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@Hasenpfote
Last active August 5, 2022 05:40
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inverse transform sampling
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/Hasenpfote/09701f65d0c841d9ead91328e84ff2ff/inverse_transform_sampling.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"source": [
"# The matplotlib in colab is an older version and needs to be updated to 3.3 or higher.\n",
"!pip install 'matplotlib>=3.3.0'"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "aYacdEwJe9d3",
"outputId": "d5aa5746-768d-4797-ddd1-2443c3f4a2ec"
},
"id": "aYacdEwJe9d3",
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/\n",
"Requirement already satisfied: matplotlib>=3.3.0 in /usr/local/lib/python3.7/dist-packages (3.5.2)\n",
"Requirement already satisfied: python-dateutil>=2.7 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (2.8.2)\n",
"Requirement already satisfied: pillow>=6.2.0 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (7.1.2)\n",
"Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (1.4.4)\n",
"Requirement already satisfied: numpy>=1.17 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (1.21.6)\n",
"Requirement already satisfied: pyparsing>=2.2.1 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (3.0.9)\n",
"Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (0.11.0)\n",
"Requirement already satisfied: packaging>=20.0 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (21.3)\n",
"Requirement already satisfied: fonttools>=4.22.0 in /usr/local/lib/python3.7/dist-packages (from matplotlib>=3.3.0) (4.34.4)\n",
"Requirement already satisfied: typing-extensions in /usr/local/lib/python3.7/dist-packages (from kiwisolver>=1.0.1->matplotlib>=3.3.0) (4.1.1)\n",
"Requirement already satisfied: six>=1.5 in /usr/local/lib/python3.7/dist-packages (from python-dateutil>=2.7->matplotlib>=3.3.0) (1.15.0)\n"
]
}
]
},
{
"cell_type": "markdown",
"id": "daecb6d3-983f-4e3e-907b-214634a1009a",
"metadata": {
"id": "daecb6d3-983f-4e3e-907b-214634a1009a"
},
"source": [
"# Inverse transform sampling"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "faeb715a-d861-472b-93ee-892cf7e08599",
"metadata": {
"id": "faeb715a-d861-472b-93ee-892cf7e08599"
},
"outputs": [],
"source": [
"import inspect\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import matplotlib.ticker as ticker\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"id": "1f004236-c3fb-459a-8eed-57a117dda634",
"metadata": {
"id": "1f004236-c3fb-459a-8eed-57a117dda634"
},
"source": [
"## 2 dimensions"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "9e84d20e-6c7f-4677-912a-f0d246d36c3b",
"metadata": {
"id": "9e84d20e-6c7f-4677-912a-f0d246d36c3b"
},
"outputs": [],
"source": [
"def plot_2d(data, *, nrows_ncols=None):\n",
" def plot(ax, **kwargs):\n",
" points = kwargs.get('points', None)\n",
" pc = ax.scatter(points[:,0], points[:,1], s=1, alpha=0.75)\n",
" #pc.remove()\n",
" #o = np.zeros_like(points)\n",
" #ax.quiver(o[:,0], o[:,1], points[:,0], points[:,1],\n",
" # angles='xy', scale=1, scale_units='xy', width=0.001)\n",
" ax.set_title(kwargs.get('title', None))\n",
" loc = ticker.MultipleLocator(base=1)\n",
" ax.xaxis.set_major_locator(loc)\n",
" ax.yaxis.set_major_locator(loc)\n",
" ax.grid()\n",
"\n",
" if nrows_ncols is None:\n",
" nrows_ncols = (1, len(data))\n",
"\n",
" width, height = plt.rcParams.get('figure.figsize')\n",
