Aproximation of Rice Correlation to Bread Demand.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import control as control\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# System Analysis and Model Creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_true=np.array([5200,5400,5800,5600,5900,5900,6200,6320,6700,8400,9600,10600])\n",
    "R_true=np.array([406.162,406.162,404.0493,410.9155,406.6901,417.7817,414.0845,427.8169,430.9859,435.7394,440.493,447.8873])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x17ec3ba2908>"
      ]
     },
     "execution_count": 3,
     "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": [
    "plt.scatter(R_true,Y_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec3c54c50>]"
      ]
     },
     "execution_count": 4,
     "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": [
    "plt.plot(R_true,Y_true)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As observed, there is linear and non-linear part for the causal model of Bread Demand output with Rice Price as input"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression for Bread Demand Model with Rice Price as Input for Linear Part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec3cbca20>]"
      ]
     },
     "execution_count": 5,
     "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": [
    "R_true_linear=np.array([406.162,406.162,404.0493,410.9155,406.6901,417.7817,414.0845,427.8169,430.9859])\n",
    "Y_true_linear=np.array([5200,5400,5800,5600,5900,5900,6200,6320,6700])\n",
    "plt.plot(R_true_linear,Y_true_linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "x = R_true_linear\n",
    "y = Y_true_linear\n",
    "linear_slope, linear_intercept, linear_r_value, linear_p_value, linear_std_err = stats.linregress(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6950358328589681"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_r_value**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# First Order Differential Equation Approximation for Bread Demand Model with Rice Price as Input for Non-Linear Part"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nonlinearity of the price is assumed to be stuck at a point due to demand resistance stochastic process, this process is calculated by observing correlation of $\\frac {dY_{i}}{dR} $ (forward gradient) with $ Y_i $ (current demand of interest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_true_non=np.array([430.9859,435.7394,440.493,447.8873])\n",
    "Y_true_non=np.array([6700,8400,9600,10600])\n",
    "dydr=np.zeros(len(R_true_non)-1)\n",
    "for i in range (len(R_true_non)-1):\n",
    "    dydr[i]=(Y_true_non[i+1]-Y_true_non[i])/(R_true_non[i+1]-R_true_non[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec4151780>]"
      ]
     },
     "execution_count": 9,
     "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": [
    "Y_i=np.array([6700,8400,9600])\n",
    "plt.plot(Y_i,dydr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "x = Y_i\n",
    "y = dydr\n",
    "non_linear_slope, non_linear_intercept, non_linear_r_value, non_linear_p_value, non_linear_std_err = stats.linregress(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9830958029292611"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "non_linear_r_value**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is observed that the correlation of $ \\frac {dY}{dR} $ with $ Y_i $ is linear with $ r^2 $ value of 0.983, therefore linear regression to find a stochastic gradient for the process is a great model for a given $Y_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "A=non_linear_slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "B=non_linear_intercept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this stochastic process, it is legal to create a non-linear model of $ \\frac {dY}{dR} $ where the minimum is 0. This is due to the boundary condition where causality of the price raise increase the probability of the demand to increase, rather than decrease."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take $Y$ as Bread Demand Output and $R$ as Rice Price Input Where $\\frac {dY}{dR} = AY + B $ (linear regression on the demand change over change on price) with minimum of zero (non-linear)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dydr(y,R,A,B):\n",
    "    if((A*y+B)<0):\n",
    "        result = 0\n",
    "    else:\n",
    "        result=A*y+B\n",
    "    return result"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Testing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predicted=np.zeros(len(R_true))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Y_predicted_linear(R):\n",
    "    return linear_slope*R+linear_intercept"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range (0,len(R_true_linear)-1):\n",
    "    Y_predicted[i]=Y_predicted_linear(R_true_linear[i])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Non-linear Part"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Y_predicted_non_linear(Y0,R,A,B):\n",
    "    yp=odeint(dydr,y0=Y0,t=R,args=(A,B))\n",
    "    return yp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "for i in range (0,len(R_true_non)):\n",
    "    Y_predicted[len(R_true_linear)-1+i]=Y_predicted_non_linear(6700,R_true_non,A,B)[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5587.58563368,  5587.58563368,  5504.17281641,  5775.26151141,\n",
       "        5608.43587687,  6046.35020642,  5900.37876323,  6442.55615324,\n",
       "        6700.        ,  8155.20606759,  9170.65514332, 10175.64640431])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec539aeb8>]"
      ]
     },
     "execution_count": 39,
     "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": [
    "plt.plot(R_true,Y_predicted)\n",
    "plt.plot(R_true,Y_true)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statistics\n",
    "Y_preddev=(abs(Y_true-Y_predicted))**2\n",
    "Y_stddev=(abs(Y_true-statistics.mean(Y_true)))**2\n",
    "rsquared=(sum(Y_stddev)-sum(Y_preddev))/sum(Y_stddev)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9723930332144516"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rsquared"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Predictive Analytics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After getting a nice model with 0.97 $ r^2 $, time to test the response afterwards using data predicted through holtz method of rice price"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_predicted=np.array([446.6279,453.2656,459.2221,465.1786,471.1351,477.0916,483.0481,489.0046,494.9611,500.9177,506.8742,512.8307,518.7872])\n",
    "Y_predicted_new=np.zeros(len(R_predicted))\n",
    "for i in range (0,len(R_predicted)):\n",
    "    Y_predicted_new[i]=Y_predicted_non_linear(10175.6464043,R_predicted,A,B)[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10175.6464043 , 10704.7397256 , 10998.90983932, 11186.3125309 ,\n",
       "       11305.69826171, 11381.75351548, 11430.20487165, 11461.07101663,\n",
       "       11480.73443089, 11493.26127935, 11501.24138246, 11506.32513963,\n",
       "       11509.56377147])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_predicted_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec541a5c0>]"
      ]
     },
     "execution_count": 44,
     "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": [
    "plt.plot(R_predicted,Y_predicted_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Final Model with Predictive Capability of System Response"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_predicted_final=np.concatenate((Y_predicted,Y_predicted_new))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5587.58563368,  5587.58563368,  5504.17281641,  5775.26151141,\n",
       "        5608.43587687,  6046.35020642,  5900.37876323,  6442.55615324,\n",
       "        6700.        ,  8155.20606759,  9170.65514332, 10175.64640431,\n",
       "       10175.6464043 , 10704.7397256 , 10998.90983932, 11186.3125309 ,\n",
       "       11305.69826171, 11381.75351548, 11430.20487165, 11461.07101663,\n",
       "       11480.73443089, 11493.26127935, 11501.24138246, 11506.32513963,\n",
       "       11509.56377147])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y_predicted_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "R_predicted_final=np.concatenate((R_true,R_predicted))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([406.162 , 406.162 , 404.0493, 410.9155, 406.6901, 417.7817,\n",
       "       414.0845, 427.8169, 430.9859, 435.7394, 440.493 , 447.8873,\n",
       "       446.6279, 453.2656, 459.2221, 465.1786, 471.1351, 477.0916,\n",
       "       483.0481, 489.0046, 494.9611, 500.9177, 506.8742, 512.8307,\n",
       "       518.7872])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "R_predicted_final"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x17ec54bf0b8>]"
      ]
     },
     "execution_count": 50,
     "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": [
    "plt.plot(R_predicted_final,Y_predicted_final)\n",
    "plt.plot(R_true,Y_true)"
   ]
  }
 ],
 "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",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}