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diff --git a/Antenna_and_Wave_Propagation/chapter1.ipynb b/Antenna_and_Wave_Propagation/chapter1.ipynb new file mode 100755 index 00000000..04654cc5 --- /dev/null +++ b/Antenna_and_Wave_Propagation/chapter1.ipynb @@ -0,0 +1,961 @@ +{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 1 : Mathematical Preliminaries"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.1,Page Number 45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 26,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "magnitude of vector: 3.74\n",
+ "direction of vector [ 0.267 0.535 0.802]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable Declaration\n",
+ "A = np.array([1,2,3]) # A is a vector\n",
+ "\n",
+ "#calculations\n",
+ "l=np.linalg.norm(A) # magnitude or length of vector A\n",
+ "a=A/l # direction of vector A\n",
+ "\n",
+ "#results\n",
+ "print \"magnitude of vector:\",round(l,2)\n",
+ "print \"direction of vector\",np.around(a,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {
+ "collapsed": true
+ },
+ "source": [
+ "## Example 1.2,Page Number 45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "summation of two vectors: [ 3 2 12]\n",
+ "subtraction of two vectors: [1 8 0]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable Declaration\n",
+ "A=np.array([2,5,6]) # vector A\n",
+ "B=np.array([1,-3,6]) # vector B\n",
+ "\n",
+ "#calculations\n",
+ "Sum = A+B # summation of two vectors\n",
+ "Sub = A-B # subtraction of two vectors\n",
+ "\n",
+ "#results\n",
+ "print \"summation of two vectors:\",Sum\n",
+ "print \"subtraction of two vectors:\",Sub\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.3,Page Number 45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dot product of vector A and B: 5\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "A = np.array([1,1,2]) # vector A\n",
+ "B = np.array([2,1,1]) # vector B\n",
+ "\n",
+ "#Calculations\n",
+ "k = np.dot(A,B) # dot product of vector A and B\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"dot product of vector A and B:\",k\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.4,Page Number 45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "cross product of vector A and B: [-3 0 3]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "A = np.array([2,1,2]) # vector A\n",
+ "B = np.array([1,2,1]) # vector B\n",
+ "\n",
+ "#Calculations\n",
+ "Cross = np.cross(A,B) # dot product of vector A and B\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"cross product of vector A and B:\",Cross\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.5,Page Number 46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "dot product of vector A and B: 9\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "A = np.array([1,3,4]) # vector A\n",
+ "B = np.array([1,0,2]) # vector B\n",
+ "\n",
+ "#Calculations\n",
+ "k = np.dot(A,B) # dot product of vector A and B\n",
+ "\n",
+ "#Results\n",
+ "\n",
+ "print \"dot product of vector A and B:\",k\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.9,Page Number 46"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "radius of cylinder is: 2.24 m\n",
+ "azimuthal angle is: 63.43 degrees\n",
+ "z coordinate is: 3 m\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "import math\n",
+ "\n",
+ "#variable declaration\n",
+ "p = [1,2,3] # coordinates of point p\n",
+ "x = 1 # x coordinate of P\n",
+ "y = 2 # y coordinate of P\n",
+ "z = 3 # z coordinate of P\n",
+ "\n",
+ "#Calculations\n",
+ "rho = math.sqrt(x**2+y**2) #radius of cylinder in m\n",
+ "phi = (math.atan(y/x))*(180/math.pi) # azimuthal angle in degrees\n",
+ "z = 3 # in m\n",
+ "\n",
+ "\n",
+ "#results\n",
+ "print \"radius of cylinder is:\",round(rho,2),\"m\"\n",
+ "print \"azimuthal angle is:\",round(phi,2),\"degrees\"\n",
