phys512/interpolation_solutions.ipynb
2023-09-25 12:46:17 -04:00

207 lines
127 KiB
Text

{
"cells": [
{
"cell_type": "markdown",
"id": "1d5fe3a8",
"metadata": {},
"source": [
"# Interpolation exercises"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "3c335a6b",
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Number of points = 11\n",
"Maximum error for linear is 8.088451e-02\n",
"Maximum error for cubic is 2.945822e-02\n",
"Maximum error for spline is 1.150823e-02\n",
"Maximum error for poly is 5.653960e-01\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.interpolate\n",
"\n",
"# function to interpolate\n",
"def func_sin(x):\n",
" f = np.sin(x) \n",
" return f\n",
"\n",
"def func_step(x):\n",
" # step function / discontinuous gradient\n",
" f = np.zeros_like(x)\n",
" for i, xx in enumerate(x):\n",
" if xx>np.pi:\n",
" f[i] = 1.0\n",
" else:\n",
" f[i] = (xx/np.pi)\n",
" return f\n",
"\n",
"def func_exp(x):\n",
" # Gaussian\n",
" return np.exp(-x**2/2)\n",
"\n",
"def func_poly(x):\n",
" # polynomial\n",
" poly = np.polynomial.Polynomial([-10, 3, 0, 0, 0, 0])\n",
" return poly(x)\n",
"\n",
"def cubic_interpolation(x, xp, fp):\n",
" # storage for the interpolated function and derivatives\n",
" f2 = np.zeros_like(x)\n",
" f2d = np.zeros_like(x)\n",
" f2dd = np.zeros_like(x)\n",
"\n",
" # do a cubic polynomial fit to each interval (except the first and last)\n",
" for i in range(len(xp)-3):\n",
" poly = np.polynomial.Polynomial.fit(xp[i:i+4], fp[i:i+4], 3) \n",
" ind = np.where(np.logical_and(x<xp[i+2],x>=xp[i+1]))\n",
" f2[ind] = poly(x[ind])\n",
" f2d[ind] = poly.deriv(m=1)(x[ind])\n",
" f2dd[ind] = poly.deriv(m=2)(x[ind])\n",
" \n",
" # exclude the first and last intervals\n",
" ind = np.where(np.logical_and(x>=xp[1],x<xp[-2]))\n",
" f2 = f2[ind]\n",
" f2d = f2d[ind]\n",
" f2dd = f2dd[ind] \n",
" x2 = x[ind]\n",
"\n",
" return x2, f2, f2d, f2dd\n",
"\n",
"# choose one of the above functions to fit\n",
"func = func_exp\n",
"x1 = -5\n",
"x2 = 5\n",
"n_points = 11 # number of sample points\n",
"add_noise = False # whether to add noise\n",
"noise_amp = 0.001 # noise amplitude\n",
"\n",
"# Sample the function\n",
"xp = np.linspace(x1, x2, num=n_points)\n",
"fp = func(xp)\n",
"# add noise\n",
"if add_noise:\n",
" fp = fp + noise_amp*np.random.normal(size = len(xp))\n",
"\n",
"# 1. Piecewise linear interpolation\n",
"x = np.linspace(x1, x2, num=10**3)\n",
"f1 = np.interp(x, xp, fp)\n",
"\n",
"# 2. Cubic interpolation\n",
"x2, f2, f2d, f2dd = cubic_interpolation(x, xp, fp)\n",
"\n",
"# 3. Spline\n",
"f3 = scipy.interpolate.CubicSpline(xp,fp) #, bc_type = 'natural')\n",
"\n",
"# 4. Lagrange polynomial fit to all points\n",
"poly = scipy.interpolate.lagrange(xp, fp)\n",
"\n",
"# Calculate the maximum errors\n",
"print('Number of points = %d' %(n_points,))\n",
"print('Maximum error for linear is %e' % (np.max(np.abs((f1-func(x))))/np.max(func(x)),) )\n",
"ind = np.where(np.logical_and(x>=xp[1],x<xp[-2]))\n",
"print('Maximum error for cubic is %e' % (np.max(np.abs((f2-func(x2))))/np.max(func(x2)),) )\n",
"print('Maximum error for spline is %e' % (np.max(np.abs((f3(x)-func(x))))/np.max(func(x)),) )\n",
"print('Maximum error for poly is %e' % (np.max(np.abs((poly(x)-func(x))))/np.max(func(x)),) )\n",
"\n",
"# Plot the function and different interpolations\n",
"plt.plot(x,func(x), label=r'$f(x)$')\n",
"plt.plot(x,poly(x),'--', label='Polynomial fit')\n",
"plt.plot(x,f1, label='Linear')\n",
"plt.plot(x2,f2,':', label='Cubic')\n",
"plt.plot(x,f3(x),':', label='Spline')\n",
"plt.plot(xp,fp, 'o')\n",
"plt.legend()\n",
"plt.show()\n",
"\n",
"# Plot the derivatives\n",
"plt.clf()\n",
"plt.plot(x, func(x), label=r'$f(x)$')\n",
"plt.plot(x2, f2, \"C0\", label = 'Cubic')\n",
"plt.plot(x2, f2d, \"C1\", label = 'Cubic 1st derivative')\n",
"plt.plot(x2, f2dd, \"C2\", label = 'Cubic 2nd derivative')\n",
"plt.plot(x, f3(x), \"C0:\", label = 'Spline')\n",
"plt.plot(x, f3(x,1), \"C1:\", label = 'Spline 1st derivative')\n",
"plt.plot(x, f3(x,2), \"C2:\", label = 'Spline 2nd derivative')\n",
"plt.plot(xp, fp, 'o')\n",
"plt.legend()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "ae9727e6",
"metadata": {},
"source": [
"Things to note:\n",
"\n",
"- For $N$ sample points, the error in linear interpolation decreases as $N^2$, cubic and spline decrease as $N^4$. This is because the largest correction term (next term in the Taylor expansion) is $\\propto (\\Delta x)^2$ for linear and $\\propto (\\Delta x)^4$ for cubic. \n",
"- The full $N-1$-order polynomial fit (Lagrange polynomial) does not behave well, often showing high frequency components, particularly near the boundaries of the domain ([Runge's phenomenon](https://en.wikipedia.org/wiki/Runge's_phenomenon)).\n",
"- The cubic fits show discontinities in the derivatives at the sampled points; the spline (by definition) has continuous first and second derivatives.\n",
"- The cubic and spline fits develop oscillations near discontinous changes in the function of derivatives. Adding Gaussian noise to the data points also can lead to oscillations in the interpolated function.\n",
"- The cubic and spline interpolations are able to fit polynomials up to 3rd order exactly. The Lagrange fit will fit up to order $N-1$ exactly. "
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