For Loops

Syntax

for index = values
statements
end

Process

x = 1;
for n = [1 2 3]
x = x + n
end

1st Iteration

n = 1
x = 1
x = x + n
x = 1 + 1
x = 2

2nd Iteration

n = 2
x = 2
x = x + n
x = 2 + 2
x = 4

3rd Iteration

n = 3
x = 4
x = x + n
x = 4 + 3
x = 7

Types of Values

Loop Through Array

m = 1;
for A = [3 6 1 5 8]
fprintf('The value of A(%d) is %.0f\n',m,A);
m = m + 1;
end

Loop through String

b = 'Boring!';
m = 1;
for A = ['B' 'o' 'o' '-' 'Y' 'a' 'h']
    fprintf('%s\n',A);
    b(m) = A
    m = m + 1;
end

Loop Through Vectorization

m = 1;
for B = 1:10
fprintf('The value of B(%d) is %.0f\n',m,B);
m = m + 1;
end

m = 1;
for B = 20:80
fprintf('The value of B(%d) is %.0f\n',m,B);
m = m + 1;
end

Loop Through Vectorization with Positive Iteration

Integer Iteration

m = 1;
for C = 1:2:10
fprintf('The value of C(%d) is %.0f\n',m,C);
m = m + 1;
end

Integer Iteration + Index

D = ones(10,1)
for C = 1:2:10
    D(C,1) = C;
    fprintf('The value of D(%d,1) is %.0f\n',C,C);
    D
end

Non-Integer Iteration

m = 1;
for C = 1:0.2:10
fprintf('The value of C(%d) is %.0f\n',m,C);
m = m + 1;
end

Loop Through Vectorization with Negative Iteration

Integer Iteration

m = 1;
for C = 10:-1:1
fprintf('The value of C(%d) is %.0f\n',m,C);
m = m + 1;
end

Integer Iteration + Index

D = ones(10,1)
for C = 10:-1:1
    D(C,1) = C;
    fprintf('The value of D(%d,1) is %.0f\n',C,C);
    D
end

Non-Integer Iteration

m = 1;
for C = 10:-0.2:1
fprintf('The value of C(%d) is %.0f\n',m,C);
m = m + 1;
end

Loop Through Matrix

View Column Vectors

m = 1;
E = zeros(4);
for D = rand(4)
    E(:,m) = D;
    disp('Column vector')
    disp(D)
    E
    m = m + 1;
end

View Unit Vectors

I = eye(4,5)
for I = eye(4,5)
disp('Current unit vector:')
disp(I)
end
I

Change Matrix Values

s = 10;
H = zeros(s);
for c = 1:s
    for r = 1:s
        H(r,c) = 1/(r+c-1);
    end
end
H

Leave a Loop

break

A = nan(20,1);
for i=10:-1:-10
    if(i <= 0)
        break;
    end
    A(i) = i;
end
A(:)

Skip Within Loop

continue

A = nan(20,1);
for i=1:20
    if(mod(i,2) == 0)
        continue;
    else
        A(i) = i;
    end
end
A

Indexing in a Loop

for i = 1:2:20
A(i) = 2;
end
A

Nested For Loops - 3 x 3

for i = 1:3
    for j = 1:3
        A(i,j) = i + j;
        fprintf('i=%d j=%d -- A(%d,%d)=%d\n',i,j,i,j,A(i,j));
    end
end
A

Nested For Loops - 3 x 3 x 3

for i = 1:3
    for j = 1:3
        for k = 1:3
            A(i,j,k) = i + j + k;
            fprintf('i=%d j=%d k=%d -- A(%d,%d,%d)=%d\n',i,j,k,i,j,k,A(i,j,k));
        end
    end
end
A

Optimization

Preallocation

tic
x = 0;
for k = 2:1000000
x(k) = x(k-1) + 5;
end
toc

tic
x = zeros(1, 1000000);
for k = 2:1000000
x(k) = x(k-1) + 5;
end
toc

Elapsed time is 0.181970 seconds.
Elapsed time is 0.011886 seconds.

