Octave Basics.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basics\n",
    "The notebook contains the following components:\n",
    "<ol><li>Vectors and Matrices</li>\n",
    "<li>Plotting</li>\n",
    "<li>Loops</li>\n",
    "<li>Functions</li></ol>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vectors and Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   2   4\n",
      "   5   6\n"
     ]
    }
   ],
   "source": [
    "#Matrix A\n",
    "A = [2,4;5,6];\n",
    "disp(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1\n",
      "   4\n",
      "   5\n",
      "   6\n",
      "   7\n"
     ]
    }
   ],
   "source": [
    "#Vector v\n",
    "v = [1;4;5;6;7];\n",
    "disp(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   10   22   32\n",
      "   17   39   56\n"
     ]
    }
   ],
   "source": [
    "%Matrix Multiplication\n",
    "B = [1,3,4;2,4,6];\n",
    "disp(A*B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  -0.75000   0.50000\n",
      "   0.62500  -0.25000\n"
     ]
    }
   ],
   "source": [
    "%Inverse of A(matrix A must be a non-singular square matrix)\n",
    "disp(pinv(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   1   2\n",
      "   3   4\n",
      "   4   6\n"
     ]
    }
   ],
   "source": [
    "%Transpose of B\n",
    "disp(B')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix A\n",
      "   2   4\n",
      "   5   6\n",
      "Matrix C\n",
      "   1   7\n",
      "   2   6\n",
      "Element-wise product\n",
      "    2   28\n",
      "   10   36\n"
     ]
    }
   ],
   "source": [
    "#Matrix C\n",
    "C = [1,7;2,6];\n",
    "%Elementwise product(dot product) of A and C\n",
    "disp('Matrix A')\n",
    "disp(A)\n",
    "disp('Matrix C')\n",
    "disp(C)\n",
    "disp('Element-wise product')\n",
    "disp(A.*C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 76\n"
     ]
    }
   ],
   "source": [
    "%to get dot product\n",
    "disp(sum(sum(A.*C)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   0.50000   0.25000\n",
      "   0.20000   0.16667\n"
     ]
    }
   ],
   "source": [
    "%Element-wise reciprocal of A\n",
    "disp(1./A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    4   16\n",
      "   25   36\n"
     ]
    }
   ],
   "source": [
    "%Element-wise power 2 of A\n",
    "disp(A.^2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Log\n",
      "   0.69315   1.38629\n",
      "   1.60944   1.79176\n",
      "Exp\n",
      "     7.3891    54.5982\n",
      "   148.4132   403.4288\n"
     ]
    }
   ],
   "source": [
    "%Element-wise functional operation\n",
    "disp('Log')\n",
    "disp(log(A))\n",
    "disp('Exp')\n",
    "disp(exp(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   17   24    1    8   15\n",
      "   23    5    7   14   16\n",
      "    4    6   13   20   22\n",
      "   10   12   19   21    3\n",
      "   11   18   25    2    9\n"
     ]
    }
   ],
   "source": [
    "%Magic matrix(matrix with sums along all rows, columns and diagonal are same)\n",
    "magic_M = magic(5);\n",
    "disp(magic_M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = [0:0.01:0.98];\n",
    "y = sin(2*pi*8*t);\n",
    "plot(t,y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%to plot another plot in the same figure\n",
    "y1 = cos(2*pi*8*t);\n",
    "plot(t,y);\n",
    "hold on;      # <-----\n",
    "plot(t,y1,'r');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%Label the plot properly\n",
    "y1 = cos(2*pi*8*t);\n",
    "plot(t,y);\n",
    "hold on;\n",
    "plot(t,y1,'r');\n",
    "xlabel('time');\n",
    "ylabel('value');\n",
    "legend('Sin', 'Cosine');\n",
    "title('Phase difference of pi/2');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%Subplot(to plot mutliple plots in a grid)\n",
    "subplot(1,2,1);     #  <---- 1,2 : row x column of grid; and 1 to access first element of grid\n",
    "plot(t,y1,'r');\n",
    "subplot(1,2,2);\n",
    "plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%axis of plot\n",
    "subplot(1,2,1);     \n",
    "plot(t,y1,'r');\n",
    "axis([-0.25 1.25 -1 1]);  #  <---- -025 1.25 : horizontal axis; -1 1 : vertical axis\n",
    "subplot(1,2,2);\n",
    "plot(t,y)\n",
    "axis([-0.25 1.25 -1 1]);  #  <---- -025 1.25 : horizontal axis; -1 1 : vertical axis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%Heat Map\n",
    "imagesc(magic_M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imagesc(magic_M), colorbar, colormap gray;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loops"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      2      4      8     16     32     64    128    256    512   1024\n"
     ]
    }
   ],
   "source": [
    "for i=1:10,\n",
    "    V(i) = 2.^i;   %indentation is not necessary\n",
    "end;\n",
    "disp(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i =  1\n",
      "    999    999    999    999    999   -999   -999   -999      0   1024\n"
     ]
    }
   ],
   "source": [
    "i=1\n",
    "while true,\n",
    "    if i < 6,\n",
    "        V(i) = 999;\n",
    "        i = i+1;\n",
    "    elseif i < 9,\n",
    "        V(i) = -999;\n",
    "        i = i+1;\n",
    "    else,\n",
    "        V(i) = 0;\n",
    "        break;\n",
    "    end;\n",
    "end;\n",
    "disp(V)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "function [y1, y2] = squareandcubeNumber(x)\n",
    "    y1 = x^2;\n",
    "    y2 = x^3;\n",
    "end;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 25\n"
     ]
    }
   ],
   "source": [
    "disp(squareandcubeNumber(5));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " 25\n"
     ]
    }
   ],
   "source": [
    "a = squareandcubeNumber(5);\n",
    "disp(a);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    25   125\n"
     ]
    }
   ],
   "source": [
    "[a, b] = squareandcubeNumber(5);\n",
    "disp([a,b]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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