math.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "enormous-disposition",
   "metadata": {},
   "source": [
    "# Mathematical calculation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "biological-broadway",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import interpolate\n",
    "import scipy\n",
    "from scipy.integrate import simps\n",
    "import scipy.linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intended-hormone",
   "metadata": {},
   "source": [
    "# 1. Interpolation (線形補間)\n",
    "- is used to estimate data points between two known points.\n",
    "- most common interpolation technique is **Linear Interpolation**\n",
    "- Other are **Quadratic**,**Cubic**,**Spline**,..\n",
    "\n",
    "<img src=\"https://i2.wp.com/www.bradleysawler.com/wp-content/uploads/2018/01/Linear-Interpolation-Equation-Graph.png?fit=838%2C659&ssl=1\" width=300 >\n",
    "\n",
    "<hr>\n",
    "\n",
    "### Interpolate a 1-D function\n",
    "\n",
    "- Numpy : [numpy.interp(x, xp, fp, left=None, right=None, period=None)](https://numpy.org/doc/stable/reference/generated/numpy.interp.html)\n",
    "- Scipy : [scipy.interpolate.interp1d(x, y, kind='linear', axis=- 1, copy=True, bounds_error=None, fill_value=nan, assume_sorted=False)](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html#scipy.interpolate.interp1d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "coordinate-sheet",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x20266358070>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [1,2,3]\n",
    "y = [3,2,0]\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.plot(x,y,marker='.',ms = 15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "postal-arnold",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Given x_new value : 2.5\n",
      "New interpolated value (y_new): 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [1,2,3]\n",
    "y = [3,2,0]\n",
    "\n",
    "x_new = 2.5 # new value of x ,so we need to find new value of y\n",
    "y_new = np.interp(x_new,x,y) # using NumPy library\n",
    "print('Given x_new value : {}'.format(x_new))\n",
    "print('New interpolated value (y_new): {}'.format(y_new))\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.plot(x,y,marker='.',ms = 15)\n",
    "\n",
    "plt.plot([x_new,x_new],[-0.1,y_new],'--',color=\"gray\")\n",
    "plt.plot([0,x_new],[y_new,y_new],'--',color=\"gray\")\n",
    "plt.plot(x_new,y_new,marker='o',ms = 10,mfc='red') # ms:markersize ,mfc:markerfacecolor\n",
    "plt.text(x_new+0.01,0,r'$x_{new}$',fontsize=14)\n",
    "plt.text(0,y_new+0.05,r'$y_{new}$',fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "political-sympathy",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Given x_new value : 2.5\n",
      "New interpolated value (y_new): 1.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [1,2,3]\n",
    "y = [3,2,0]\n",
    "f = interpolate.interp1d(x,y)  # using SciPy library , take 2 arrays as arguments\n",
    "\n",
    "x_new = 2.5 # new value of x ,so we need to find new value of y\n",
    "y_new = f(x_new) \n",
    "print('Given x_new value : {}'.format(x_new))\n",
    "print('New interpolated value (y_new): {}'.format(y_new))\n",
    "\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.plot(x,y,marker='.',ms = 15)\n",
    "\n",
    "plt.plot([x_new,x_new],[-0.1,y_new],'--',color=\"gray\")\n",
    "plt.plot([0,x_new],[y_new,y_new],'--',color=\"gray\")\n",
    "plt.plot(x_new,y_new,marker='o',ms = 10,mfc='red') # ms:markersize ,mfc:markerfacecolor\n",
    "plt.text(x_new+0.01,0,r'$x_{new}$',fontsize=14)\n",
