Delta Method.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ab319438-c44e-47a0-a7cc-8c70c1910128",
   "metadata": {},
   "source": [
    "# Purpose:\n",
    "Compute the slope at a point on a function using the delta method.  Plot the user defined function and get the slop of the point.  The compare the output of the slope to getting the derivative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "897c0aeb-e5d7-49fd-b48d-80625d60e3af",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "abd7fa54-6410-4789-be02-1eeeba9a1518",
   "metadata": {},
   "outputs": [],
   "source": [
    "class delta_method():\n",
    "    '''The delta method is used to approximate the slope of a points on a function's curve.\n",
    "    This method will be used to find the slope of two points that are extrememly close to each other.\n",
    "    \n",
    "    Fit the model with two x & y pairs of your choosing using the fit_slope method.\n",
    "    Plot your function along with the slope of the fitted points.\n",
    "    '''\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.x = np.linspace(-10,10,1000) # change this if you would like\n",
    "        \n",
    "    def fit_slope(self,x2, y2, x1, y1):\n",
    "        '''fit_slope method:\n",
    "        computes the slope between two different x & y values\n",
    "        These two points should be extremely close.\n",
    "        For example:\n",
    "            (2,10) & (2.0000001,10.000000600000009)\n",
    "            \n",
    "        Returns: slope\n",
    "        '''\n",
    "        self.x2 = x2\n",
    "        self.x1 = x1\n",
    "        self.y2 = y2\n",
    "        self.y1 = y1\n",
    "        self.slope = (self.y2-self.y1)/(self.x2-self.x1)\n",
    "        return self.slope\n",
    "    \n",
    "    def plot(self, y_fun):\n",
    "        '''plot method:\n",
    "        y_fun: the y values from your self created function.\n",
    "        The x values used in your function should be the same as\n",
    "        the x values initialized here, x = np.linspace(-10,10,1000).\n",
    "        You can change those x values in the code to suit your needs.\n",
    "        \n",
    "        Returns: the plots of your function and the slope's line at the points. \n",
    "        '''\n",
    "        b = self.y2 - self.slope*self.x2 # the y intercept with respect to the slope\n",
    "        y3 = self.slope*self.x + b # computing the y values with respect to the intercept\n",
    "        plt.plot(self.x,y3, label=f'Slope {self.slope:.2f}') # plotting the line of the slope\n",
    "        \n",
    "        plt.plot(self.x, y_fun, label='Function') # plotting the function's curve\n",
    "        plt.scatter(self.x2,self.y2, c='orange') # plotting the points\n",
    "        plt.scatter(self.x1,self.y1, c='green') # plotting the points\n",
    "        # these points should overlap since they are basically the same\n",
    "        plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ede31d8a-977e-445e-b3d7-4351fac7213a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# user defined function\n",
    "\n",
    "x = np.linspace(-10,10,1000) # x values to create the function's line plot\n",
    "\n",
    "def f(x):\n",
    "    y = x**2 + 2*x + 2\n",
    "    return y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "255ceb79-f51d-48e6-8dd1-86dcb5dbfc93",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this will be used to plot the main curve of the function and all the different \n",
    "# points of the x value created with np.linspace(-10,10,1000)\n",
    "y_fun = f(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "176e34d3-7a02-4e6a-9256-74604c77c78a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# getting the y value when x = 2\n",
    "# this is to plot a point to get the slope at said point\n",
    "# (2, 10)\n",
    "f(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "325f5158-c88a-4b9f-9d47-6a885c83ea04",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.000000600000009"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# getting the y value when x = 2.0000001\n",
    "# this will be the delta change (0.0000001) in the x value\n",
    "# this point is meant to be extremely close to the other point above\n",
    "# (2.0000001, 10.000000600000009)\n",
    "f(2.0000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f98fc85f-cb9d-46e7-80a6-3ea80b4868e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.000000097699626"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# example of x & y pairs for getting the slope\n",
    "\n",
    "d = delta_method()\n",
    "\n",
    "d.fit_slope(x2=2.0000001, y2=10.000000600000009, x1=2, y1=10)\n",
    "# the same points we computed above\n",
    "# slope is ~ 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a75c76ac-d383-435d-9b0a-9b87b1efd93b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting the user defined function in context to the x & y pairs and the slope\n",
    "\n",
    "d.plot(y_fun=y_fun)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "bdef60ea-6daa-4b5d-992d-9dad49930377",
   "metadata": {},
   "outputs": [],
   "source": [
    "# this method shows us that the slope for (2,10) is 6\n",
    "\n",
    "# now lets compute the derivative of the function to see if the results \n",
    "# agree with the delta method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "8e6fbce2-eafd-460b-b902-2b3ba5fb88ce",
   "metadata": {},
   "outputs": [],
   "source": [
    "# the function: \n",
    "# y = x^2 + 2x + 2\n",
    "# dy/dx = 2(x) + 2(x^0) + 0\n",
    "\n",
    "# dy/dx = 2(x) + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9497fd38-b4f6-4478-91a3-dbf5a6f1df1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# using the same x value from the plot above x_ = 2\n",
    "x_ = 2\n",
    "dy_wrt_x = 2*x_ + 2\n",
    "dy_wrt_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "39cbe600-4b66-4736-99a6-3202ad0da7b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# here we see the derivative of y wrt x when x = 2 is 6\n",
    "# this agrees with the delta method plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "269281e2-ba8a-4cd8-826c-dab34a422c57",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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