewPause()

ca ll msFreeArgs(tri, x, y, z, c, h)


Result


See Also mfTriMesh


mfPatch, msPatch Add patches on 2-D or 3-D coordinates.

Module fgl

Syntax handle = mfPatch(x, y, c) handle = mfPatch(x, y, z, c) call msPatch(x, y, c) call msPatch(x, y, z, c) Descriptions Procedure mfPatch adds a patch (filled 2-D polygon) on the coordinates specified by arguments x and y. Notice that only convex polygons can be accepted. call msPatch(x, y) call msPatch(x, y, c)

• Add patches on the vertices defined by arguments x and y. • If arguments x and y are matrices, then each column defines a single patch. • Argument c defines the color scale for the vertices that determine the interior color of the

patch.

• The shapes of the three mfArrays x,y and c should be conformed. call msPatch(x, y, z) call msPatch(x, y, z, c)

• Add patches on the 3-D coordinates defined by arguments x,y and z. • If x,y and z are matrices of the same size, then each column defines a single patch. • The color scale is assumed to be proportional to the surface height specified by vertex z

and is used to determine the interior color of the added patch.

• If argument c is defined, it overrides the default color specification and defines the new color scale for the vertices.

• The shapes of the four mfArrays x,y,z and c should be conformed. Example Code pr ogram example

use fml use fgl


im plicit none

type (mfArray) :: x, y, c, h re al(8) :: p, q

p = 0.5d0*sqrt(3.0d0) q = 1.5d0

x = (/0.0d0, p, p, 0.0d0, -p, -p /) .vc. & (/2*p, 3*p, 3*p, 2*p, p, p /) .vc. & (/4*p, 5*p, 5*p, 4*p, 3*p, 3*p/) .vc. & (/p, 2*p, 2*p, p, 0.0d0, 0.0d0/) .vc. & (/3*p, 4*p, 4*p, 3*p, 2*p, 2*p/) .vc. & (/p, 2*p, 2*p, p, 0.0d0, 0.0d0/) .vc. & (/3*p, 4*p, 4*p, 3*p, 2*p, 2*p/)

y = (/-1.0d0, -0.5d0, 0.5d0, 1.0d0, 0.5d0, -0.5d0/) .vc. & (/-1.0d0, -0.5d0, 0.5d0, 1.0d0, 0.5d0, -0.5d0/) .vc. & (/-1.0d0, -0.5d0, 0.5d0, 1.0d0, 0.5d0, -0.5d0/) .vc. & (/-1.0d0+q, -0.5d0+q, 0.5d0+q, 1.0d0+q, 0.5d0+q, -0.5d0+q/) .vc. & (/-1.0d0+q, -0.5d0+q, 0.5d0+q, 1.0d0+q, 0.5d0+q, -0.5d0+q/) .vc. & (/-1.0d0-q, -0.5d0-q, 0.5d0-q, 1.0d0-q, 0.5d0-q, -0.5d0-q/) .vc. & (/-1.0d0-q, -0.5d0-q, 0.5d0-q, 1.0d0-q, 0.5d0-q, -0.5d0-q/)

c = (/1, 1, 1, 1, 1, 1/) .vc. & (/2, 2, 2, 2, 2, 2/) .vc. & (/3, 3, 3, 3, 3, 3/) .vc. & (/4, 4, 4, 4, 4, 4/) .vc. & (/5, 5, 5, 5, 5, 5/) .vc. & (/6, 6, 6, 6, 6, 6/) .vc. &

(/7, 7, 7, 7, 7, 7/)

x = .t. x y = .t. y c = .t. c

h = mfPatch(x, y, c) call msView('2') call msAxis('equal') ca ll msViewPause()

ca ll msFreeArgs(x, y, c, h)


Result

See Also


Unstructured Grids


mfTetSurf, msTetSurf Create polyhedral surface plots.

Module fgl

Syntax handle = mfTetSurf(tet, x, y, z[, c]) handle = mfTetSurf(tet, xyz[, c]) call msTetSurf(tet, x, y, z[, c]) call msTetSurf(tet, xyz[, c]) Descriptions Procedure mfTetSurf displays polyhedrons defined by a cell matrix. call msTetSurf(tet, x, y, z) call msTetSurf(tet, x, y, z, c)

• Display the polyhedrons defined by an m-by-k cell matrix tet as a polyhedral object, where m is the number of polyhedrons to be drawn. There are four different types of polyhedrons depending on the value of k, as illustrated below.

12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)


• Each row of cell matrix tet contains indices to x,y and z vertex vectors that define a

single polyhedron.

• As with procedure mfSurf, the edge color is assumed to be proportional to the surface height specified by vertex z.

• Argument c overrides the default color specification. • The shapes of the four mfArrays x,y,z and c should be conformed. • Note that you can use either mfTetSurf or mfTetMesh to plot the polygons and

switch the shading mode using the toolbar function shading mode. call msTetSurf(tet, xyz) call msTetSurf(tet, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz where n is the number of vertices. h = mfTetSurf(...)

• Handle h retrieves a handle to the polyhedral object created by mfTetSurf(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the polyhedral object through handle h with procedure msGSet. The properties available are: 1. tet 2. xyz Example Code pr ogram example


ty pe (mfArray) :: tet, x, y, z, c

x = mfRand(500,1) y = mfRand(500,1) z = mfRand(500,1) c = 1 - ((x - 0.5d0) ** 2 + (y - 0.5d0) ** 2 + (z - 0.5d0) ** 2)

te t = mfGetDelaunay3(x, y, z)

call msTetSurf(tet, x, y, z) ca ll msViewPause()

ca ll msFreeArgs(tet, x, y, z, c)



Result

See Also mfTetMesh


mfTetMesh, msTetMesh Create polyhedral mesh plots.

Module fgl

Syntax handle = mfTetMesh(tet, x, y, z[, c]) handle = mfTetMesh(tet, xyz[, c]) Descriptions Procedure mfTetMesh displays polyhedrons defined by a cell matrix. call msTetMesh(tet, x, y, z) call msTetMesh(tet, x, y, z, c)

• Display the polyhedrons defined by an m-by-k cell matrix tet as a meshed polyhedral object, where m is the number of polyhedrons to be drawn. There are four different types of polyhedrons depending on the value of k as illustrated below.

12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)

• Each row of cell matrix tet contains indices to x,y and z vertex vectors that define a

single polyhedron.


• As with procedure mfTetMesh,the edge color is assumed to be proportional to the surface height specified by vertex z.

• Argument c overrides the default color specification and defines the new edge color. • The shapes of the four mfArrays x,y,z and c should be conformed. • Note that you can use either mfTetSurf or mfTetMesh to plot the polygons and

switch the shading mode using the toolbar function shading mode. call msTetMesh(tet, xyz) call msTetMesh(tet, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTetMesh(...)

• Handle h retrieves a handle to the polyhedral object created by mfTetMesh(...). • Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the

current graphics object. You can specify properties of the polyhedral object through handle h with procedure msGSet. The properties available are: 1. tet 2. xyz Example See Also mfTetSurf


mfTetContour, msTetContour Create contours on polyhedral plots.

Module fgl

Syntax handle = mfTetContour(tet, x, y, z[, c]) handle = mfTetContour(tet, xyz[, c]) call msTetContour(tet, x, y, z[, c]) call msTetContour(tet, xyz[, c]) Descriptions Procedure mfTetSurface plots contour lines on the surface of the polyhedral object defined by a face matrix. call msTetContour(tet, x, y, z) call msTetContour(tet, x, y, z, c)


12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)


• Generate contour lines of matrix z on the surface of the polyhedral object for selected

scalar values. The values plotted are selected automatically.

• Similar to procedures mfTetSurf and mfTetMesh,the polyhedral object is the combination of the polyhedrons defined by a m-by-n face matrix tet.Each row of face matrix tet contains indices into x,y and z vertex vectors to define a single polyhedron.

• The color scale is assumed to be proportional to the surface height specified by vertex z. • Argument c overrides the default color specification and defines the new edge color. • The shapes of the four mfArrays x,y,z and c should be conformed. call msTetContour(tet, xyz) call msTetContour(tet, xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfTetContour(...)

• Handle h retrieves a handle to the contour line objects created by mfTetContour(...).

• Alternatively, use procedure h = mfGetCurrentDraw()to retrieve the handle of the current graphics object.

You can specify properties of the contour line objects through handle h with procedure msGSet. The properties available are: 1. tet 2. xyz 3. iso: iso-values, a vector containing iso-value set. Setting this property will replace default set of contour lines. 4. autolevel: given number of levels, it will generate the iso-value set automatically. 5. clipping: "on" or "off" 6. label " "on" or "off" Example Code pr ogram example


ty pe (mfArray) :: tet, x, y, z, c, h


tet = mfGetDelaunay3(x, y, z)


h = mfTetContour(tet, x, y, z, c) call msGSet(h,'label','on') ca ll msViewPause()

ca ll msFreeArgs(tet, x, y, z, c, h)


Result

See Also mfTetMesh


mfTetIsoSurface, msTetIsoSurface Create polyhedral isosurface plots.

Module fgl

Syntax handle = mfTetIsoSurface(tet, x, y, z, c, isovalue) handle = mfTetIsoSurface(tet, xyz, c, isovalue) call msTetIsoSurface(tet, x, y, z, c, isovalue) call msTetIsoSurface(tet, xyz, c, isovalue) Descriptions Procedure mfTetIsoSurface creates 3-D graphs composed of isosurface data from the polyhedral data c at the isosurface value specified in argument isovalue. call msTetIsoSurface(x, y, z, c, isovalue)

• Display the polyhedrons defined by a m-by-k cell matrix tet as a meshed polyhedral object, where m is the number of polyhedrons to be drawn. There are four different types of polyhedrons depending on the value of k as illustrated below.

12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)


• The arguments x,y and z define the coordinates for the volume c. h = mfTetIsoSurface(...)

• Handle h retrieves a handle to the isosurface object created by mfTetIsoSurface(...).


You can specify properties of the isosurface object through handle h with procedure msGSet. The properties available are: 1. iso: iso-value, a vector containing iso-value sets. Example Code pr ogram example


type (mfArray) :: tet, x, y, z, c ty pe(mfArray) :: g_tri,g_x,g_y,g_z,g_c,v2,h



call msSubplot(1,2,1) call msTetIsoSurface(tet, x, y, z, c, mf((/0.8d0, 0.7d0, 0.6d0/))) ca ll msColorbar('on')

call msSubplot(1,2,2) !Get IsoSurface data and draw it. call msGetTetIsoSurface(mfOut(g_tri,g_x,g_y,g_z,g_c),& tet, x, y, z, c, mf(0.75d0)) v2 = 1 - ((g_x - 0.5d0) ** 2 + (g_y - 0.5d0) ** 2 - (g_z - 0.5d0) ** 2) h = mfTriSurf(g_tri,g_x,g_y,g_z,v2)

call msDrawMaterial(h, mf('edge'),mf('visible'),mf('off')) call msDrawMaterial(h,mf('surf'),mf('smooth'),mf('on'),& mf('ambient'),mf(0),& mf('diffuse'),mf(100),& mf('specular'),mf(0)) ca ll msColorbar('on')

ca ll msViewPause()

call msFreeArgs(tet, x, y, z, c) call msFreeArgs(g_tri,g_x,g_y,g_z,g_c,v2,h) e nd program example

Result


See Also


mfTetSliceXYZ, msTetSliceXYZ Display orthogonal slice-planes through volumetric data.

Module fgl

Syntax handle = mfTetSliceXYZ(tet, x, y, z, c, Sx, Sy, Sz) handle = mfTetSliceXYZ(tet, xyz, c, Sx, Sy, Sz) call msTetSliceXYZ(tet, x, y, z, c, Sx, Sy, Sz) call msTetSliceXYZ(tet, xyz, c, Sx, Sy, Sz) Descriptions Procedure mfTetSliceXYZ displays orthogonal slice-planes of a specified set of polyhedral data. The information on the slice-planes can be retrieved by using procedure mfGetTetSliceXYZ. call msTetSliceXYZ(tet, x, y, z, c, Sx, Sy, Sz)


12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)


• Displays orthogonal slice-planes along the x, y and z directions specified by points in

vector mfArrays Sx,Sy and Sz

• Use mf() to substitute any of the direction vectors Sx, Sy or Sz if you are not drawing any slice along the respective direction. E.g. call msSliceXYZ(x, y, z, v, Sx, mf(), Sz) draws slices along the x-axis as specified by Sx and z-axis as specified by Sz.

• The arguments x,y and z define the corresponding coordinates of scalar values mfArray c, where c is an m-by-n-by-p three-dimensional array.

• The arguments x,y and z must be of the same shape as c and are monotonic and three-dimensional plaid as if produced by procedure mfMeshgrid.

• The color at each point is determined by three-dimensional interpolation into the elements of volume c, mapped to the current colormap.

call msTetSliceXYZ(tet, xyz, c, Sx, Sy, Sz)

• Vertex vectors are defined in the n-by-3 matrix xyz where n is the number of vertices. h = mfTetSliceXYZ(...)

• Handle h retrieves a handle to the volumetric slice object created by mfTetSliceXYZ(...).


You can specify properties of the volumetric slice objects through handle h with procedure msGSet. The properties available are: 1. tet 2. slicex: specifies the slice-planes along the x direction. 3. slicey: specifies the slice-planes along the y direction. 4. slicez: specifies the slice-planes along the z direction. Example Code pr ogram example


type(mfArray) :: nx, ny, nz, x, y, z, c, tet type(mfArray) :: stri,sx,sy,sz,sc nx = mfLinspace(-2, 2.2d0, 21) ny = mfLinspace(-2, 2.25d0, 17) nz = mfLinspace(-1.5d0, 1.6d0, 31) call msMeshgrid(mfout(y, x, z), ny, nx, nz)


c = 2*mfCos(x**2)*mfExp(-(y**2)-(z**2))

te t = mfGetDelaunay3(x, y, z);

call msTetSliceXYZ(tet, x, y, z, c, mf((/-1.0d0, 1.0d0/)), & mf(0), mf())

call msHold('on') call msGetTetSliceXYZ(mfOut(stri,sx,sy,sz,sc), & tet, x, y, z, c, mf(),mf(),mf(-.75d0)) call msTriContour(stri,sx,sy,sz,sc) ca ll msHold('off')

ca ll msViewPause()

call msFreeArgs(nx, ny, nz, x, y, z, c) ca ll msFreeArgs(stri,sx,sy,sz,sc)


Result

See Also mfTetSlicePlane, mfTetIsoSurface, msGetTetSliceXYZ


mfTetSlicePlane, msTetSlicePlane Display orthogonal slice-planes along an arbitrary direction.

Module fgl

Syntax handle = mfTetSlicePlane(tet, x, y, z, c, plane) handle = mfTetSlicePlane(tet, xyz, c, plane) call msTetSlicePlane(tet, x, y, z, c, plane) call msTetSlicePlane(tet, xyz, c, plane) Descriptions Procedure mfTetSlicePlane displays orthogonal slice-planes of a specified set of polyhedral data along arbitrary direction. The information on the slice-planes can be retrieved by using procedure mfGetTetSlicePlane. call msTetSlicePlane(tet, x, y, z, c, plane)


12

4

6

35

Wedge (k=6)

1

23

4

Tetrahedron (k=4)

2

34

5

1Pyramid (k=5)

12

345

6

78

Hexahedron (k=8)


• Displays orthogonal slice-planes along the direction specified by plane. • The arguments x,y and z are structured grid data which define the corresponding

coordinates of scalar values specified in argument c, where c is a m-by-n-by-p



• The arguments x,y and z must be of the same shape as c and are monotonic and three-dimensional plaid as if produced by procedure mfMeshgrid.

• The color at each point is determined by three-dimensional interpolation into the elements of volume c, mapped to the current colormap.

call msTetSlicePlane(tet, xyz, c, plane)

• Vertex vectors are defined in the n-by-3 matrix xyz where n is the number of vertices. h = mfTetSlicePlane(...)

• Handle h retrieves a handle to the volumetric slice objects created by mfTetSlicePlane(...).


You can specify properties of the volumetric slice objects through handle h with procedure msGSet. The properties available are: 1. tet 2. plane Example Code pr ogram Example_msTetSlicePlane


type(mfArray) :: nx, ny, nz, x, y, z, c, tet ty pe(mfArray) :: stri,sx,sy,sz,sc



call msTetSlicePlane(tet, x, y, z, c, mf((/1, 0, -1, 0/))) call msHold('on') call msGetTetSlicePlane(mfOut(stri,sx,sy,sz,sc), &


tet, x, y, z, c, mf((/1, 1, 0, 0/))) call msTriContour(stri,sx,sy,sz,sc) call msHold('off') ca ll msViewPause()

call msFreeArgs(nx, ny, nz, x, y, z, c, tet) e nd program Example_msTetSlicePlane

Result

See Also mfSlicePlane, mfGetSlicePlane, mfGetTetSlicePlane


msGetTetIsoSurface Retrieve three-dimensional iso-value surface plots from polyhedral data.