    "plt.text(0,y_new+0.05,r'$y_{new}$',fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "widespread-train",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "### Interpolate a 2-D function\n",
    "- Scipy : [scipy.interpolate.interp2d(x, y, z, kind='linear', copy=True, bounds_error=False, fill_value=None)[source]](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp2d.html#scipy.interpolate.interp2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cloudy-electronics",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-5.01, 5.01, 0.25)\n",
    "y = np.arange(-5.01, 5.01, 0.25)\n",
    "xx, yy = np.meshgrid(x, y)\n",
    "z = np.sin(xx**2+yy**2)\n",
    "f = interpolate.interp2d(x, y, z,kind='cubic')\n",
    "\n",
    "xnew = np.arange(-5.01, 5.01, 1e-2)\n",
    "ynew = np.arange(-5.01, 5.01, 1e-2)\n",
    "znew = f(xnew, ynew)\n",
    "plt.plot(x, z[0, :], 'ro-', xnew, znew[0, :], 'b-')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "global-selection",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# Numerical intergration using trapezoidal rule and Simpson (数値積分：台形公式とシンプソン則)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "caroline-bahamas",
   "metadata": {},
   "source": [
    "<img src=\"https://www.bragitoff.com/wp-content/uploads/2015/08/TrapezoidRule1.png\" width=300 >\n",
    "$${\\int\\limits_a^b {f\\left( x \\right)dx} \\approx {T_n} }={ {\\frac{{\\Delta x}}{2}}\\left[ {{f\\left( {{x_0}} \\right)} + {2f\\left( {{x_1}} \\right)} }\\right.}+{\\left.{ {2f\\left( {{x_2}} \\right)} + \\cdots }\\right.}+{\\left.{ {2f\\left( {{x_{n – 1}}} \\right)} + {f\\left( {{x_n}} \\right)}} \\right],}$$\n",
    "$$\\Delta x=h=\\frac{b-a}{n}\\; ,\\;  {x_i} = a + i\\Delta x.$$\n",
    "<hr>\n",
    "\n",
    "Numpy : [numpy.trapz(y, x=None, dx=1.0, axis=-1)](https://numpy.org/doc/stable/reference/generated/numpy.trapz.html) <br>\n",
    "      : [numpy.linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None, axis=0)](https://numpy.org/doc/stable/reference/generated/numpy.linspace.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "juvenile-decline",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h =  0.314159\n",
      "Integral = 1.0082654169662284\n"
     ]
    }
   ],
   "source": [
    "from math import sin,pi\n",
    "#TRAPEZOIDAL RULE\n",
    "f = lambda x: x*sin(x)\n",
    "a = 0         # lower limit\n",
    "b = pi/2      # upper limit\n",
    "n = 5         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "S = 0.5*(f(a)+f(b))\n",
    "for i in range(1,n): #this loop will run until (n-1)\n",
    "    S+=f(a+i*h)\n",
    "integral = h*S\n",
    "\n",
    "print('h = ',round(h,6))\n",
    "print(\"Integral = {}\".format(integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "three-seeking",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h=  0.314159\n",
      "Integral = 1.0082654169662284\n"
     ]
    }
   ],
   "source": [
    "#TRAPEZOIDAL RULE\n",
    "a = 0         # lower limit\n",
    "b = pi/2         # upper limit\n",
    "n = 5         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "x = np.linspace(a,b,num=n+1)\n",
    "y = x*np.sin(x)\n",
    "\n",
    "trap = np.trapz(y,x,dx=h)\n",
    "print('h= ',round(h,6))\n",
    "print(\"Integral = {}\".format(trap))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "pregnant-pipeline",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h=  0.666667\n",
      "Integral = 2.814814814814815\n"
     ]
    }
   ],
   "source": [
    "f = lambda x: x**2\n",
    "#TRAPEZOIDAL RULE\n",
    "a = 0         # lower limit\n",
    "b = 2         # upper limit\n",
    "n = 3         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "S = 0.5*(f(a)+f(b))\n",
