{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <a href='https://www.gnu.org/software/octave/'>GNU Octave </a>\n",
    "<ul>\n",
    "<li> A high-level interpreted language </li>\n",
    "<li> primarily uses for numerical computations </li> \n",
    "<li> a tool of data visualization and manipulation </li> \n",
    "<li> Octave language is quite similar to Matlab </li> </ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Basic Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  12\n"
     ]
    }
   ],
   "source": [
    "5+7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  1.5000\n"
     ]
    }
   ],
   "source": [
    "6/4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans = -1\n"
     ]
    }
   ],
   "source": [
    "5-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  16\n"
     ]
    }
   ],
   "source": [
    "2^4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  25\n"
     ]
    }
   ],
   "source": [
    "5*5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans = -0.95892\n"
     ]
    }
   ],
   "source": [
    "sin(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  0.28366\n"
     ]
    }
   ],
   "source": [
    "cos(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =   -1.2246e-16\r\n"
     ]
    }
   ],
   "source": [
    "tan(pi)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  3.1416\r\n"
     ]
    }
   ],
   "source": [
    "pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "format long"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  3.14159265358979\r\n"
     ]
    }
   ],
   "source": [
    "pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "format short"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  2.7183\r\n"
     ]
    }
   ],
   "source": [
    "exp(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  1\r\n"
     ]
    }
   ],
   "source": [
    "log(exp(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  1\r\n"
     ]
    }
   ],
   "source": [
    "log10(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  27.290\r\n"
     ]
    }
   ],
   "source": [
    "sinh(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  0.99505\r\n"
     ]
    }
   ],
   "source": [
    "tanh(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1 =  80\n",
      "ans =  12\n"
     ]
    }
   ],
   "source": [
    "x1 = sqrt(100^2 -60^2)\n",
    "x1*15*(60^2 + x1^2)^(-1/2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# vector and matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      "\n",
      "   1   2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "% row vector\n",
    "x=[1 2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y =\n",
      "\n",
      "   3\n",
      "   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "% column vector \n",
    "y=[3;4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   3   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "% transpose\n",
    "y'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y =\n",
      "\n",
      "   3   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "y=[3 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   1   2\n",
      "   3   4\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=[1 2; 3 4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A*A and A^2 are same but A.^2 is different! A*A or A^2 are the multiplication of A with A; however, A.^2 is the component wise pultiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "    7   10\n",
      "   15   22\n",
      "\n",
      "ans =\n",
      "\n",
      "    7   10\n",
      "   15   22\n",
      "\n",
      "ans =\n",
      "\n",
      "    1    4\n",
      "    9   16\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A*A\n",
    "A^2\n",
    "A.^2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "B =\n",
      "\n",
      "   5   6\n",
      "   7   8\n",
      "\n"
     ]
    }
   ],
   "source": [
    "B = [5 6; 7 8]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C =\n",
      "\n",
      "  -4.0000   3.0000\n",
      "   3.5000  -2.5000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "C=B^(-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   3.00000  -2.00000\n",
      "   2.00000  -1.00000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   1.00000   0.00000\n",
      "   0.00000   1.00000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "B*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "  -20.000   18.000\n",
      "   24.500  -20.000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "% component wise multiplication \n",
    "B.*C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "  -4.0000   3.0000\n",
      "   3.5000  -2.5000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "inv(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans = -2.0000\r\n"
     ]
    }
   ],
   "source": [
    "% determinant\n",
    "det(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "'eig' is a built-in function from the file libinterp/corefcn/eig.cc\n",
      "\n",
      " -- Built-in Function: LAMBDA = eig (A)\n",
      " -- Built-in Function: LAMBDA = eig (A, B)\n",
      " -- Built-in Function: [V, LAMBDA] = eig (A)\n",
