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BEH.420 Matlab Tutorial

BEH.420 Matlab Tutorial. Bambang Adiwijaya 09/20/01. Starting Matlab. On athena: Athena% add matlab Athena% matlab On PC: Point and click. Matlab basic. Functions: Matrix formulation: fast calculation Strong in numerical, but weak in analytical

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BEH.420 Matlab Tutorial

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  1. BEH.420 Matlab Tutorial Bambang Adiwijaya 09/20/01

  2. Starting Matlab • On athena: • Athena% add matlab • Athena% matlab • On PC: • Point and click

  3. 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

  4. 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 = 1:N, for J = 1:N, A(I,J) = 1/(I+J-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 Basic Syntax

  5. Basic Matlab Commands

  6. 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)-2*x(2);

  7. 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=(1:10); b=a.^2; c=a.^0.5; figure; subplot(2,1,1), semilogx(a,b,’bx-’); subplot(2,1,2), plot(a,c, ‘rs:’);

  8. Fsolve: solving nonlinear equations • FSOLVE solves equations of the form: F(X)=0 where F and X may be vectors or matrices. • Syntax: X=fsolve('FUN',X0,OPTIONS, P1,P2,...) • Problem: Solve: x(1)*x(2)-3=0 x(1)-2*x(2)=0

  9. 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 y’=F(t,y). • ODE file must be in the form of: dydt=F(t,y,flag,p) • Syntax: [T,Y] = ode45('F',TSPAN,Y0,OPTIONS,P1,P2,...)

  10. ODE solvers: how to solve higher order ODE? • Example: how to solve: y’’+2y’+3=0? • Answer: make substitution. Y1=y Y2=y’ New formulation: Y1’=Y2 Y2’=-2Y2-3

  11. Curvefitting • CURVEFIT solves problems of the form: min sum {(FUN(X,XDATA)-YDATA).^2} where FUN, XDATA and YDATA are X vectors. • Syntax: X=curvefit('FUN',X,XDATA,YDATA,OPTIONS,'GRADFUN',P1,P2,..) • Examples: Fit the following data into the following model and regress x parameters: ydata=p*x(1)+x(2)*exp(-xdata);

  12. 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');

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