Module fgl

Syntax call msGetTetIsoSurface(mfOut(tri,x,y,z,c),tet, xyz, c, iso) call msGetTetIsoSurface(mfOut(tri,xyz,c),tet, x, y, z, c, iso) Descriptions Procedure mfGetTetIsoSurface retrieves 3-D graphs composed of isosurface data from the data c. It returns the triangular mesh tri and the vertex vectors of isosurface defined in the n-by-3 matrix xyz. For details on the input arguments, please refer to the description of procedure mfTetIsoSurface. Example To be referred to mfTetIsoSurface See Also mfTetIsoSurface


msGetTetSliceXYZ Retrieve orthogonal slice-planes through polyhedral data.

Module fgl

Syntax call msGetTetSliceXYZ(mfOut(tri,x,y,z,c), tet, x, y, z, c, Sx, Sy, Sz) Descriptions Procedure mfGetTetSliceXYZ retrieves orthogonal slice-planes of a specified set of polyhedral data. It returns the triangular mesh tri and the vertex vectors of the sliced-planes defined in the n-by-3 matrix xyz. For details on the input arguments, refer to the description of procedure mfTetSliceXYZ. Example To be referred to mfTetSliceXYZ See Also mfTetSliceXYZ


msGetTetSlicePlane Retrieve orthogonal slice-planes along an arbitrary direction.

Module fgl

Syntax call msGetTetSlicePlane(mfOut(tri,x,y,z,c), tet, x, y, z, c, planes) Descriptions Procedure mfGetTetSlicePlane retrieves orthogonal slice-planes of a specified set of polyhedral data along an arbitrary direction. It returns the triangular mesh tri and the vertex vectors of the sliced-planes defined in the n-by-3 matrix xyz. call msGetTetSlicePlane(mfOut(tri,x,y,z,c), x, y, z, c, planes)


• The arguments x, y and z are structured grid data which define the corresponding coordinates of scalar values specified in argument c, where c is an m-by-n-by-p




For details on the input arguments, refer to the description of procedure mfTetSlicePlane. Example To be referred to mfTetSlicePlane See Also mfTetSlicePlane


Unstructured Streamlines


mfTriStreamLine, msTriStreamLine Create streamlines from two-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTriStreamline(tri, x, y, u, v, Sx, Sy) handle = mfTriStreamline(tri, xy, uv, Sxy) call msTriStreamline(tri, x, y, u, v, Sx, Sy) call msTriStreamline(tri, xy, uv, Sxy) Descriptions Procedure mfTriStreamLine creates streamlines from two-dimensional unstructured mesh data. handel = mfTriStreamLine(tri, x, y, u, v, Sx, Sy)

• Argument tri is an m-by-n face matrix, where m is the number of polygons and n is the number of edges on each polygon. For example; a 4-by-3 face matrix tri draws a streamline object of 4 triangles, while a 3-by-4 face matrix tri draws a streamline object

of 3 quadrilaterals.

• Arguments x and y are n-by-1 vectors contain the x- and y- coordinates of the respective points.

• Arguments u and w are two-dimensional orthogonal vector components corresponding to the x- and y- directions respectively.

• Arguments Sx and Sy are vectors defining starting positions of the streamlines. handel = mfTriStreamLine(tri, xy, uv, Sxy)

• Argument xy and uv are both defined in the n-by-2 matrix where n is the number of vertices.

• Argument Sxy is an s-by-2 matrix where s is the number of streamlines. You can also specify properties of the streamline objects through handle h with procedure msGSet. The properties available are: 1. start: an s-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the streamlines. 3. steplength: step length of the streamlines. By default, sizefactor=1 and steplength=0.5.


Example Code program Example use fml use fgl implicit none type(mfArray) :: h, tri, tet, x, y, z, u, v, w, sx, sy, sz x = mfRand( 500, 1 ) * 4 - 2 y = mfRand( 500, 1 ) * 4 - 2 z = mfZeros( 500, 1 )

u = mfSin( 2 * x * y ) v = mfCos( 2 * x - y ) w = z


tri = mfGetDelaunay( x, y )

call msSubplot(2,2,1) call msTitle("Tri Stream Line") call msColormapRange(-2d0,2d0) h = mfTriStreamLine(tri, x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.2d0 )

call msSubplot(2,2,2) call msTitle("Tri Stream Dashed Line") call msColormapRange(-2d0,2d0) h = mfTriStreamDashedLine(tri, x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.2d0 ) call msDrawMaterial(h,mf('surf'),mf('colormap'), & mf('off'),mf('color'),mf((/0,0,0/)))

call msSubplot(2,2,3) call msTitle("Tri Stream Ribbon") call msColormapRange(-2d0,2d0) h = mfTriStreamRibbon(tri, x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.2d0 )

call msGSet( h, "sizefactor", 0.01d0 )

call msSubplot(2,2,4) call msTitle("Tri Stream Tube") call msQuiver( x, y, u, v, mf(0.15) ) call msHold("on")

h = mfTriMesh( tri, x, y, z ) call msDrawMaterial( h, "edge", "trans", 90d0 ) call msDrawMaterial( h, "surf", "visible", "off")

h = mfTriStreamTube( tri, x, y, u, v, sx, sy ) call msGSet( h, "steplength", 0.2d0 ) call msGSet( h, "sizefactor", 0.003d0 ) call msAxis("2") call msColormapRange( -2, 2 )

call msViewPause() call msFreeArgs(h, tri, tet, x, y, z, u, v, w, sx, sy, sz) e nd program Example

Result


See Also mfTriMesh, mfTriStreamDashLine, mfTriStreamRibbon, mfTriStreamTube, mfTriStreamArrow


mfTriStreamDashLine, msTriStreamDashLine Create stream dashed-lines from two-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTriStreamDashLine(tri, x, y, u, v, Sx, Sy) handle = mfTriStreamDashLine(tri, xy, uv, Sxy) call msTriStreamline(tri, x, y, u, v, Sx, Sy) call msTriStreamline(tri, xy, uv, Sxy) Descriptions Procedure mfTriStreamDashLine creates stream dashed-lines from two-dimensional unstructured mesh data. handel = mfTriStreamDashLine(tri, x, y, u, v, Sx, Sy)

• Argument tri is an m-by-n face matrix, where m is the number of polygons and n is the number of edges on each polygon. For example; a 4-by-3 face matrix tri draws a stream dashed-line object of 4 triangles, while a 3-by-4 face matrix tri draws a stream

dashed-line object of 3 quadrilaterals.



• Arguments Sx and Sy are vectors defining starting positions of the stream dashed-lines. handel = mfTriStreamDashLine(tri, xy, uv, Sxy)


• Argument Sxy is an s-by-2 matrix where s is the number of stream dashed-lines. You can also specify properties of the streamline objects through handle h with procedure msGSet. The properties available are: 1. start: an s-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream dashed-lines. 3. steplength: step length of the stream dashed-lines. By default, sizefactor=1 and steplength=0.5.


Example To be referred to mfTriStreamLine See Also mfTriMesh, mfTriStreamLine, mfTriStreamRibbon, mfTriStreamTube, mfTriStreamArrow


mfTriStreamRibbon, msTriStreamRibbon Create stream ribbons from two-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTriStreamRibbon(tri, x, y, u, v, Sx, Sy) handle = mfTriStreamRibbon(tri, xy, uv, Sxy) call msTriStreamRibbon(tri, x, y, u, v, Sx, Sy) call msTriStreamRibbon(tri, xy, uv, Sxy) Descriptions Procedure mfTriStreamRibbon creates stream ribbons from two-dimensional unstructured mesh data. handel = mfTriStreamRibbon(tri, x, y, u, v, Sx, Sy)

• Argument tri is an m-by-n face matrix, where m is the number of polygons and n is the number of edges on each polygon. For example; a 4-by-3 face matrix tri draws a stream ribbon object of 4 triangles, while a 3-by-4 face matrix tri draws a stream ribbon object




• Arguments Sx and Sy are vectors defining starting positions of the stream ribbons. handel = mfTriStreamRibbon(tri, xy, uv, Sxy)


• Argument Sxy is an s-by-2 matrix where s is the number of stream ribbons. You can also specify properties of the streamline objects through handle h with procedure msGSet. The properties available are: 1. start: an s-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream ribbons. 3. steplength: step length of the stream ribbons. By default, sizefactor=1 and steplength=0.5.


Example To be referred to mfTriStreamLine

See Also mfTriMesh, mfTriStreamDashLine, mfTriStreamLine, mfTriStreamTube, mfTriStreamArrow


mfTriStreamTube, msTriStreamTube Create stream tubes from two-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTriStreamTube(tri, x, y, u, v, Sx, Sy) handle = mfTriStreamTube(tri, xy, uv, Sxy) call msTriStreamTube(tri, x, y, u, v, Sx, Sy) call msTriStreamTube(tri, xy, uv, Sxy) Descriptions Procedure mfTriStreamTube creates stream tubes from two-dimensional unstructured mesh data. handel = mfTriStreamTube(tri, x, y, u, v, Sx, Sy)

• Argument tri is an m-by-n face matrix, where m is the number of polygons and n is the number of edges on each polygon. For example; a 4-by-3 face matrix tri draws a stream tube object of 4 triangles, while a 3-by-4 face matrix tri draws a stream tube object of 3

quadrilaterals.



• Arguments Sx and Sy are vectors defining starting positions of the stream tubes. handel = mfTriStreamTube(tri, xy, uv, Sxy)


• Argument Sxy is an s-by-2 matrix where s is the number of stream tubes. You can also specify properties of the streamline objects through handle h with procedure msGSet. The properties available are: 1. start: an s-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream tubes. 3. steplength: step length of the stream tubes. By default, sizefactor=1 and steplength=0.5.


Example To be referred to mfTriStreamLine See Also mfTriMesh, mfTriStreamDashLine, mfTriStreamRibbon, mfTriStreamLine, mfTriStreamArrow


mfTriStreamArrow, msTriStreamArrow Create stream arrows from two-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTriStreamArrow(tri, x, y, u, v, Sx, Sy) handle = mfTriStreamArrow(tri, xy, uv, Sxy) call msTriStreamArrow(tri, x, y, u, v, Sx, Sy) call msTriStreamArrow(tri, xy, uv, Sxy) Descriptions Procedure mfTriStreamArrow creates stream arrows from two-dimensional unstructured mesh data. handel = mfTriStreamArrow(tri, x, y, u, v, Sx, Sy)

• Argument tri is an m-by-n face matrix, where m is the number of polygons and n is the number of edges on each polygon. For example; a 4-by-3 face matrix tri draws a stream arrow object of 4 triangles, while a 3-by-4 face matrix tri draws a stream arrow object




• Arguments Sx and Sy are vectors defining starting positions of the stream arrows. handel = mfTriStreamArrow(tri, xy, uv, Sxy)


• Argument Sxy is an s-by-2 matrix where s is the number of stream arrows. You can also specify properties of the streamline objects through handle h with procedure msGSet. The properties available are: 1. start: an s-by-2 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream arrows. 3. steplength: step length of the stream arrows. By default, sizefactor=1 and steplength=0.5.


Example Code program Example use fml use fgl implicit none type(mfArray) :: h, tri, x, y, z, u, v, w, sx, sy, sz

x = mfRand( 500, 1 ) * 4 - 2 y = mfRand( 500, 1 ) * 4 - 2 z = mfZeros( 500, 1 )

u = mfSin( 2 * x * y ) v = mfCos( 2 * x - y ) w = z


tri = mfGetDelaunay( x, y ) call msTitle("Tri Stream Arrow")

call msColormapRange(-2, 2)

h = mfTriStreamArrow(tri, x, y, u, v, sx, sy) call msGSet( h, "arrowsize", 0.15d0 )


call msHold("on")

h = mfTriMesh( tri, x, y, z ) call msDrawMaterial( h, mf("edge"), mf("colormap"), mf("off"), & mf("color"), mf((/0.8,0.8,0.8/)) ) call msDrawMaterial( h, "surf", "visible", "off")

h = mfTriStreamTube(tri, x, y, u, v, sx, sy) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0 )


call msAxis("2")

call msViewPause() call msFreeArgs(h, tri, x, y, z, u, v, w, sx, sy, sz) e nd program Example

Result


See Also mfTriMesh, mfTriStreamDashLine, mfTriStreamRibbon, mfTriStreamTube, mfTriStreamLine


mfTetStreamLine, msTetStreamLine Create streamlines from three-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTetStreamline(tet, x,y,z, u,v,w, Sx,Sy,Sz) handle = mfTetStreamline(tet, xyz, uvw, Sxyz) call msTetStreamline(tet, x,y,z, u,v,w, Sx,Sy,Sz) call msTetStreamline(tet, xyz, uvw, Sxyz) Descriptions Procedure mfTetStreamLine creates streamlines from three-dimensional unstructured mesh data. handel = mfTetStreamLine(tet, x, y, z, u, v, w, Sx, Sy, Sz)

• Argument tet is an m-by-k cell matrix, where m is the number of polyhedrons and k is the number of vertices on each polyhedron.

• Arguments x, y and z are n-by-1 vectors contain the x-, y-, and z- coordinates of the respective unstructured grid points.

• Arguments u, v and w are three-dimensional orthogonal vector components corresponding to x, y and z.

• Arguments Sx, Sy and Sz are vectors defining starting positions of the streamlines. handel = mfTetStreamLine(tet, xyz, uvw, Sxyz)

• Argument xyz and uvw are both defined in the n-by-3 matrix where n is the number of vertices.

• Argument Sxyz is an s-by-3 matrix where s is the number of streamlines. You can also specify properties of the streamlines through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the streamlines. 3. steplength: step length of the streamlines. By default, sizefactor=1 and steplength=0.5. Example


Code program Example use fml use fgl implicit none type(mfArray) :: h, tet, x, y, z, u, v, w, sx, sy, sz

x = mfRand( 4000, 1 ) * 4 - 2 y = mfRand( 4000, 1 ) * 4 - 2 z = mfRand( 4000, 1 ) * 4 - 2



tet = mfGetDelaunay3( x, y, z )

call msSubplot(2,2,1) call msTitle("Tet Stream Line") call msColormapRange(-2d0,2d0) h = mfTetStreamLine(tet, x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.2d0 )

call msSubplot(2,2,2) call msTitle("Tet Stream Dashed Line") call msColormapRange(-2d0,2d0) h = mfTetStreamDashedLine(tet, x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.2d0 ) call msDrawMaterial(h,mf('surf'),mf('colormap'), & mf('off'),mf('color'),mf((/0,0,0/)))

call msSubplot(2,2,3) call msTitle("Tet Stream Ribbon") call msColormapRange(-2d0,2d0) h = mfTetStreamRibbon(tet, x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.2d0 )

call msGSet( h, "sizefactor", 0.01d0 )

call msSubplot(2,2,4) call msTitle("Tet Stream Tube") h = mfTetSurf( tet, x, y, z ) call msDrawMaterial( h, "both", "trans", 90d0 ) call msHold("on")

h = mfTetStreamTube( tet, x, y, z, u, v, w, sx, sy, sz ) call msGSet( h, "steplength", 0.1d0 ) call msGSet( h, "sizefactor", 0.005d0 ) call msColormapRange( -2, 2 )

call msViewPause() call msFreeArgs(h, tet, x, y, z, u, v, w, sx, sy, sz) e nd program Example

Result


See Also mfTetMesh, mfTetStreamDashLine, mfTetStreamRibbon, mfTetStreamTube, mfTetStreamArrow


mfTetStreamDashLine, msTetStreamDashLine Create stream dashed-lines from three-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTetStreamDashline(tet, x,y,z, u,v,w, Sx,Sy,Sz) handle = mfTetStreamDashline(tet, xyz, uvw, Sxyz) call msTetStreamDashline(tet, x,y,z, u,v,w, Sx,Sy,Sz) call msTetStreamDashline(tet, xyz, uvw, Sxyz) Descriptions Procedure mfTetStreamDashline creates stream dashed-lines from three-dimensional unstructured mesh data. handel = mfTetStreamDashline(tet, x, y, z, u, v, w, Sx, Sy, Sz)




• Arguments Sx, Sy and Sz are vectors defining starting positions of the stream dashed-lines.

handel = mfTetStreamDashline(tet, xyz, uvw, Sxyz)


• Argument Sxyz is an s-by-3 matrix where s is the number of stream dashed-lines. You can also specify properties of the stream dashed-lines through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream dashed-lines. 3. steplength: step length of the stream dashed-lines. By default, sizefactor=1 and steplength=0.5.