" fig, axes = plt.subplots(nrows=nrows_ncols[0],\n",
" ncols=nrows_ncols[1],\n",
" sharex='all',\n",
" sharey='all',\n",
" subplot_kw={'aspect': 'equal', 'xlabel': 'x', 'ylabel': 'y'},\n",
" figsize=(width*nrows_ncols[1]/2, height*nrows_ncols[0]/1.33),\n",
" constrained_layout=True)\n",
"\n",
" fig.set_constrained_layout_pads(hspace=0.1, wspace=0.1)\n",
"\n",
" if type(axes) != np.ndarray:\n",
" axes = np.array([axes])\n",
"\n",
" for ax, datum in zip(axes.reshape(-1), data):\n",
" if not datum: # skip\n",
" ax.axis('off')\n",
" continue\n",
" # Generate random variables.\n",
" rv_size = datum.get('rv_size')\n",
" fn = datum.get('fn')\n",
" args = datum.get('args')\n",
" u_args = {'{}'.format(name): np.random.uniform(low=0, high=1, size=rv_size)\n",
" for name in inspect.getfullargspec(fn).args}\n",
"\n",
" plot(ax, title=datum.get('title'), points=fn(**u_args, **args))\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "9d90b1c6-64a2-4036-a765-0ed6ba0786d3",
"metadata": {
"id": "9d90b1c6-64a2-4036-a765-0ed6ba0786d3"
},
"source": [
"### About circles\n",
"#### Distribution on an arc\n",
"$$\n",
"\\begin{aligned}\n",
"x\n",
"&=\\mathrm{R} \\cos{\\theta}\\\\\n",
"y\n",
"&=\\mathrm{R} \\sin{\\theta}\\\\\n",
"\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u)=2\\pi u\n",
"\\end{aligned}\n",
"$$\n",
"#### Distribution inside a circle\n",
"$$\n",
"\\begin{aligned}\n",
"x\n",
"&=r \\cos{\\theta}\\\\\n",
"y\n",
"&=r \\sin{\\theta}\\\\\n",
"\\\\\n",
"r\n",
"&=F_{R}^{-1}(u_{1})=\\mathrm{R} \\sqrt{u_{1}}\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{2})=2\\pi u_{2}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "832fbaca-0b03-43b9-abcf-75f4a5963282",
"metadata": {
"id": "832fbaca-0b03-43b9-abcf-75f4a5963282"
},
"outputs": [],
"source": [
"def rand_on_circle(u, *, radius=1.0):\n",
" theta = 2 * np.pi * u\n",
" x = radius * np.cos(theta)\n",
" y = radius * np.sin(theta)\n",
" return np.stack((x, y), axis=-1)\n",
"\n",
"def rand_inside_circle(u0, u1, *, radius=1.0):\n",
" radius *= np.sqrt(u0)\n",
" theta = 2 * np.pi * u1\n",
" x = radius * np.cos(theta)\n",
" y = radius * np.sin(theta)\n",
" return np.stack((x, y), axis=-1)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "8b101996-ac5e-41e9-9bae-92e7249fabf7",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 241
},
"id": "8b101996-ac5e-41e9-9bae-92e7249fabf7",
"outputId": "3f75072b-3999-46cd-f166-48ea4c96f60d"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x216.541 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"rv_size = (400, 1200)\n",
"radius = 1.5\n",
"\n",
"data = [{'title': 'rand_on_circle\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_on_circle,\n",
" 'rv_size': rv_size[0],\n",
" 'args': {'radius': radius}},\n",
" {'title': 'rand_inside_circle\\n{} samples'.format(rv_size[1]),\n",
" 'fn': rand_inside_circle,\n",
" 'rv_size': rv_size[1],\n",
" 'args': {'radius': radius}},]\n",
"\n",
"plot_2d(data)"
]
},
{
"cell_type": "markdown",
"id": "beb1fb97-fb6f-409b-8a6f-33e5810326f2",
"metadata": {
"id": "beb1fb97-fb6f-409b-8a6f-33e5810326f2"
},
"source": [
"### About circular sectors\n",
"#### Distribution on an arc\n",
"$$\n",
"\\begin{aligned}\n",
"x\n",
"&=\\mathrm{R} \\cos{\\theta}\\\\\n",
"y\n",
"&=\\mathrm{R} \\sin{\\theta}\\\\\n",
"\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u)=a + (b - a) u\n",
"\\end{aligned}\n",
"$$\n",
"#### Distribution inside a sector\n",
