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ANum/QUESTION1.ipynb
2024-12-03 18:02:14 +01:00

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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "f47a3a4d-fe62-4803-8531-e5e377497546",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "572458f7-700e-454a-9e3d-d323065bd0ea",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"POINTS = np.array( [ [0, 0], [1, 0], [2, 1], [4, 1], [5, 0], [6, 0], [7, 1], [9, 1], [10, 0], [11, 0] ])"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "c0a91729-9698-4e18-90ed-67b9618329cd",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def InterpolLagrange(xp,x,y):\n",
" s = 0\n",
" \n",
" for i in range(len(x)):\n",
" t = 1\n",
" for j in range(len(y)):\n",
" if j != i:\n",
" t *= (xp - x[j])\n",
" t /= (x[i] - x[j])\n",
" s += y[i]*t\n",
" \n",
" return s"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "274a8789-8db0-47a1-9e56-a271ebe93cdc",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def CoeffSplinesCubNaturelles(x, y):\n",
" N = len(x)\n",
" M = np.zeros(N**2)\n",
" M.shape = (N, N)\n",
" \n",
" b = np.zeros(N)\n",
" for i in range(N-2):\n",
" b[i] = 6*((y[i+2]-y[i+1])/(x[i+2] - x[i+1]) - (y[i+1]-y[i])/(x[i+1]-x[i]) )\n",
" \n",
" M[i, i] = (x[i+1]-x[i])\n",
" M[i, i+1] = 2*(x[i+1]-x[i] + x[i+2] - x[i+1])\n",
" M[i, i+2] = (x[i+2] - x[i+1])\n",
" \n",
" M[N-2, 0] = 1\n",
" M[N-1, N-1] = 1\n",
" \n",
" \n",
" M = np.linalg.solve(M, b)\n",
" print(\"M=\",M)\n",
" a = np.zeros(N-1)\n",
" b = np.zeros(N-1)\n",
" c = np.zeros(N-1)\n",
" d = np.zeros(N-1)\n",
" \n",
" for i in range(N-1):\n",
" a[i] = (M[i+1] - M[i])/(6*(x[i+1] - x[i]))\n",
" b[i] = M[i]/2\n",
" c[i] = ((y[i+1]-y[i])/(x[i+1]-x[i])) - ((x[i+1]-x[i])/6)*(M[i+1]+2*M[i])\n",
" d[i] = y[i]\n",
" print(\"a=\",a,\"b=\",b,\"c=\",c,\"d=\",d)\n",
" return a,b,c, d"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "1417bd86-672b-4926-920a-984231027a93",
"metadata": {
"tags": []
},
"outputs": [],
"source": [
"def RegressionPolynomiale(x,y,m):\n",
" # min || Ax - b ||\n",
" # A.T * A * x = A.T * B\n",
" \n",
" A = np.zeros((len(x), m+1))\n",
" b = np.zeros(len(x))\n",
" for i in range(len(x)):\n",
" for j in range(m+1):\n",
" A[i, j] = (x[i])**j\n",
" b[i] = y[i]\n",
" \n",
" return np.linalg.solve(A.T @ A, A.T @ b)\n",
" \n",
" "
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "549233bb-6150-47df-8175-04a44ac827ba",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"M= [ 0. 1.74787053 -0.99148211 -0.89948893 1.37989779 1.37989779\n",
" -0.89948893 -0.99148211 1.74787053 0. ]\n",
"a= [ 2.91311755e-01 -4.56558773e-01 7.66609881e-03 3.79897785e-01\n",
" -3.70074342e-17 -3.79897785e-01 -7.66609881e-03 4.56558773e-01\n",
" -2.91311755e-01] b= [ 0. 0.87393526 -0.49574106 -0.44974446 0.68994889 0.68994889\n",
" -0.44974446 -0.49574106 0.87393526] c= [-0.29131175 0.58262351 0.96081772 -0.93015332 -0.68994889 0.68994889\n",
" 0.93015332 -0.96081772 -0.58262351] d= [0. 0. 1. 1. 0. 0. 1. 1. 0.]\n"
]
},
{
"data": {
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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X, Y = POINTS[:,0], POINTS[:,1]\n",
"\n",
"x = np.linspace(0, 11, 500)\n",
"\n",
"plt.plot(X, Y, 'o')\n",
"\n",
"y = InterpolLagrange(x, X, Y)\n",
"plt.plot(x, y, color='b', label='Polynôme d''interpolation')\n",
"\n",
"a,b,c,d = CoeffSplinesCubNaturelles(POINTS[:,0], POINTS[:,1])\n",
"\n",
"xspline = np.array([])\n",
"yspline = np.array([])\n",
"for i in range(len(POINTS) - 1):\n",
" x = np.linspace(X[i], X[i+1], 50)\n",
" y = (x - X[i])**3 * a[i] + (x - X[i])**2 * b[i] + (x - X[i]) * c[i] + d[i]\n",
" xspline = np.concatenate([xspline, x])\n",
" yspline = np.concatenate([yspline, y])\n",
"\n",
"plt.plot(xspline,yspline, color='r', label='Spline naturelle')\n",
" \n",
"a = RegressionPolynomiale(POINTS[:,0], POINTS[:,1], 4) \n",
"x = np.linspace(0, 11, 500)\n",
"y = np.zeros(len(x))\n",
"\n",
"for i in range(4, 0, -1):\n",
" y += x**i * a[i]\n",
" \n",
"plt.plot(x, y, color='g', label='Moindres carrés')\n",
"\n",
"plt.legend(loc='upper left')\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "78b1910e-a552-4794-aa1d-1734d0fe92a2",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}