School  of  Physics  and  Astronomy,  University  of  Manchester  

PHYS20762  ComputaAonal  Physics  

Hywel  Owen  

Part  1:  MATLAB  and  Data  Analysis  Lecture  1:  IntroducAon  to  ComputaAonal  Physics  

What  is  this  course?  

•  This  is  a  course  on  ComputaAonal  Physics:  –  The  use  of  algorithms  and  numerical  methods  to  perform  data  analysis  and  

simulaAon  in  support  of  experimental  and  theoreAcal  physics    

•  There  are  3  pillars  of  physics:  –  Theory  –  Experiment  –  SimulaAon  

PHYS20762  Lecture  1  

Course  Informa3on  

•  The  real  course  website:  –  hPp://theory.physics.manchester.ac.uk/~hywel/teaching/phys20762/  

 •  But  material  is  also  posted  on  Blackboard  

–  Blackboard  is  linked  to  the  website  above    

PHYS20762  Lecture  1  

Should  you  be  here?  

•  If  you  are  a  TheoreAcal  Physics  student:  –  Go  away.  You  should  be  on  PHYS20872  Theory  CompuAng  Project.  –  Were  you  at  the  orientaAon  session  yesterday?  No?  Then  talk  to  Niels  Walet.  

•  If  you  not  a  TheoreAcal  Physics  student:  –  CongratulaAons!  –  You  should  be  here.  

•  Can  you  do  both  PHYS20762  and  PHYS20872?  –  No.  

•  Can  you  do  both  AddiAonal  Lab  and  PHYS20762?  –  No.  

•  What  is  the  difference  between  PHYS20762  and  PHYS20872?  –  PHYS20762  is  for  Normal  students  –  PHYS20872  is  for  Theory  students  

PHYS20762  Lecture  1  

Why  should  you  do  this  course?  

•  Technical  compuAng  underlies  prePy  much  all  of  the  jobs  you  are  likely  to  do  a]er  graduaAng  

•  You  are  about  90%  likely  to  be  doing  scienAfic  programming  a]er  you  leave  

Manchester  Graduate  Des3na3ons  

ScienAc/CompuAng  

Finance/Management  

Postgrad/Research  

Other  

PHYS20762  Lecture  1  

A  couple  of  examples  

•  My  best  friend  ScoP  

•  Graduate  physics  (Edinburgh)  •  PhD  in  crystallography,  including  

wriAng  of  experimental  control  and  data  analysis  

•  Then  programming  GUIs  in  C++  for  mobile  phone  manufacturer  

•  Now  wriAng  trading  so]ware  in  C++  for  CiAbank  in  London  

•  ££££  

•  Me  

•  Graduate  physics  (Manchester!)  •  PhD  in  liquid  crystals,  wriAng  data  

acquisiAon  and  data  analysis  •  WriAng  control  so]ware  for  

diagnosAc  staAon  on  parAcle  accelerators  (e.g.  SRS);  VB,  LabVIEW,  etc.  

•  WriAng  so]ware  to  simulate  behaviour  of  new  parAcle  accelerators  (e.g.  DIAMOND)  www.diamond.ac.uk  

•  Carrying  this  on  at  Manchester  

PHYS20762  Lecture  1  

What  languages/plaAorms  are  actually  used  in  the  ‘real  world’?  

Commercial  •  Compiled  

–  C/C++  (esp.  Finance)  •  Vis-­‐C,  C#,  Obj-­‐C,  Java  

•  Interpreted  –  Python  (e.g.  Google)  –  (Ruby,  Javascript)  

•  Environments  –  LabVIEW  (esp.  for  DAQ)  –  Excel  

Research/Scien3fic  •  Compiled  

–  C/C++  –  Fortran  

•  F90,  F95  etc.  

•  Interpreted  –  Python  

•  Environments  –  MATLAB  –  MathemaAca  

PHYS20762  Lecture  1  

Other languages (Pascal, Visual Basic, Perl, Tcl)

Other packages (Maple, Mathcad, IDL, Origin)

Structure  of  the  Course  

•  Part  1:  MATLAB  and  Data  Analysis  –  Lecture  1:  The  MATLAB  environment  –  Lecture  2:  Working  with  data  in  MATLAB  –  Lecture  3:  Data  analysis  and  fiong  in  

