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@rodluger
Created June 8, 2020 16:43
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%run notebook_setup.py"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from scipy.special import binom"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [],
"source": [
"class SquareRoot(object):\n",
" \n",
" def __init__(self, N, z0=0.5):\n",
" self._N = N\n",
" self._z0 = z0\n",
" self._get_u0()\n",
" \n",
" def _get_u0(self):\n",
" self._u0 = np.zeros(self._N + 1)\n",
" for n in range(self._N + 1):\n",
" fac1 = binom(0.5, n) * self._z0 ** 0.5\n",
" for k in range(n + 1):\n",
" fac2 = binom(n, k) * (-1) ** (n - k) * self._z0 ** -k\n",
" self._u0[k] += fac1 * fac2\n",
" \n",
" def _get_u(self, c, d):\n",
" u = d * self._u0\n",
" u[0] += 1 - c - d\n",
" u[1] += c\n",
" return u\n",
" \n",
" def exact(self, z, c, d):\n",
" return 1 - c * (1 - z) - d * (1 - np.sqrt(z))\n",
" \n",
" def __call__(self, z, c, d):\n",
" Z = np.vander(np.atleast_1d(z), self._N + 1, increasing=True)\n",
" return Z.dot(self._get_u(c, d))\n",
" \n",
"\n",
"class Logarithmic(object):\n",
" \n",
" def __init__(self, N, z0=0.5):\n",
" self._N = N\n",
" self._z0 = z0\n",
" self._get_u0()\n",
" \n",
" def _get_u0(self):\n",
" self._u0 = np.zeros(self._N + 1)\n",
" self._u0[0] = -self._z0\n",
" self._u0[1] = 1 + np.log(self._z0)\n",
" for n in range(2, self._N + 1):\n",
" fac1 = (-1) ** n * self._z0 / (n * (n - 1))\n",
" for k in range(n + 1):\n",
" fac2 = binom(n, k) * (-1) ** (n - k) * self._z0 ** -k\n",
" self._u0[k] += fac1 * fac2\n",
" \n",
" def _get_u(self, e, f):\n",
" u = -f * self._u0\n",
" u[0] += 1 - e\n",
" u[1] += e\n",
" return u\n",
" \n",
" def exact(self, z, e, f):\n",
" return 1 - e * (1 - z) - f * z * np.log(z)\n",
" \n",
" def __call__(self, z, e, f):\n",
" Z = np.vander(np.atleast_1d(z), self._N + 1, increasing=True)\n",
" return Z.dot(self._get_u(e, f))"
]
},
{
"cell_type": "code",
"execution_count": 158,
"metadata": {},
"outputs": [
{
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"text/plain": [
"<Figure size 1200x800 with 2 Axes>"
]
},
"metadata": {
"image/png": {
"height": 697,
"width": 1031
}
},
"output_type": "display_data"
}
],
"source": [
"S = SquareRoot(10)\n",
"z = np.linspace(0, 1, 1000)\n",
"c = 0.3\n",
"d = 0.5\n",
"I_exact = S.exact(z, c, d)\n",
"I_taylor = S(z, c, d)\n",
"\n",
"fig, ax = plt.subplots(2, figsize=(12, 8))\n",
"ax[0].plot(z, I_exact, label=\"exact\")\n",
"ax[0].plot(z, I_taylor, label=\"polynomial\")\n",
"ax[1].plot(z, np.abs((I_exact - I_taylor)))\n",
"ax[1].set_yscale(\"log\");\n",
"ax[1].set_ylim(1e-15, 1e0);\n",
"ax[1].set_xlabel(r\"$\\mu$\", fontsize=20)\n",
"ax[0].set_ylabel(\"intensity\")\n",
"ax[0].legend()\n",
"ax[1].set_ylabel(\"rel. error\");"
]
},
{
"cell_type": "code",
"execution_count": 157,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<Figure size 1200x800 with 2 Axes>"
]
},
"metadata": {
"image/png": {
"height": 697,
"width": 1031
}
},
"output_type": "display_data"
}
],
"source": [
"S = Logarithmic(10)\n",
"z = np.linspace(1e-5, 1, 1000)\n",
"c = 0.8\n",
"d = 0.5\n",
"I_exact = S.exact(z, c, d)\n",
"I_taylor = S(z, c, d)\n",
"\n",
"fig, ax = plt.subplots(2, figsize=(12, 8))\n",
"ax[0].plot(z, I_exact, label=\"exact\")\n",
"ax[0].plot(z, I_taylor, label=\"polynomial\")\n",
"ax[1].plot(z, np.abs((I_exact - I_taylor)))\n",
"ax[1].set_yscale(\"log\");\n",
"ax[1].set_ylim(1e-15, 1e0);\n",
"ax[1].set_xlabel(r\"$\\mu$\", fontsize=20)\n",
"ax[0].set_ylabel(\"intensity\")\n",
"ax[0].legend()\n",
"ax[1].set_ylabel(\"rel. error\");"
]
}
],
"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": "3.7.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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