BEH.420 Matlab Tutorial

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BEH.420 Matlab Tutorial

• Bambang Adiwijaya
• 09/20/01

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Starting Matlab

• On athena
• Athena add matlab
• Athena matlab
• On PC
• Point and click

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Matlab basic

• Functions
• Matrix formulation fast calculation
• Strong in numerical, but weak in analytical
• General purpose math solvers nonlinear
  equations, ODEs, PDEs, optimization
• Basic mode of usage
• Interactive mode
• M-script
• Functions
• M-script and Functions must be written in
  separate files

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Basic Syntax

• Case sensitive variable name
• Ending a statement with a
• Vector Vec(i)
• Matrix Mat(i,j,)
• Element by element matrix operations
• ., ./, .2
• General matrix operations
• Cross product ()

• Looping in matlab
• for I 1N,
• for J 1N,
• A(I,J) 1/(IJ-1)
• end
• end
• If statement
• if I J
• A(I,J) 2
• elseif abs(I-J) 1
• A(I,J) -1
• else
• A(I,J) 0
• end

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Basic Matlab Commands
Matlab commands Functions and descriptions
help functionname Matlab on-line help for functions
lookfor searchphrase To find matlab function with descriptions containing the search phrase
who To list all variables currently used
size(matrix) To identify the dimensionality of the matrix
ones(m,n) To create a unit matrix of size m x n
print depsc filename.ps To print an active plot (later use lpr to print in athena)
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Function

• A function must be created under a separate file
• Function name and filename should be the same
• Example
• function res no1fun(x,p1)
• res(1)x(1)x(2)-p1
• res(2)x(1)-2x(2)

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Plotting

• figure to create a new popup window
• plot(X,Y,'c) semilogx(X,Y,bx-)
• subplot(row,col,figno), title(example title)
• ylabel(temp) xlabel(conc)
• axis(minX maxX minY maxY)
• Example
• a(110)
• ba.2
• ca.0.5
• figure
• subplot(2,1,1), semilogx(a,b,bx-)
• subplot(2,1,2), plot(a,c, rs)

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Fsolve solving nonlinear equations

• FSOLVE solves equations of the form
• F(X)0 where F and X may be vectors or
  matrices.
• Syntax
• Xfsolve('FUN',X0,OPTIONS, P1,P2,...)
• Problem
• Solve
• x(1)x(2)-30
• x(1)-2x(2)0

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ODE solvers solving ordinary differential
equations

• ODE23, ODE45, ODE113, ODE15S, ODE23S
• ODE45 Runge Kutta (4,5) formula, best first try
  function
• ODE23 Runge Kutta (2,3) formula.
• ODE113 variable order Adams-Bashforth-Moulton
  PECE solver. More efficient when the function
  evaluation is expensive.
• Stiff vs non-stiff ODEs
• Function solving yF(t,y).
• ODE file must be in the form of
  dydtF(t,y,flag,p)
• Syntax
• T,Y ode45('F',TSPAN,Y0,OPTIONS,P1,P2,...)

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ODE solvers how to solve higher order ODE?

• Example how to solve
• y2y30?
• Answer make substitution.
• Y1y
• Y2y
• New formulation
• Y1Y2
• Y2-2Y2-3

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Curvefitting

• CURVEFIT solves problems of the form
• min sum (FUN(X,XDATA)-YDATA).2 where
  FUN, XDATA and YDATA are
• X
  vectors.
• Syntax
• Xcurvefit('FUN',X,XDATA,YDATA,OPTIONS,'GRADFUN',P
  1,P2,..)
• Examples
• Fit the following data into the following model
  and regress x parameters
• ydatapx(1)x(2)exp(-xdata)

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Importing data

• Textread, dlmread
• DLMREAD read ASCII delimited file.
• M dlmread(FILENAME,DLM)
• TEXTREAD read text file in a certain format
• A B textread(datafile','f f')