Example To be referred to mfTetStreamLine See Also mfTetMesh, mfTetStreamLine, mfTetStreamRibbon, mfTetStreamTube, mfTetStreamArrow


mfTetStreamRibbon, msTetStreamRibbon Create stream ribbons from three-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTetStreamRibbon(tet, x,y,z, u,v,w, Sx,Sy,Sz) handle = mfTetStreamRibbon(tet, xyz, uvw, Sxyz) call msTetStreamRibbon(tet, x,y,z, u,v,w, Sx,Sy,Sz) call msTetStreamRibbon(tet, xyz, uvw, Sxyz) Descriptions Procedure mfTetStreamRibbon creates stream ribbons from three-dimensional unstructured mesh data. handel = mfTetStreamRibbon(tet, x, y, z, u, v, w, Sx, Sy, Sz)




• Arguments Sx, Sy and Sz are vectors defining starting positions of the stream ribbons. handel = mfTetStreamRibbon(tet, xyz, uvw, Sxyz)


• Argument Sxyz is an s-by-3 matrix where s is the number of stream ribbons. You can also specify properties of the stream ribbons through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream ribbons. 3. steplength: step length of the stream ribbons. By default, sizefactor=1 and steplength=0.5. Example


To be referred to mfTetStreamLine See Also mfTetMesh, mfTetStreamDashLine, mfTetStreamLine, mfTetStreamTube, mfTetStreamArrow


mfTetStreamTube, msTetStreamTube Create stream tubes from three-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTetStreamTube(tet, x,y,z, u,v,w, Sx,Sy,Sz) handle = mfTetStreamTube(tet, xyz, uvw, Sxyz) call msTetStreamTube(tet, x,y,z, u,v,w, Sx,Sy,Sz) call msTetStreamTube(tet, xyz, uvw, Sxyz) Descriptions Procedure mfTetStreamTube creates stream tubes from three-dimensional unstructured mesh data. handel = mfTetStreamTube(tet, x, y, z, u, v, w, Sx, Sy, Sz)




• Arguments Sx, Sy and Sz are vectors defining starting positions of the stream tubes. handel = mfTetStreamTube(tet, xyz, uvw, Sxyz)


• Argument Sxyz is an s-by-3 matrix where s is the number of stream tubes. You can also specify properties of the stream tubes through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream tubes. 3. steplength: step length of the stream tubes. By default, sizefactor=1 and steplength=0.5. Example


To be referred to mfTetStreamLine See Also mfTetMesh, mfTetStreamDashLine, mfTetStreamRibbon, mfTetStreamLine, mfTetStreamArrow


mfTetStreamArrow, msTetStreamArrow Create stream arrows from three-dimensional unstructured mesh data.

Module fgl

Syntax handle = mfTetStreamArrow(tet, x,y,z, u,v,w, Sx,Sy,Sz) handle = mfTetStreamArrow(tet, xyz, uvw, Sxyz) call msTetStreamArrow(tet, x,y,z, u,v,w, Sx,Sy,Sz) call msTetStreamArrow(tet, xyz, uvw, Sxyz) Descriptions Procedure mfTetStreamArrow creates stream arrows from three-dimensional unstructured mesh data. handel = mfTetStreamArrow(tet, x, y, z, u, v, w, Sx, Sy, Sz)




• Arguments Sx, Sy and Sz are vectors defining starting positions of the stream arrows. handel = mfTetStreamArrow(tet, xyz, uvw, Sxyz)


• Argument Sxyz is an s-by-3 matrix where s is the number of stream arrows. You can also specify properties of the stream arrows through handle h with procedure msGSet. The properties available are: 1. start: an n-by-3 matrix containing starting points coordinates. 2. sizefactor: thickness of the stream arrows. 3. steplength: step length of the stream arrows. By default, sizefactor=1 and steplength=0.5. Example


Code program Example use fml use fgl implicit none type(mfArray) :: h, tet, x, y, z, u, v, w, sx, sy, sz

x = mfRand( 4000, 1 ) * 4 - 2 y = mfRand( 4000, 1 ) * 4 - 2 z = mfRand( 4000, 1 ) * 4 - 2



tet = mfGetDelaunay3( x, y, z )

call msTitle("Tet Stream Arrow")

call msColormapRange(-2,2)

h = mfTetStreamArrow(tet, x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "arrowsize", 0.15d0 )


call msHold("on")

h = mfTetMesh( tet, x, y, z ) call msDrawMaterial( h, mf("edge"), mf("colormap"), mf("off"), & mf("color"), mf((/0.8,0.8,0.8/)) )

call msDrawMaterial( h, "surf", "visible", "off")

h = mfTetStreamTube(tet, x, y, z, u, v, w, sx, sy, sz) call msGSet( h, "steplength", 0.25d0 ) call msGSet( h, "sizefactor", 0.01d0 )


call msViewPause() call msFreeArgs(h, tet, x, y, z, u, v, w, sx, sy, sz) e nd program Example

Result


See Also mfTetMesh, mfTetStreamDashLine, mfTetStreamRibbon, mfTetStreamTube, mfTetStreamLine


Unstructured Point Set


mfPoint, msPoint Display input points in three-dimensional space.

Module fgl

Syntax handle = mfPoint(x, y, z[, c]) handle = mfPoint(xyz[, c]) call msPoint(x, y, z[, c]) call msPoint(xyz[, c]) Descriptions Procedure mfPoint plots a set of input points in three-dimensional space. call msPoint(x, y, z) call msPoint(x, y, z, c)

• Arguments x, y and z contain the x-, y-, and z- coordinates of the respective points. They can be either matrices or vectors of the same shape.

• By default, the scalar value of each point is the height specified in argument z. Specifying the scalar vector c overrides the default scalar values.

call msPoint(xyz) call msPoint(xyz, c)

• Vertex vectors are defined in the n-by-3 matrix xyz. h = mfPoint(...)

• Handle h retrieves a handle to the points created by mfPoint(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the points through handle h with procedure msGSet. The property available is: 1. xyz 2. point_size Example Code program Example


use fml use fgl implicit none type(mfArray) :: x, y, xy, z, xyz

integer nPoint,i,j

nPoint = 2000

! Specify locations of three balls x = mfRand(nPoint,1) * MF_PI * 2 - MF_PI y = mfRand(nPoint,1) * MF_PI * 2 - MF_PI xy = x + y z = mfSin(x) * mfCos(y) - mfSin(xy)

xyz = x.hc.y.hc.z

call msPoint(xyz)

! Pause program to view

call msViewPause()

call msFreeArgs(x, y, xy, z, xyz) end program Example

Result

See Also


mfDelaunay, msDelaunay, mfGetDelaunay, msGetDelaunay 2-D Delaunay triangulation of input points.

Module fgl

Syntax h = mfDelaunay(x, y[, bx1, bx2, ...]) tri = mfGetDelaunay(x, y[, p1, p2, ...]) call msGetDelaunay(mfOut(tri), x, y[, p1, p2, ...]) Descriptions Procedure mfDelaunay is a filter that constructs a two-dimensional Delaunay triangulation from a set of input points. You may use procedure mfGetDelaunay to retrieve the triangular mesh output of the filter. h = mfDelaunay(x, y, bx1, by1, bx2, by2, bx3, by3)

• Arguments x and y specify the x- and y- coordinates of the input points.

• You may define the boundaries which the Delaunay triangulation is constructed upon. Each boundary is defined by two vertex vectors specified in the arguments. For instance, arguments bx1 and by1 define the first boundary, arguments bx2 and by2 define the

second boundary and so on.

• Notice that the order of the boundary points determines how the Delaunay triangulation is constructed. If the boundary points are specified counterclockwise, then the Delaunay triangulation is constructed within the boundary; if the boundary points are specified clockwise, then the Delaunay triangulation is constructed beyond the boundary. On the other hand, an unexpected result may arise if a false order of boundary points is given.

tri = mfGetDelaunay(x, y, bx1, by1, bx2, by2, bx3, by3) call msGetDelaunay(mfOut(tri), x, y, bx1, by1, bx2, by2, bx3, by3)


h = mfDelaunay(...)

• Handle h retrieves a handle to the polygonal surface object created by mfDelaunay(...).



You can specify properties of the polygonal surface object through handle h with procedure msGSet. Example Code pr ogram example


type (mfArray) :: x, y, n, h type (mfArray) :: bx1, by1, bx2, by2, bx3, by3 integer :: i re al(8) :: rx, ry

bx1 = .t. (/ -5, 5, 5, 1, 1, -1, -1, -5/) by1 = .t. (/ -5, -5, 5, 5, 2, 2, 5, 5/) bx2 = .t. (/ -3, -3, -1 /) by2 = .t. (/ -3, -1, -3 /) n = .t. mfLinspace(0, -1.9*MF_PI, 10) bx3 = 2.5d0 + mfCos(n) by3 = mfSin(n) x = mfZeros(30,1) y = mfZeros(30,1) call random_seed() do i=1,30 do while (.true.) call random_number(rx) call random_number(ry) rx= rx*10 - 5 ry= ry*10 - 5 if ( (rx<5 .or. rx>-5 ) .and. (ry<5 .or. ry>-5) .and. (rx<-1 .or. rx>1 .or. ry<2) & .and. (rx<-3 .or. ry<-3 .or. rx + ry > -2) .and. ( (rx-2.5d0)**2 + ry**2 > 1) ) then exit end if

end do

call msAssign(mfS(x,i,1), rx) call msAssign(mfS(y,i,1), ry) en d do

call msFigure('Delaunay'); call msSubplot(1, 2, 1) call msTitle('Delaunay') h = mfDelaunay(x, y) ca ll msAxis('equal')

call msSubplot(1, 2, 2) call msTitle('Constrained Delaunay') h = mfDelaunay(x, y, bx1, by1, bx2, by2, bx3, by3) call msHold('on') h = mfPlot(bx1, by1, "or", bx2, by2, "or", x, y, "xb") ca ll msAxis('equal')

call msViewPause() ca ll msFreeArgs(x, y, n, h, bx1, by1, bx2, by2, bx3, by3)


Result


See Also


mfDelaunay3, msDelaunay3, mfGetDelaunay3,

msGetDelaunay3 3-D Delaunay triangulation of input points.

Module fgl

Syntax h = mfDelaunay3(x, y, z) h = mfDelaunay3(xyz) tet = mfGetDelaunay3(x, y, z) tet = mfGetDelaunay3(xyz) call msGetDelaunay3(mfOut(tet), x, y, z) Descriptions Procedure mfDelaunay3 is a filter that constructs a three-dimensional Delaunay triangulation from a set of input points. You may use procedure to retrieve the tetrahedral mesh output of the filter. h = mfDelaunay3(x, y, z) tet = mfGetDelaunay3(x, y, z)

• Arguments x,y and z specify the x-, y- and z- coordinates of the input points. h = mfDelaunay3(xyz) tet = mfGetDelaunay3(xyz)

• Vertex vectors xyz are defined in the n-by-3 matrix. tet = mfGetDelaunay3(xyz)

• Retrieve the tetrahedral mesh tet. With tet and the coordinates xyz, you may use mfTetSurf to plot the tetrahedral surface.

h = mfDelaunay3(...)

• Handle h retrieves a handle to the polyhedral object created by mfDelaunay3(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the polyhedral object through handle h with procedure msGSet.


Example Code Pr ogram example


ty pe(mfArray) :: xyz, h

xy z = mfRand(30, 3)

call msFigure('Delaunay 3D') call msTitle('Delaunay 3D') h = mfDelaunay3( xyz ) call msDrawMaterial(h, 'surf', 'trans', 50) call msDrawMaterial(h,'edge','line_style','dashed') call msHold('on') !h = mfSphere( xyz, mf(0.02), mf((/0, 0, 1/)) ) ca ll msViewPause()

ca ll msFreeArgs(xyz, h)

e nd Program example

Result

See Also


Velocity Vectors


mfQuiver, msQuiver Plot two-dimensional velocity vectors.

Module fgl

Syntax handle = mfQuiver(x, y, u, v[, scale]) handle = mfQuiver(u, v[, scale]) Descriptions Procedure mfQuiver plots velocity vectors as arrows with components (u, v) at the points (x, y). handle = mfQuiver(x, y, u, v) handle = mfQuiver(x, y, u, v, scale)

• mfArrays x and y contain positions of the velocity vectors, while the mfArrays u and v contain the corresponding velocity components.

• You can control the vector scaling by specifying argument scale. Specifying scale as 0.5 would reduce the relative length of the vector by half.

• The shapes of the four mfArrays x,y,u and v must conform, i.e. all are m-by-n mfArrays.

handle = mfQuiver(u, v) handle = mfQuiver(u, v, scale)

• Velocity vectors are plotted over a geometrically rectangular grid where x = mfColon(1, n) and y = mfColon(1, m).

h = mfQuiver(...)

• Handle h retrieves a handle to the quiver object created by mfQuiver(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the quiver object through handle h with procedure msGSet. Example Code pr ogram example

use fml use fgl


im plicit none

ty pe(mfArray) :: u, v, x, y, a

a = mfLinspace(1, 10, 8) call msMeshgrid(mfout(x, y), a) u = 4*mfCos(y) v = 4*mfOnes(8, 8)

call msQuiver(x, y, u, v, mf(0.2)) call msAxis('equal') call msCamZoom(0.8d0) ca ll msViewPause()

ca ll msFreeArgs(u, v, x, y, a)


Result

See Also mfQuiver3


mfQuiver3, msQuiver3 Plot three-dimensional velocity vectors.

Module fgl

Syntax handle = mfQuiver3(x, y, z, u, v, w[, scale]) handle = mfQuiver3(z, u, v, w[, scale]) Descriptions Procedure mfQuiver3 plots velocity vectors as arrows with components (u, v, w) at the points (x, y, z)in three-dimensional space. handle = mfQuiver3(x, y, z, u, v, w) handle = mfQuiver3(x, y, z, u, v, w, scale)

• mfArrays x, y and z contain corresponding positions of velocity vectors, which are specified by mfArrays u, v and w corresponding to the three-dimensional orthogonal

velocity components.

• You can control the vector scaling by specifying argument scale. Specifying scale as 0.5 would reduce the relative length of the vector by half. By default, scale = 0.

• The shapes of the four mfArrays x, y, u and v must be conformed, i.e. All are m-by-n mfArrays.

call msQuiver3(z, u, v, w) call msQuiver3(z, u, v, w, scale)

• mfArray z, u, v, w are assumed to be defined over a geometrically rectangular grid [x,y], where x = mfColon(1, n) and y = mfColon(1, m).

h = mfQuiver3(...)

• Handle h retrieves a handle to the velocity vector objects created by mfQuiver3(...).


You can specify properties of the velocity vector objects through handle h with procedure msGSet. The property available is: 1. symbol: "arrow", "cone" or "flat_arrow"


Example Code program Example_mfQuiver3 use fml use fgl implicit none type(mfArray) :: a, b, c, x, y, z, v, u, w, h1, h2, t,p

a = mfLinspace(-2, 1.6d0, 4) b = mfLinspace(-2, 1, 3) c = mfLinspace(-2, 1.84d0, 5) call msMeshgrid(mfout(x, y, z), a, b, c) u = mfOnes(3, 4, 5) v = 0.4d0*(z**2) w = mfExp(0.5d0*x)

call msFigure('Quiver3') h1=mfQuiver3(x, y, z, u, v, w) ! Let vector color as colomap call msDrawMaterial(h1, mf('edge'), mf('colormap'), mf('on')) call msColormapRange(0, 3) call msColorbar('on') call msView(-30, 50)

call msFigure('Quiver Surf') call msMeshgrid(mfout(t,p), a, b) t = mfCos(t) call msMesh(t) call msHold('on') h2 = mfQuiver3(t, mfS(u,MF_COL,MF_COL,5), & mfS(v,MF_COL,MF_COL,5), mfS(w,MF_COL,MF_COL,5)) call msDrawMaterial(h2, mf('edge'), mf('colormap'), mf('on')) call msColormapRange(0, 3) call msColorbar('on') call msView(-30, 50)

call msViewPause() call msFreeArgs(a, b, c, x, y, z, v, u, w, h1, h2, t, p) e nd program Example_mfQuiver3

Result


See Also mfQuiver


Image


mfImage, msImage Displays image files.

Module fgl

Syntax handle = mfImage(img [, pos]) handle = mfImage(filename [, pos]) Descriptions Procedure mfImage displays an image file in the plot space. handle = mfImage(img [, pos])

• Argument img is an m-by-n-by-3 matrix containing the image pixel and the rgb color codes. Use m-by-n matrix for gray scale image.

• img can be saved into mfArray format using Procedure mfLoad.

