{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Loops"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fibonacci Sequence\n",
    "$F_1 = 1$, $F_2 = 1$ and $F_i = F_{i-1} + F_{i-2}$, $i = 3, 4, ...$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F =\n",
      "\n",
      " Columns 1 through 11:\n",
      "\n",
      "      1      1      2      3      5      8     13     21     34     55     89\n",
      "\n",
      " Columns 12 through 20:\n",
      "\n",
      "    144    233    377    610    987   1597   2584   4181   6765\n",
      "\n"
     ]
    }
   ],
   "source": [
    "n=20;\n",
    "F(1)=1;\n",
    "F(2)=1;\n",
    "for i=3:n\n",
    "    F(i)=F(i-1)+F(i-2);\n",
    "end\n",
    "F\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F =\n",
      "\n",
      "    1    1    2    3    5    8   13   21   34   55\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clear all\n",
    "F(1)=1;\n",
    "F(2)=1;\n",
    "n=3;\n",
    "F(3) = F(1) + F(2);\n",
    "while n<=10\n",
    "    F(n)=F(n-1)+F(n-2);\n",
    "    n=n+1;\n",
    "end\n",
    "F"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple while loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =  1\n",
      "x =  2\n",
      "x =  4\n",
      "x =  8\n",
      "x =  16\n"
     ]
    }
   ],
   "source": [
    "x=1\n",
    "while x<=10\n",
    "    x=2*x\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sum of two matrices without loop\n",
      "ans =\n",
      "\n",
      "    6    8   10\n",
      "   12   14    6\n",
      "   10   12   14\n",
      "\n",
      "sum of two matrices using for loop\n",
      "C =\n",
      "\n",
      "    6    8   10\n",
      "   12   14    6\n",
      "   10   12   14\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=[1 2 3; 4 5 6; 7 8 9];\n",
    "B=[5 6 7;8 9 0;3 4 5];\n",
    "disp('sum of two matrices without loop')\n",
    "A+B\n",
    "for i=1:3\n",
    "    for j=1:3\n",
    "        C(i,j)=A(i,j)+B(i,j);\n",
    "    end\n",
    "end\n",
    "disp('sum of two matrices using for loop')\n",
    "C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix multiplication without loop\n",
      "    42    36    30\n",
      "    96    81    66\n",
      "   150   126   102\n",
      "Matrix multiplication using for loop\n",
      "    42    36    30\n",
      "    96    81    66\n",
      "   150   126   102\n"
     ]
    }
   ],
   "source": [
    "A=[1 2 3; 4 5 6; 7 8 9];\n",
    "B= [3 2 1; 6 5 4; 9 8 7];\n",
    "C=zeros(3);\n",
    "disp('Matrix multiplication without loop')\n",
    "disp(A*B)\n",
    "for i=1:3\n",
    "    for j=1:3\n",
    "       % C(i,j)=0;\n",
    "        for k=1:3\n",
    "            C(i,j)=C(i,j)+A(i,k)*B(k,j);\n",
    "        end\n",
    "    end\n",
    "end\n",
    "disp('Matrix multiplication using for loop')\n",
    "disp(C)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find factorial $n! = 1. 2. 3. ... (n-1)n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "using for loop\n",
      " 120\n",
      "using while loop\n",
      " 120\n"
     ]
    }
   ],
   "source": [
    "n=5;\n",
    "f=1;\n",
    "i = 1;\n",
    "for i=1:n\n",
    "    f=f*i;\n",
    "    i=i+1;\n",
    "end\n",
    "disp('using for loop')\n",
    "disp(f)\n",
    "\n",
    "f1=1;\n",
    "i=1;\n",
    "while i<=n\n",
    "    f1=f1*i;\n",
    "    i=i+1;\n",
    "end\n",
    "disp('using while loop')\n",
    "disp(f1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "function f = fact(n)\n",
    "    f = prod(1:n);\n",
    "endfunction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  120\r\n"
     ]
    }
   ],
   "source": [
    "fact(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fixed point iteration,\n",
    "$x = \\phi(x)$, $x_n =\\phi(x_{n-1})$. \n",
    "For example $x = cosh(x/4)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fixed point iteration\n",
      "x =  1.0336\n",
      "k =  7\n"
     ]
    }
   ],
   "source": [
    "disp('Fixed point iteration');\n",
    "phi = @(x) cosh(x/4);\n",
    "x=1;\n",
    "er = 1;\n",
    "k=0;\n",
    "while ((er > 1e-8) && (k < 100))\n",
    "    xnew = phi(x);\n",
    "    er = abs(xnew-x);\n",
    "    x = xnew;\n",
    "    k = k+1;\n",
    "end\n",
    "x\n",
    "k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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    {
     "text": "MetaKernel Magics",
     "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
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