    "for i in range(1,n): #this loop will run until (n-1)\n",
    "    S+=f(a+i*h)\n",
    "    \n",
    "integral = h*S\n",
    "print('h= ',round(h,6))\n",
    "print(\"Integral = {}\".format(integral))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "comprehensive-recorder",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h=  0.666667\n",
      "Integral = 2.814814814814815\n"
     ]
    }
   ],
   "source": [
    "#TRAPEZOIDAL RULE\n",
    "a = 0         # lower limit\n",
    "b = 2         # upper limit\n",
    "n = 3         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "x = np.linspace(a,b,num=n+1)\n",
    "y = x**2\n",
    "\n",
    "trap = np.trapz(y,x,dx=h)\n",
    "print('h= ',round(h,6))\n",
    "print(\"Integral = {}\".format(trap))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "simple-ivory",
   "metadata": {},
   "source": [
    "Reference \n",
    "- [Trapezoidal Rule](https://www.math24.net/trapezoidal-rule#:~:text=Another%20useful%20integration%20rule%20is,little%20trapezoids%20rather%20than%20rectangles.&text=a%3Dx0%3Cx1,%E2%8B%AF%3Cxn%3Db)\n",
    "- [Simpson's Rule](https://www.math24.net/simpsons-rule)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "naked-manual",
   "metadata": {},
   "source": [
    "<img src=\"https://www.aplustopper.com/wp-content/uploads/2017/06/What-are-the-Trapezoidal-rule-and-Simpsons-rule-in-Numerical-Integration-1.jpg\" width=300 >\n",
    "\n",
    "( $h$ is width of subinterval, $n$ must be even )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "raising-shoulder",
   "metadata": {},
   "source": [
    "$$\\int _0^5\\:x^3dx \\approx [\\frac{1}{4}x^4]_0^5 = 156.25$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "imported-daniel",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "156.25\n"
     ]
    }
   ],
   "source": [
    "a = 0         # lower limit\n",
    "b = 5        # upper limit\n",
    "n = 100         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "x = np.linspace(a,b,num=n+1)\n",
    "y = x**3\n",
    "\n",
    "Integral = scipy.integrate.simpson(y, x,dx=h)\n",
    "\n",
    "print(Integral)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "proof-prime",
   "metadata": {},
   "source": [
    "$$\\int\\limits_0^\\pi {sin (x)\\;dx} \\approx [-\\sin x]_0^\\pi = 2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "black-spring",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.0001095173150043\n"
     ]
    }
   ],
   "source": [
    "a = 0         # lower limit\n",
    "b = np.pi       # upper limit\n",
    "n = 10         # number of divisions/subintervals\n",
    "h = (b-a)/n   # step size\n",
    "\n",
    "x = np.linspace(a,b,num=n+1)\n",
    "y = np.sin(x)\n",
    "\n",
    "Integral = scipy.integrate.simpson(y, x,dx=h)\n",
    "\n",
    "print(Integral)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "sufficient-tuition",
   "metadata": {},
   "source": [
    "# Addition / Subtraction / Multiplication of matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "tough-rouge",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix A :\n",
      "[[1 2 1]\n",
      " [3 4 1]]\n",
      "Matrix B :\n",
      "[[5 6 1]\n",
      " [7 8 1]]\n",
      " \n",
      "Matrix A + Matrix B\n",
      "[[ 6  8  2]\n",
      " [10 12  2]]\n"
     ]
    }
   ],
   "source": [
    "#create first matrix\n",
    "A = np.array([[1,2,1],[3,4,1]])\n",
    "print(\"Matrix A :\")\n",
    "print(A)\n",
    "\n",
    "#create second matrix\n",
    "B = np.array([[5,6,1],[7,8,1]])\n",
    "print(\"Matrix B :\")\n",
    "print(B)\n",
    "print(\" \")\n",
    "\n",
    "# adding two matrix\n",
    "print('Matrix A + Matrix B')\n",
