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Intro to Matlab
1. Using scalar variables
2. Vectors, matrices, and arithmetic
3. Plotting
4. Solving Systems of Equations
Can be found at: http://www.cs.unc.edu/~kim/matlab.ppt
New Class--for Engineers
• ENGR196.3
• SPECIAL TOPICS: INTRODUCTION TO MATLAB
• Description: Fundamentals of MATLAB programming applied to problems in science and mathematics. Solving systems of equations, basic scripting, functions, vectors, data files, and graphics. (Credit course for grade or CR/NC)
Why use Matlab?
• Drawbacks:
Slow (execution) compared to C or Java
• Advantages:
Handles vector and matrices very nice
Quick plotting and analysis
EXTENSIVE documentation (type ‘help’)
Lots of nice functions: FFT, fuzzy logic, neural nets, numerical integration, OpenGL (!?)
One of the major tools accelerating tech change
A tour of Matlab’s features• Click on Help>Full Product Family Help:
Check out Fuzzy Logic
Genetic Algorithms
Symbolic Math
Scalars
• The First Time You Bring Up MATLAB
• MATLAB as a Calculator for Scalars
• Fetching and Setting Scalar Variables
• MATLAB Built-in Functions, Operators, and Expressions
• Problem Sets for Scalars
3-1 The First Time You Bring Up MATLAB
Basic windows in MATLAB are:• Command - executes single-line commands• Workspace - keeps track of all defined variables• Command History - keeps a running record of all single
line programs you have executed• Current Folder - lists all files that are directly available for
MATLAB use• Array Editor - allows direct editing of MATLAB arrays• Preferences - for setting preferences for the display of
results, fonts used, and many other aspects of how MATLAB looks to you
3-2 MATLAB as a Calculator for Scalars
• A scalar is simply a number…
• In science the term scalar is used as opposed to a vector, i.e. a magnitude having no direction.
• In MATLAB, scalar is used as opposed to arrays, i.e. a single number.
• Since we have not covered arrays (tables of numbers) yet, we will be dealing with scalars in MATLAB.
,4,7
22,5.3
3-3 Fetching and Setting Scalar Variables
• Think of computer variables as named containers.
• We can perform 2 types of operations on variables:
we can set the value held in the container: x = 22we can set the value held in the container: x = 22
we can look at the value held in the container: xwe can look at the value held in the container: x
The Assignment Operator (=)
• The equal sign is the assignment operator in MATLAB.
>> x = 22places number 22 in container x
• How about:>> x = x + 1
• Note the difference between the equal sign in mathematics and the assignment operator in MATLAB!
Useful Constants
• Inf infinity• NaN Not a number (div by zero)• eps machine epsilon• ans most recent unassigned answer• pi 3.14159….• i and j Matlab supports imaginary
numbers!
3-4 MATLAB Built-in Functions, Operators, and Expressions
• MATLAB comes with a large number of built-in functions (e.g.. sin, cos, tan, log10, log, exp)
• A special subclass of often-used MATLAB functions is called operators– Assignment operator (=)– Arithmetic operators (+, -, *, /, ^)– Relational operators (<, <=, = =, ~=, >=, >)– Logical operators (&, |, ~)
Vector Operations
• Vector Creation
• Accessing Vector Elements
• Row Vectors and Column Vectors, and the Transpose Operator
• Vector Built-in Functions, Operators, and Expressions
Vectors and Matrices• Can be to command line or from *.m file
scalar: x = 3vector: x = [1 0 0]2D matrix: x = [1 0 0; 0 1 0; 0 0 1]arbitrarily higher dimensions (don’t use much)
• Can also use matrices / vectors as elements:
x = [1 2 3]
y = [ x 4 5 6]
2-D Plotting and Help in MATLAB
• Using Vectors to Plot Numerical Data
• Other 2-D plot types in MATLAB
• Problem Sets for 2-D Plotting
6-2 Using Vectors to Plot Numerical Data• Mostly from observed data - your goal is to
understand the relationship between the variables of a system.
• Determine the independent and dependent variables and plot:
speed = 20:10:70;stopDis = [46,75,128,201,292,385];plot(speed, stopDis, '-ro') % note the ‘-ro’ switch
• Don’t forget to properly label your graphs:title('Stopping Distance versus Vehicle Speed', 'FontSize', 14)xlabel('vehicle speed (mi/hr)', 'FontSize', 12)ylabel('stopping distance (ft)', 'FontSize', 12)grid on
Speed (mi/hr) 20 30 40 50 60 70
Stopping Distance (ft) 46 75 128 201 292 385
3D Plotting• 3D plots – plot an outer product
x = 1:10y = 1:10z = x’ * ymesh(x,y,z)
Single quote ‘ means transpose (can’t cut and paste though…)
Flow Constructs
• IF block
if (<condition>)
<body>
elseif
<body>
end
• WHILE block
while (<condition>)
<body>
end
Conditions same as C, ( ==, >=, <=) except != is ~=
More Flow Constructs
• FOR block
for i = 1:10
<body>
end
• SWITCH statement
switch <expression>
case <condition>,
<statement>
otherwise <condition>,
<statement>
end
Other Language Features
• Matlab language is pretty sophisticated– Functions
Stored in a *.m file of the same name:
function <return variable> = <function name>(<args>)
<function body>
– Structs• point.x = 2; point.y = 3; point.z = 4;
– Even has try and catch (never used them)
Solving Systems of Equations
• Consider a system of simultaneous equations
3x + 4y + 5z = 32
21x + 5y + 2z = 20
x – 2y + 10z = 120
• A solution is a value of x, y, and z that satisfies all 3 equations
• In general, these 3 equations could have
1 solution, many solutions, or NO solutions
Using Matlab to Solve Simultaneous Equations
• Set up the equation in matrix/vector form:
A = [3 4 5; 21 5 2; 1 -2 10] u = [ x y z]’ b = [ 32 20 120]’In other words, A u = b (this is linear algebra)
3 4 5
21 5 2
1 -2 10
x
y
z
*
32
20
120
=
The solution uses matrix inverse
• If you multiply both sides by 1/A you get
u = 1/A * b
• In the case of matrices, order of operation is critical (WRONG: u = b/A )
• SO we have “Left division” u = A \ b
(recommended approach)
• OR use inv( ) function: u = inv(A) * b
The solution>> u = A\b
u =
1.4497 ( value of x)
-6.3249 ( value of y)
10.5901 ( value of z)
• You can plug these values in the original equation test = A * u and see if you get b