• Argument pos is a 4 by 3 or a 4 by 2 (with z value equals to 0) matrix specifying the location of the image. By default, the pos value is [0,0,0; w,0,0; 0,h,0; w,h,0] where w

and h are the width and height of the input image respectively. handle = mfImage(filename [, pos])

• Argument filename is the name of the image file. You can specify properties of the image objects through handle h with procedure msGSet. The properties available are: 1. position 2. filename 3. cdata Example Code pr ogram example


type(mfArray) :: ax, h, bx, pos in teger i

call msSubplot(1,2,1) ax = mfImRead('ancad.bmp') h = mfImage(ax) call msAssign(bx,mfS(ax, 320.to.350, 25.to.200, MF_COL) )


ca ll msAxis("equal")

call msSubplot(1,2,2) call msImWrite('test.bmp',bx) pos = mf((/15,0,-10/)).vc.mf((/185,0,-10/)).vc.mf((/0,60,10/)).vc.mf((/200,60,0/)) h = mfImage(mfImRead('test.bmp'),pos) ca ll msView("3")

!Pauses the program to display graph. ca ll msViewPause()

do i=1,5 call msSubplot(1,2,2) call msAssign(mfS(pos,1,1),mfS(pos,1,1)-5*i) call msAssign(mfS(pos,1,2),mfS(pos,1,2)-10*i) call msAssign(mfS(pos,3,2),mfS(pos,3,2)+10*i) call msGSet(h,"position",pos) call msDrawNow() en d do

ca ll msViewPause()

!Deallocate mfArray ca ll msFreeArgs(ax,h,bx,pos)


Result

See Also mfImRead, mfImWrite


mfImRead Read in an image file.

Module fgl

Syntax ax = mfImRead(filename) Descriptions Procedure mfImRead reads in an image file with the name specified by argument filename and stores it in argument ax which is an m-by-n-by-3 matrix storing the rgb color codes. The supported file formats are: bmp, jpeg and png. Example To be referred to mfImage See Also mfImage, mfImWrite


msImWrite Write to an image file.

Module fgl

Syntax call msImWrite(filename, ax) Descriptions Procedure msImWrite writes the rgb color codes stored in the m-by-n-by-3 matrix ax into a file with the name specified by argument filename. The supported file formats are: bmp, jpeg and png. Example To be referred to mfImage See Also


Elementary 2D/3D Objects


mfCircle, msCircle Draw a circle.

Module fgl

Syntax h = mfCircle([loc][, rad][, color][, resolution]) call msCircle([loc][, rad][, color][, resolution]) Descriptions Procedure mfCircle draws a circle with center at loc, radius specified as rad, color specified as color and resolution level specified as resolution. All arguments are optional. call msCircle(loc, rad, color, resolution)

Argument Meaning

loc A 1-by-2 mfArray containing the x- and y- coordinates of the circle center. By default, argument loc is set to [0,0].

rad An mfArray containing a real number specifies the radius of the circle. By default, argument radius is set to 0.5.

color An mfArray containing a string specifies the color, e.g. “y” for yellow, or a 1-by-3 mfArray contains the rgb codes. By

default, argument color is set to white.

resolution An mfArray containing the number of polygons used for modeling the circular object. The higher the polygon number, the smoother a circle appears. The lower the polygon number, the faster a circle is rendered. By default, the circle is set to a resolution = 64.

h = mfCircle(...)

• Handle h retrieves a handle to the circle object created by mfCircle(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the circle object through handle h with procedure msGSet. The properties available are:


1. location 2. radius 3. color 4. resolution Example Code pr ogram example


type(mfArray) :: loc,color,rad ! Center at (10,20), (17.5,20), (32.5,20) lo c = (/10d0, 20d0/).vc.(/17.5d0,20d0/).vc.(/32.5d0,20d0/)

! Color is red, green, blue co lor = (/1,0,0/).vc.(/0,1,0/).vc.(/0,0,1/)

!radius is 2.5, 5, 10 ra d = .t.(/2.5d0,5d0,10d0/)

! resolution = 64 by default ca ll msCircle(loc, rad, color)

ca ll msAxis('equal')


! Deallocate mfArrays call msFreeArgs(loc,color,rad) e nd program example

Result

See Also mfShpere


mfSquare, msSquare Draw a square.

Module fgl

Syntax h = mfSquare([loc][, size][, color]) call msSquare([loc][, size][, color]) Descriptions Procedure mfSquare draws a square with center at loc, size specified as size, and color specified as color. All arguments are optional. call msSquare(loc, size, color)

Argument Meaning

loc A 1-by-2 mfArray contains the x- and y- coordinates of the square center By default, argument loc is set to [0,0].

size A 1-by-2 mfArray specifies the length and width of a square. By default, argument Size is set to [1,1].

color An mfArray containing a string specifies the color, e.g. “y”, or a

1-by-3 mfArray containing the rgb codes. By default, argument color is set to grey.

h = mfSquare(...)

• Handle h retrieves a handle to the square object created by mfSquare(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the square object through handle h with procedure msGSet. The properties available are: 1. location 2. size 3. color




type(mfArray) :: loc, size,color ! Center at (10,20), (17.5,20), (32.5,20) lo c = (/10d0, 20d0/).vc.(/17.5d0,20d0/).vc.(/32.5d0,20d0/)

si ze = .t.(/5d0,10d0,20d0/)

! Color is red, green, blue co lor = (/1,0,0/).vc.(/0,1,0/).vc.(/0,0,1/)

ca ll msSquare(loc, size, color)

ca ll msAxis('equal')


! Deallocate mfArrays ca ll msFreeArgs(loc, size,color)


Result

See Also mfCube


mfMolecule, msMolecule Draw stick-and-ball models of molecules.

Module fgl

Syntax h = mfMolecule(loc, conn[, rad][, color][, stick_rad][, stick_col][, resolution]) call msMolecule(loc, conn[, rad][, color][, stick_rad][, stick_col][, resolution]) Descriptions Procedure mfMolecule enables you to create three-dimensional stick and ball models of molecules. call msMolecule(loc, conn, rad, color, stick_rad, stick_col, resolution)

• Draw n balls specified by argument loc and m sticks specified by argument conn. Argument rad specifies the radius of each ball, argument color specifies the color of each ball, argument stick_rad specifies the cylindrical radius of each stick, argument stick_col specifies the color of the sticks, and argument resolution specifies the

smoothness of the ball objects.

• Argument loc is an n-by-3 array containing the three-dimensional Cartesian coordinates (x, y, z) of each ball center, hence specifying the spatial relationship of each ball. Each ball is numbered according to their respective row index. Thus, row number 1 specifies ball number 1. The first column contains the x-coordinates, the second column contains the y-coordinates, and the third the z-coordinates. For example, the array below specifies three balls whose centers are located at (0,0,0), (1,1,1) and (0,1,0) respectively.

Argument loc:

x y z ball 1 0 0 0 ball 2 1 1 1 ball 3 0 1 0

• Argument conn is an m-by-2 array specifying m number of sticks and the balls

connected by each stick. Each stick connects two balls and is labeled according to its row


number. Columns of the argument conn contain the indices of the balls that each stick

connects. For example, the array below specifies 3 sticks connecting ball 1 and ball 2, ball 3 and ball 1, ball 2 and ball 3.

Argument conn:

ball index ball indexstick 1 1 2 stick 2 3 1 stick 3 2 3

• Argument rad is a scalar specifying the radius of all balls or an n-by-1 array specifying

the radius of each individual ball. By default, all balls are drawn with a radius of 0.5. As an example, the array below specifies three balls of different sizes, with radius 1, 2, and 3 respectively.

Argument rad:

radius ball 1 1 ball 2 2 ball 3 3

• Argument color contains a string specifying the color of all the balls or an n-by-3 array

containing the rgb color code of each ball. The rgb color code is specified as [r, g, b] where 0 < r, g, b < 1. For example, the array below specifies three balls of red, green and blue respectively.

Argument color:

r g b ball 1 0.8 0.1 0.1 ball 2 0.1 0.8 0.1 ball 3 0.1 0.1 0.8

h = mfMolecule(...)

• Handle h retrieves a handle to the molecule objects created by mfMolecule(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the molecule objects through handle h with procedure msGSet.


The properties available are: 1. location 2. connective 3. radius 4. color 5. stick_radius 6. stick_color 7. resolution Example Code pr ogram example


ty pe(mfArray) :: loc, conn, rad, color, stick_rad, stick_col, h

! Specify locations of three balls using vcat loc = reshape((/0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0/), & (/3,3/))

! Specify three sticks and their connections conn = reshape((/1.0, 1.0, 2.0, 2.0, 3.0, 3.0/), & (/3,2/))

! Specify the radius of each ball at radius=0.25,0.35,0.5 ra d = (/0.25, 0.35, 0.5/)

! Set the color of each ball to red, green and blue color = reshape((/0.8, 0.1, 0.1, 0.1, 0.8, 0.1, 0.1, 0.1, 0.8/), & (/3,3/))

! Set the cylindrical radius to 0.1 st ick_rad = 0.1d0

! Set the color of the stick to grey st ick_col = (/0.7, 0.7, 0.7/)

ca ll msAxis(mf((/-0.5d0, 1.6d0, -0.3d0, 1.6d0, -0.5d0, 1.35d0/)))

! Draw the molecules h = mfMolecule(loc, conn, rad, color, stick_rad, stick_col)

! Pause program to view ca ll msViewPause()

! Deallocate mfArrays ca ll msFreeArgs(loc, conn, rad, color, stick_rad, stick_col)


Result


See Also mfSphere


mfFastMolecule, msFastMolecule Draw stick-and-ball models of molecules.

Module fgl

Syntax h = mfFastMolecule(loc, conn[, rad][, color]) call msFastMolecule(loc, conn[, rad][, color]) Descriptions Procedure mfFastMolecule enables you to quickly create three-dimensional stick-and-ball models of molecules. call msFastMolecule(loc, conn, rad, color)

• Draw n balls specified by argument loc and m sticks specified by argument conn. Argument rad specifies the radius of each ball, argument color specifies the color of

each ball.

• Argument loc is an n-by-3 array containing the three-dimensional Cartesian coordinates (x, y, z) of each ball center, hence specifying the spatial relationship of each ball. Each ball is numbered according to their respective row index. Thus, row number 1 specifies ball number 1. The first column contains the x-coordinates, the second column contains the y-coordinates, and the third the z-coordinates. For example, the array below specifies three balls whose center are located at (0,0,0), (1,1,1) and (0,1,0) respectively.

Argument loc:

x y z ball 1 0 0 0 ball 2 1 1 1 ball 3 0 1 0

• Argument conn is an m-by-2 array specifying m number of sticks and the balls

connected by each stick. Each stick connects two balls and is labeled according to its row number. Columns of the argument conn contain the indices of the balls that each stick

connects. For example, the array below specifies 3 sticks connecting ball 1 and ball 2, ball 3 and ball 1, ball 2 and ball 3.

Argument conn:


ball index ball indexstick 1 1 2 stick 2 3 1 stick 3 2 3

• Argument rad is a scalar specifying the radius of all balls or an n-by-1 array specifying

the radius of each individual ball respectively. By default, all balls are drawn with a radius of 0.5. As an example, the array below specifies three balls of different sizes, with radius 1, 2 and 3 respectively.

Argument rad:

radius ball 1 1 ball 2 2 ball 3 3

• Argument color contains a string specifying the color of all the balls or an n-by-3 array

containing the rgb color code of each ball. The rgb color code is specified as [r, g, b] where 0 < r, g, b < 1. For example, the array below specifies three balls of red, green and blue respectively.

Argument color:

r g b ball 1 0.8 0.1 0.1 ball 2 0.1 0.8 0.1 ball 3 0.1 0.1 0.8

h = mfFastMolecule(...)

• Handle h retrieves a handle to the molecule objects created by mfFastMolecule(...).


You can specify properties of the molecule objects through handle h with procedure msGSet. The properties available are: 1. location


2. connective 3. radius 4. color Example Code program Example_msFastMolecule use fml use fgl implicit none

type(mfArray) :: loc, conn, rad, color, h

! Specify locations of three balls using vcat loc = Reshape((/0.0, 1.0, 0.0, 0.0, 1.0, 1.0, 0.0, 1.0, 0.0/), &

(/3,3/))

! Specify three sticks and their connections conn = Reshape((/1.0, 1.0, 2.0, 2.0, 3.0, 3.0/), &

(/3,2/))

! Specify the radius of each ball at radius=0.5,0.7,1.0

rad = (/0.25, 0.35, 0.5/)

! Set the color of each ball to red, green and blue color = Reshape((/0.8, 0.1, 0.1, 0.1, 0.8, 0.1, 0.1, 0.1, 0.8/), &

(/3,3/))

call msAxis(-0.5d0, 1.6d0, -0.3d0, 1.6d0, -0.5d0, 1.35d0)

! Draw the molecules

h = mfFastMolecule(loc, conn, rad, color)

! Pause program to view

call msViewPause()

e nd program Example_msFastMolecule

Result


See Also mfSphere


mfSphere, msSphere Draw a sphere.

Module fgl

Syntax h = mfSphere([loc][, radius][, color][, resolution]) call msSphere([loc][, radius][, color][, resolution]) Descriptions Procedure mfSphere draws a sphere with center at loc, radius specified by radius, color specified by color and resolution level specified by resolution. All arguments are optional. call msSphere(loc, radius, color, resolution)

Argument Meaning

loc A 1-by-3 mfArray containing the x-, y- and z- coordinates of the sphere center. By default, argument loc is set to [0,0,0].

radius An mfArray containing a real number specifies the radius of the sphere. By default, argument radius is set to 0.5.

color An mfArray containing a string specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the rgb codes. By default, argument color is set to grey.

resolution An mfArray containing the number of polygons used for modeling the circular object. The higher the polygon number, the smoother a sphere appears. The lower the polygon number, the faster a sphere is rendered. By default, the sphere is set to a resolution = 64.

h = mfSphere(...)

• Handle h retrieves a handle to the sphere object created by mfSphere(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the sphere object through handle h with procedure msGSet.


The properties available are: 1. location 2. radius 3. color 4. resolution Example Code pr ogram example


ty pe(mfArray) :: zeros, color

zeros =(/0, 0, 0/) co lor = (/0, 1, 0/)

! Center at (0,0,0), Radius = 0.5, Color = 'green' ca ll msSphere(zeros, mf(1), color)

! Remove current Axis call msAxis('off') ca ll msAxis('equal')


! Deallocate mfArray ca ll msFreeArgs(zeros)


Result

See Also mfCylinder, mfMolecule, mfCube


mfCube, msCube Draw a cube.

Module fgl

Syntax h = mfCube([loc][, size][, color]) call msCube([loc][, size][, color]) Descriptions Procedure mfCube draws a cube with center at loc, size specified by size, and color specified by color. All arguments are optional. call msCube(loc, size, color)

Argument Meaning

loc A 1-by-3 mfArray contains the x-, y- and z- coordinates of the cube center. By default, argument loc is set to [0,0,0].

size A 1-by-3 mfArray specifies the length , width and height of a cube. By default, argument Size is set to [1,1,1].

color An mfArray containing a string specifies the color, e.g. “y”, or a

1-by-3 mfArray containing the rgb codes. By default, argument color is set to grey.

h = mfCube(...)

• Handle h retrieves a handle to the cube object created by mfCube(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the cube object through handle h with procedure msGSet. The properties available are: 1. location 2. size 3. color




ty pe(mfArray) :: zeros, cubesize, color

zeros = (/ 0, 0, 0 /) cubesize = (/ 0.2, 0.3, 0.4 /) co lor = (/ 0, 1, 0 /)

! Cube with center at (0,0,0), size of 0.2x0.3x0.4, ! and green in color call msCube(zeros, cubesize, color) ca ll msAxis('equal')


! Deallocate mfArrays ca ll msFreeArgs(zeros, cubesize, color)


Result

See Also mfCylinder, mfSphere, mfCone


mfCylinder, msCylinder Draw a cylinder.

Module fgl

Syntax h = mfCylinder([loc][, radius][, height][, color][, resolution]) call msCylinder([loc][, radius][, height][, color][, resolution]) Descriptions Procedure mfCylinder draws a cylinder with center at loc, radius specified by radius, height specified by height, color specified by color and resolution level specified by resolution. All arguments are optional. call msCylinder(loc, radius, height, color, resolution)

Argument Meaning

loc A 1-by-3 mfArray contains the x-, y- and z- coordinates of the cylinder center. By default, argument loc is set to [0, 0, 0].

radius An mfArray containing a real number specifies the radius of the cylinder. By default, argument radius is set to 0.5.

height An mfArray containing a real number specifies the height of the cylinder. By default, argument height is set to 1.0.

color An mfArray containing a string specifies the color, e.g. “y”, or a 1-by-3 mfArray contains the rgb codes. By default, argument color is set to grey.

resolution An mfArray contains the number of polygons used for modeling the circular object. The higher the polygon number, the smoother a sphere appears. The lower the polygon number, the faster a sphere is rendered. By default, the sphere is set to a resolution = 64.

h = mfCylinder(...)

• Handle h retrieves a handle to the cylinder object created by mfCylinder(...).