      " -- Built-in Function: [V, LAMBDA] = eig (A, B)\n",
      "     Compute the eigenvalues (and optionally the eigenvectors) of a\n",
      "     matrix or a pair of matrices\n",
      "\n",
      "     The algorithm used depends on whether there are one or two input\n",
      "     matrices, if they are real or complex and if they are symmetric\n",
      "     (Hermitian if complex) or non-symmetric.\n",
      "\n",
      "     The eigenvalues returned by 'eig' are not ordered.\n",
      "\n",
      "     See also: eigs, svd.\n",
      "\n",
      "\n",
      "Additional help for built-in functions and operators is\n",
      "available in the online version of the manual.  Use the command\n",
      "'doc <topic>' to search the manual index.\n",
      "\n",
      "Help and information about Octave is also available on the WWW\n",
      "at http://www.octave.org and via the help@octave.org\n",
      "mailing list.\n"
     ]
    }
   ],
   "source": [
    "help eig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "    1    2    3\n",
      "    4    5    6\n",
      "    7    8   98\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=[1 2 3; 4 5 6; 7 8 98]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "eigvec =\n",
      "\n",
      "  -0.031944  -0.812694  -0.329567\n",
      "  -0.065196   0.582597  -0.938125\n",
      "  -0.997361   0.010440   0.106334\n",
      "\n",
      "eigval =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   98.74715          0          0\n",
      "          0   -0.47228          0\n",
      "          0          0    5.72513\n",
      "\n"
     ]
    }
   ],
   "source": [
    "[eigvec, eigval] = eig(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$a_{1,1} \\quad   a_{1,2}  \\quad  a_{1,3}$\n",
    "\n",
    "$a_{2,1} \\quad   a_{2,2}  \\quad  a_{2,3}$\n",
    "\n",
    "$a_{3,1} \\quad   a_{3,2}  \\quad  a_{3,3}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "    3\n",
      "    6\n",
      "   98\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A(1:3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   3   3\n",
      "\n"
     ]
    }
   ],
   "source": [
    "size(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   0   0   0\n",
      "   0   0   0\n",
      "   0   0   0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=zeros(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "Diagonal Matrix\n",
      "\n",
      "   1   0   0   0\n",
      "   0   1   0   0\n",
      "   0   0   1   0\n",
      "   0   0   0   1\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A = eye(4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A =\n",
      "\n",
      "   0.691284   0.458066   0.969734   0.981280\n",
      "   0.523134   0.193470   0.780486   0.076756\n",
      "   0.414799   0.367310   0.369840   0.400804\n",
      "   0.431737   0.505204   0.080192   0.592407\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=rand(4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solve the linear system $Ax =b$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      "\n",
      "  -0.50000\n",
      "   1.50000\n",
      "  -0.50000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "A=[1 2 3; 3 3 4; 2 3 3];\n",
    "b=[1; 1; 2];\n",
    "x=A\\b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## more vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      "\n",
      "   1   2   3   4   5\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = 1:5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      "\n",
      " Columns 1 through 8:\n",
      "\n",
      "    1.0000    1.5000    2.0000    2.5000    3.0000    3.5000    4.0000    4.5000\n",
      "\n",
      " Column 9:\n",
      "\n",
      "    5.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = 1:0.5:5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =  9\r\n"
     ]
    }
   ],
   "source": [
    "length(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x =\n",
      "\n",
      " Columns 1 through 8:\n",
      "\n",
      "   0.00000   0.50000   1.00000   1.50000   2.00000   2.50000   3.00000   3.50000\n",
      "\n",
      " Columns 9 through 11:\n",
      "\n",
      "   4.00000   4.50000   5.00000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x = linspace(0,5,11)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "index =\n",
      "\n",
      "    6    7    8    9   10   11\n",
      "\n"
     ]
    }
   ],
   "source": [
    "index = find(x>2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ans =\n",
      "\n",
      "   2.5000   3.0000   3.5000   4.0000   4.5000   5.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "x(index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run a script file \n",
    "For example plottest.m is an script file. We can run plottest.m by simply write plottest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "%plot gnuplot\n",
    "plottest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Octave",
   "language": "octave",
   "name": "octave"
  },
  "language_info": {
   "file_extension": ".m",
   "help_links": [
    {
     "text": "GNU Octave",
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