"$$\n",
"\\begin{aligned}\n",
"x\n",
"&=r \\cos{\\theta}\\\\\n",
"y\n",
"&=r \\sin{\\theta}\\\\\n",
"\\\\\n",
"r\n",
"&=F_{R}^{-1}(u_{1})=\\mathrm{R} \\sqrt{u_{1}}\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{2})=a + (b - a) u_{2}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "541ca43a-49f5-4817-b510-0cdef8b02cc4",
"metadata": {
"id": "541ca43a-49f5-4817-b510-0cdef8b02cc4"
},
"outputs": [],
"source": [
"def rand_on_circular_sector(u, *, a=0, b=2*np.pi, radius=1.0):\n",
" theta = a + (b - a) * u\n",
" x = radius * np.cos(theta)\n",
" y = radius * np.sin(theta)\n",
" return np.stack((x, y), axis=-1)\n",
"\n",
"def rand_inside_circular_sector(u0, u1, *, a=0, b=2*np.pi, radius=1.0):\n",
" radius *= np.sqrt(u0)\n",
" theta = a + (b - a) * u1\n",
" x = radius * np.cos(theta)\n",
" y = radius * np.sin(theta)\n",
" return np.stack((x, y), axis=-1)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a26cfbb6-66c8-4f92-8ebc-5a80818cf6d1",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 675
},
"id": "a26cfbb6-66c8-4f92-8ebc-5a80818cf6d1",
"outputId": "30d8835a-4225-4e10-86f3-b024d8cfe19e"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x649.624 with 6 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# rv_size, limits\n",
"params = [((100, 300), (0.25 * np.pi, 0.75 * np.pi)),\n",
" ((200, 600), (0.00 * np.pi, 1.00 * np.pi)),\n",
" ((400, 1200), (0.00 * np.pi, 2.00 * np.pi))]\n",
"\n",
"radius = 1.5\n",
"\n",
"data = []\n",
"for rv_size, limits in params:\n",
" # rand_on_circular_sector\n",
" data.append({'title': 'rand_on_circular_sector\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_on_circular_sector,\n",
" 'rv_size': rv_size[0],\n",
" 'args': {'a': limits[0], 'b': limits[1], 'radius': radius}})\n",
" # rand_inside_circular_sector\n",
" data.append({'title': 'rand_inside_circular_sector\\n{} samples'.format(rv_size[1]),\n",
" 'fn': rand_inside_circular_sector,\n",
" 'rv_size': rv_size[1],\n",
" 'args': {'a': limits[0], 'b': limits[1], 'radius': radius}})\n",
"\n",
"plot_2d(data, nrows_ncols=(len(data)//2, 2))"
]
},
{
"cell_type": "markdown",
"id": "b19d0abd-9cd6-4796-ade1-3d1bbcf82b04",
"metadata": {
"id": "b19d0abd-9cd6-4796-ade1-3d1bbcf82b04"
},
"source": [
"### About triangles\n",
"$$\n",
"\\begin{aligned}\n",
"\\boldsymbol{r}\n",
"&=s \\boldsymbol{p}_{1} + t \\boldsymbol{p}_{2} + (1 - s - t) \\boldsymbol{p}_{3}\\\\\n",
"\\\\\n",
"s\n",
"&=F_{S}^{-1}(u_{1})=1 - \\sqrt{1 - u_{1}}=1 - \\sqrt{u_{1}}\\\\\n",
"t\n",
"&=F_{T}^{-1}(u_{2})=(1 - s) u_{2}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "b35e9f9c-6a41-44f2-af2b-b6a5ca384b5d",
"metadata": {
"id": "b35e9f9c-6a41-44f2-af2b-b6a5ca384b5d"
},
"outputs": [],
"source": [
"def rand_inside_triangle(u0, u1, *, p0, p1, p2):\n",
" s = 1 - np.sqrt(u0)\n",
" t = (1 - s) * u1\n",
" return s * p0 + t * p1 + (1 - s - t) * p2"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "bcd5b4c7-bb90-4118-93d7-f6f558af54ba",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 241
},
"id": "bcd5b4c7-bb90-4118-93d7-f6f558af54ba",
"outputId": "a7f225aa-5f31-4423-bb39-7d11c75645d3"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 216x216.541 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"rv_size = (500, 1)\n",
"p0 = np.array([-1, -1])\n",
"p1 = np.array([2, 0])\n",
"p2 = np.array([0, 2])\n",
"\n",
"data = [{'title': 'rand_inside_triangle\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_inside_triangle,\n",
