1. MATLAB 程式設計 Learning Loops and Logic
方煒 台大生機系

2. Ex9_1 Summing a series with a for loop
s=0; % set a variable to 0 so that 1/n^2 can be repeatedly added to it
N=10000; % set the upper limit of the sum
for n=1:N % start of the loop
% add 1/n^2 to s each time, then put the answer back into s
s=s+1/n^2;
end % end of the loop
fprintf(’ Sum = %g \n’,s) % print the answer
% calculate the sum of the squares of the reciprocals of the
% integers from 1 to 10,000
n=1:10000;
sum(1./n.^2)

3. Ex9_2 Products with a for loop
P=1; % set the first term in the product
N=20; % set the upper limit of the product
for n=2:N % start the loop at n=2 because we already loaded n=1
P=P*n; % multiply by n each time and put the answer back into P
end
fprintf(’ N! = %g \n’,P) % print the answer
factorial(20)
gamma(21)

4. Ex9_3 Recursion relations with for loops
a(1)=1; % put the first element into the array
N=19; % the first one is loaded, so let’s load 19 more
for n=1:N % start the loop
a(n+1)=(2*n-1)/(2*n+1)*a(n); % the recursion relation
end
disp(a) % display the resulting array of values

5. Ex9_4 Logic clear; a=1;b=3;
% If the number a is positive set c to 1; if a is 0 or negative set c to 0
if a>0
c=1
else
c=0
end
% if either a or b is non-negative, add them to obtain c;
% otherwise multiply a and b to obtain c
if a>=0 | b>=0 % either non-negative
c=a+b
c=a*b % otherwise multiply them to obtain c

6. Ex9_5 Secant method % set chk, the error, to 1 so it won’t trigger
clear;close all;
%************************************
% Define the function as an in line function
func=inline(’exp(-x)-x’,’x’);
% First plot the function
x=0:.01:2;
f=func(x);
plot(x,f,’r-’,x,0*x,’b-’)
% From the plot the solution is near x=.6
% Secant method to solve the exp(-x)-x = 0
% Use an initial guess of x1=0.6
x1=0.6;
% find f(x1)
f1=func(x1);
% find a nearby second guess
x2=0.99*x1;
% set chk, the error, to 1 so it won’t trigger
% the while before the loop starts
chk=1;
% start the loop
while chk>1e-8
% find f(x2)
f2=func(x2);
% find the new x from the straight line approximation and print it
xnew = x2 - f2*(x2-x1)/(f2-f1)
% find chk the error by seeing how closely f(x)=0 is approximated
chk=abs(f2);
% load the old x2 and f2 into x1 and f1; then put the new x into x2
x1=x2;f1=f2;x2=xnew;
end

7. Ex9_6 Using fzero function f=fz(x) % evaluate the function fz(x) whose
% roots are being sought
f=exp(-x)-x;
%****************************************% Here is the matlab code that uses fz.m to find
% a zero of f(x)=0 near the guess x=.7
% Note that sign is used to tell Matlab that
% the name of an M-file is being passed into fzero
%***************************************