Loops

In [4]:
n=5;
s=0;
for i=1:n
 s = s+i;   
end
s

s =

    15

Fibonacci Sequence

$F_1 = 1$, $F_2 = 1$ and $F_i = F_{i-1} + F_{i-2}$, $i = 3, 4, ...$

In [8]:
n=10;
F(1)=1;
F(2)=1;
for i=3:n
    F(i)=F(i-1)+F(i-2);
end
F

F =

     1     1     2     3     5     8    13    21    34    55
In [11]:
clear all
F(1)=1;
F(2)=1;
n=3;
while n<=10
    F(n)=F(n-1)+F(n-2);
    n=n+1;
end
F

F =

     1     1     2     3     5     8    13    21    34    55
In [12]:
A=[1 2 3; 4 5 6; 7 8 9];
B=[5 6 7;8 9 0;3 4 5];
disp('sum of two matrices without loop')
A+B
for i=1:3
    for j=1:3
        C(i,j)=A(i,j)+B(i,j);
    end
end
disp('sum of two matrices using for loop')
C

sum of two matrices without loop

ans =

     6     8    10
    12    14     6
    10    12    14

sum of two matrices using for loop

C =

     6     8    10
    12    14     6
    10    12    14

Matrix multiplication

In [6]:
A=[1 2 3; 4 5 6; 7 8 9];
B= [3 2 1; 6 5 4; 9 8 7];
C=zeros(3);
disp('Matrix multiplication without loop')
disp(A*B)
for i=1:3
    for j=1:3
       % C(i,j)=0;
        for k=1:3
            C(i,j)=C(i,j)+A(i,k)*B(k,j);
        end
    end
end
disp('Matrix multiplication using for loop')
disp(C)

Matrix multiplication without loop
    42    36    30
    96    81    66
   150   126   102

Matrix multiplication using for loop
    42    36    30
    96    81    66
   150   126   102

Find factorial $n! = 1. 2. 3. ... (n-1)n$

In [13]:
n=5;
f=1;
for i=1:n
    f=f*i;
    i=i+1;
end
disp('using for loop')
disp(f)

f1=1;
i=1;
while i<=n
    f1=f1*i;
    i=i+1;
end
disp('using while loop')
disp(f1)

using for loop
   120

using while loop
   120

Fixed point iteration, $x = \phi(x)$, $x_n =\phi(x_{n-1})$. For example $x = cosh(x/4)$

In [14]:
clear all
disp('Fixed point iteration');
phi = @(x) cosh(x/4);
xf=1;
er = 1;
k=0;
while ((er > 1e-8) && (k < 100))
    xnew = phi(xf);
    er = abs(xnew-xf);
    xf = xnew;
    k = k+1;
end
xf
k

Fixed point iteration

xf =

    1.0336


k =

     7
In [9]:
f = @(x) x - phi(x);
x=0:0.05:10;
y1=x;
y2=phi(x);
plot(x,y1,'r',x,y2,'b')
hold on 
plot(x,f(x),'g',x,0*x,'k',xf*ones(length(-2:0.05:10),1),-2:0.05:10,'k')
plot(xf,xf,'ob',xf,0,'og')
hold off

Leibniz formula for $\pi$,

$\frac{\pi}{4} = \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}$

In [10]:
clear piapprox
n=100;
piq=0;
piapprox = 0;
for i=0:n
    piq=piq+((-1)^i)/(2*i+1);
    piapprox = [piapprox, piq*4];
end
piapprox(end)
%plot gnuplot
plot(piapprox,'b')
hold on
plot(0:n,pi*ones(length(0:n),1),'r')
hold off

ans =

    3.1515
In [11]:
x=1
while x<=10
    x=2*x
end

x =

     1


x =

     2


x =

     4


x =

     8


x =

    16

Infinite Loop!

In [ ]:
x=1
while 1
    x=2*x
    pause
end