" 'rv_size': rv_size,\n",
" 'args': {'p0': p0, 'p1': p1, 'p2': p2}},]\n",
"\n",
"plot_2d(data)"
]
},
{
"cell_type": "markdown",
"id": "40981c65-1d56-401a-9dbc-5e02b6b7fd08",
"metadata": {
"id": "40981c65-1d56-401a-9dbc-5e02b6b7fd08"
},
"source": [
"### About parallelograms\n",
"$$\n",
"\\begin{aligned}\n",
"\\boldsymbol{r}\n",
"&=s \\boldsymbol{a} + t \\boldsymbol{b}\\\\\n",
"\\\\\n",
"s\n",
"&=F_{S}^{-1}(u_{1})=u_{1}\\\\\n",
"t\n",
"&=F_{T}^{-1}(u_{2})=u_{2}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "f1c986e7-7583-4483-9577-52c649a1c744",
"metadata": {
"id": "f1c986e7-7583-4483-9577-52c649a1c744"
},
"outputs": [],
"source": [
"def rand_inside_parallelogram(u0, u1, *, a, b):\n",
" return u0 * a + u1 * b"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "c4f13443-39e4-4316-ad9c-e629a47fc020",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 231
},
"id": "c4f13443-39e4-4316-ad9c-e629a47fc020",
"outputId": "dcc04494-844c-491f-d598-a05d7a6e14cc"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 216x216.541 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"rv_size = (500, 1)\n",
"a = np.array([3, 1])\n",
"b = np.array([1, 2])\n",
"\n",
"data = [{'title': 'rand_inside_parallelogram\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_inside_parallelogram,\n",
" 'rv_size': rv_size,\n",
" 'args': {'a': a, 'b': b}},]\n",
"\n",
"plot_2d(data)"
]
},
{
"cell_type": "markdown",
"id": "5cb3e9c8-f749-4c35-90cb-9a0b818f0546",
"metadata": {
"id": "5cb3e9c8-f749-4c35-90cb-9a0b818f0546"
},
"source": [
"## 3 dimensions"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "786f118b-b8a5-4e90-b969-6b34fb98abbf",
"metadata": {
"id": "786f118b-b8a5-4e90-b969-6b34fb98abbf"
},
"outputs": [],
"source": [
"# https://stackoverflow.com/a/50664367\n",
"def set_axes_equal(ax: plt.Axes):\n",
" \"\"\"Set 3D plot axes to equal scale.\n",
"\n",
" Make axes of 3D plot have equal scale so that spheres appear as\n",
" spheres and cubes as cubes. Required since `ax.axis('equal')`\n",
" and `ax.set_aspect('equal')` don't work on 3D.\n",
" \"\"\"\n",
" limits = np.array([\n",
" ax.get_xlim3d(),\n",
" ax.get_ylim3d(),\n",
" ax.get_zlim3d(),\n",
" ])\n",
" origin = np.mean(limits, axis=1)\n",
" radius = 0.5 * np.max(np.abs(limits[:, 1] - limits[:, 0]))\n",
"\n",
" x, y, z = origin\n",
" ax.set_xlim3d([x - radius, x + radius])\n",
" ax.set_ylim3d([y - radius, y + radius])\n",
" ax.set_zlim3d([z - radius, z + radius])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "40b333a9-4401-41a0-8590-12b010b8f826",
"metadata": {
"id": "40b333a9-4401-41a0-8590-12b010b8f826"
},
"outputs": [],
"source": [
"def plot_3d(data, *, nrows_ncols=None):\n",
" def plot(ax, **kwargs):\n",
" points = kwargs.get('points', None)\n",
" pc = ax.scatter(points[:,0], points[:,1], points[:,2], s=1, alpha=0.75)\n",
" set_axes_equal(ax)\n",
" #pc.remove()\n",
" #o = np.zeros_like(points)\n",
" #ax.quiver(o[:,0], o[:,1], o[:,2], points[:,0], points[:,1], points[:,2], linewidths=0.5)\n",
" ax.set_title(kwargs.get('title', None))\n",
" loc = ticker.MultipleLocator(base=1)\n",
" ax.xaxis.set_major_locator(loc)\n",
" ax.yaxis.set_major_locator(loc)\n",
" ax.zaxis.set_major_locator(loc)\n",
" ax.grid()\n",
" #ax.view_init(elev=ax.elev, azim=135)\n",
"\n",
" if nrows_ncols is None:\n",
" nrows_ncols = (1, len(data))\n",
"\n",
" width, height = plt.rcParams.get('figure.figsize')\n",