MATLAB  –  Lecture  4:  File  input  and  output  in  MATLAB  

•  Part  2:  Numerical  Methods  –  Lecture  5:  IntroducAon  to  numerical  

methods  –  Lecture  6:  Numerical  soluAon  of  equaAons  –  Lecture  7:  Numerical  methods  in  MATLAB  –  Lecture  8:  User-­‐defined  funcAons  in  

MATLAB  •  Part  3:  Monte-­‐Carlo  Techniques  

–  Lecture  9:  Random  Numbers  and  Monte  Carlo  IntegraAon  

–  Lecture  10:  Monte  Carlo  ParAcle  Transport  

•  MATLAB  PracAce  (Week  1)  •  Projects:  

–  Project  1  (Weeks  2-­‐4):  Analysis  of  experimental  spectrum  data  

–  Project  2  (Weeks  5-­‐8):  Numerical  integraAon  of  the  damped  oscillator  equaAon  

–  Project  3  (Weeks  9-­‐12):  PenetraAon  of  neutron  through  shielding  

•  12  Half  days  in  the  laboratory  3.58  (½  on  Tue,  ½  on  Fri)    

PHYS20762  Lecture  1  

Course  Aims  and  Learning  Outcomes  

•  To  familiarise  the  students  with  pracAcal  techniques  for  using  computers  in  physics.  

•  On  compleAon  successful  students  will  be  able  to:    1.  write  MATLAB  programs  involving  computaAons  and  graphics;    2.  use  MATLAB  to  analyse  and  fit  experimental  data;    3.  use  numerical  methods  (Euler,  Verlet)  to  find  soluAons  of  an  ordinary  

differenAal  equaAon  and  thereby  to  analyse  the  behaviour  of  a  physical  system  (e.g.  damped  oscillator);    

4.  understand  the  principles  of  the  Monte  Carlo  method  and  its  applicaAon  to  parAcle  transport  

5.  use  the  Monte  Carlo  method  to  simulate  parAcle  transport  through  a  given  physical  system  (e.g.  neutrons  through  shielding)  

 

PHYS20762  Lecture  1  

Assessments  •  You  will  write  3  project  reports  •  Assessment  is  based  on  the  content  of  these  reports  •  Read  each  project  brief  (on  the  module  website)  and  follow  it!  •  All  the  project  briefs  and  assessment  forms  (with  criteria)  are  already  on  

the  website.    •  Each  project  has  a  bonus  secAon  –  you  are  encouraged  to  try  them,  

they’re  not  that  hard.  (hint:  don’t  think  of  them  as  bonuses…)  •  Extra  marks  may  be  awarded  for  invenAveness  –  we  want  you  to  think!  

•  Projects  are  to  be  submiPed  in  paper  form:  –  Sorry,  what?  This  is  a  compuAng  course,  and  you  want  a  report,  in  paper  

format???  –  We  tried  electronic,  and  it’s  too  much  hassle  both  for  you  and  for  us  –  We  have  to  print  them  out  to  mark  them  up  for  your  feedback  anyway  

PHYS20762  Lecture  1  

Some  Recommended  Texts  

•  Chapman,  S.J.  MATLAB  Programming  for  Engineers  (Brooks  and  Cole  2000)    •  Higham,  D.J.  &  Higham,  N.J.  MATLAB  Guide  (Philadelphia:  Society  for  

Industrial  and  Applied  MathemaAcs)  2nd  ediAon  (2005)    •  Garcia,  A.L.  Numerical  Methods  for  Physics  (PrenAce  Hall  1994)    •  Kerningham,  B.W.  &  Ritchie,  D.M.  The  C  programming  Language  (PrenAce  

Hall)  2nd  ediAon  (1988)    •  Barlow,  R.J.  &  BarneP,  A.R.  Compu>ng  for  Scien>sts,  Principles  of  

Programming  with  Fortran  90  and  C++  (John  Wiley  and  Sons  Ltd  ,  1998)    

•  There  are  not  a  lot  of  good  texts  for  what  we’re  doing.  

PHYS20762  Lecture  1  

Two  Basic  Messages  About  This  Course  

•  Not  everything  you  need  to  know  for  the  projects  is  in  the  lecture  notes  –  APend  the  lectures,  ask  quesAons!  –  You  will  learn  a  lot  by  doing  the  projects:  get  feedback  in  the  lab  sessions  

•  Not  everything  in  the  lectures  is  about  the  projects  –  We’re  trying  to:  –  a)  Make  the  rest  of  your  degree  easier  –  b)  Expose  you  to  ideas  that  you  can  learn  more  about  by  yourselves  later  –  c)  Generally  educate  you  in  this  topic  

PHYS20762  Lecture  1  

Rubin  Landau’s  Rules  of  Educa3on  

1.  Most  of  educaAon  is  learning  what  the  words  mean;  the  concepts  are  usually  quite  simple  once  you  understand  what  you  are  being  told.      2.  Confusion  is  the  first  step  to  understanding.    3.  TraumaAc  experiences  tend  to  be  the  most  educaAonal  ones.    