+ "print \"z coordinate is:\",z,\"m\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.10,Page Number 47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 27,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "cylindrical coordinates of vector A: [ 4.472 0. 1. ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import cos,sin,pi,atan\n",
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "A = np.array([4,2,1]) # vector A\n",
+ "A_x = 4 # x coordinate of P\n",
+ "A_y = 2 # y coordinate of P\n",
+ "A_z = 1 # z coordinate of P\n",
+ "\n",
+ "\n",
+ "#calculations\n",
+ "phi = atan(A_y/A_x) # azimuthal in radians\n",
+ "A_rho = (A_x*cos((phi)))+(A_y*sin((phi))) # x coordinate of cylinder\n",
+ "A_phi = (-A_x*sin(phi))+(A_y*cos(phi)) # y coordinate of cylinder\n",
+ "A_z = 1 # z coordinate of cylinder\n",
+ "A = [A_rho,A_phi,A_z] # cylindrical coordinates if vector A\n",
+ "\n",
+ "#Result\n",
+ "print \"cylindrical coordinates of vector A:\",np.around(A,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.12,Page Number 47"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 22,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "radius of sphere is: 3.742 m\n",
+ "angle of elevation is: 0.641 radians\n",
+ "azimuthal angle is: 0.464 radians\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import sqrt,acos,atan\n",
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "P = np.array([1,2,3]) # coordinates of point P in cartezian system\n",
+ "x = 1 # x coordinate of point P in cartezian system\n",
+ "y = 2 # y coordinate of point P in cartezian system\n",
+ "z = 3 # z coordinate of point P in cartezian system\n",
+ "\n",
+ "#calculations\n",
+ "r = sqrt(x**2+y**2+z**2) # radius of sphere in m\n",
+ "theta = acos(z/r) # angle of elevation in degrees\n",
+ "phi = atan(x/y) # azimuthal angle in degrees\n",
+ "\n",
+ "#results\n",
+ "print \"radius of sphere is:\",round(r,3),\"m\"\n",
+ "print \"angle of elevation is:\",round(theta,3),\"radians\"\n",
+ "print \"azimuthal angle is:\",round(phi,3),\"radians\"\n",
+ "\n",
+ "\n",
+ "# note : answer in the book is incomplete they find only one coordinate but there are three\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.17,Page Number 48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "power gain is: 13.424 dB\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable declaration\n",
+ "A_p=22 # power gain\n",
+ "\n",
+ "#calulation\n",
+ "A_p_dB=10*(np.log10(A_p)) # power gain in dB\n",
+ "\n",
+ "#result\n",
+ "print \"power gain is:\",round(A_p_dB,3),\"dB\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.18,Page Number 48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "voltage gain is: 39.554 dB\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable declaration\n",
+ "A_v=95 # voltage gain\n",
+ "\n",
+ "#calculation\n",
+ "A_v_dB=20*(np.log10(A_v)) # voltage gain in dB\n",
+ "\n",
+ "#result\n",
+ "print \"voltage gain is:\",round(A_v_dB,3),\"dB\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.19,Page Number 48"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "power gain is: 1.386 Np\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "from math import sqrt\n",
+ "\n",
+ "#variable declaration\n",
+ "A_p = 16 # power gain\n",
+ "\n",
+ "#calculations\n",
+ "A_p_Np = np.log(sqrt(A_p)) # power gain in Np\n",
+ "\n",
+ "#results\n",
+ "print \"power gain is:\",round(A_p_Np,3),\"Np\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.20,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "power gain is: 3.526 Np\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable declaration\n",
+ "A_i = 34 # current gain\n",
+ "\n",
+ "#calculations\n",
+ "A_i_Np = np.log(A_i) # current gain in Nepers\n",
+ "\n",
+ "#result\n",
+ "print \"power gain is:\",round(A_i_Np,3),\"Np\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.21,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "magnitude of complex number A is: 4.472\n",
+ "phase of complex number A is: 63.435 degrees\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "import cmath \n",