" fig, axes = plt.subplots(nrows=nrows_ncols[0],\n",
" ncols=nrows_ncols[1],\n",
" #sharex='all',\n",
" #sharey='all',\n",
" subplot_kw={'projection': '3d', 'box_aspect': (1,1,1),\n",
" 'xlabel': 'x', 'ylabel': 'y', 'zlabel': 'z'},\n",
" figsize=(width*nrows_ncols[1]/2, height*nrows_ncols[0]/1.33),\n",
" constrained_layout=True)\n",
"\n",
" fig.set_constrained_layout_pads(hspace=0.15, wspace=0.15)\n",
"\n",
" if type(axes) != np.ndarray:\n",
" axes = np.array([axes])\n",
"\n",
" zlimits = np.array([np.PINF, np.NINF])\n",
"\n",
" for ax, datum in zip(axes.reshape(-1), data):\n",
" if not datum: # skip\n",
" ax.set_axis_off() # ax._axis3don=False\n",
" continue\n",
" # Generate random variables.\n",
" rv_size = datum.get('rv_size')\n",
" fn = datum.get('fn')\n",
" args = datum.get('args')\n",
" u_args = {'{}'.format(name): np.random.uniform(low=0, high=1, size=rv_size)\n",
" for name in inspect.getfullargspec(fn).args}\n",
"\n",
" plot(ax, title=datum.get('title'), points=fn(**u_args, **args))\n",
"\n",
" zmin, zmax = ax.get_zlim3d()\n",
" zlimits[0] = zlimits[0] if zlimits[0] < zmin else zmin\n",
" zlimits[1] = zlimits[1] if zlimits[1] > zmax else zmax\n",
"\n",
" # sharez\n",
" for ax in axes.reshape(-1):\n",
" ax.set_zlim3d(*zlimits)\n",
" set_axes_equal(ax)\n",
"\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "71e1caf1-1c53-4b91-be29-9a4d07dac504",
"metadata": {
"id": "71e1caf1-1c53-4b91-be29-9a4d07dac504"
},
"source": [
"### About spheres\n",
"#### Distribution on a surface\n",
"$$\n",
"\\begin{aligned}\n",
"x&=\\mathrm{R}\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=\\mathrm{R}\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=\\mathrm{R}\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{1})=\\arccos{(1 - 2 u_{1})}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{2})=2 \\pi u_{2}\n",
"\\end{aligned}\n",
"$$\n",
"#### Distribution inside a sphere\n",
"$$\n",
"\\begin{aligned}\n",
"x&=r\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=r\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=r\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"r\n",
"&=F_{R}^{-1}(u_{1})=\\mathrm{R} \\sqrt[3]{u_{1}}\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{2})=\\arccos{(1 - 2 u_{2})}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{3})=2 \\pi u_{3}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "2d03926f-90ed-488a-9ef0-bae39a2cbdd7",
"metadata": {
"id": "2d03926f-90ed-488a-9ef0-bae39a2cbdd7"
},
"outputs": [],
"source": [
"def rand_on_sphere(u0, u1, *, radius=1.0):\n",
" cos_theta = 1 - 2 * u0\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta) \n",
" phi = 2 * np.pi * u1\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * sin_theta * np.sin(phi)\n",
" z = radius * cos_theta\n",
" return np.stack((x, y, z), axis=-1)\n",
"\n",
"def rand_inside_sphere(u0, u1, u2, *, radius=1.0):\n",
" radius *= np.cbrt(u0)\n",
" cos_theta = 1 - 2 * u1\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta) \n",
" phi = 2 * np.pi * u2\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * cos_theta\n",
" z = radius * sin_theta * np.sin(phi)\n",
" return np.stack((x, y, z), axis=-1)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "99193a67-98bd-44a6-8f12-f6297938905b",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 263
},
"id": "99193a67-98bd-44a6-8f12-f6297938905b",
