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@rodluger
Created February 21, 2021 21:52
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Eigendecomposition trick for applying covariance matrix inverses w/ different white noise
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{
"cells": [
{
"cell_type": "code",
"execution_count": 233,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.linalg import cho_factor, cho_solve, eigh\n",
"from celerite import terms, GP\n",
"import time"
]
},
{
"cell_type": "code",
"execution_count": 286,
"metadata": {},
"outputs": [],
"source": [
"class Solver:\n",
" \n",
" def __init__(self, C):\n",
" self.C = C\n",
" self.s, self.U = eigh(C)\n",
" self.UT = np.array(self.U.T)\n",
" \n",
" def apply_inverse_chol(self, sigma, x):\n",
" K = self.C + sigma ** 2 * np.eye(self.C.shape[0])\n",
" choK = cho_factor(K, lower=True)\n",
" return cho_solve(choK, x)\n",
" \n",
" def apply_inverse_eigh(self, sigma, x):\n",
" sinv = 1.0 / (self.s + sigma ** 2)\n",
" return (self.U * sinv) @ (self.UT @ x)"
]
},
{
"cell_type": "code",
"execution_count": 312,
"metadata": {},
"outputs": [],
"source": [
"# Quasi-periodic covariance matrix\n",
"npts = 1000\n",
"gp = GP(terms.SHOTerm(log_S0=1, log_Q=2, log_omega0=0))\n",
"gp.compute(np.linspace(0, 10, npts))\n",
"C = gp.get_matrix()\n",
"\n",
"# Cholesky / Eigendecomp solver\n",
"solver = Solver(C)"
]
},
{
"cell_type": "code",
"execution_count": 313,
"metadata": {},
"outputs": [],
"source": [
"sigmas = np.logspace(-6, 0, 10)\n",
"max_error = np.zeros_like(sigmas)\n",
"med_error = np.zeros_like(sigmas)\n",
"x = np.ones(C.shape[0])\n",
"for k, sigma in enumerate(sigmas):\n",
" z1 = solver.apply_inverse_chol(sigma, x)\n",
" z2 = solver.apply_inverse_eigh(sigma, x)\n",
" max_error[k] = np.max(np.abs((z1 - z2)/ z1))\n",
" med_error[k] = np.median(np.abs((z1 - z2)/ z1))"
]
},
{
"cell_type": "code",
"execution_count": 314,
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
"<Figure size 1200x400 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 390,
"width": 1037
}
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(sigmas, max_error, label=\"max\")\n",
"plt.plot(sigmas, med_error, label=\"med\")\n",
"plt.yscale(\"log\")\n",
"plt.xscale(\"log\")\n",
"plt.legend()\n",
"plt.ylim(1e-10, 1e0)\n",
"plt.xlabel(r\"$\\sigma$\")\n",
"plt.ylabel(r\"frac error in apply inverse\");"
]
},
{
"cell_type": "code",
"execution_count": 309,
"metadata": {},
"outputs": [],
"source": [
"npts = [100, 300, 500, 1000, 3000, 5000, 10000]\n",
"ntimes = 1\n",
"tc = np.zeros(len(npts))\n",
"te = np.zeros(len(npts))\n",
"for n in range(len(npts)):\n",
" gp.compute(np.linspace(0, 10, npts[n]))\n",
" solver = Solver(gp.get_matrix())\n",
" x = np.ones(npts[n])\n",
" ts = time.time()\n",
" for k in range(ntimes):\n",
" solver.apply_inverse_chol(1e-2, x)\n",
" tc[n] = (time.time() - ts) / ntimes\n",
" ts = time.time()\n",
" for k in range(ntimes):\n",
" solver.apply_inverse_eigh(1e-2, x)\n",
" te[n] = (time.time() - ts) / ntimes"
]
},
{
"cell_type": "code",
"execution_count": 310,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1200x400 with 1 Axes>"
]
},
"metadata": {
"image/png": {
"height": 382,
"width": 1029
}
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(npts, tc, label=\"chol\")\n",
"plt.plot(npts, te, label=\"eigh\")\n",
"plt.legend()\n",
"plt.xscale(\"log\")\n",
"plt.yscale(\"log\")\n",
"plt.xlabel(\"npts\")\n",
"plt.ylabel(\"compute time [s]\");"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.8.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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