analyzeStrengthDuration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1672b53e",
   "metadata": {},
   "source": [
    "# Analyze Strength Duration\n",
    "\n",
    "This notebook will help you generate your strength duration curve from the earthworm.\n",
    "\n",
    "**Note**: If you're new to Jupyter Notebooks and/or Python, please be sure to work through the Introduction notebook before this one.\n",
    "    \n",
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa2f211c",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "At the start of almost every coding notebook, we'll import the packages we need."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "15d677c6",
   "metadata": {},
   "source": [
    "To generate the trendline on our plot, we need a couple of additional packages. Currently, the Datahub has the wrong package versions though! Run the cell below to install the correct versions in your datahub. When you're done, restart the notebook. **You do not need to run this cell after you have already completed this step**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78315d2d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "!pip install scipy=='1.10.0' numpy=='1.24.1'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d5319d2d",
   "metadata": {},
   "source": [
    "To plot our scatter plot, we just need package: `matplotlib.pyplot`. \n",
    "\n",
    "> **Task**: Import the `matplotlib.pyplot` package as `plt`, just as you did in the introduction notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b5627e3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import necessary packages here\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.optimize import curve_fit\n",
    "\n",
    "# These lines are additional configuration steps for matplotlib\n",
    "%matplotlib inline \n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5200e250",
   "metadata": {},
   "source": [
    "## Define values to plot\n",
    "With matplotlib imported, we can now use the scatter function by calling `plt.scatter()`. However, we need to define what to plot first. One straightforward way to think about this is to define an x variable and a y variable. Below, there are **lists** of values (defined in brackets `[ ]`) assigned to `x` and `y`. Replace these with your own values, depending on what you'd like to plot on the x and y axis of your strength duration curve.\n",
    "\n",
    "**Note**: Remember that in a scatterplot, each dot has both an x and a y value. Therefore, these lists should be the same length. The coordinate for each point will be the values at the same **index** in `x` and `y`. For example, the coordinate for the very first point will be `x[0],y[0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "53dc0802",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Replace your scatterplot values here\n",
    "x = [1,2,3,4,5,6]\n",
    "y = [1,0.8,0.5,0.45,0.4,0.4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "01196ae2",
   "metadata": {},
   "source": [
    "## Plot & label\n",
    "We can now plot our values using the code below. Remember that you can add axis labels using `plt.xlabel()`. If you need a reminder for how to do this, refer to the Introduction notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "de064aab",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)\n",
    "\n",
    "# Add labels here\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3ca35305",
   "metadata": {},
   "source": [
    "## Fit a hyperbolic curve\n",
    "\n",
    "The strength-duration curve should follow a **hyperbolic** function:\n",
    "\n",
    "$$\n",
    "a = r + \\frac{r+c}{t}\n",
    "$$\n",
    "\n",
    "where **a** is the stimulus amplitude (in amps or volts), **r** is the rheobase, **c** is the chronaxie, and **t** is time (the width of the stimulus).\n",
    "\n",
    "We'll first define that function below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3eecdad6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a curve function\n",
    "def func(t, r, c):\n",
    "    return r+((r*c)/t) #hyperbolic function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7be1cfdd",
   "metadata": {},
   "source": [
    "To demonstrate what this function looks like, we'll use `np.linspace()` to generate a list of 100 numbers from 0 to 1, with 0.01 spacing. We'll also define a sample rheobase and chronaxie. Then, from those points, we'll fit a hyperbolic curve using `scipy.optimize.curve_fit()`, which uses non-linear least squares to fit a function to data. [[curve_fit documentation](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.curve_fit.html)]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "500d01db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 261,
       "width": 376
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pulse_width = np.linspace(0.01,1,100)\n",
    "rheobase = .5 # in V\n",
    "chronaxie = 0.1 # in ms\n",
    "\n",
    "amplitude = rheobase+((rheobase*chronaxie)/pulse_width)\n",
    "\n",
    "# Fit the curve!\n",
    "sample_popt, sample_pcov = curve_fit(func,pulse_width,amplitude)\n",
    "\n",
    "# Plot a regression line, using the slope & intercept\n",
    "plt.plot(pulse_width, func(pulse_width, *sample_popt), 'black')\n",
    "\n",
    "# Plot chronaxie & rheobase lines\n",
    "plt.vlines(chronaxie,amplitude.min(),amplitude.max(),color='blue',linestyle='--')\n",
    "plt.hlines(rheobase,pulse_width.min(),pulse_width.max(),color='red',linestyle='--')\n",
    "\n",
    "# Label the axes & show plot\n",
    "plt.ylabel('Stimulus Amplitude (Volts)')\n",
    "plt.xlabel('Stimulus Width (Seconds)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cce0a46",
   "metadata": {},
   "source": [
    "Above, you can see a perfectly fit curve, with the rheobase (red) and chronaxie (blue) labeled. Now, let's do the same, but with your data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "a3865aec",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fit the curve with your data!\n",
    "popt, pcov = curve_fit(func,x,y)\n",
    "\n",
    "# Plot a regression line, using the slope & intercept\n",
    "plt.plot(x, func(x, *popt), 'black')\n",
    "plt.scatter(x,y)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae289ea4",
   "metadata": {},
   "source": [
    "It is also important to know how well our curve fits. To do so, we'll calculate the residuals and then the sum of squares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "eeda09d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 =  0.9239011751642454\n",
      "Rheobase:  0.278745874411597\n",
      "Chronaxie:   2.749230408204977\n"
     ]
    }
   ],
   "source": [
    "#  Calculate the distance (on y axis) from data to curve\n",
    "residuals = y - func(x, *popt)\n",
    "\n",
    "# Calculate the residual sum of squares\n",
    "ss_res = np.sum(residuals**2)\n",
    "\n",
    "# Calculate the total sum of squares\n",
    "ss_tot = np.sum((y-np.mean(y))**2)\n",
    "\n",
    "# Calculate r-squared\n",
    "r_squared = 1 - (ss_res / ss_tot)\n",
    "\n",
    "print('R^2 = ',r_squared)\n",
    "print('Rheobase: ' , popt[0])\n",
    "print('Chronaxie:  ', popt[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d89ecb7",
   "metadata": {},
   "source": []
  }
 ],
 "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": 5
}