notebooks/Math/Linear Algebra/Linear operator and linear tranformations.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cartesian_product(x,y):\n",
    "    \"\"\"\n",
    "    retrun catesian product\n",
    "    \"\"\"\n",
    "    return np.transpose([np.tile(x, len(y)), np.repeat(y, len(x))])\n",
    "\n",
    "\n",
    "\n",
    "class VectorGround:\n",
    "    def __init__(self, range=[-3,10], fig_size=(20,20),**kwargs):\n",
    "        self.plt = plt\n",
    "        self.plt.figure(figsize=fig_size)\n",
    "        self.range=range\n",
    "        self.ax = self.plt.gca()\n",
    "        self.ax.set_aspect('equal')\n",
    "        plt.grid()\n",
    "        self.ax.arrow(0, 0, 1, 0, head_width=0.1, head_length=0.1, fc='blue', ec='black')\n",
    "        self.ax.arrow(0, 0, 0, 1, head_width=0.1, head_length=0.1, fc='blue', ec='black')\n",
    "\n",
    "        self.ax.text(1, -0.3, r'$\\vec{e}_1$',fontsize=16,color='red')\n",
    "        self.ax.text(-0.4, 1, r'$\\vec{e}_2$',fontsize=16,color='red')\n",
    "        self.plt.xlim(range[0],range[1])\n",
    "        self.plt.ylim(range[0],range[1])\n",
    "        self.ax.set_xlabel('X',fontsize=20)\n",
    "        \n",
    "        self.ax.set_ylabel('Y',fontsize=30)\n",
    "        self.plt.title('',fontsize=10)\n",
    "\n",
    "        self.plt.savefig('fig1.png', bbox_inches='tight')\n",
    "    \n",
    "    def add_v(self,x_0,y_0,x,y,index='1',show_cord=True,font_size=15):\n",
    "        self.ax.arrow(x_0, y_0, x, y, head_width=0.1, head_length=0.1, fc='black', ec='black')\n",
    "    \n",
    "        if show_cord:\n",
    "            #self.ax.text(x, y-0.2, r'$\\vec{r}_{%s}(%1.1f:%1.1f)$' % (index,x, y),fontsize=font_size,color='blue')\n",
    "            self.ax.text(x, y-0.2, r'$\\vec{r}_{%s}(%1.0f:%1.0f)$' % (index,x, y),fontsize=font_size,color='blue')\n",
    "    def plot_points(self,points,color='b'):\n",
    "        for p in points:\n",
    "            self.plt.scatter(p[0],p[1],color=color)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/home/daodeiv/GIT_PROJECTS/Machine-Learning/daoutil\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "import os,sys,inspect\n",
    "currentdir = os.path.dirname(os.path.abspath(inspect.getfile(inspect.currentframe())))\n",
    "parentdir = os.path.dirname(currentdir)\n",
    "parentdir =parentdir+'/'+'daoutil'\n",
    "print( parentdir)\n",
    "sys.path.insert(0,parentdir) \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "\n",
    "#my libs\n",
    "from dplot import Dplot2D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear operator and linear tranformations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear opeartor\n",
    "###  The operator A acts on linear space $L^n$ is linear if for every x,y $\\in $ $L^n$ and $\\gamma x,\\beta \\in R $ is  satify $A(\\gamma x+ \\beta y)=\\gamma A(x) + \\beta A(y)$ \n",
    "exmaple : \n",
    "  The matrix $$ \\begin{bmatrix} 1 & 2 \\\\ 2 & 3  \\end{bmatrix}$$ is the linear operator over vecors $x_i \\in L^2 $ \n",
    "  $$ \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; x = \\begin{bmatrix} 3 \\\\ 2   \\end{bmatrix},y=\\begin{bmatrix} 1 \\\\ 3   \\end{bmatrix}  $$  then \n",
    "  $$ \\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\;\\; x = \\begin{bmatrix} 3 \\\\ 2   \\end{bmatrix},y=\\begin{bmatrix} 1 \\\\ 3   \\end{bmatrix}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Mappling\n",
    "#### Rotation (antismetric matrix)\n",
    "Let to have linear opearator  <br> <br> \n",