"outputId": "1d865971-38a9-499a-cfad-8acc72ca1d2f"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x216.541 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"rv_size = (1000, 3000)\n",
"radius = 1.5\n",
"\n",
"data = [{'title': 'rand_on_sphere\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_on_sphere,\n",
" 'rv_size': rv_size[0],\n",
" 'args': {'radius': radius}},\n",
" {'title': 'rand_inside_sphere\\n{} samples'.format(rv_size[1]),\n",
" 'fn': rand_inside_sphere,\n",
" 'rv_size': rv_size[1],\n",
" 'args': {'radius': radius}},]\n",
"\n",
"plot_3d(data)"
]
},
{
"cell_type": "markdown",
"id": "06b68a62-b194-475a-963f-5382649099d2",
"metadata": {
"id": "06b68a62-b194-475a-963f-5382649099d2"
},
"source": [
"### About hemispheres\n",
"#### Distribution on a surface\n",
"$$\n",
"\\begin{aligned}\n",
"x&=\\mathrm{R}\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=\\mathrm{R}\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=\\mathrm{R}\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{1})=\\arccos{(1 - u_{1})}=\\arccos{(u_{1})}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{2})=2 \\pi u_{2}\n",
"\\end{aligned}\n",
"$$\n",
"#### Distribution inside a hemisphere\n",
"$$\n",
"\\begin{aligned}\n",
"x&=r\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=r\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=r\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"r\n",
"&=F_{R}^{-1}(u_{1})=\\mathrm{R} \\sqrt[3]{u_{1}}\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{2})=\\arccos{(1 - u_{2})}=\\arccos{(u_{2})}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{3})=2 \\pi u_{3}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "a8fe422a-cecb-4cda-81c7-51a91c547a44",
"metadata": {
"id": "a8fe422a-cecb-4cda-81c7-51a91c547a44"
},
"outputs": [],
"source": [
"def rand_on_hemisphere(u0, u1, *, radius=1.0):\n",
" cos_theta = u0\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta)\n",
" phi = 2 * np.pi * u1\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * sin_theta * np.sin(phi)\n",
" z = radius * cos_theta\n",
" return np.stack((x, y, z), axis=-1)\n",
"\n",
"def rand_inside_hemisphere(u0, u1, u2, *, radius=1.0):\n",
" radius *= np.cbrt(u0)\n",
" cos_theta = u1\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta)\n",
" phi = 2 * np.pi * u2\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * sin_theta * np.sin(phi)\n",
" z = radius * cos_theta\n",
" return np.stack((x, y, z), axis=-1)"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "1ae1a88a-456b-46c3-b417-118a806f9444",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 263
},
"id": "1ae1a88a-456b-46c3-b417-118a806f9444",
"outputId": "8bf37c58-c676-447d-d5d6-eba71473571d"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x216.541 with 2 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"rv_size = (500, 1500)\n",
"radius = 1.5\n",
"\n",
"data = [{'title': 'rand_on_hemisphere\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_on_hemisphere,\n",
" 'rv_size': rv_size[0],\n",
" 'args': {'radius': radius}},\n",
" {'title': 'rand_inside_hemisphere\\n{} samples'.format(rv_size[1]),\n",
" 'fn': rand_inside_hemisphere,\n",
" 'rv_size': rv_size[1],\n",
" 'args': {'radius': radius}},]\n",
"\n",
"plot_3d(data)"
]
},
{
"cell_type": "markdown",
"id": "b0bd9be8-e249-4f23-9840-ba717d851bb7",
"metadata": {
"id": "b0bd9be8-e249-4f23-9840-ba717d851bb7"
},
"source": [
"### About spherical sectors\n",
"#### Distribution on a surface\n",
"$$\n",
"\\begin{aligned}\n",