+ "from math import sqrt,pi\n",
+ "\n",
+ "\n",
+ "#variable declaration\n",
+ "A=2+4j # complex number A\n",
+ "\n",
+ "#calculations\n",
+ "magnitude = abs(A) # magnitude of complex number A\n",
+ "phi = cmath.phase(A)*(180/pi) # phase of complex number A in degrees\n",
+ "\n",
+ "#results\n",
+ "print \"magnitude of complex number A is:\",round(magnitude,3)\n",
+ "print \"phase of complex number A is:\",round(phi,3),\"degrees\"\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.22,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "magnitude of complex number A is: 3.162\n",
+ "phase of complex number A in degrees: 71.565\n",
+ "conjugate of complex no. A: (1-3j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import pi\n",
+ "import cmath\n",
+ "\n",
+ "#variable declaration\n",
+ "A = 1+3j # complex no. A\n",
+ "\n",
+ "#calculations\n",
+ "c = A.conjugate() # conjugate of complex no. A\n",
+ "magnitude = abs(A) # magnitude of complex number A\n",
+ "phi = cmath.phase(A)*(180/pi) # phase of complex number A in degrees\n",
+ "\n",
+ "\n",
+ "#results\n",
+ "print \"magnitude of complex number A is:\",round(magnitude,3)\n",
+ "print \"phase of complex number A in degrees:\",round(phi,3)\n",
+ "print \"conjugate of complex no. A:\",c\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.23,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 24,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "real part of complex number A: 3.536\n",
+ "imaginary part of complex number A: 3.536\n",
+ "complex number A: (3.536+3.536j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "from __future__ import division\n",
+ "from math import cos,sin,radians\n",
+ "import numpy as np\n",
+ "\n",
+ "#variable declaration\n",
+ "rho = 5 # magnitude of the complex number A\n",
+ "phi = 45 # phase of a complex number A in Degrees\n",
+ "\n",
+ "#calculations\n",
+ "x = rho*cos(radians(phi)) # real part of complex number A\n",
+ "y = rho*sin(radians(phi)) # imaginary part of complex number A\n",
+ "A = complex(x,y) # complex number A\n",
+ "\n",
+ "#results\n",
+ "print \"real part of complex number A:\",round(x,3)\n",
+ "print \"imaginary part of complex number A:\",round(y,3)\n",
+ "print \"complex number A:\",np.around(A,3)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.24,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "sum of complex numbers A_1 and A_2 is: (6+8j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Variable Declaration\n",
+ "\n",
+ "A_1 = 2+3j # complex number A_1\n",
+ "A_2 = 4+5j # complex number A_2\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "A = A_1 + A_2\n",
+ "\n",
+ "#Result\n",
+ "print \"sum of complex numbers A_1 and A_2 is:\",A\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.25,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Difference of complex numbers A_1 and A_2 is: (-1+8j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Variable Declaration\n",
+ "\n",
+ "A_1 = 6j # complex number A_1\n",
+ "A_2 = 1-2j # complex number A_2\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "A = A_1 - A_2\n",
+ "\n",
+ "#Result\n",
+ "print \"Difference of complex numbers A_1 and A_2 is:\",A\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.26,Page Number 49"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Product of complex numbers A and B is: (-14.2+11.2j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "#Variable Declaration\n",
+ "\n",
+ "A = 0.4 + 5j # complex number A\n",
+ "B = 2+3j # complex number B\n",
+ "\n",
+ "\n",
+ "#calculation\n",
+ "P = A*B\n",
+ "\n",
+ "#Result\n",
+ "print \"Product of complex numbers A and B is:\",P\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.27,Page Number 50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 25,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Division of complex numbers A and B is: (0.154+3.231j)\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#Variable Declaration\n",