You can specify properties of the cylinder object through handle h with procedure msGSet. The properties available are: 1.location 2.radius 3.height 4.color 5.resolution Example Code pr ogram example



zeros = (/ 0, 0, 0 /) co lor = (/ 1, 0, 0 /)

! Cube with center at (0,0,0), radius = 0.5, height = 0.5, ! and red in color ca ll msCylinder(zeros, mf(0.5), mf(0.5), color)


! Deallocate mfArrays zeros, color ca ll msFreeArgs(zeros, color)

e nd program

Result


See Also mfSphere, mfCone, mfCube


mfCone, msCone Draw a cone.

Module fgl

Syntax h = mfCone([loc][, radius][, height][, color][, resolution]) call msCone([loc][, radius][, height][, color][, resolution]) Descriptions Procedure mfCone draws a cone with center at loc, radius specified by radius, height specified by height, color specified by color and resolution level specified by resolution. All arguments are optional. call msCone(loc, radius, height, color, resolution)

h = mfCone(...)

• Handle h retrieves a handle to the cone object created by mfCone(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the cone object through handle h with procedure msGSet. The properties available are: 1.location 2.radius 3.height 4.color 5.resolution Example Code pr ogram example



zeros = (/ 0., 0., 0. /) co lor = (/ 0., 1., 0. /)

! Cone with location (0,0,0), radius = 0.5, height = 1.0,


! color = green. ca ll msCone(zeros, mf(0.5), mf(1.0), color)


! Deallocate mfArrays ca ll msFreeArgs(zeros, color)

e nd program

Result

See Also mfCylinder, mfSphere, mfCube


mfAxisMark, msAxisMark 3-directional axis mark on arbitrary point.

Module fgl

Syntax h = mfAxisMark([loc][, length][, radius]) call msAxisMark([loc][, length][, radius]) Descriptions Procedure mfAxisMark draws a 3-directional axis mark on any arbitrary point in the plot space. call msAxisMark(loc, length, radius)

• Draws a 3-directional axis mark on the point specified by argument loc with length specified by argument length and thickness specified by argument radius.

• By default, location is [0, 0, 0], length is 1 and radius is 0.1. h = mfAxisMark(...)

• Handle h retrieves a handle to the axis mark object created by mfAxisMark(...). • Alternatively, use procedure h = mfGetCurrentDraw() to retrieve the handle of the

current graphics object. You can specify properties of the molecules object through handle h with procedure msGSet. The properties available are: 1. symmetric = "on" or "off". If symmetric is on, the axes extend to negative values. 2. location 3. length 4. radius Example Code pr ogram example


ty pe (mfArray) :: cubesize, center, h, loc, length, radius


cubesize = (/4, 4, 4/) center = (/0, 0, 0/) loc = mf((/-1.0d0, -3.0d0, 2.1d0/)) length = 1 ra dius = 0.05

h = mfCube(center, cubesize, 'b') ca ll msObjOrientation(h, 15, 15, 15)

call msHold('on') h = mfAxisMark(loc, length, radius) call msObjOrientation(h, 15, 15, 15) call msGSet(h,'symmetric',mf(1)) ca ll msViewPause()

ca ll msFreeArgs(cubesize, center, h)


Result

See Also


Property Setting


msGSet Set property of specified graph.

Module fgl

Syntax call msGSet(handle, property, value[, property2, value2, ...]) Descriptions Procedure msGSet sets the property of a graphics object whose handle is given by handle. You can set various properties of a graph object through the procedure. call msGSet(handle, property, value)

• Argument property is a string specifying the target property to be updated. Argument value is an mfArray containing the data to be updated. For example, you can input "xdata" for x-coordinate, "ydata" for y-coordinate, "zdata" for z-coordinate if

you want to update the coordinates of a graphics object. call msGSet(handle, property, value, property2, value2, ...)

• Multiple properties can be updated in one statement as above. • The table below lists the common properties available for updating through procedure

msGSet.

Property Description Apply to

"xdata" Specify x data as target for

updating Almost all two-dimensional and three-dimensional graphics objects

"ydata" Specify y data as target for

updating Almost all two-dimensional and three-dimensional graphics objects

"zdata" Specify z data as target for

updating Almost all three-dimensional graphics objects


"cdata" Specify color vector, c as target

for updating Almost all two-dimensional and three-dimensional graphics objects

"udata" Specify velocity in x-direction, u

as target for updating.

mfQuiver, mfQuiver3,

mfStreamLine, etc.

"vdata" Specify velocity in y-direction, v


mfQuiver, mfQuiver3,

mfStreamLine, etc.

"wdata" Specify velocity in z-direction, w


mfQuiver3,

mfStreamLine

Note: Not all of the available properties are listed here. Please refer to the description of each graphical procedure for a supplementary list of properties. Example Code pr ogram example


type(mfArray):: x, y, h in teger::i

!Construct and initialize the mfArrays for plotting. x = mfLinspace(-MF_PI, MF_Pi, 30) y = mfCos(x)

!Plot the initial figure and get its handle. call msPlot(x, y, 'ro') h= mfGetCurrentDraw()

!Set up an iteration loop for the range of data you !wish to observe through animation. Do i=1,1000 y=mfCos(x+0.02d0*i)

!Within the iteration loop, use procedure msGSet to update !the targeted data of the current draw. call msGSet(h, 'ydata', y)

!Update the current Graphics Viewer by using procedure !msDrawNow. call msDrawNow()

en d do

!Pause the program to observe figure. ca ll msViewPause()

!Deallocate mfArray ca ll msFreeArgs(x, y, h)



Result

See Also


msDrawMaterial Set transparency, ambient, diffuse and specular reflectance of a draw object.

Module fgl

Syntax call msDrawMaterial(handle, target, property1, value1[, property2, value2, ...]) Descriptions Procedure msDrawMaterial sets the color component, transparency reflectance, ambient reflectance, diffuse reflectance and specular reflectance of the draw object's surface and edges. Each reflectance is specified as a level of intensity ranging from 0 to 100. The resultant lighting effect is produced by applying the intensity levels of the reflectance to the color component. For example, if the intensity of the draw object's ambient reflectance is set to be 50 and the color component is set to be [1, 1, 1], the draw object's ambient color component becomes [0.5, 0.5, 0.5]. call msDrawMaterial(handle, target, property, value)

• You can perform the operation on the draw object's surface, edge or both by specifying argument target as "surf", "edge" or "both".


Property Meaning

“trans” Transparency reflectance. The

corresponding argument value can be an

integer or an mfArray containing an integer

that ranges from 0 to 100.

“ambient” Ambient reflectance. The corresponding

argument value can be an integer or an

mfArray containing an integer that ranges

from 0 to 100.

“diffuse” Diffuse reflectance. The corresponding argument value can be an integer or an mfArray

containing an integer that ranges from 0 to


100.

“specular” Specular reflectance. The corresponding


mfArray containing an integer that ranges

from 0 to 100.

“color” Color component. The corresponding

argument value can be an mfArray containing

the rgb vector [r, g, b].

“colormap” Turn the colormap on or off. The


mfArray containing the string that is

specified as “on” or “off”.

“visible” Turn the surface or edge on or off. The




“smooth”Interpolate to Gouraud shading. The corresponding argument value can be an



“line_width” Line width of edge. The corresponding


mfArray containing an integer.

“line_style” Line style of edge. The corresponding

argument value can be an mfArray containing

a string that is specified as "solid",

"dashed", "dotted" or "dashdot".


use fgl use fml


im plicit none

ty pe (mfArray) :: a, x, y, z, h, v


h = mfSurf(x, y, z)

call msDrawMaterial(h, mf('surf'), mf('visible'), mf('on'), & mf('smooth'), mf('on'), & mf('colormap'), mf('on'), & mf('ambient'), mf(0), & mf('diffuse'), mf(75), & mf('specular'), mf(25)) call msDrawMaterial(h, mf('edge'), mf('color'), mf((/1,0,0/)), & mf('smooth'), mf('on'), & mf('colormap'), mf('off'), & mf('ambient'), mf(0), & mf('diffuse'), mf(0), & mf('diffuse'), mf(0), & mf('specular'), mf(0), & mf('trans'), mf(90)) !Set name of draw object call msSetDrawName(h,'My Surf 1') ca ll msViewPause()

!Get Object handle's status v = mfIsValidDraw(h) if (mfAny(v)) print *,'Draw object is valid'

!Remove Object handle call msRemoveDraw(h) v = mfIsValidDraw(h) if (.not.mfAny(v))print *,'Draw object is invalid'

ca ll msFreeArgs(a, x, y, z, h, v)


Result

See Also


msDrawTexture Set texture mapping.

Module fgl

Syntax call msDrawTexture(handle, property1, value1[, property2, value2, ...]) Descriptions Procedure msDrawTexture places a texture on a graphics object by mapping the texture coordinates to the object's coordinates. The texture coordinates comprise of two coordinates, namely the s- and t-coordinates, which are vectors of values ranging from 0 to 1. They correspond to the object's x- and y-coordinates in order to determine which texel (texture element) in the texture is mapped to which vertex. call msDrawTexture(handle, property, value)


Property Meaning

"enable" Enabling or disabling the texture-mapping. The

corresponding argument value can be “on” or

“off”.

"map" Specifying the texture file. The corresponding

argument value specifies the name of a bitmap

file (e.g. texture.bmp).

"coord_s" Texture’s s-coordinate. The corresponding argument value is a vector of values ranging from 0 to

1, which specifies the way of mapping.

"coord_t" Texture’s t-coordinate. The corresponding

argument value is a vector of values ranging

from 0 to 1, which specifies the way of mapping.




ty pe (mfArray) :: a, x, y, z, h


h = mfSurf(x, y, z) call msDrawTexture(h, 'map', 'ancad.bmp') call msDrawMaterial(h, mf('surf'), mf('smooth'), mf('on'), & mf('colormap'), mf('on'), & mf('ambient'), mf(0), & mf('diffuse'), mf(15), & mf('specular'), mf(85)) call msDrawMaterial(h, 'edge', 'visible', 'off') ca ll msViewPause()

ca ll msFreeArgs(a, x, y, z, h)


Result

See Also


mfIsValidDraw Check validity of draw object.

Module fgl

Syntax validity = mfIsValidDraw(handle) Descriptions Procedure mfIsValidDraw returns the validity of a draw object which is associated with argument handle. The output is an mfArray containing logical data. It returns true if the draw object still exists, false otherwise. Example To be referred to msDrawMaterial See Also


mfGetCurrentDraw Return handle of current draw object.

Module fgl

Syntax handle = mfGetCurrentDraw() Descriptions Procedure mfGetCurrentDraw returns the handle of current draw object. Example Code pr ogram example


type (mfArray) :: a, b, c, x, y, z, theta, phi, h in teger :: i

a = mfLinspace(-MF_PI/2, MF_PI/2, 31) b = mfLinspace(-MF_PI, MF_PI, 31) c = mfOnes(31, 31) call msMeshgrid(mfout(phi, theta), a, b) x = mfCos(phi)*mfCos(theta) y = mfCos(phi)*mfSin(theta) z = mfSin(phi)

! Plot the graph you wish to animate call msSurf(x, y, z) call msAxis(mf((/-MF_PI, MF_PI, -MF_PI, MF_PI, -MF_PI, MF_PI/))) call msShading('interp') ca ll msAxis('off')

! Get handle of current draw h = mfGetCurrentDraw()

! Use a Do Loop to change the value of x, y and z. do i =1 ,30 x = mfCos(phi)*mfCos(theta+i*0.1d0) y = mfCos(phi)*mfSin(theta+i*0.1d0)+0.05d0*i z = mfSin(phi)+mfSin(c*i) ! Set the x,y, and z-data of the current graph call msGSet(h, mf('xdata'), x, mf('ydata'), y, mf('zdata'), z) ! Draw graph on Graphics Viewer call msDrawNow() en d do

! Pause program to view graph. If this statement is ! not added, the Graphics Viewer closes once animation ! is completed. Ca ll msViewPause()


! Deallocate mfArrays Ca ll msFreeArgs(a, b, c, x, y, z, theta, phi, h)


See Also


msRemoveDraw Remove draw object from plot space.

Module fgl

Syntax call msRemoveDraw(handle1[, handle2, ...]) Descriptions Procedure msRemoveDraw removes specific draw objects from the plot space. call msRemoveDraw(handle1, handle2, ...)

Removes the draw objects associated with the handles specified in the arguments.

Example To be referred to msDrawMaterial See Also


msSetDrawName Name draw object.

Module fgl

Syntax call msSetDrawName(handle, name) Descriptions Procedure msSetDrawName sets the name of the draw object associated with argument handle. By default, the name of a draw object is set to its draw type followed by an incremental integer. The purpose of giving each draw object a name is to distinguish between the draw objects. It allows you to perform operations (e.g. custom shading or view draw object data) on a specific draw object from object list view window when there are multiple draw objects presented in the same subplot. All the draw objects are listed in Object List View Window. Example To be referred to msDrawMaterial See Also


Graphics Viewer Manipulation


msPrintPreview Pop up print preview dialog box.

Module fgl

Syntax call msPrintPreview() Descriptions Procedure msPrintPreview pops up a dialog box showing current figure as it will be printed. Example Code pr ogram example


ty pe (mfArray) :: x, y, z

!Create surface data for plot ca ll msCreateSurfData( mfOut(x, y, z), 1, 30, 30 )

!Plot a surf using mfArray x, y and z call msSubplot(1,2,1) ca ll msSurf(x, y, z)

call msSubplot(1,2,2) ca ll msSolidContour(x, y, z)

!Show print preview window ca ll msPrintPreview()

!Pause to display the graph ca ll msViewPause()


Result


See Also


msEditorDrawList Pop up draw-list editor.

Module fgl

Syntax call msEditorDrawList() Descriptions Procedure msEditorDrawList creates a draw-list dialog box that enables the user to edit objects' material, colormap, and transformation settings from the global scope. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorMaterial Pop up material editor.

Module fgl

Syntax call msEditorMaterial() Descriptions Procedure msEditorMaterial creates a dialog box that enables the user to edit objects' material settings. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorColormap Pop up colormap editor.

Module fgl

Syntax call msEditorColormap() Descriptions Procedure msEditorColormap creates a dialog box that enables the user to edit objects' colormap settings. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorTransform Pop up transformation editor.

Module fgl

Syntax call msEditorTransform() Descriptions Procedure msEditorTransform creates a dialog box that enables the user to edit objects' transformation settings. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorAxis Pop up axis editor.

Module fgl

Syntax call msEditorAxis() Descriptions Procedure msEditorAxis creates a dialog box that enables the user to edit objects' axis settings. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorColorbar Pop up colorbar editor.

Module fgl

Syntax call msEditorColorbar() Descriptions Procedure msEditorColorbar creates a dialog box that enables the user to edit colorbar settings. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


msEditorBackground Pop up background editor.

Module fgl

Syntax call msEditorBackground() Descriptions Procedure msEditorBackground creates a dialog box that enables the user to manipulate background colors. Example Code P lease refer to the gsurf demo under <MATFOR4>\gui_demo

Result

See Also


Simple GUI


msShowMessage Pop up message dialog box.

Module fgl

Syntax call msShowMessage(msg) Descriptions Procedure msShowMessage pops up a dialog box displaying a message. Example Code pr ogram example


call msShowMessage("Show Message Test")

e nd program

Result

See Also


mfInputString Pop up input string insertion dialog box.

Module fgl

Syntax call msInputString(mfOut(str, is_ok),msg ,string_value) Descriptions Procedure mfInputString pops up a dialog box displaying the prompt msg, with string_value in the textbox. This procedure has two return arguments; str returns the entered string value, is_ok returns 1 if the OK button is clicked, and 0 if the Cancel button is clicked. Example Code pr ogram example


type(mfArray) :: str, is_ok; ca ll msInputString(mfOut(str, is_ok), "Input Name", "Ancad")

call msShowMessage(str); ca ll msDisplay(is_ok,"Is ok")

e nd program

Result

See Also


mfInputValue Pop up value insertion dialog box.

Module fgl

Syntax call msInputValue(mfOut(num, is_ok),msg ,number_value) Descriptions Procedure mfInputValue pops up a dialog box displaying the prompt msg, with number_value in the textbox. This procedure has two return arguments; num returns the entered number value, is_ok returns 1 if the OK button is clicked, and 0 if the Cancel button is clicked. Example Code pr ogram example


ty pe(mfArray) :: val, is_ok;

call msInputValue(mfOut(val, is_ok), "Input Number", 10) ca ll msDisplay(val, "Number", is_ok, "Is ok")

e nd program

Result

See Also


mfInputVector Pop up vector insertion dialog box.

