%% we want to show how "preallocation" speed up the code!!
%dynamic array growth:
tic
fibonacci = [0,1];
for idx = 3 : 40000
   fibonacci(idx) = fibonacci(idx-1) + fibonacci(idx-2); %dynamically changes size
end
toc
 %@MatlabTips 
% use preallocation – 9x faster in my machine(dual_core)
tic
fibonacci = zeros(40000,1); %preallocation
fibonacci(1)=0; fibonacci(2)=1;
for idx = 3 : 40000, 
   fibonacci(idx) = fibonacci(idx-1) + fibonacci(idx-2);
end
toc

A=rand(100,1);
B=rand(100,1);
for i=1:100
C(i)=A(i)*B(i);
end

A=rand(100,1);
B=rand(100,1);
C=A.*B;

R = 1:10000;        %radious 
H = 1:400;          %Height
V = zeros(10000,4000);  %preallocate V(volume) to speed up
 
for i = 1:numel(H)
    for j = 1:numel(R)
        V(j,i) = pi * R(j).^2 * H(i);
    end
end

R = 1:10000;
H = 1:400;
[matR, matH] = meshgrid(R,H);
V = pi.*matR.^2.*matH;

%@MatlabTips
% Using a loop(element by element)
tic
R = 1:10000;        %radious 
H = 1:400;          %Height
V = zeros(10000,4000);  %preallocate V(volume) to speed up

for i = 1:numel(H)
    for j = 1:numel(R)
        V(j,i) = pi * R(j).^2 * H(i);
    end
end
toc
clear all
%@MatlabTips
% Vectorized code , 6x faster in my machine

tic
R = 1:10000;
H = 1:400;
[matR, matH] = meshgrid(R,H);
V = pi.*matR.^2.*matH;
toc

»which myname

 ‘myname’ not found.

X = randn(N);
Y = zeros(N);
for row = 1:N % Row
    for col = 1:N % Column
        if X(row,col) >= 0
            Y(row,col) = X(row,col);
        end
    end
end

N = 5e3;
X = randn(N);
Y = zeros(N);
for col = 1:N % Column
    for row = 1:N % Row
        if X(row,col) >= 0
            Y(row,col) = X(row,col);
        end
    end
end

>> bench

%% slow approach using a.^n
a = 0.9999; n = 10000;
for idx=1:1000
    y=a.^(1:n);
end

%% Using exp(log(a)*n) - 8x faster
for idx=1:1000
    y=exp(log(a)*(1:n)); 
end

%% Using cumprod(a) - 40x faster
for idx=1:1000
    y=cumprod(zeros(1,n)+a);
end

N = 1e7;
tic
w = zeros(1, N);
for i = 1:N
    w(i) = i*5;
end
fprintf('For loop: %.4fs\n', toc);
 
tic
y = (1:N)*5;
fprintf('Vectorized: %.4fs\n', toc);

feature('accel','off')  %this line shuts down the JIT
N = 1e7;
tic
w = zeros(1, N);
for i = 1:N
    w(i) = i*5;
end
fprintf('For loop: %.4fs\n', toc);
 
tic
y = (1:N)*5;
fprintf('Vectorized: %.4fs\n', toc);

a=3%scalar
x=[1,2,3]% row vector
y=[1;2;3]% column vector
A=[1,2,3;4,5,6]% matrix

a = 3;
b = 4;
a * b %scalar by scalar
 
a = 3;
x = [1, 3, 7];
a * x %scalar by vector
 
a = 3;
X = [1, 2 ,4 ;5, 2, 3];
a * X %scalar by matrix