+ "\n",
+ "A = 10+6j # complex number A\n",
+ "B = 2-3j # complex number B \n",
+ "\n",
+ "#calculation\n",
+ "D = A/B\n",
+ "\n",
+ "#Result\n",
+ "print \"Division of complex numbers A and B is:\",np.around(D,3)\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.28,Page Number 50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The roots of the given quadratic equation are: [-1 - sqrt(3)*I, -1 + sqrt(3)*I]\n",
+ "Root 1 = -1.0 - 1.732*I\n",
+ "Root 2 = -1.0 + 1.732*I\n"
+ ]
+ }
+ ],
+ "source": [
+ "from sympy import Symbol,solve\n",
+ "\n",
+ "#variable Declaration\n",
+ "\n",
+ "x = Symbol('x')\n",
+ "p = (x)**2 + 2*x + 4\n",
+ "\n",
+ "#calculations\n",
+ "Roots = solve(p,x)\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print \"The roots of the given quadratic equation are:\",Roots\n",
+ "\n",
+ "for i in range(len(Roots)):\n",
+ " print \"Root %i = %s\" % (i + 1, str(Roots[i].n(5)))\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example 1.29,Page Number 50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The minor of 8 is: [[1 3]\n",
+ " [4 6]]\n",
+ "the determinant of minor of 8 is: -6.0\n",
+ "The minor of 8 is: [[1 2]\n",
+ " [4 5]]\n",
+ "the determinant of minor of 9 is: -3.0\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable Declaration\n",
+ "a = np.array([[1,2,3],[4,5,6],[7,8,9]]) # Determinant\n",
+ "i = 2 # Third row of the determinant \n",
+ "j = 1 # second column of the determinant\n",
+ "\n",
+ "#Calculations\n",
+ "\n",
+ "b = np.delete(np.delete(a, i, axis=0), j, axis=1) # minor of 8\n",
+ "m = np.linalg.det(b) # determinant of minor of 8\n",
+ "\n",
+ "i = 2 # Third row of the determinant \n",
+ "j = 2 # Third column of the determinant\n",
+ "c = np.delete(np.delete(a, i, axis=0), j, axis=1) # minor of 9\n",
+ "n = np.linalg.det(c) # determinant of minor of 9\n",
+ "\n",
+ "\n",
+ "#Result\n",
+ "print \"The minor of 8 is:\",b\n",
+ "print \"the determinant of minor of 8 is:\",m\n",
+ "print \"The minor of 8 is:\",c\n",
+ "print \"the determinant of minor of 9 is:\",n\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "##Example 1.30,Page Number 50-51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "The cofactor of 6 is: [[-3 -2]\n",
+ " [-9 -8]]\n",
+ "The cofactor of 5 is: [[-1 -3]\n",
+ " [-7 -9]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "import numpy as np\n",
+ "\n",
+ "#variable declaration and Calculations\n",
+ "a = np.array([[1,3,2],[6,1,5],[7,9,8]]) # Determinant\n",
+ "i = 1 # second row of the determinant \n",
+ "j = 0 # first column of the determinant\n",
+ "b = np.delete(np.delete(a, i, axis=0), j, axis=1) # minor of 6\n",
+ "b_c = (-1)**(i+j) * b #cofactor of 6 \n",
+ "\n",
+ "\n",
+ "i = 1 # second row of the determinant \n",
+ "j = 2 # Third column of the determinant\n",
+ "c = np.delete(np.delete(a, i, axis=0), j, axis=1) # minor of 5\n",
+ "c_c = (-1)**(i+j) * c #cofactor of 5\n",
+ "\n",
+ "#Result\n",
+ "print \"The cofactor of 6 is:\",b_c\n",
+ "print \"The cofactor of 5 is:\",c_c\n",
+ "\n",
+ "\n",
+ "## note : the answer of cofactor of 5 is wrong in the book.The sign should be negative. \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 1.31,Page Number 51"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {
+ "collapsed": false
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "factorial of 4 is: 24\n",
+ "factorial of 6 is: 720\n"
+ ]
+ }
+ ],
+ "source": [
+ "from math import factorial\n",
+ "\n",
+ "f1 = factorial(4) # factorial of 4\n",
+ "f2 = factorial(6) # factorial of 6\n",
+ "print \"factorial of 4 is:\",f1\n",
+ "print \"factorial of 6 is:\",f2\n"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 2",
+ "language": "python",
+ "name": "python2"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 2
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython2",
+ "version": "2.7.8"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
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