Vectorization

tic
i = 0;
for t = 0:.01:100000
i = i + 1;
y(i) = sin(t);
end
toc

tic
t = 0:.01:100000;
y = sin(t);
toc

Elapsed time is 2.255200 seconds.
Elapsed time is 0.141934 seconds.

Keep Loops Lean

tic
i = 0;
for t = 0:.01:100000
    i = i + 1;
    y(i) = sin(t);
end
toc

tic
i = 0;
for t = 0:.01:100000
    i = i + 1;
    y(i) = sin(t);
    z = linspace(0,2*pi);
    r = cos(z);
end
toc

Elapsed time is 2.211985 seconds.
Elapsed time is 88.842359 seconds.

Mathematical Series

1/(1-x) for -1 < x < 1

x = 0;
s = 1/2;
upper = 1000;

for i = 0:upper
x = x + (s)^i;
end
fprintf('Let x = %.4f\n\n',s);
fprintf('sum(x^n/n!) = %.4f\n\n',x);
fprintf('where n = 0 to %d\n\n',upper);

y = 1/(1-s);

fprintf('1/(1-x) = %.4f\n\n',y);

e^x for -inf < x < inf

x = 0;
s = 1/2;
upper = 1000;

for i = 0:upper
x = x + (s)^i/factorial(i);
end
fprintf('Let x = %.4f\n\n',s);
fprintf('sum(x^n) = %.4f\n\n',x);
fprintf('where n = 0 to %d\n\n',upper);

y = exp(s);

fprintf('1/(1-x) = %.4f\n\n',y);

Plots Within Loop

Build Variable then Plot

tic
hold on
b = 0:.00001:2*pi;
for i = 0:.01:2*pi
    x(m) = sin(i);
    y(m) = cos(i);
    z(m) = i*sin(i);
    m = m + 1;
end
plot(b,x,':b')
plot(b,y,':r')
plot(b,z,':g')
toc

Plot then Clear Variable

tic
hold on
for i = 0:.01:2*pi
    clear x
    clear y
    clear z
    x = sin(i);
    y = cos(i);
    z = i*sin(i);
    plot(i,x,':b')
    plot(i,y,':r')
    plot(i,z,':g')
end
toc

Fractals

Mandelbrot

tic
n = 800;
niter = 40;

x0 = -2; x1 = 1;
y0 = -1.5; y1 = 1.5;

[x,y] = meshgrid(linspace(x0, x1, n), linspace(y0, y1, n));

c = x + 1i * y;
z = zeros(size(c));
k = zeros(size(c));

for ii = 1:niter
z = z.^2 + c;
k(abs(z) > 2 & k == 0) = niter - ii;
end

figure,
imagesc(k),
colormap jet
axis square
toc

Algorism and Bushism of the Day


"My job is a decision-making job, and as a result, I make a lot of decisions."	"I tell you that Michael Jackson is unbelievable, isn’t he? He’s just unbelievable." This statement was made just after the Chicago Bulls won their sixth championship.

Loops

OODA Loop?

Cool Loop?

Four Loops?

Infinite Loops?

Learning Loops?

For Loops

Syntax

Process

1st Iteration

2nd Iteration

3rd Iteration

Types of Values

Loop Through Array

Loop through String

Loop Through Vectorization

Loop Through Vectorization with Positive Iteration

Integer Iteration

Integer Iteration + Index

Non-Integer Iteration

Loop Through Vectorization with Negative Iteration

Integer Iteration

Integer Iteration + Index

Non-Integer Iteration

Loop Through Matrix

View Column Vectors

View Unit Vectors

Change Matrix Values

Leave a Loop

break

Skip Within Loop

continue

Indexing in a Loop

Nested For Loops - 3 x 3

Nested For Loops - 3 x 3 x 3

Optimization

Preallocation

Vectorization

Keep Loops Lean

Mathematical Series

1/(1-x) for -1 < x < 1

e^x for -inf < x < inf

Plots Within Loop

Build Variable then Plot

Plot then Clear Variable

Fractals

Mandelbrot

Algorism and Bushism of the Day

Lesson of the Day

Integrity

It's what you do when no one is looking

Word of the day

Color Me

Badd

The End