Numerical Methods for Civil Engineers

Transcription

1 Numerical Methods for Civil Engineers Lecture 3 - MATLAB 3 Programming with MATLAB : - Script m-filesm - Function m-filesm - Input and Output - Flow Control Mongkol JIRAVACHARADET S U R A N A R E E UNIVERSITY OF TECHNOLOGY INSTITUTE OF ENGINEERING SCHOOL OF CIVIL ENGINEERING

2 Creating m-filesm MATLAB scripts and functions are stored in plain text files ed with extension.m To open the built-in editor, select menu: File > New > M-file hello.m % hello.m greets you and asks for your name. disp( Hello! Who are you? ) >> help hello >> hello

3 A Script to Plot Functions trigplot.m t = linspace(0,2*pi); y1 = sin(t); y2 = cos(t); y3 = y1.*y2; plot(t,y1, -,t,y2,.,t,y3, ); >> trigplot Replace the plot statement with plot(t,y1, -,t,y2, :,t,y3, ); axis([0 2*pi ]) leg( sin(t), cos(t), sin(t)*cos(t) ); >> close all; trigplot

4 Use T E X notation to display θ leg( sin(\theta), cos(\theta), sin(\theta)*cos(\theta) ); xlabel( \theta (radius), FontName, Times, FontSize,14) >> close all; trigplot >> x = linspace(0,2*pi); >> y1 = sin(x); >> y2 = cos(x); >> y3 = y1.*y2; >> plot(x,y1,'-',x,y2,':',x,y3,'--'); >> axis([0 2*pi ]) >> leg('sin(\theta)','cos(\theta)','sin(\theta)*cos(\theta)') >> xlabel('\theta (radius)','fontname','times','fontsize',14) >> title('plot of simple trigonometric functions',... 'FontName','Times','FontSize',12)

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6 Function m-files Command Window >> input parameters function output parameters function [outputparameterlist] = functionname(inputpramaterlist) pyt.m function h = pyt(a, b) % PYT hypotenuse of a right-angled triangle h = sqrt(a.^2 + b.^2); >> pyt(3,4)

7 addmult.m function [s,p] = addmult(x,y) % addmult Compute sum and product of two matrices s = x+y; p = x*y; >> clear >> [a,b] = addmult(3,2) >> addmult(3,2) >> v = addmult(3,2) Number of output parameters used to call a function must match the number of output parameters that is expexted to return.

8 INPUT AND OUTPUT Prompting for User Input >> x = input( Enter a value for x ); By default, the input function returns a numerical value. To obtain a string input, a second parameter, s, must be provided. >> yourname = input( Enter your name, s ); function s = inputabuse % inputabuse Use input messages to compute sum of 3 variables x = input( Enter the first variable to be added ); y = input( Enter the second variable to be added ); z = input( Enter the third variable to be added ); s = x+y+z;

9 Text Output The disp Function >> disp( My favorite color is red ) Since disp requires only one argument, the message and variable must be combined into a single string. >> yourname = input( enter your name, s ); >> disp([ Your name is,yourname]) The fprintf Function fprintf(format) fprintf(format,variables) fprintf(fid,format,variables) >> fprintf( Warning: x is negative\n ) \n is the newline string

10 fprintf(format,variables) >> name = Elvis ; age = str2num(datestr(now,10)-1935; >> fprintf( %s is %d years old\n,name,age); Elvis is 65 years old %s format as a string %d format as an integer %f format as a floating point %e format as a floating point in scientific notation %g format in the most compact form of either %f or %e \n insert newline in output string \t insert tab in output string

11 fprintf(fid,format,variables) >> x =... >> fout = fopen( myfile.dat, wt ); >> fprintf(fout, k x(k)\n ); >> for k = 1:length(x) >> fprintf(fout, %4d %5.2f\n,k,x(k)); >> >> fclose(fout)

12 FLOW CONTROL MATLAB has several flow control constructs: if switch & case for while continue break

13 if Conditional Control The if statement evaluates a logical expression and executes a group of statements when the expression is true. The optional elseif and else keywords provide for the execution of alternate groups of statements. An keyword, which matches the if, terminates the last group of statements. if condition expression elseif condition expression else expression Condition: Equal A == B Not equal A ~= B Greater A > B Smaller A < B Greater or equal A >= B Smaller or equal A <= B AND & OR

14 Example 1: if a < 0 disp( a is negative ); Example 2: if a < 0, disp( a is negative ); Example 3: if x >= y c = x^2 - y; elseif y/x > 2.0 c = log(y/x); else c = x + y;

15 switch & case The switch statement executes groups of statements based on the value of a variable or expression. The keywords case and otherwise delineate the groups. Only the first matching case is executed. There must always be an to match the switch. switch expression case value1 block of statements case value2 block of statements... otherwise block of statements switch sign(x) case -1 disp( x is negative ); case 0 disp( x is exactly zero ); case 1 disp( x is positive ); otherwise disp( sign test fail );

16 for The for loop repeats a group of statements a fixed, predetermined number of times. A matching delineates the statements. >> P = zeros(5, 5); >> for k = 1:5 for l = 1:5 P(k, l) = pyt(k, l); >> P

17 while The while loop repeats a group of statements an indefinite number of times under control of a logical condition. A matching delineates the statements. while condition expressions >> x=1; >> while 1+x > 1 x = x/2; >> x Break Loops Return Loops break return LOOP return break

18 Here is a complete program, illustrating while, if, else, and, that uses interval bisection to find a zero of a polynomial. a = 0; fa = -Inf; b = 3; fb = Inf; while b-a > eps*b x = (a+b)/2; fx = x^3-2*x-5; if sign(fx) == sign(fa) a = x; fa = fx; else b = x; fb = fx; x a fa x fb b The result is a root of the polynomial x 3-2x - 5, namely x =