    "C = np.add(A,B)\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ahead-vaccine",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix A :\n",
      "[[5 6 1]\n",
      " [7 8 1]]\n",
      "Matrix B :\n",
      "[[1 2 1]\n",
      " [3 4 1]]\n",
      " \n",
      "Matrix A - Matrix B = \n",
      "[[4 4 0]\n",
      " [4 4 0]]\n"
     ]
    }
   ],
   "source": [
    "#create first matrix\n",
    "A = np.array([[5,6,1],[7,8,1]])\n",
    "\n",
    "print(\"Matrix A :\")\n",
    "print(A)\n",
    "\n",
    "#create second matrix\n",
    "B = np.array([[1,2,1],[3,4,1]])\n",
    "print(\"Matrix B :\")\n",
    "print(B)\n",
    "print(\" \")\n",
    "\n",
    "# adding two matrix\n",
    "print('Matrix A - Matrix B = ')\n",
    "C = np.subtract(A,B)\n",
    "print(C)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "dimensional-gallery",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix X :\n",
      "[[12, 7, 3], [4, 5, 6], [7, 8, 9]]\n",
      "Matrix Y :\n",
      "[[5, 8, 1, 2], [6, 7, 3, 0], [4, 5, 9, 1]]\n",
      " \n",
      "Multiplication of matrix X and matrix Y : \n",
      "[23, 34, 11, 0]\n",
      "[31, 46, 15, 0]\n",
      "[0, 0, 0, 0]\n"
     ]
    }
   ],
   "source": [
    "# take a 3x3 matrix\n",
    "X = [[12,7,3],\n",
    "     [4,5,6],\n",
    "     [7,8,9]]\n",
    "\n",
    "# take a 3x4 matrix\n",
    "Y = [[5,8,1,2],\n",
    "     [6,7,3,0],\n",
    "     [4,5,9,1]]\n",
    "\n",
    "result = [[0,0,0,0],\n",
    "         [0,0,0,0],\n",
    "         [0,0,0,0]]\n",
    "\n",
    "# iterating by rows of A\n",
    "for i in range(len(A)):\n",
    "  \n",
    "    # iterating by columns of B \n",
    "    for j in range(len(B[0])):\n",
    "  \n",
    "        # iterating by rows of B\n",
    "        for k in range(len(B)):\n",
    "            result[i][j] += A[i][k] * B[k][j]\n",
    "  \n",
    "            \n",
    "print(\"Matrix X :\")\n",
    "print(X)\n",
    "\n",
    "print(\"Matrix Y :\")\n",
    "print(Y)\n",
    "print(\" \")\n",
    "\n",
    "print('Multiplication of matrix X and matrix Y : ')\n",
    "for r in result:\n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "sporting-rings",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix X :\n",
      "[[12, 7, 3], [4, 5, 6], [7, 8, 9]]\n",
      "Matrix Y :\n",
      "[[5, 8, 1, 2], [6, 7, 3, 0], [4, 5, 9, 1]]\n",
      " \n",
      "Multiplication of matrix X and matrix Y : \n",
      "[114 160  60  27]\n",
      "[74 97 73 14]\n",
      "[119 157 112  23]\n"
     ]
    }
   ],
   "source": [
    "# take a 3x3 matrix\n",
    "X = [[12,7,3],\n",
    "     [4,5,6],\n",
    "     [7,8,9]]\n",
    "\n",
    "# take a 3x4 matrix\n",
    "Y = [[5,8,1,2],\n",
    "     [6,7,3,0],\n",
    "     [4,5,9,1]]\n",
    "\n",
    "# this will be 3x4 matrix\n",
    "result = np.dot(X,Y)\n",
    "            \n",
    "print(\"Matrix X :\")\n",
    "print(X)\n",
    "\n",
    "print(\"Matrix Y :\")\n",
    "print(Y)\n",
    "print(\" \")\n",
    "\n",
    "print('Multiplication of matrix X and matrix Y : ')\n",
    "for r in result:\n",
    "    print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "continental-token",
   "metadata": {},
   "source": [
    "# Eigenvector and eigenvalue (固有ベクトル・固有値)\n",
    "#### Reference :\n",
    "- [Mathematical Python : Eigenvalues and Eigenvectors](https://www.math.ubc.ca/~pwalls/math-python/linear-algebra/eigenvalues-eigenvectors/)\n",
    "- [Eigenvector and Eigenvalue](https://www.mathsisfun.com/algebra/eigenvalue.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "julian-collar",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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