    "$$T(\\alpha) =  \\begin{bmatrix}cos(45^*) & -sin(45^*) \\\\ sin(45^*) & cos(45^*)  \\end{bmatrix}=  \\begin{bmatrix} 0.7  & 0.7 \\\\ 0.7 & 0.7  \\end{bmatrix}$$\n",
    "$$x =\\begin{bmatrix} 3 \\\\ 3   \\end{bmatrix}$$ <br> <br>\n",
    "$$x_2=T(x)= T(\\alpha) =  \\begin{bmatrix}cos(45^*) & -sin(45^*) \\\\ sin(45^*) & cos(45^*)  \\end{bmatrix}=  \\begin{bmatrix} 0.7  & 0.7 \\\\ 0.7 & 0.7  \\end{bmatrix}.\\begin{bmatrix} 3 \\\\ 3   \\end{bmatrix}=\\begin{bmatrix} 0 \\\\ 7   \\end{bmatrix}$$ <br> <br>\n",
    "if we make one more tranformation $$x_3=  T(x_2)= T(\\alpha) =  \\begin{bmatrix}cos(45^*) & -sin(45^*) \\\\ sin(45^*) & cos(45^*)  \\end{bmatrix}=  \\begin{bmatrix} 0.7  & -0.7 \\\\ 0.7 & 0.7  \\end{bmatrix}.\\begin{bmatrix} 0 \\\\ 7   \\end{bmatrix}=\\begin{bmatrix} -4.9 \\\\ 4.9   \\end{bmatrix}$$\n",
    "### The linear tranformation T rotate every vector with 45 degree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. ]\n",
      " [4.2]]\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = VectorGround(range=[-5,5])\n",
    "A = np.array([[0.7,-0.7],[0.7,0.7]])\n",
    "b = np.transpose(np.array([[3,3]]))\n",
    "g.add_v(0,0,b[0][0],b[1][0])\n",
    "t_v = A.dot(b)\n",
    "print(t_v)\n",
    "g.add_v(0,0,t_v[0][0],t_v[1][0],index='2')\n",
    "t2_v = A.dot(t_v)\n",
    "g.add_v(0,0,t2_v[0][0],t2_v[1][0],index='3')\n",
    "t2_v = A.dot(t2_v)\n",
    "g.add_v(0,0,t2_v[0][0],t2_v[1][0],index='4')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above example shows that the matrix $$T(x_2)= T(\\alpha) =  \\begin{bmatrix}cos(\\alpha) & -sin(\\alpha) \\\\ sin(\\alpha) & cos(\\alpha)  \\end{bmatrix}$$ rotates the every vector $x \\in L^2 $ with degree alpha that is the rotating tranformations <br>\n",
    "\n",
    "### Scaling tranfomration (symtric matrix):\n",
    "lets to have symetric \n",
    "$$T(x)=  \\begin{bmatrix} x & 0 \\\\ 0 & x  \\end{bmatrix}$$ <br>\n",
    "and x-1.5 we have $$ T(x)=  \\begin{bmatrix} 2 & 0 \\\\ 0 & 2 \\end{bmatrix} * \\begin{bmatrix} 3 \\\\ 3   \\end{bmatrix} = =\\begin{bmatrix} 6 \\\\ 6 \\end{bmatrix} $$ <be> <br>\n",
    " $$ T(x)=  \\begin{bmatrix} 2 & 0 \\\\ 0 & 2 \\end{bmatrix} * \\begin{bmatrix} 6 \\\\ 6   \\end{bmatrix} = =\\begin{bmatrix} 12 \\\\ 12 \\end{bmatrix} $$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[6]\n",
      " [6]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = VectorGround(range=[-7,16])\n",
    "A = np.array([[2,0],[2,0]])\n",
    "b = np.transpose(np.array([[3,3]]))\n",
    "g.add_v(0,0,b[0][0],b[1][0])\n",
    "t_v = A.dot(b)\n",
    "print(t_v)\n",
    "g.add_v(0,0,t_v[0][0],t_v[1][0],index='2')\n",
    "t2_v = A.dot(t_v)\n",
    "g.add_v(0,0,t2_v[0][0],t2_v[1][0],index='3')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### we can see that the linear traformation just scaling the vector with 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Roation + Scaling\n",
    "We see that the antisymetric matrix make rotation over vector and symtrix matrix making a scaling we can combine both matrix to achieve new matrix wich will make scaling and rotating \n",
    "lets to have tranformations $T_1,T_2$ <br>\n",
    "$$ T(\\alpha) = \\begin{bmatrix}cos(\\alpha) & -sin(\\alpha) \\\\ sin(\\alpha) & cos(\\alpha)  \\end{bmatrix} $$ <br> <br>\n",
    "$$T_2(x)=  \\begin{bmatrix} x & 0 \\\\ 0 & x  \\end{bmatrix}$$ <br>\n",
    "$$T_1.(T_2.(x)) = (T_1*T_2).(x)= T_3(x)$$ <br> <br>\n",
    "$$T_3(x) = \\begin{bmatrix}cos(\\alpha) & -sin(\\alpha) \\\\ sin(\\alpha) & cos(\\alpha)  \\end{bmatrix}*  \\begin{bmatrix} x & 0 \\\\ 0 & x  \\end{bmatrix}=\\begin{bmatrix}cos(\\alpha)*x & -sin(\\alpha)*x \\\\ sin(\\alpha)*x & cos(\\alpha)*x  \\end{bmatrix}$$\n",
