{
 "cells": [
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    "# Solutions"
   ]
  },
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    ":\n",
    "# Activation (sigmoid) function\n",
    "def sigmoid(x):\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "def output_formula(features, weights, bias):\n",
    "    return sigmoid(np.dot(features, weights) + bias)\n",
    "\n",
    "def error_formula(y, output):\n",
    "    return - y*np.log(output) - (1 - y) * np.log(1-output)\n",
    "\n",
    "def update_weights(x, y, weights, bias, learnrate):\n",
    "    output = output_formula(x, weights, bias)\n",
    "    d_error = y - output\n",
    "    weights += learnrate * d_error * x\n",
    "    bias += learnrate * d_error\n",
    "    return weights, bias"
   ]
  }
 ],
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