Why  MATLAB?  

•  MATLAB  is  a  terrible  programming  language  

•  You  could  do  this  course  in,  for  example,  C++  

•  BUT….  

–  This  is  not  a  course  in  programming  (you  did  that  last  semester)  –  This  is  a  course  on  algorithms,  i.e.  implemenAng  physics  using  compuAng  –  The  language  is  secondary  –  Speed  does  not  maPer  for  our  course  (hint:  it  does  a  bit)  

PHYS20762  Lecture  1  

PHYS20762  Lecture  1  

Interlude…  

Interlude:  How  do  programmers  spend  their  3me?  

•  Q:  How  much  of  a  typical  programmer’s  day  is  spent  actually  programming?    

PHYS20762  Lecture  1  

Interlude:  How  do  programmers  spend  their  3me?  

•  Q:  How  much  of  a  typical  programmer’s  day  is  spent  actually  programming?    

PHYS20762  Lecture  1  

Programming  25%  

Debugging  25%  Documenta3on  

10%  

Design  20%  

Mee3ngs  20%  

PHYS20762  Lecture  1  

Onward…

C++  is  great,  but…  

•  There  is  an  overhead  of  ‘structure’  needed  in  your  code  •  There  are  no  ‘scienAfic/math’  libraries  built  in  to  the  language  

–  Plenty  of  add-­‐ons  •  It’s  fairly  plaxorm-­‐dependent  

–  You  can’t  send  the  source  code  to  your  friend  easily  •  It’s  fast,  but  you  o]en  don’t  need  that  parAcularly  

PHYS20762  Lecture  1  

MATLAB  

•  MATLAB  is  the  most  widely-­‐used  interpreted  scienAfic  compuAng  package  –  i.e.  you  will  probably  need  to  know  it  later  –  It’s  also  VERY  handy  to  know  how  to  use  it  for  your  degree  

•  A]er  this  course  I  don’t  want  to  hear  people  moaning  about  Easyplot!  

•  MATLAB’s  advantages  –  Interpreted  –  no  messing  around  between  wriAng,  compiling  and  running  –  Lots  of  built-­‐in  libraries  for  scienAsts  –  Plaxorm  independent.  ‘Write  once,  run  anywhere’  (nearly)  

•  MATLAB’s  disadvantages  –  Interpreted,  so  somewhat  slower  than  compiled  languages  for  big  tasks  –  Like  many  library-­‐heavy  commercial  packages,  it’s  expensive  –  But  you  won’t  noAce  either  of  these!  

PHYS20762  Lecture  1  

Reminders:  Workspace/Command  Window  

PHYS20762  Lecture  1  

Reminders:  Edit  Window  

PHYS20762  Lecture  1  

Reminders:  Variables  in  MATLAB  

•  (Reminder:  A  variable  is  a  unit  of  data  with  a  name,  which  is  available  to  the  program)  

•  Simple  variables  –  comment = ‘This is a string’; % Can put comments

after the definition!–  a = 1; % Integers!–  b = 2.883; % Reals!–  c = 1.2*a + b; % Formulae!–  x = 1; y = 2; % Multiple definitions per line!–  v = [1 5 2 6]; % vector(row vector)–square brackets!!–  m = [1 5;3 8]; % 2x2 matrix!–  n = [0 1+7]; % Expression in a definition!–  p = [y(2) 7 y(3)]; % Array indexing!

PHYS20762  Lecture  1  

Reminders:  Defining  and  indexing  arrays  

x = 1:2:10 % First:increment:last!!x = 1 3 5 7 9!!g = 1:4; % Row vector!h = g’; % Transpose makes column vector!i = [1;3;4;5]; % Or define column vector explicitly!!!This is all quite different from other languages!!!

PHYS20762  Lecture  1  

Reminders:  Indexing  

x = [1.1 -2.2 3.3 -4.4 5.5];!!x(3) is 3.3!x(1:2) is [1.1 -2.2]!x(1:2:5) is [1.1 3.3 5.5]!!!m = [1 2 3;-2 -3 -4;3 4 5];!m(6) is 4 – weird but true…!m(2,3) is -4!m(3,:) is [3 4 5]!m(:,2) is [2;-3;4]!m(1:2,3:4) is [2 3;-3 -4]  

PHYS20762  Lecture  1  

1 2 3!-2 -3 -4!3 4 5!