Module fgl

Syntax call msInputVector(mfOut(vec, is_ok),msg ,vector_value) Descriptions Procedure mfInputVector pops up a dialog box displaying the prompt msg, with vector_value in the textbox. This procedure has two return arguments; vec returns the entered vector value, is_ok returns 1 if the OK button is clicked, and 0 if the Cancel button is clicked. Example Code pr ogram example

use fml use fgl implicit none type(mfArray) :: vec, is_ok; call msInputVector(mfOut(vec,is_ok), "Input Vector", mf((/1, 2, 3, 4, 5/))) ca ll msDisplay(vec,"Vector",is_ok,"Is ok")

end program Result

See Also


mfInputMatrix Pop up matrix insertion dialog box.

Module fgl

Syntax call msInputMatrix(mfOut(matrix, is_ok),msg ,matrix_value)

Descriptions Procedure mfInputMatrix pops up a dialog box displaying the prompt msg, with matrix_value in the table. This procedure has two return arguments; matrix returns the entered matrix value, is_ok returns 1 if the OK button is clicked, and 0 if the Cancel button is clicked. Example Code pr ogram example


type(mfArray) :: x, m, is_ok real(8) :: a(5, 3) in teger :: i

x=reshape((/(i, i=1,15)/),(/5,3/)) call msInputMatrix(mfOut(m,is_ok), "Input Matrix", x) ca ll msDisplay(m,"Matrix",is_ok,"Is ok")

end program Result


See Also


mfFileDialog, mfOpenFileDialog Pop up file open dialog box.

Module fgl

Syntax string = mfFileDialog(filename, filefilter)

Descriptions Procedure mfFileDialog pops up a file open dialog box for locating a file. Example Code pr ogram example


ty pe(mfArray) :: a, str, is_ok;

str = mfFileDialog("x.txt", "*.txt") a = mfLoadAscii(str)

call msDisplay(a, "a")

call msSaveFileDialog(mfOut(str, is_ok), "y.txt", "*.txt") !If user press save button if (mfAny(is_ok)) then a = a + 1 call msSaveAscii(str, a) call msDisplay(mfLoadAscii(str), "a+1", is_ok, "Is ok") end if end program Result


See Also mfSaveFileDialog


mfSaveFileDialog Pop up file save dialog box.

Module fgl

Syntax call msSaveFileDialog(mfOut(str,is_ok),filename, filefilter)

Descriptions Procedure mfSaveFileDialog pops up a file-save dialog box for locating the directory the file filename will be saved. This procedure has two return arguments; str returns the directory of the saved file, is_ok returns 1 if the OK button is clicked, and 0 if the Cancel button is clicked. Example To be referred to mfFileDialog See Also mfFileDialog


mfInputYesNo Pop up yes-no query dialog box.

Module fgl

Syntax value = mfInputYesNo(msg, default_value)

Descriptions Procedure mfInputYesNo pops up a yes-no dialog box. The chosen option is passed back to the output argument value. Argument default_value can be either 0 or 1. Example Code pr ogram example


ty pe(mfArray) :: val;

val = mfInputYesNo("yes or no") if(mfAny(val))then print *,'You press Yes.' else print *,'You press No.' end if

call msDisplay(val, "val")

end program Result

See Also


Chapter 10 MATFOR Extensions 605

C H A P T E R 1 0

Extensions of MATFOR

This chapter introduces advanced MATFOR routines that enable users to use external data or programs.

Tecplot FileIO

mfTecOpenFile/

mfTecCloseFile

Open Tecplot files for reading or writing

mfTecReadTitle/

mfTecWriteTitle

Read and write title of Tecplot files.

mfTecReadVarName/

mfTecReadBlock

Retrieve data information from Tecplot files.

mfTecReadVarCount/ mfTecReadBlockCount

Retrieve number of variables and blocks from Tecplot files.

mfTecWriteVarNames Write variable names to Tecplot files.

mfTecWriteIJKBlock/

mfTecWriteTriBlock/ mfTecWriteTetBlock

Write data information to Tecplot files.

MATLAB Interface

mfDoMATLAB Execute MATLAB functions.

mfMATLABServer Perform MATLAB actions in MATFOR programs.


Tecplot FileIO


mfTecOpenFile, msTecCloseFile Open a Tecplot file for reading or writing.

Module fgl

Syntax h = mfTecOpenFile( filename, 'r' ) h = mfTecOpenFile( filename, 'w' ) call msTecCloseFile(h) Descriptions Procedure mfTecOpenFile opens a Tecplot file for reading 'r', or writing 'w'. This procedure returns a file handler. When opening a file in write mode, the file will be created automatically if it does not exist. When finishing working with the file, you can close it using procedure msTecCloseFile. Example Code Pr ogram TecPlot

use fml us e fgl

im plicit none

type(mfArray) :: tri, tet, x, y, z, c type(mfArray) :: h, tec type(mfArray) :: fname, title type(mfArray) :: values, atype in teger(4) :: nb, nv

! create unstructure tetra data x = mfRand(500,1) y = mfRand(500,1) z = mfRand(500,1) c = 1 - (x-0.5d0)**2d0 - (y-0.5d0)**2d0 - (z-0.5d0)**2d0 te t = mfGetDelaunay3(x, y, z)

! write to Tecplot file tec = mfTecOpenFile( 'tetsurf.plt', 'w' ) call msTecWriteTitle( tec, 'TET-SURF' ) call msTecWriteVarNames( tec, 'X', 'Y', 'Z', 'C' ) call msTecWriteTetBlock( tec, tet, x, y, z, c ) ca ll msTecCloseFile( tec )

!read from Tecplot file tec = mfTecOpenFile( 'tetsurf.plt', 'r' ) title = mfTecReadTitle( tec ) nb = mfTecReadBlockCount( tec ) nv = mfTecReadVarCount( tec ) call msDisplay( title, 'title', mf(nb), 'nb', mf(nv), 'nv' )


call msTecReadBlock( mfOut( values, atype, tri ), tec, 1 ) ca ll msTecCloseFile( tec )

x = mfS( values, MF_COL, 1.to.1 ) y = mfS( values, MF_COL, 2.to.2 ) z = mfS( values, MF_COL, 3.to.3 ) c = mfS( values, MF_COL, 4.to.4 ) call msTetSurf( tri, x, y, z, c ) call msTitle( title ) ca ll msViewPause

call msFreeArgs(tri, tet, x, y, z, c) ca ll msFreeArgs(h, tec, fname, title, values, atype)

e nd Program TecPlot

See Also


mfTecReadTitle, mfTecWriteTitle Read and write title of a Tecplot file.

Module fgl

Syntax title = mfTecReadTitle( h ) call msTecReadTitle(mfOut(title),h) call msTecWriteTitle( h, title ) Descriptions Procedure mfTecReadTitle reads the title from a Tecplot file. It returns a string or an mfArray that contains a string. Procedure mfTecWriteTitle appends the title to the Tecplot file given file handler h. Example To be referred to mfTecOpenFile See Also mfTecOpenFile, mfTecCloseFile


msTecReadVarName, msTecReadBlock Retrieve data information from a Tecplot file.

Module fgl

Syntax call msTecReadVarName( mfOut( varname, min_max ), h, var_idx) call msTecReadBlock( mfOut( values, type, tri ), h, block_idx) Descriptions Procedure msTecReadVarName retrieves variable information from a Tecplot file given a file handler h and the variable index. It returns a variable name and a 2 by 1 vector that contains minimum and maximum values of the variable. Procedure mfTecReadBlock retrieves block information from a Tecplot file given a file handler h and the block index. It returns block values, type of polyhedrons and connectivity values in the shapes specified below: Element Type values type tri

Triangle nn x nv MF_TEC_TRI ne x 3

Quadrilateral

nn x nv MF_TEC_QUAD ne x 4

Tetrahedron

nn x nv MF_TEC_TET ne x 4

Brick

nn x nv MF_TEC_BRICK ne x 8

IJK m x n x p x nv MF_TEC_IJK Mf() or MF_NULL

*nn = number of nodes. *nv = number of variables. *ne = number of elements. *m = number of points in 1st dimension. *n = number of points in 2nd dimension. *p = number of points in 3rd dimension. Example Code


Pr ogram tecread

use fml us e fgl

im plicit none

type(mfArray) :: x, y, z, c, h type(mfArray) :: fname, title type(mfArray) :: tec type(mfArray) :: values1, values2, atype, tri type(mfArray) :: min_max in teger(4) :: nb, nv, tectype

! ****************************************************************** ! load data ! ******************************************************************

fn ame = mfFileDialog( '', '*.plt;*.dat' )

tec = mfTecOpenFile( fname, mf('r') ) title = mfTecReadTitle( tec ) nb = mfTecReadBlockCount( tec ) nv = mfTecReadVarCount( tec ) ca ll msDisplay( title, 'title', mf(nb), 'nb', mf(nv), 'nv' )

if (nb<1 .or. nv<3) then call msShowMessage( 'No valid block') stop en d if

call msTecReadBlock( mfOut( values1, atype, tri ), tec, 1 ) call msTecReadVarName(mfOut( values2, min_max ), tec, 4) call msGDisplay( values1, 'values1' ) ca ll msDisplay( atype, 'atype' )

ca ll msTecCloseFile( tec )

! ****************************************************************** ! draw data ! ****************************************************************** tectype = atype select case (tectype) case (MF_TEC_IJK) x = mfS( values1, MF_COL, MF_COL, MF_COL, 1.to.1 ) y = mfS( values1, MF_COL, MF_COL, MF_COL, 2.to.2 ) z = mfS( values1, MF_COL, MF_COL, MF_COL, 3.to.3 ) if (nv<4) then c = z else c = mfS( values1, MF_COL, MF_COL, MF_COL, 4.to.4 ) end if call msSurf( x, y, z, c ) case (MF_TEC_TRI, MF_TEC_QUAD, MF_TEC_TET, MF_TEC_BRICK) x = mfS( values1, MF_COL, 1.to.1 ) y = mfS( values1, MF_COL, 2.to.2 ) z = mfS( values1, MF_COL, 3.to.3 ) if (nv<4) then c = z else c = mfS( values1, MF_COL, 4.to.4 ) end if if (tectype==MF_TEC_TRI .or. tectype==MF_TEC_QUAD) then call msTriSurf( tri, x, y, z, c ) call msGDisplay( tri, 'tri' ) else call msTetSurf( tri, x, y, z, c ) call msGDisplay( tri, 'tet' ) end if end select


call msTitle( title ) ca ll msViewPause

e nd Program tecread

See Also msTecWriteVarNames, mfTecWriteIJKBlock, mfTecWriteTriBlock, mfTecWriteTetBlock


mfTecReadVarCount, mfTecReadBlockCount Retrieve number of variables and blocks from a Tecplot file.

Module fgl

Syntax nv = mfTecReadVarCount( h ) nb = mfTecReadBlockCount( h ) Descriptions Procedure mfTecReadVarCount returns a scalar mfArray containing number of variables in the Tecplot file specified by the file handler h. Procedure mfTecReadBlockCount returns a scalar mfArray containing number of blocks in the Tecplot file specified by the file handler h. Example To be referred to mfTecReadVarName See Also msTecReadVarName, msTecReadBlock


msTecWriteVarNames Write variable names to a Tecplot file.

Module fgl

Syntax call msTecWriteVarNames( h, name1[, name2, name3...] ) Descriptions Procedure msTecWriteVarNames writes variable names to a Tecplot file given the file handler h. Example To be referred to mfTecWriteIJKBlock See Also msTecReadVarName


msTecWriteIJKBlock, msTecWriteTriBlock,

msTecWriteTetBlock Write data information to a Tecplot file.

Module fgl

Syntax call msTecWriteIJKBlock( h, var1[, var2, var3...]) call msTecWriteTriBlock( h, tri[, var1, var2, var3...]) call msTecWriteTetBlock( h, tet[, var1, var2, var3...]) Descriptions Procedure msTecWriteIJKBlock writes data values to a Tecplot file given the file handler h. • The shapes of all variables should be conformed. Procedure msTecWriteTriBlock writes data values and connectivity values to a Tecplot file given the file handler h. • tri is a surface object defined by an m-by-n face matrix, where m is the number of polygons

to be drawn and n is the number of edges of each polygon.

• The shapes of all variables should be conformed. Procedure msTecWriteTetBlock writes data values and connectivity values to a Tecplot file given the file handler h. • tet is a polyhedral object defined by an m-by-k cell matrix, where m is the number of

polyhedrons to be drawn and k is the number nodes of each polyhedron.

• The shapes of all variables should be conformed. Example Code Pr ogram tecwrite

use fml us e fgl

im plicit none

type(mfArray) :: tri, tet, x, y, z, c ty pe(mfArray) :: h, tec

!******************************************************************


! create surf data !* *****************************************************************

call msFigure('Surf') call msCreateSurfData( mfOut( x, y, z ), 6, 30, 28 ) c = mfCreateSurfData( 1, 30, 28 )

h = mfSolidContour3( x, y, z, c ) call msDrawMaterial( h, 'surf', 'smooth', 'on' ) ca ll msDrawMaterial( h, mf('edge'), mf('trans'), mf(70) )

!****************************************************************** ! write to Tecplot !****************************************************************** tec = mfTecOpenFile( 'surf.plt', 'w' ) call msTecWriteTitle( tec, 'SURF' ) call msTecWriteVarNames( tec, 'X', 'Y', 'Z', 'C' ) call msTecWriteIJKBlock( tec, x, y, z, c ) ! write multi-block call msTecWriteIJKBlock( tec, x, y, z * 2, c ) ca ll msTecCloseFile( tec )

call msDrawNow() ca ll msShowMessage( 'Data has been written to the Tecplot file: surf.plt' )

!****************************************************************** ! create unstructure surf data !* *****************************************************************

ca ll msFigure('TriSurf')

x = mfRand(400,1) y = mfRand(400,1) z = 1 - (x-0.5d0)**2d0 - (y-0.5d0)**2d0 c = mfSin(x) * mfCos(y) * z tr i = mfGetDelaunay(x, y)

h = mfTriContour(tri, x, y, z, c) call msDrawMaterial( h, 'surf', 'smooth', 'on' ) ca ll msDrawMaterial( h, mf('edge'), mf('trans'), mf(70) )

!****************************************************************** ! write to Tecplot !****************************************************************** tec = mfTecOpenFile( 'trisurf.plt', 'w' ) call msTecWriteTitle( tec, 'TRI-SURF' ) call msTecWriteVarNames( tec, 'X', 'Y', 'Z', 'C' ) call msTecWriteTriBlock( tec, tri, x, y, z, c ) ca ll msTecCloseFile( tec )

call msDrawNow() call msShowMessage( 'Data has been written to the Tecplot file: isurf.plt' ) tr

!****************************************************************** ! create unstructure tetra data !* *****************************************************************

ca ll msFigure('TetSurf')

x = mfRand(500,1) y = mfRand(500,1) z = mfRand(500,1) c = 1 - (x-0.5d0)**2d0 - (y-0.5d0)**2d0 - (z-0.5d0)**2d0 te t = mfGetDelaunay3(x, y, z)

h = mfTetContour(tet, x, y, z, c) call msDrawMaterial( h, 'surf', 'smooth', 'on' ) ca ll msDrawMaterial( h, mf('edge'), mf('trans'), mf(70) )

!****************************************************************** ! write to Tecplot


!****************************************************************** tec = mfTecOpenFile( 'tetsurf.plt', 'w' ) call msTecWriteTitle( tec, 'TET-SURF' ) call msTecWriteVarNames( tec, 'X', 'Y', 'Z', 'C') call msTecWriteTetBlock( tec, tet, x, y, z, c ) ca ll msTecCloseFile( tec )

call msDrawNow() call msShowMessage( 'Data has been written to the Tecplot file: tsurf.plt' ) te

ca ll msViewPause

e nd Program tecwrite

See Also msTecReadBlock


MATLAB Interface


mfDoMATLAB, msDoMATLAB Execute MATLAB functions.

Module fml

Syntax h = mfDoMATLAB( func_str, p[, p2, .... ]) Descriptions Procedure mfDoMATLAB executes MATLAB functions and MATLAB script files from MATFOR programs. h = mfDoMATLAB(func_str, p[, p2, .... ])

• Argument func_str is a string containing the name of the MATLAB function. • Argument p is the input argument(s) corresponding to the function func_str. Example Code pr ogram example


ty pe(mfArray):: x, y

!Create 5*5 magic matrix in MATLAB and save result to mfArray x call msMATLABServer( "setvar", "in0", 5 ) call msMATLABServer( "command", "out0 = magic( in0 );" ) call msMATLABServer(mfOut(x), "getvar", "out0" ) !x = mfDoMATLAB("magic", mf(5)) ca ll msDisplay(x)

!Execute eig function in MATLAB y = mfDoMATLAB("eig", x) ca ll msDisplay(y)

!Execute surf function in MATLAB to show magic matrix ca ll msDoMATLAB("surf", x)

!The same graphic result in MATFOR call msSurf(x) ca ll msViewPause()


Result


See Also mfMATLABServer


mfMATLABServer, msMATLABServer Perform MATLAB actions from MATFOR programs.

