{ "cells": [ { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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zgKXd3h6jqmdFpBBYKyL7VLX8PTtUfRx4HGDOnDm6bNmya5a/+ps9pA67wITc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\nUVEWeyovcrml3elQHLepvBY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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\"\"\"The sigmoid function (or the logistic curve) is a \n", "function that takes any real number, z, and outputs a number (0,1).\n", "It is useful in neural networks for assigning weights on a relative scale.\n", "The value z is the weighted sum of parameters involved in the learning algorithm.\"\"\"\n", "\n", "import numpy\n", "import matplotlib.pyplot as plt\n", "import math as mt\n", "\n", "z = numpy.arange(-5, 5, .1)\n", "sigma_fn = numpy.vectorize(lambda z: 1/(1+numpy.exp(-z)))\n", "sigma = sigma_fn(z)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.plot(z, sigma)\n", "ax.set_ylim([-0.1, 1.1])\n", "ax.set_xlim([-5,5])\n", "ax.grid(True)\n", "ax.set_xlabel('z')\n", "ax.set_title('sigmoid function')\n", "\n", "plt.show()\n", "\n", "\"\"\"Step Function\"\"\"\n", "z = numpy.arange(-5, 5, .02)\n", "step_fn = numpy.vectorize(lambda z: 1.0 if z >= 0.0 else 0.0)\n", "step = step_fn(z)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.plot(z, step)\n", "ax.set_ylim([-0.5, 1.5])\n", "ax.set_xlim([-5,5])\n", "ax.grid(True)\n", "ax.set_xlabel('z')\n", "ax.set_title('step function')\n", "\n", "plt.show()\n", "\n", "\"\"\"Sine Function\"\"\"\n", "z = numpy.arange(-2*mt.pi, 2*mt.pi, 0.1)\n", "t = numpy.sin(z)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.plot(z, t)\n", "ax.set_ylim([-1.0, 1.0])\n", "ax.set_xlim([-2*mt.pi,2*mt.pi])\n", "ax.grid(True)\n", "ax.set_xlabel('z')\n", "ax.set_title('sine function')\n", "\n", "plt.show()\n", "\n", "\"\"\"Plots a graph of the squashing function used by a rectified linear\n", "unit\"\"\"\n", "z = numpy.arange(-2, 2, .1)\n", "zero = numpy.zeros(len(z))\n", "y = numpy.max([zero, z], axis=0)\n", "\n", "fig = plt.figure()\n", "ax = fig.add_subplot(111)\n", "ax.plot(z, y)\n", "ax.set_ylim([-2.0, 2.0])\n", "ax.set_xlim([-2.0, 2.0])\n", "ax.grid(True)\n", "ax.set_xlabel('z')\n", "ax.set_title('Rectified linear unit')\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "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": "3.6.3" } }, "nbformat": 4, "nbformat_minor": 2 }