mrfarhadir

function [retval] = isPositiveDefinit(A)

FLAG = 1;

IS_SYMMETRIC = isequal(A,A.');

if (IS_SYMMETRIC == 0)
    retval = 0;
else

mrfarhadir

const algo = arr => {
  let sum_half = 0
  let i = 0
  let p = 0
  while(i < arr.length)
    sum_half += arr[i++]
  sum_half /= 2
  let left_side_sum = 0
  let last_diff = 0
  for(i in arr) {

mrfarhadir

function ImprovedEuler(F)
% Improved Euler Method
% blog.mrfarhad.ir
% author: Farhad Mehryari
a = 0;          
b = 200;

% محدوده مورد نظر

n = 100;            % ـعداد دفعات تکرار حلقه

mrfarhadir

% matlab eular method
% Author: Farhad Mehryari
% blog.mrfarhad.ir
function [y t] = euler(f,a,b,ya,n)
    h = (b - a) / n;
    y(1,:) = ya;
    t(1) = a;
    for i = 1 : n
        y(i+1,:) = y(i,:) + h * f(t(i),y(i,:));
        t(i+1) = t(i) + h;

mrfarhadir

% play piano with matlab
% "soltan qalba" ha song
% author: Farhad Mehryari
notecreate = @(frq,dur,v) sin(2*pi* [1:dur]/v * (440*2.^((frq-1)/12)));
notename = {'A' 'A#' 'B' 'C' 'C#' 'D' 'D#' 'E' 'F' 'F#' 'G' 'G#'};
song =      {'A' 'B' 'C' 'E' 'F' 'E' 'F' 'E' 'F' 'E' 'D' 'E' 'D' 'E' 'D' 'E' 'D' 'C' 'D' 'C' 'D' 'C' 'B' 'A' 'A' 'B'};
durations = [1 1 1 3 1 2 1 2 1 1 1 1 2 1 2 1 1 1 1 2 1 2 1 2 1 0.5 1]
for k1 = 1:length(song)
    if (string(song(k1)) == '0') 
        songidx(k1) = 0

mrfarhadir

function root = newton(f,df)
  % Newton-Raphson method
  % Author: Farhad Mehryari
  i = 1;
  p0 = 0.5*pi;            %شرایط اولیه
  N = 100;                %حداکثر تعداد تکرار
  error = 0.0001;         %خطا
  while i <= N
      p = p0 - (f(p0)/df(p0));          %روش نیوتن
      if (abs(p - p0)/abs(p)) < error % شرط خروج از حلقه

mrfarhadir

% Romberg Integration in Numerical Analysis
% Author: Farhad Mehryari
% Web: blog.mrfarhad.ir
function r = romberg(f,a,b,n)
h = (b - a) ./ (2.^(0:n-1));
r(1,1) = (b - a) * (f(a) + f(b)) / 2;
for j = 2:n
    subtotal = 0;
    for i = 1:2^(j-2)
        subtotal = subtotal + f(a + (2 * i - 1) * h(j));

mrfarhadir

% LU Matrix decomposition algorithm
% Author: Farhad Mehryari
% Web: blog.mrfarhad.ir
function [ L, U ] = LU(A)
% A شرط بررسی مربعی بودن ماتریس 
sz = size(A);
if sz(1)~=sz(2)
    fprintf('A is not square !\n');
    clear x;
    return;

mrfarhadir

%Cholesky matrix decompression
function [retval] = Cholesky (A)
n = length( A );
L = zeros( n, n );
for i=1:n
   L(i, i) = sqrt(A(i, i) - L(i, :)*L(i, :)');
   for j=(i + 1):n
      L(j, i) = (A(j, i) - L(i,:)*L(j ,:)')/L(i, i);
   end
end

mrfarhadir

function [eigValue,eigVector] = EigPowerMethod (A, epsilon)
[m,n]=size(A);
if (m != n) 
  disp("Matrix Should Be Square");
else
  u = [];
  t = 0;
  r = ones(m);
  u = [u transpose(r(1,:))];
  i = 2;