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

– 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

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 = 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 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)

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);

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:’);

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

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,...)

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

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);

Importing data

• Textread, dlmreadDLMREAD read ASCII delimited file.

M = dlmread(FILENAME,DLM)

TEXTREAD read text file in a certain format

[A B] = textread(‘datafile','%f %f');