{
 "cells": [
  {
   "cell_type": "code",
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   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1.25, 2.25]\n"
     ]
    },
    {
     "ename": "AttributeError",
     "evalue": "'list' object has no attribute 'replace'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-a9c4883c08fd>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'x'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     26\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minterpolate_lagrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.25\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'u1'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'u2'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 27\u001b[0;31m \u001b[0mpoly\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msimplify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minterpolate_lagrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1.25\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'u1'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mSymbol\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'u2'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     28\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     29\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoly\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/homebrew/lib/python3.9/site-packages/sympy/simplify/simplify.py\u001b[0m in \u001b[0;36msimplify\u001b[0;34m(expr, ratio, measure, rational, inverse, doit, **kwargs)\u001b[0m\n\u001b[1;32m    602\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0m_eval_simplify\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    603\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 604\u001b[0;31m     \u001b[0moriginal_expr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mexpr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcollect_abs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msignsimp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    605\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    606\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mexpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mBasic\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mexpr\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m:\u001b[0m  \u001b[0;31m# XXX: temporary hack\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/homebrew/lib/python3.9/site-packages/sympy/simplify/radsimp.py\u001b[0m in \u001b[0;36mcollect_abs\u001b[0;34m(expr)\u001b[0m\n\u001b[1;32m    604\u001b[0m       \u001b[0;32mreturn\u001b[0m \u001b[0mMul\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_from_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_commutative\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mnot\u001b[0m \u001b[0mnc\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    605\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 606\u001b[0;31m     return expr.replace(\n\u001b[0m\u001b[1;32m    607\u001b[0m         \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mMul\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    608\u001b[0m         \u001b[0;32mlambda\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0m_abs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreplace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'list' object has no attribute 'replace'"
     ]
    }
   ],
   "source": [
    "from sympy import Symbol, simplify, lambdify\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from functools import reduce\n",
    "import operator\n",
    "\n",
    "\n",
    "def interpolate_lagrange(x, x_values, y_values):\n",
    "    \"\"\"\n",
    "    x : value at which to evaluate y, should be between min and max x_values\n",
    "    x_values: list or numpy array containing values of x\n",
    "    y_values: list or numpy array contaning values of y\n",
    "    \"\"\"\n",
    "    def _basis(j):\n",
    "        p = [(x - x_values[m])/(x_values[j] - x_values[m]) for m in range(k) if m != j]\n",
    "        return reduce(operator.mul, p)\n",
    "    assert len(x_values) != 0 and (len(x_values) == len(y_values)), 'x and y cannot be empty and must have the same length'\n",
    "    k = len(x_values)\n",
    "    basis = []\n",
    "    for j in range(k):\n",
    "        basis.append(_basis(j))\n",
    "    #return sum(_basis(j)*y_values[j] for j in range(k)) \n",
    "    return basis\n",
    "\n",
    "x = Symbol('x')\n",
    "print(interpolate_lagrange(1.25,[-1, 0],[Symbol('u1'),Symbol('u2')]))\n",
    "poly = simplify(interpolate_lagrange(1.25,[-1, 0],[Symbol('u1'),Symbol('u2')]))\n",
    "\n",
    "print(poly)\n",
    "\n",
    "x1 = np.linspace(-1, 2, 100)\n",
    "y1 = lambdify(x, poly)(x1)\n",
    "\n",
    "#fig, ax = plt.subplots()\n",
    "#ax.plot(x1, y1)\n",
    "#ax.scatter([-1, 0, 1, 2],[3,-4, 5, -6], c = 'r')\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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