1 2 3!-2 -3 -4!3 4 5!

Reminders:  Func3ons  

There  are  lots  of  funcAons  and  constants  available  to  you:    Math:      +  -­‐  *  /  ^  ()  Comparison:  ==    <    >    ~=    (these  return  1/0  for  ‘true’/’false’)  Logical:    &  |      (also  return  1/0  for  ‘true’/’false’)  Numerical:  Inf  j  NaN  pi  FuncAons:  abs  exp  log  log2  log10  mod  real  imag  round  sign    Trig:    sin  cos  tan  asin  acos  atan  (etc.)  Specialised:  besselj  factorial  legendre  �  (etc.)    Use  the  Quick  Reference  Booklets    BIG  TIP:    Someone  will  probably  have  wanted  to  do  the  same  job  as  you.  That  

funcAon  already  exists,  you  just  have  to  FIND  IT.  PHYS20762  Lecture  1  

Reminders:  Let’s  plot  some  data  

x = 0:pi/20:2*pi; % Make some x values!y = sin(x); % Make some y values as a fn. of x!!plot(x,y);  

PHYS20762  Lecture  1  Hint: also try linspace

Reminders:  How  about  another  one?  

x = 0:pi/20:2*pi; % Make some x values!z = (x-2).^2+2; % Make some z!% (x-2)^2+2 doesn’t work!!plot(x,z); % Over-writes first figure  

PHYS20762  Lecture  1  

Matrix  and  Array  Mul3ply/Power  –  ‘a  Gotcha’  

This is something *very* particular to MATLAB: •  * is used for matrix multiplication •  .* is used for element-by-element (array) multiplication •  ^ is used for matrix powers •  .^ is used for element-by-element (array) powers

PHYS20762  Lecture  1  

>> a = [1 2;3 4]!a =! 1 2!

3 4  

>> a^2!ans =! 7 10!

15 22!>> a.^2!ans =! 1 4! 9 16!

a^2 is equivalent to a*a (matrix multiplication)

…and  for  mul3plica3on  

>> a = [1 2;3 4]!!a =!! 1 2! 3 4!!>> b=[1 1;1 1]!!b =!! 1 1! 1 1!

PHYS20762  Lecture  1  

>> a*b!!ans =!! 3 3! 7 7!!>> a.*b!!ans =!! 1 2! 3 4!

Some  other  plot  types  

•  (Use  the  Quick  Reference  Booklets)  PHYS20762  Lecture  1  

polar(x,y) bar(x,y)

loglog(x,y) semilogx(x,y)

Code  recommenda3ons  

•  Microso]  Excel  –  part  of  Office,  okay  for  basic  work  and  data  collecAon  

•  MATLAB  (hPp://www.mathworks.co.uk/  )  –  Students  can  use  this  anywhere  you’re  connected  to  the  Uni  network  –  Including  VPN  (hPp://www.itservices.manchester.ac.uk/vpn/)  

•  MathemaAca  (hPp://www.wolfram.com/)  –  Awesome  so]ware,  but  less  used  than  MATLAB  –  Also  have  a  site  license,  but  easier  to  use  Cluster  computers  

•  Python  (hPp://www.python.org/  )  –  Use  Python  2.7.x  (not  3.x)  as  there’s  more  code  made  for  it  –  Get  the  excellent  Canopy  package  (any  OS):  

hPps://www.enthought.com/products/canopy/    

PHYS20762  Lecture  1  

Lab  Sessions  

•  Today:  MATLAB  Refresher  and  PracAce  

•  Lab  Sessions  are  10am  to  1pm  on  Tuesdays  or  Fridays  –  (about)  Half  of  you  on  Tuesdays,  Half  of  you  on  Fridays.  –  Computer  Lab  3.58  –  Demonstrators  are  on  hand  only  at  these  Ames;  make  use  of  them  

•  At  other  Ames  you  may  carry  out  work  on  any  of  the  Schuster  cluster  computers  

 •  Refer  to  the  Ametable  and  deadlines  to  work  out  when  to  hand  in  your  

project  work:  –  hPp://theory.physics.manchester.ac.uk/~hywel/phys20762/phys20762-­‐

Ametable/  

PHYS20762  Lecture  1