    "example :\n",
    "$$T_1=\\begin{bmatrix}cos(30^*) & -sin(30^*) \\\\ sin(30^*) & cos(30^*)  \\end{bmatrix}$$\n",
    "$$T_2=  \\begin{bmatrix} 2 & 0 \\\\ 0 & 2  \\end{bmatrix}$$ <br> <br>\n",
    "\n",
    "$$T_3=\\begin{bmatrix}cos(30^*) & -sin(30^*) \\\\ sin(30^*) & cos(30^*)  \\end{bmatrix}*\\begin{bmatrix} 2 & 0 \\\\ 0 & 2  \\end{bmatrix}=\\begin{bmatrix}  2*cos(30^*) & - 2*sin(30^*) \\\\  2*sin(30^*) & 2*cos(30^*)  \\end{bmatrix}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$T_3=\\begin{bmatrix} 1.7 & - 0.9 \\\\ 0.9 & 1.7  \\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.4]\n",
      " [7.8]]\n",
      "[[-2.94]\n",
      " [15.42]]\n",
      "[[-18.876]\n",
      " [ 23.568]]\n",
      "[[-53.3004]\n",
      " [ 23.0772]]\n",
      "[[-111.38016]\n",
      " [  -8.73912]]\n",
      "[[-181.481064]\n",
      " [-115.098648]]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = VectorGround(range=[-150,20])\n",
    "A = np.array([[1.7,-0.9],[0.9,1.7]])\n",
    "b = np.transpose(np.array([[3,3]]))\n",
    "g.add_v(0,0,b[0][0],b[1][0],font_size=4)\n",
    "for i in range(6) :\n",
    "    b = A.dot(b)\n",
    "    print(b)\n",
    "    g.add_v(0,0,b[0][0],b[1][0],index=str(i),font_size=4)\n",
    "\n",
    "\n",
    "     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(81, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = VectorGround(range=[-10,12])\n",
    "def linear_tranformation(points,matrix):\n",
    "    sh = points.shape\n",
    "    print(sh)\n",
    "    A = np.array([0,0])\n",
    "    for i in points[:][:]:\n",
    "        row = matrix.dot(i)\n",
    "        A=np.vstack([A, row])\n",
    "    return A\n",
    "x_args=y_args = np.linspace(0,10,9)\n",
    "points = np.meshgrid(x_args,y_args)\n",
    "result = cartesian_product(x_args,y_args)\n",
    "print(type(result))\n",
    "g.plot_points(result)\n",
    "new_points = linear_tranformation(result,np.array([[0.2,0],[0,1]]))  \n",
    "g.plot_points(new_points,color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(81, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_args=y_args = np.linspace(0,10,9)\n",
    "points = np.meshgrid(x_args,y_args)\n",
    "result = cartesian_product(x_args,y_args)\n",
    "print(type(result))\n",
    "\n",
    "g = VectorGround(range=[-10,30])\n",
    "\n",
    "g.plot_points(result)\n",
    "new_points = linear_tranformation(result,np.array([[1,0],[0,3]]))  \n",
    "g.plot_points(new_points,color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "let to have matrix $$A =  \\begin{bmatrix} 1.5 & 0.5 \\\\ 0.5 & 1.5  \\end{bmatrix}$$\n",
    "Eingvalues and eing vectors of A\n",
    "$$\\gamma_1 = 1,\\vec{v_1} =  \\begin{bmatrix} -0.7  \\\\ 0.7   \\end{bmatrix},\\vec{v_2} =  \\begin{bmatrix} 0.7  \\\\ 0.7   \\end{bmatrix} $$  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "(81, 2)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_args=y_args = np.linspace(0,10,9)\n",
    "points = np.meshgrid(x_args,y_args)\n",
    "result = cartesian_product(x_args,y_args)\n",
    "print(type(result))\n",
    "g = VectorGround(range=[-10,30])\n",
    "g.plot_points(result)\n",
    "new_points = linear_tranformation(result,np.array([[1.5,0.5],[0.5,1.5]]))  \n",
    "g.plot_points(new_points,color='r')\n",
    "g.add_v(0,0,-10*-0.7,10*0.7)\n",
    "g.add_v(0,0,-10*0.7,10*0.7)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
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