{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import drjit as dr\n",
    "import mitsuba as mi \n",
    "mi.set_variant(\"cuda_ad_rgb\")\n",
    "from PDE2D.Sampling.sampling_wos import *\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_points = 1000\n",
    "threshold = Float(dr.pi * 0.49)\n",
    "t = dr.arange(Float, num_points) / num_points * dr.pi/2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "pdf = pdf_sec_angle(t, threshold)\n",
    "n = 1000000\n",
    "pcg = PCG32(initstate=dr.arange(UInt32, n))\n",
    "sample = pcg.next_float32()\n",
    "sampled = sample_sec_angle(sample, threshold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.995358]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dr.sum(pdf) * dr.pi /2 / num_points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,1,figsize = (8,4))\n",
    "ax.plot(t.numpy(), pdf.numpy())\n",
    "ax.set_xticks([0, np.pi/8, np.pi/4, 3*np.pi/8, np.pi/2])\n",
    "ax.set_xticklabels([\"0\",r\"$\\pi/8$\",r\"$\\pi/4$\", r\"$3\\pi/8$\", r\"$\\pi/2$\" ])\n",
    "ax.hist(sampled.numpy(), density = True, bins = 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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