{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0f18ddb6-6f8f-44b1-9083-c86b9ae657ac",
   "metadata": {},
   "source": [
    "# Step"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fb0ada15-3643-4b61-b962-af80bd318097",
   "metadata": {},
   "source": [
    "`lamatrix` provides a Step model to capture step functions and breaks in data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ae5d5c89-f880-4c50-9a53-bc4171ec3086",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "x = np.arange(-10, 10, 0.01)\n",
    "\n",
    "\n",
    "from lamatrix import Step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3241dc64-c209-4971-8a2c-f036d0324b47",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\\[f(\\mathbf{x}) = w_{0} \\mathbb{I}_{[{-\\infty}, {0}]}(\\mathbf{x}) + w_{1} \\mathbb{I}_{[{0}, {\\infty}]}(\\mathbf{x})\\]</div>"
      ],
      "text/plain": [
       "'\\\\[f(\\\\mathbf{x}) = w_{0} \\\\mathbb{I}_{[{-\\\\infty}, {0}]}(\\\\mathbf{x}) + w_{1} \\\\mathbb{I}_{[{0}, {\\\\infty}]}(\\\\mathbf{x})\\\\]'"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Step().equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "d100b342-9f43-4277-aad2-aa1eb431a776",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = Step('x', breakpoints=[0])\n",
    "w = np.random.normal(size=model.width)\n",
    "sample = model.design_matrix(x=x).dot(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e32159da-2a24-43cc-9550-d53afcf403e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(x, sample, c='k')\n",
    "ax.set(xlabel='$x$', ylabel='$y$', title='Step model sample');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}