Module fml

Syntax call msMATLABServer(action, input[, input2, ...]) call msMATLABServer("setvar", "var", val) val = mfMATLABServer("getvar", "var") Descriptions Procedure mfMATLABServer performs MATLAB actions from MATFOR programs. call msMATLABServer(action, input[, intput2, ...])

• Argument action specifies the type of the MATLAB action used. The action types currently supported by MATFOR are:

Action Inputs Meaning

“visible” “on” or “off” Control the visibility of MATLAB Command Window.

“command” “command_name” Execute the given MATLAB command.

“script” “file_name” Execute the given MATLAB script file.

call msMATLABServer("setvar", "var", val)

• Set the variable to the given value val under MATLAB Command Window. val = mfMATLABServer("getvar", "var")

• Retrieve the value of the variable under MATLAB Command Window. Example To be referred to mfDoMATLAB. See Also mfDoMATLAB


Chapter 11 MATFOR GUI System 623

C H A P T E R 1 1

MATFOR GUI System


Initialization


msUIInitialize Initialize the MATFOR GUI system.

Module mxui

Syntax call msUIInitialize Descriptions Procedure msUIInitialize is to initialize the MATFOR GUI system. It would create a main window according to a given MFUI file. The default MFUI filename is the same as the name of the executable but with the extension name ".mfui". The user can assign a custom MFUI file by adding the parameters "-ui custom.mfui" in the command line, where the name custom.mfui is the name of the custom MFUI file. This procedure should be called before other MATFOR graphics procedures. If this procedure is not called in the whole program and some graphics procedures are used, the system will automatically create a MATFOR Graphic Viewer to represent the visualization results. Example See Also mfUIMainLoop


msUIMainLoop Enters the main event loop of the MATFOR GUI system.

Module mxui

Syntax call msUIMainLoop Descriptions Enters the main event loop and waits until the main window is closed. It is necessary to call this function to start event handling. The main event loop receives events from the MATFOR GUI system and dispatches them to the application callback functions. Generally speaking, procedure msUIMainLoop is a correspondence of procedure msUIInitialize. Users should call msUIMainLoop when all initialization is done. Also, users should avoid calling mfViewPause if the function mfUIMainLoop has been called. Example See Also mfUIInitialize, mfViewPause


Property Setting


mfUIGetPropertyString Get the string property of a UI component.

Module mxui

Syntax value = mfUIGetPropertyString( ctrlname, propname[, defvalue] ) Descriptions Function mfUIGetPropertyString gets the string property of a given UI component. value = mfUIGetPropertyString( ctrlname, propname[, defvalue] )

• ctrlname is a string name of a UI component.

• propname describes the property being inquired.

• defvalue is the default value if the inquired property doesn't exist.

• value is the returned value of the inquired property.

Example See Also mfUISetPropertyString, mfUIGetPropertyInteger, mfUISetPropertyInteger, mfUIGetPropertyDouble, mfUISetPropertyDouble


msUISetPropertyString Set the string property of a UI component.

Module mxui

Syntax call msUISetPropertyString( ctrlname, propname, value ) Descriptions Function mfUISetPropertyString sets the string property of a given UI component. call msUISetPropertyString( ctrlname, propname, value )


• propname describes the property to be set.

• value is the value the property is set to.

Example See Also mfUIGetPropertyString, mfUIGetPropertyInteger, mfUISetPropertyInteger, mfUIGetPropertyDouble, mfUISetPropertyDouble


mfUIGetPropertyInteger Get the integer property of a UI component

Module mxui

Syntax value = mfUIGetPropertyInteger( ctrlname, propname[, defvalue] ) Descriptions Function mfUIGetPropertyInteger gets the integer property of a given UI component. value = mfUIGetPropertyInteger( ctrlname, propname[, defvalue] )





Example See Also mfUISetPropertyInteger, mfUIGetPropertyString, mfUISetPropertyString, mfUIGetPropertyDouble, mfUISetPropertyDouble


msUISetPropertyInteger Set the integer property of a UI component

Module mxui

Syntax call msUISetPropertyInteger( ctrlname, propname, value ) Descriptions Function mfUISetPropertyInteger sets the integer property of a given UI component call msUISetPropertyInteger( ctrlname, propname, value )




Example See Also mfUIGetPropertyInteger, mfUIGetPropertyString, mfUISetPropertyString, mfUIGetPropertyDouble, mfUISetPropertyDouble


mfUIGetPropertyDouble Get the double property of UI component

Module mxui

Syntax value = mfUIGetPropertyDouble( ctrlname, propname[, defvalue] ) Descriptions Function mfUIGetPropertyDouble gets the double property of a given UI component value = mfUIGetPropertyDouble( ctrlname, propname[, defvalue] )





Example See Also mfUISetPropertyDouble, mfUIGetPropertyString, mfUISetPropertyString, mfUIGetPropertyInteger, mfUISetPropertyInteger


msUISetPropertyDouble Set the double property of a UI component

Module mxui

Syntax call msUISetPropertyDouble( ctrlname, propname, value ) Descriptions Function mfUISetPropertyDouble sets the double property of a given UI component call msUISetPropertyDouble( ctrlname, propname, value )




Example See Also mfUIGetPropertyDouble, mfUIGetPropertyString, mfUISetPropertyString, mfUIGetPropertyInteger, mfUISetPropertyInteger


Callback Setting


msUISetOnClick Set the callback function of a UI component for a Click event.

Module mxui

Syntax call msUISetOnClick( ctrlname, callback ) Descriptions Function mfUISetOnClick sets the callback function of a UI component for a Click event. Once the user clicks the UI component, the callback function will be called to handle this event. The Click event is available for the MenuItem, Panel, Button, Label, RadioButton, CheckBox, ListBox, ProgressBar and Image components. call msUISetOnClick( ctrlname, callback )


• callback is the callback function that handles the corresponding event. Please refer to the

callback function section to see how to declare the prototype of a callback function.

Example See Also


msUISetOnDoubleClick Set the callback function of a UI component for a DoubleClick event.

Module mxui

Syntax call msUISetOnDoubleClick( ctrlname, callback ) Descriptions Function mfUISetOnDoubleClick sets the callback function of a UI component for a DoubleClick event. Once the user double-clicks the UI component, the callback function will be called to handle this event. The DoubleClick event is available for the Panel, Label, ListBox, ProgressBar and Image components. call msUISetOnDoubleClick( ctrlname, callback )




Example See Also


msUISetOnTabChanged Set the callback function of a UI component for a TabChanged event.

Module mxui

Syntax call msUISetOnTabChanged( ctrlname, callback ) Descriptions Function mfUISetOnTabChanged sets the callback function of a UI component for a TabChanged event. Once the user switches the tabsheet of the TabControl component, the callback function will be called to handle this event. The TabChanged event is available for the TabControl component. call msUISetOnTabChanged( ctrlname, callback )




Example See Also


msUISetOnResize Set the callback function of a UI component for a Resize event.

Module mxui

Syntax call msUISetOnResize( ctrlname, callback ) Descriptions Function mfUISetOnResize sets the callback function of a UI component for a Resize event. Once the user resizes the UI component, the callback function will be called to handle this event. The Resize event is available for the MainForm and Panel components. call msUISetOnResize( ctrlname, callback )




Example See Also


msUISetOnTextChanged Set the callback function of a UI component for a TextChanged event.

Module mxui

Syntax call msUISetOnTextChanged( ctrlname, callback ) Descriptions Function mfUISetOnTextChanged sets the callback function of a UI component for a TextChanged event. Once the user changes the text in the UI component, the callback function will be called to handle this event. The TextChanged event is available for the Edit and ComboBox components. call msUISetOnTextChanged( ctrlname, callback )




Example See Also


msUISetOnReturnPressed Set the callback function of a UI component for a ReturnPressed event.

Module mxui

Syntax call msUISetOnReturnPressed( ctrlname, callback ) Descriptions Function mfUISetOnReturnPressed sets the callback function of a UI component for a ReturnPressed event. Once the user presses the return key in the Edit component, the callback function will be called to handle this event. The ReturnPressed event is available for the Edit component. call msUISetOnReturnPressed( ctrlname, callback )




Example See Also


msUISetOnValueChanged Set the callback function of a UI component for a ValueChanged event.

Module mxui

Syntax call msUISetOnValueChanged( ctrlname, callback ) Descriptions Function mfUISetOnValueChanged sets the callback function of a UI component for a ValueChanged event. Once user changes the value of the UI component, the callback function will be called to handle this event. The ValueChanged event is available in the SpinEdit, Slider and ScrollBar components. call msUISetOnValueChanged( ctrlname, callback )




Example See Also


msUISetOnScrollReleased Set the callback function of a UI component for a ScrollReleased event.

Module mxui

Syntax call msUISetOnScrollReleased( ctrlname, callback ) Descriptions Function mfUISetOnScrollReleased sets the callback function of a UI component for a ScrollReleased event. Once user releases the scroll button of the Slider or ScrollBar components, the callback function will be called to handle this event. The ScrollReleased event is available in the Slider and ScrollBar components. call msUISetOnScrollReleased( ctrlname, callback )




Example See Also


UI Components


MainForm The base main window of the application. When this main window is closed, the application exits.

Properties

Property Value Description

caption string specifies the caption of the window

color string, e.g. "#FF0000" for red specifies the background color of the component

font font specifies the font of the component

fontcolor string, e.g. "#FF0000" for red specifies the font color of the

component

height integer specifies the vertical size of the

component in pixels.

icon encoded image specifies the icon that appears when the

form is minimized.

name string specifies the name of the component.

Use name to refer to this component

when getting or setting property values.

tag integer has no predefined meaning. It is

provided for the convenience of

developers, which can be used for

storing an additional integer value.

width integer specifies the horizontal size of the


Event(s)

Event Description

OnResize Occurs immediately after the component is resized.


MenuItem The menu item of the window menu

Properties


caption string specifies the caption of menu item



when getting or setting property values.





Event(s)

Event Description

OnClick Occurs when the user clicks the component.


MatforWindow A customized MATFOR component in which Matfor graphics functions represent their visualization results.

Properties


align "alNone", "alClient", "alTop", "alBottom", "alLeft", "alRight"

specifies the alignment of the

component. height integer specifies the vertical size of the




when getting or setting property

values.







x integer specifies the horizontal coordinate of

the component relative to its parent.

y integer specifies the vertical coordinate of the

component relative to its parent.

Event(s)

Event Description

None


TabControl A tab set that has the appearance of notebook dividers.

Properties




component.

currentpage integer determines which page displays in the

TabControl. The first page starts from

1.



component



margin integer specifies the size of the margin around

the inner page.




values.

pagetitle string specifies the text that identify the

individual page of the TabControl.

tabposition "tpTop", "tpBottom" determines whether tabs appear at the

top or bottom.











Event(s)


Event Description

OnTabChanged Occurs after a new tab is selected.


Panel A panel component.

Properties




component.

alignspace integer specifies the distance, in pixels,

between the aligned components on

this panel.

bevelstyle "bsRaised", "bsPlain", "bsSunken", "bsGroove", "bsRidge"

determines the display style of the

panel.

bevelwidth integer determines the width, in pixels, of the

panel bevels.

borderwidth integer specifies the distance, in pixels,

between the inner component and the

panel bevels..

caption string specifies the caption of the component.




component






values.












Event(s)

Event Description


OnDoubleClick Occurs when the user double-clicks the component.

OnResize Occurs immediately after the component is resized.


Button A button component.

Properties




component.

allowallup boolean specifies whether all buttons in the

same group can be unselected at the

same time.

caption string specifies the caption of the component.


down boolean specifies whether the button is selected

(down) or unselected (up).

flat boolean determines whether the button

removes the raised border when the

button is unselected.



component

glyph encoded image specifies the bitmap that appears on

the button.

groupindex integer allows buttons to work together as a

group. When groupindex is 0, the

button behaves as a normal

pushbutton. When groupindex is greater than 0, the buttons which have

the same groupindex are regarded as the same group. When the user clicks

one of these buttons, it remains

selected until the user clicks another

button belonging to the same group.







values.











Event(s)

Event Description



Label A label component.

Properties




component.

caption string specifies the text to display.




component

halign "haLeft", "haCenter", 'haRight" specifies the horizontal placement of

the text within the label






values.





valign "vaTop", "vaMiddle", "vaBottom"

specifies the vertical placement of the

text within the label







Event(s)

Event Description





RadioButton A radio button component.

Properties




component.


checked boolean determines whether the option

represented by the radio button is

selected.




component






values.











Event(s)

Event Description



CheckBox A check box component.

Properties




component.


checked boolean determines whether the option

represented by the check box is

selected.




component






values.

state "cbUnchecked", "cbChecked", "cbGrayed"

indicates whether the check box is

deselected, selected, or grayed.





tristate boolean determines whether check box can be

in a "grayed" state.








Event(s)

Event Description



Edit An edit component.

Properties




component.




component






values.





text string specifies the text in the component







Event(s)

Event Description

OnReturnPressed Occurs when return key pressed.

OnTextChanged Occurs when the text of the component has changed.


SpinEdit A spin edit component.

Properties




component.




component



max integer specifies the maximum value the user

can enter into the spin edit component.

min integer specifies the minimum value the user

can enter into the spin edit component.




values.












Event(s)

Event Description

OnValueChanged Occurs when the value of the component has changed.



ListBox A list box component.

Properties




component.




component



itemindex integer specifies the ordinal number of the selected item in the list box.

items string contains the strings that appear in the list box. The items are separated by linefeed character "\n".




values.





text string specifies the text of the selected item.







Event(s)

Event Description





ComboBox A combo box component.

Properties




component.




component



itemindex integer specifies the ordinal number of the selected item in the list box.

items string contains the strings that appear in the list box. The items are separated by linefeed character "\n".




values.





text string specifies the text of the selected item.







Event(s)

Event Description


OnTextChanged Occurs when the text of the component has changed.


Slider A slider component.

Properties






max integer specifies the maximum value of the

component.

min integer specifies the minimum value of the

component.




values.

orientation "otHorizontal", "otVertical" specifies whether the component is

horizontal or vertical.

position integer specifies the current position (value)

of the progress bar.





tickinterval integer specifies the tick interval on the slider.

tickmarks "tmNone", "tmTopLeft", "tmBottomRight", "tmBoth"

specifies the location of the tick

marks.

value integer is the same as the property

position.







Event(s)


Event Description

OnScrollReleased Occurs when the user finishes the scrolling. (Windows only)



ScrollBar A scroll bar component.

Properties







component.


component.




values.

orientation "otHorizontal", "otVertical" specifies whether the component is

horizontal or vertical.








position.







Event(s)

Event Description

OnScrollReleased Occurs when the user finishes the scrolling. (Windows Only)




ProgressBar A progress bar component.

Properties




component.




component



labelpos "lpNone", "lpCenter", "lpRight" specifies the label position of the

progress bar.


component.


component.




values.








position.








Event(s)

Event Description



(XWindow Only)


Image A image component.

Properties




component.

halign "haLeft", "haCenter", 'haRight" specifies the horizontal placement of

the text within the label






values.

picture encoded image specifies the bitmap that appears on

the image.

stretch boolean indicates whether the image should be

resized to fit the bounds of the image

component.





valign "vaTop", "vaMiddle", "vaBottom"

specifies the vertical placement of the

text within the label







Event(s)

Event Description





Memo A multiline edit component.

Properties




component.




component






values.

readonly boolean determines whether the user can

change the text of the component.








wordwrap boolean determines whether the component

inserts soft linefeed text wraps at the

right margin.





