{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5ee7ff02-7b28-4141-aec9-8d848cd2645c",
   "metadata": {},
   "source": [
    "# Time measurements for the different MTF solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d1333d-f72b-4d1e-8c0b-d8eb425cf164",
   "metadata": {},
   "source": [
    "This routine measures the time taken for solving the problem presented in [e1.laplace_transmission_mtf.ipynb](./e1.laplace_transmission_mtf.ipynb) with the routines `mtf_laplace_n_spheres_point_source_direct_solver` and `mtf_laplace_n_spheres_point_source_indirect_solver`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6da62af-814e-477a-ae58-a6034df47ee5",
   "metadata": {},
   "source": [
    "## Setup of the parameters and environment"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd9fe33b-3d5b-47c0-b321-734d12a00569",
   "metadata": {},
   "source": [
    "The following block is to control some environment variables. Specifically the threads allowed to use for some underlying libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "cd821fb7-5603-4ef7-9105-b44a213a5d00",
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "number = \"1\"\n",
    "os.environ[\"OMP_NUM_THREADS\"] = number\n",
    "os.environ[\"OPENBLAS_NUM_THREADS\"] = number\n",
    "os.environ[\"MKL_NUM_THREADS\"] = number\n",
    "os.environ[\"VECLIB_MAXIMUM_THREADS\"] = number\n",
    "os.environ[\"NUMEXPR_NUM_THREADS\"] = number"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b2a9744d-af6f-4cc1-8f0d-60215f789726",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import biosspheres.miscella.spherearrangements as pos\n",
    "import biosspheres.formulations.mtf.solvertemplates as solver\n",
    "import biosspheres.formulations.mtf.solvertemplates as solver\n",
    "import time\n",
    "\n",
    "n = 8\n",
    "big_l = 15\n",
    "big_l_c = 55\n",
    "\n",
    "r = 0.875\n",
    "radii = np.ones(n) * r\n",
    "\n",
    "d = 1.15\n",
    "center_positions = pos.cube_vertex_positions(int(n**(1/3)), r, d)\n",
    "\n",
    "sigma_e = 1.75\n",
    "sigma_i = 0.75\n",
    "sigmas = np.ones(n+1) * sigma_i\n",
    "sigmas[0] = sigma_e\n",
    "\n",
    "p0 = np.ones(3)*-5.\n",
    "p0\n",
    "\n",
    "tolerance = 10**(-10)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a123537-4b49-453c-8e52-ee9a12b6342d",
   "metadata": {},
   "source": [
    "## Time measurements"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40d41770-06f6-4887-b30a-2061c5d2f0a1",
   "metadata": {},
   "source": [
    "We are going to measure (approximately) the time taken to solve a certain number of times using both methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "08b5b3b6-4d68-486b-a637-d61925425f92",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n",
      "0\n",
      "1\n",
      "2\n",
      "3\n",
      "4\n",
      "5\n",
      "6\n",
      "7\n",
      "8\n",
      "9\n"
     ]
    }
   ],
   "source": [
    "number_of_times = 10\n",
    "times_taken_direct = np.empty(number_of_times)\n",
    "t0 = 0.\n",
    "for i in np.arange(0, number_of_times):\n",
    "    print(i)\n",
    "    t0 = time.time()\n",
    "    traces = solver.mtf_laplace_n_spheres_point_source_direct_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0)\n",
    "    times_taken_direct[i] = time.time()-t0\n",
    "\n",
    "times_taken_indirect = np.empty(number_of_times)\n",
    "for i in np.arange(0, number_of_times):\n",
    "    print(i)\n",
    "    t0 = time.time()\n",
    "    traces = solver.mtf_laplace_n_spheres_point_source_indirect_solver(n, big_l, big_l_c, radii, center_positions, sigmas, p0, tolerance)\n",
    "    times_taken_indirect[i] = time.time()-t0"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28c38177-848a-4f6f-8cdf-c7d56026b97b",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fe6249f-9c7c-44de-b4f8-4857e573935b",
   "metadata": {},
   "source": [
    "Averages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "565359d5-ce3b-4dac-a1b6-ce12338eda87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct method average:    9.47792592048645\n",
      "Indirect method average:  2.7520662546157837\n"
     ]
    }
   ],
   "source": [
    "print(\"Direct method average:   \", np.mean(times_taken_direct))\n",
    "print(\"Indirect method average: \", np.mean(times_taken_indirect))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9981a3f6-39a6-4842-9043-536be6046091",
   "metadata": {},
   "source": [
    "Standart deviations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "41ce8cbd-d550-4add-8386-4212589e9bbe",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct method std:    0.16462314321045604\n",
      "Indirect method sdt:  0.05972414899239749\n"
     ]
    }
   ],
   "source": [
    "print(\"Direct method std:   \", np.std(times_taken_direct))\n",
    "print(\"Indirect method sdt: \", np.std(times_taken_indirect))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a238ba39-c058-4559-b518-24790b79413f",
   "metadata": {},
   "source": [
    "Minimum and maximum values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "dcaa1d02-2eb5-4fbf-b67a-7ea5baeebc3b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Direct method min:    9.244473934173584\n",
      "Indirect method min:  2.6842405796051025\n",
      "Direct method max:    9.244473934173584\n",
      "Indirect method max:  2.6842405796051025\n"
     ]
    }
   ],
   "source": [
    "print(\"Direct method min:   \", np.min(times_taken_direct))\n",
    "print(\"Indirect method min: \", np.min(times_taken_indirect))\n",
    "print(\"Direct method max:   \", np.max(times_taken_direct))\n",
    "print(\"Indirect method max: \", np.max(times_taken_indirect))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff48fb9d-23b8-40ab-b13c-ce4f50c3c32e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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