"x&=\\mathrm{R}\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=\\mathrm{R}\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=\\mathrm{R}\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{1})=\\arccos{\\left(1 - \\frac{\\mathrm{\\Omega}}{2\\pi} u_{1}\\right)}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{2})=2 \\pi u_{2}\n",
"\\end{aligned}\n",
"$$\n",
"#### Distribution inside a sector\n",
"$$\n",
"\\begin{aligned}\n",
"x&=r\\,\\sin{\\theta}\\,\\cos{\\phi}\\\\\n",
"y&=r\\,\\sin{\\theta}\\,\\sin{\\phi}\\\\\n",
"z&=r\\,\\cos{\\theta}\\\\\n",
"\\\\\n",
"r\n",
"&=F_{R}^{-1}(u_{1})=\\mathrm{R} \\sqrt[3]{\\frac{\\omega_{0}}{2\\pi\\left(1 - \\cos{\\frac{\\mathrm{\\Omega}}{4}}\\right)} u_{1}}\\\\\n",
"\\theta\n",
"&=F_{\\Theta}^{-1}(u_{2})=\\arccos{\\left(1 - \\left(1 - \\cos{\\frac{\\mathrm{\\Omega}}{4}}\\right) u_{2}\\right)}\\\\\n",
"\\phi\n",
"&=F_{\\Phi}^{-1}(u_{3})=2 \\pi u_{3}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "a141e53d-e649-4243-a573-6ccadd89297d",
"metadata": {
"id": "a141e53d-e649-4243-a573-6ccadd89297d"
},
"outputs": [],
"source": [
"def rand_on_spherical_sector(u0, u1, *, solid_angle=4*np.pi, radius=1.0):\n",
" cos_theta = 1 - (solid_angle / (2 * np.pi)) * u0\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta) \n",
" phi = 2 * np.pi * u1\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * sin_theta * np.sin(phi)\n",
" z = radius * cos_theta\n",
" return np.stack((x, y, z), axis=-1)\n",
"\n",
"def rand_inside_spherical_sector(u0, u1, u2, *, solid_angle=4*np.pi, radius=1.0):\n",
" coef = 1 - np.cos(solid_angle / 4)\n",
" radius *= np.cbrt((solid_angle / (2 * np.pi * coef)) * u0)\n",
" cos_theta = 1 - coef * u1\n",
" sin_theta = np.sqrt(1 - cos_theta * cos_theta) \n",
" phi = 2 * np.pi * u2\n",
" x = radius * sin_theta * np.cos(phi)\n",
" y = radius * sin_theta * np.sin(phi)\n",
" z = radius * cos_theta\n",
" return np.stack((x, y, z), axis=-1)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "0451da8e-28af-4f39-b21e-053237492b92",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 698
},
"id": "0451da8e-28af-4f39-b21e-053237492b92",
"outputId": "8ac47626-f662-4e8e-e8fd-3c82c97b4e8a"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 432x649.624 with 6 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
],
"source": [
"# rv_size, solid_angle\n",
"params = [((250, 750), 4 * (0.25 * np.pi)),\n",
" ((500, 1500), 4 * (0.50 * np.pi)),\n",
" ((1000, 3000), 4 * (1.00 * np.pi))]\n",
"\n",
"radius = 1.5\n",
"\n",
"data = []\n",
"for rv_size, solid_angle in params:\n",
" # rand_on_spherical_sector\n",
" data.append({'title': 'rand_on_spherical_sector\\n{} samples'.format(rv_size[0]),\n",
" 'fn': rand_on_spherical_sector,\n",
" 'rv_size': rv_size[0],\n",
" 'args': {'solid_angle': solid_angle, 'radius': radius}})\n",
" # rand_inside_spherical_sector\n",
" data.append({'title': 'rand_inside_spherical_sector\\n{} samples'.format(rv_size[1]),\n",
" 'fn': rand_inside_spherical_sector,\n",
" 'rv_size': rv_size[1],\n",
" 'args': {'solid_angle': solid_angle, 'radius': radius}})\n",
"\n",
"plot_3d(data, nrows_ncols=(3, 2))"
]
}
],
"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": "3.8.3"
},
"colab": {
"name": "inverse_transform_sampling.ipynb",
"provenance": [],
"collapsed_sections": [],
"include_colab_link": true
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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