Event(s)

Event Description


None

Index 675

Index

A

All .................................................119 Any..................................................119 Arithmetic & Relational Operators.109 Arithmetic Operators ......109, 112, 119 Axis Control....................................341

B

Basic..................................................76 Button..............................................651

C

Callback Setting ..............................634 Camera Manipulation......................376 Cartographic Functions.....................96 CheckBox........................................656 ComboBox ......................................663 Complex..........................................159 Configuration ..................................303

D

Data Manipulation Functions............75 Display ................................24, 61, 299 Documentations ................................15

E

Edit..................................................658 Eigenvalues and singular values .....229 Elementary 2D/3D Objects .............546 Elementary Math Functions............121 Elementary Matrix-manipulation Functions.........................................181 Equivalency.................................23, 50 Essential Functions ...........................23 Exponential .....................................150 Extensions of MATFOR .................605

F

Factorization Utilities .....................240 Fast Fourier Transform .....................89 Figure..............................................290 FileIO................................................65

G

Graphics Viewer Manipulation.......584

I

Image ......................................541, 671 Initialization....................................624 Introduction.......................................15

L

Label ...............................................653 Linear Equations.............................216 Linear Graphs .................................388 Linespec..389, 398, 401, 404, 406, 408 ListBox ...........................................661

M

MainForm .......................................644 MATFOR Visualization Routines...281 MatforWindow................................646 MATLAB Interface.........................618 Matrices ..................................181, 183 Matrix Analysis...............................209 Matrix Function ..............................207 Matrix Manipulation...............181, 195 Memo..............................................673 Memory Management.................24, 56 MenuItem........................................645 mf......................................................28 mfAbs .....................................122, 160 mfACos...................................121, 124


mfACosh .................................121, 125 mfACot ...................................121, 126 mfACoth .................................121, 127 mfACsc ...................................121, 128 mfACsch .................................121, 129 mfAll .........................................38, 119 mfAngle ..................................122, 161 mfAnnotation ..................................325 mfAny .......................................40, 119 mfArray access..................................43 mfArray manipulation.................23, 25 mfAsec ............................................121 mfASec ...........................................130 mfASech .................................121, 131 mfASin....................................121, 132 mfASinh..................................121, 134 mfATan....................................121, 135 mfATan2..................................121, 136 mfATanh..................................121, 137 mfAxis.............................................342 mfAxis2DRange .............................353 mfAxis3DRange .............................354 mfAxisMark....................................568 mfBackgroundColor .......................340 mfBalance .......................208, 241, 244 mfBar ..............................................401 mfBar3 ............................................406 mfBar3h ..........................................408 mfBarh ............................................404 mfCamAngle...................................380 mfCamAzElRoll .............................381 mfCamDistance...............................382 mfCamFocal....................................384 mfCamProj......................................383 mfCamZoom...................................385 mfCeil .....................................122, 167 mfChol ....................207, 217, 243, 605 mfCircle ..........................................547

mfColon ..........................................185 mfColormapRange..........................334 mfComplex .............................122, 162 mfCond ...................207, 219, 243, 605 mfCone ...........................................566 mfConj ....................................122, 163 mfContour.......................................423 mfContour3.....................................425 mfCos......................................121, 138 mfCosh....................................121, 139 mfCot ......................................121, 140 mfCoth ....................................121, 141 mfCsc......................................121, 142 mfCsch....................................121, 143 mfCube ...........................................561 mfCylinder......................................563 mfDelaunay.....................................530 mfDelaunay3...................................533 mfDet ......................................207, 210 mfDiag ....................................181, 196 mfDoMATLAB...............................619 mfEig ..............................208, 230, 243 mfEquiv ............................................54 mfExp .....................................122, 151 mfEye......................................181, 184 mfFastMolecule ..............................555 mfFastPColor..................................421 mfFFT...............................................90 mfFFT2.............................................92 mfFFTShift .......................................94 mfFigure .........................................291 mfFigureCount................................294 mfFileDialog...................................601 mfFind.....................................181, 198 mfFix.......................................122, 169 mfFloor ...................................122, 171 mfFullToSp .....................................276 mfGetCamViewParam....................386

Index 677

mfGetCurrentDraw .........................580 mfGetDelaunay ...............................530 mfGetDelaunay3 .............................533 mfHess ............................208, 232, 243 mfIFFT..............................................90 mfIFFT2............................................92 mfIFFTShift ......................................94 mfImag....................................122, 164 mfImage ..........................................542 mfImRead .......................................544 mfInputMatrix.................................599 mfInputString..................................596 mfInputValue...................................597 mfInputVector .................................598 mfInputYesNo.................................604 mfInv...............................207, 221, 243 mfIsComplex.....................................26 mfIsEmpty.........................................26 mfIsHold .........................................320 mfIsLogical .......................................26 mfIsNumeric .....................................26 mfIsoSurface ...................................433 mfIsReal............................................26 mfIsValidDraw................................579 mfLDiv............................................228 mfLength...........................................42 mfLinspace..............................181, 186 mfLoad..............................................66 mfLoad.m..........................................67 mfLoadAscii .....................................68 mfLoadCsv........................................70 mfLog......................................122, 152 mfLog10..................................122, 153 mfLog2....................................122, 154 mfLogical................................181, 200 mfLu................................207, 223, 243 mfMagic..................................181, 187 mfMATLABServer .........................621

mfMatSub .........................................44 mfMax...............................................77 mfMesh ...........................................413 mfMeshc .........................................417 mfMeshgrid.............................181, 188 mfMin ...............................................79 mfMod ....................................122, 173 mfMolecule.....................................551 mfMul .............................................227 mfNDims ..........................................34 mfNorm...................207, 211, 243, 605 mfObjectModel...............................374 mfObjOrientation............................372 mfObjOrigin ...................................370 mfObjPosition.................................368 mfObjScale .....................................366 mfOnes....................................181, 190 mfOpenFileDialog ..........................601 mfOut................................................30 mfOutline........................................431 mfPatch ...........................................479 mfPColor.........................................419 mfPlot .............................................389 mfPlot3 ...........................................392 mfPoint ...........................................528 mfPow2...................................122, 156 mfProd ..............................................81 mfQr........................207, 225, 243, 605 mfQuiver.........................................536 mfQuiver3.......................................538 mfQz ...............................208, 234, 243 mfRand ...................................181, 191 mfRank ...................207, 213, 243, 605 mfRcond .................207, 222, 243, 605 mfRDiv ...........................................228 mfReal.....................................122, 165 mfRem ....................................122, 175 mfRepmat ...............................181, 192


mfReshape...............................181, 201 mfRibbon ........................................394 mfRound .................................122, 177 mfS....................................................44 mfSave.m ..........................................72 mfSaveFileDialog ...........................603 mfSchur...................................208, 236 mfSec ......................................121, 144 mfSech ....................................121, 145 mfShape ............................................36 mfSign.....................................122, 179 mfSin.......................................122, 146 mfSinh.....................................122, 147 mfSize ...............................................32 mfSliceIJK ......................................440 mfSlicePlane ...................................442 mfSliceXYZ....................................437 mfSolidContour...............................427 mfSolidContour3.............................429 mfSort ...............................................83 mfSortRows ......................................85 mfSpCreate .....................................246 mfSpEigs.........................................266 mfSpGet ..........................................251 mfSpGetCol ....................................257 mfSpGetM.......................................253 mfSpGetN .......................................253 mfSpGetNNZ..................................255 mfSpGetRow...................................257 mfSpGetVal.....................................259 mfSphere .........................................559 mfSpImport .....................................265 mfSpLDiv .......................................268 mfSpMul .........................................270 mfSpSize .........................................272 mfSpToFull .....................................274 mfSpy..............................................278 mfSqrt .....................................122, 158

mfSquare.........................................549 mfStem............................................398 mfStreamArrow ..............................468 mfStreamArrow2 ............................457 mfStreamArrow3 ............................468 mfStreamDashedLine .....................462 mfStreamDashedLine2 ...................451 mfStreamDashedLine3 ...................462 mfStreamLine .................................459 mfStreamLine2 ...............................448 mfStreamLine3 ...............................459 mfStreamRibbon.............................464 mfStreamRibbon2...........................453 mfStreamRibbon3...........................464 mfStreamTube.................................466 mfStreamTube2...............................455 mfStreamTube3...............................466 mfSubplot .......................................314 mfSum...............................................87 mfSurf .............................................411 mfSurfc ...........................................415 mfSvd..............................208, 238, 244 mfTan......................................122, 148 mfTanh....................................122, 149 mfTecOpenFile ...............................607 mfTecReadBlockCount...................613 mfTecReadTitle ..............................609 mfTecReadVarCount.......................613 mfTecWriteTitle..............................609 mfTetContour..................................487 mfTetIsoSurface..............................490 mfTetMesh......................................485 mfTetSlicePlane..............................496 mfTetSliceXYZ...............................493 mfTetStreamArrow .........................524 mfTetStreamDashLine ....................518 mfTetStreamLine ............................515 mfTetStreamRibbon........................520

Index 679

mfTetStreamTube............................522 mfTetSurf ........................................482 mfText .............................................324 mfTitle.............................................322 mfTrace ...................207, 215, 243, 605 mfTriContour ..................................476 mfTril ......................................181, 202 mfTriMesh ......................................474 mfTriStreamArrow..........................512 mfTriStreamDashLine.....................506 mfTriStreamLine.............................503 mfTriStreamRibbon ........................508 mfTriStreamTube ............................510 mfTriSurf ........................................472 mfTriu .....................................181, 204 mfTube ............................................396 mfUIGetPropertyDouble.................632 mfUIGetPropertyInteger .................630 mfUIGetPropertyString...................628 mfWindowCaption..........................296 mfWindowPos.................................298 mfWindowSize................................297 mfXLabel ........................................322 mfYLabel ........................................322 mfZeros ...................................181, 194 mfZLabel.........................................322 msAbs .............................................160 msACos...........................................124 msACosh.........................................125 msACot ...........................................126 msACoth .........................................127 msACsc ...........................................128 msACsch .........................................129 msAddLegend.................................338 msAll.................................................38 msAngle ..........................................161 msAnnotation..................................325 msAny...............................................40

msASec ...........................................130 msASech .........................................131 msASin ...........................................132 msASinh .........................................134 msAssign...........................................51 msATan ...........................................135 msATan2 .........................................136 msATanh .........................................137 msAxis ............................................342 msAxis2DDependency ...................349 msAxis2DMode..............................347 msAxis2DPosition ..........................355 msAxis3DDependency ...................351 msAxis3DMode..............................348 msAxisGrid.....................................359 msAxisMark ...................................568 msAxisWall.....................................357 msBackgroundColor .......................340 msBalance.......................................241 msCamAngle ..................................380 msCamProj .....................................383 msCamZoom...................................385 msCeil .............................................167 msChol............................................217 msCircle..........................................547 msClearSubplot...............................317 msCloseFigure ................................293 msColon..........................................185 msColorbar .....................................329 msColormap....................................331 msColormapRange .........................334 msComplex .....................................162 msCone ...........................................566 msConj............................................163 msContour.......................................423 msContour3.....................................425 msCos .............................................138 msCosh ...........................................139


msCot ..............................................140 msCoth ............................................141 msCreateCoastline3Data.................106 msCreateCoastlineData...................104 msCreateGeoid3Data ......................103 msCreateGeoidData ........................102 msCsc..............................................142 msCsch............................................143 msCube ...........................................561 msCylinder......................................563 msDelaunay.....................................530 msDelaunay3...................................533 msDiag ............................................196 msDisplay .........................................62 msDoMATLAB...............................619 msDrawColormap ...........................335 msDrawMaterial .............................574 msDrawNow ...................................301 msDrawTexture...............................577 msEditorAxis ..................................591 msEditorBackground ......................593 msEditorColorbar............................592 msEditorColormap..........................589 msEditorDrawList...........................587 msEditorMaterial ............................588 msEditorTransform .........................590 msEig ..............................................230 msExp .............................................151 msExportImage ...............................311 msEye..............................................184 msFastMolecule ..............................555 msFastPColor..................................421 msFigure .........................................291 msFind.............................................198 msFix...............................................169 msFloor ...........................................171 msFormat ..........................................64 msFreeArgs .......................................59

msGDisplay ....................................300 msGetDelaunay...............................530 msGetDelaunay3.............................533 msGetIsoSurface.............................435 msGetSlicePlane .............................446 msGetSliceXYZ..............................445 msGetTetIsoSurface........................499 msGetTetSlicePlane........................501 msGetTetSliceXYZ.........................500 msGSet............................................571 msHess............................................232 msHold............................................318 msImag ...........................................164 msImage..........................................542 msImWrite ......................................545 msInitArgs ........................................59 msIsoSurface...................................433 msLegendBox.................................336 msLinspace .....................................186 msLoadConfig ................................305 msLog .............................................152 msLog10 .........................................153 msLog2 ...........................................154 msLogical .......................................200 msLu ...............................................223 msMagic .........................................187 msMATLABServer.........................621 msMax ..............................................77 msMesh...........................................413 msMeshc .........................................417 msMeshgrid ....................................188 msMin ...............................................79 msMod ............................................173 msMolecule.....................................551 msObjectModel...............................374 msObjOrientation ...........................372 msObjOrigin ...................................370 msObjPosition.................................368

Index 681

msObjRotateWXYZ .......................364 msObjRotateX.................................362 msObjRotateY.................................362 msObjRotateZ.................................362 msObjScale .....................................366 msOnes............................................190 msOutline........................................431 msPatch ...........................................479 msPColor.........................................419 msPlot .............................................389 msPlot3 ...........................................392 msPoint ...........................................528 msPointer ..........................................52 msPow2...........................................156 msPrintPreview...............................585 msProd ..............................................81 msProj4 .............................................97 msProj4Inv........................................97 msQr................................................225 msQuiver.........................................536 msQuiver3.......................................538 msQz ...............................................234 msRand ...........................................191 msReal.............................................165 msRecordEnd..................................307 msRecordStart.................................307 msRem ............................................175 msRemoveAllLegend .....................339 msRemoveDraw..............................582 msRemoveLegend...........................339 msRepmat .......................................192 msReshape ......................................201 msReturnArray..................................57 msRibbon ........................................394 msRound .........................................177 msSave ..............................................71 msSaveAscii......................................73 msSaveConfig .................................304

msSaveCsv........................................74 msSchur ..........................................236 msSec..............................................144 msSech............................................145 msSetCamViewParam ....................387 msSetDrawName ............................583 msShading.......................................327 msShowMessage.............................595 msSign ............................................179 msSin ..............................................146 msSinh ............................................147 msSize...............................................32 msSliceIJK......................................440 msSlicePlane...................................442 msSliceXYZ ...................................437 msSolidContour ..............................427 msSolidContour3 ............................429 msSort ...............................................83 msSortRows......................................85 msSpAdd.........................................247 msSpDisplay ...................................263 msSpExport.....................................264 msSpGetIdx ....................................261 msSphere.........................................559 msSpSet ..........................................249 msSpy .............................................278 msSqrt .............................................158 msSquare.........................................549 msStem ...........................................398 msStreamArrow..............................468 msStreamArrow2............................457 msStreamArrow3............................468 msStreamDashedLine .....................462 msStreamDashedLine2 ...................451 msStreamDashedLine3 ...................462 msStreamLine .................................459 msStreamLine2 ...............................448 msStreamLine3 ...............................459


msStreamRibbon.............................464 msStreamRibbon2...........................453 msStreamRibbon3...........................464 msStreamTube.................................466 msStreamTube2...............................455 msStreamTube3...............................466 msSubplot .......................................314 msSum...............................................87 msSurf .............................................411 msSurfc ...........................................415 msSvd..............................................238 msTan..............................................148 msTanh............................................149 msTecCloseFile...............................607 msTecReadBlock ............................610 msTecReadVarName.......................610 msTecWriteIJKBlock......................615 msTecWriteTetBlock.......................615 msTecWriteTriBlock.......................615 msTecWriteVarNames.....................614 msTetContour..................................487 msTetIsoSurface..............................490 msTetMesh......................................485 msTetSlicePlane..............................496 msTetSliceXYZ...............................493 msTetStreamArrow .........................524 msTetStreamDashLine ....................518 msTetStreamLine ............................515 msTetStreamRibbon........................520 msTetStreamTube ...........................522 msTetSurf ........................................482 msText.............................................324 msTrace...........................................215 msTriContour ..................................476 msTriMesh ......................................474 msTriStreamArrow .........................512 msTriStreamLine.....................503, 506 msTriStreamRibbon ........................508

msTriStreamTube............................510 msTriSurf ........................................472 msTube............................................396 msUIInitialize .................................625 msUIMainLoop...............................626 msUISetOnClick.............................635 msUISetOnDoubleClick .................636 msUISetOnResize...........................638 msUISetOnReturnPressed ..............640 msUISetOnScrollReleased .............642 msUISetOnTabChanged .................637 msUISetOnTextChanged ................639 msUISetOnValueChanged ..............641 msUISetPropertyDouble.................633 msUISetPropertyInteger .................631 msUISetPropertyString...................629 msView ...........................................377 msViewPause..................................302 msWindowCaption .........................296 msWindowPos ................................298 msWindowSize ...............................297 msZeros...........................................194

O

Object Manipulation .......................361 Operator Precedence.........21, 109, 110

P

Panel ...............................................649 Plot Annotation and Appearance ....321 Plot Creation and Control ...............313 Procedure Descriptions Convention .17 ProgressBar.....................................669 Property Setting ......................570, 627

R

RadioButton....................................655 Recording........................................306 Relational Operators ....... 109, 116, 117

Index 683

Rounding and Remainder ...............166

S

ScrollBar .........................................667 Simple GUI .....................................594 Slice Graphs ....................................436 Slider ...............................................665 Sparse Array....................................243 Sparse Array....................................245 SpinEdit...........................................659 Streamline Graphs...........................447 Surface Graphs................................410

T

TabControl ......................................647 Tecplot FileIO .................................606

Triangular Surface Graphs..............471 Trigonometry ..................................123 Typographical Conventions ..............16

U

UI Components...............................643 Unstructured Grids..........................481 Unstructured Point Set....................527 Unstructured Streamlines................502

V

Velocity Vectors ..............................535

W

Window Frame ...............................295

Documents

MATFOR4 Ref Fortran