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@ridlo
Last active August 3, 2021 13:26
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "5ea070ef",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy import integrate\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "104a065f",
"metadata": {},
"outputs": [],
"source": [
"def func(x):\n",
" return 0.5 + np.sin(np.pi * x)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "836d6dc7",
"metadata": {},
"outputs": [],
"source": [
"xmin = 0.25\n",
"xmax = 1.95"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0be747ea",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# plot the function\n",
"x = np.linspace(xmin, xmax, 100)\n",
"y = func(x)\n",
"\n",
"plt.plot(x, y, 'm-')\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.xlim([xmin, xmax])\n",
"plt.grid(True)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "2393c6c1",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.7606881157593811, 1.3309649938119312e-14)"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# find the integral using `scipy.integrate` function\n",
"integrate.quad(func, xmin, xmax)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "b8ba67a4",
"metadata": {},
"outputs": [],
"source": [
"def integrate_mc(f, xmin, xmax, N, N_init=1000, c=1.05, plot=False):\n",
" \"\"\"Monte Carlo integration\"\"\"\n",
" \n",
" ### find the maximum of f(x) in the range of integral using monte carlo\n",
" xr_init = np.random.uniform(xmin, xmax, N_init)\n",
" yr_init = f(xr_init)\n",
" ymin, ymax = np.min(yr_init), np.max(yr_init)\n",
" ylim = np.max(np.abs([ymin, ymax]))\n",
" \n",
" ### the integral part\n",
" xr = np.random.uniform(xmin, xmax, N)\n",
" yr = c * np.random.uniform(0, ylim, N)\n",
" sign = np.where(f(xr) < 0, -1, 1) # positive or negative section\n",
" yr = sign * yr\n",
" \n",
" insidecurve = np.where(np.abs(yr) <= np.abs(f(xr)), 1, 0)\n",
" result = sign*insidecurve # 0 outside, +1 and -1 inside\n",
" \n",
" integral_result = np.sum(result)/N * (xmax-xmin) * (ylim * c)\n",
" \n",
" ### plot the result\n",
" if plot:\n",
" x = np.linspace(xmin, xmax, 100)\n",
" y = f(x)\n",
" plt.plot(xr[np.where(result == 1)], yr[np.where(result == 1)], 'b,')\n",
" plt.plot(xr[np.where(result == -1)], yr[np.where(result == -1)], 'r,')\n",
" plt.plot(xr[np.where(result == 0)], yr[np.where(result == 0)], 'k,')\n",
" plt.plot(x, y, 'm-')\n",
" plt.xlabel(\"x\")\n",
" plt.ylabel(\"y\")\n",
" plt.xlim([xmin, xmax])\n",
" plt.grid(True)\n",
" \n",
" return integral_result #, result, xr, yr, ylim"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "374f92b3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.7703166523860584"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"integrate_mc(func, xmin, xmax, N=10000, plot=True)"
]
},
{
"cell_type": "markdown",
"id": "c4a2a8d9",
"metadata": {},
"source": [
"Test to other function"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "b0087acd",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(-4.0, 4.440892098500626e-14)\n"
]
},
{
"data": {
"text/plain": [
"-3.981343497209112"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def func2(x):\n",
" return -2.5 + np.sin(np.pi * x)\n",
"\n",
"print(integrate.quad(func2, 0.2, 1.8))\n",
"integrate_mc(func2, 0.2, 1.8, N=10000, plot=True)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "c3c974ad",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(0.40299456487885466, 7.72575924813062e-12)\n"
]
},
{
"data": {
"text/plain": [
"0.40303181771156193"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def func2(x):\n",
" return np.sin(2*x) * np.exp(-x)\n",
"\n",
"print(integrate.quad(func2, 0, 5))\n",
"integrate_mc(func2, 0, 5, N=10000, plot=True)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8c577aac",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"id": "f126c520",
"metadata": {},
"outputs": [],
"source": []
}
],
"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": "3.8.8"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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