{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a8d15cee",
   "metadata": {},
   "source": [
    "# Benchmarking"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "b7d64184",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import jax\n",
    "import jax.numpy as jnp\n",
    "import time\n",
    "import WDM"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a2ce23c",
   "metadata": {},
   "source": [
    "We will time some of the dwt methods on a time series of length $N=2^{16}=32768$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d51fd3b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "wdm = WDM.WDM.WDM_transform(dt=1., \n",
    "                            Nf=2**8, \n",
    "                            N=2**15)\n",
    "\n",
    "x = np.random.normal(size=wdm.N) # white noise"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f68fc199",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 1369.47 milliseconds\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "w = wdm.forward_transform_exact(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "436a751a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 94.96 milliseconds\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "w = wdm.forward_transform_short_fft(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "19864f32",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 44.54 milliseconds\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "w = wdm.forward_transform_fft(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5a13939",
   "metadata": {},
   "source": [
    "Compilation means subsequent calls can be much faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9d207ee1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 21.80 milliseconds\n",
      "Time taken: 0.92 milliseconds\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "w = wdm.dwt(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")\n",
    "\n",
    "t0 = time.time()\n",
    "w = wdm.dwt(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9a77c473",
   "metadata": {},
   "source": [
    "Vectorisation means that batched transforms can also be much faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c26fe209",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 66.06 milliseconds\n",
      "Time taken: 8.31 milliseconds\n"
     ]
    }
   ],
   "source": [
    "x = np.random.normal(size=(20, wdm.N)) # white noise\n",
    "\n",
    "t0 = time.time()\n",
    "w = wdm.dwt(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")\n",
    "\n",
    "t0 = time.time()\n",
    "w = wdm.dwt(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b302ca9",
   "metadata": {},
   "source": [
    "Let's compare this with the cost of an FFT on the same set of time series."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b0510401",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 41.41 milliseconds\n",
      "Time taken: 11.78 milliseconds\n"
     ]
    }
   ],
   "source": [
    "t0 = time.time()\n",
    "w = jnp.fft.fft(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")\n",
    "\n",
    "t0 = time.time()\n",
    "w = jnp.fft.fft(x).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "661a5fd7",
   "metadata": {},
   "source": [
    "Let's also time the inverse transform."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c41f80f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 1057.09 milliseconds\n"
     ]
    }
   ],
   "source": [
    "x = np.random.normal(size=wdm.N) # white noise\n",
    "\n",
    "w = wdm.dwt(x)\n",
    "\n",
    "t0 = time.time()\n",
    "x_recovered = wdm.idwt(w).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3ee2f57",
   "metadata": {},
   "source": [
    "The inverse transforms are also vectorised."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9c121db7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Time taken: 5842.13 milliseconds\n"
     ]
    }
   ],
   "source": [
    "x = np.random.normal(size=(20, wdm.N)) # white noise\n",
    "\n",
    "w = wdm.dwt(x)\n",
    "\n",
    "t0 = time.time()\n",
    "x_recovered = wdm.idwt(w).block_until_ready()\n",
    "t1 = time.time()\n",
    "\n",
    "print(f\"Time taken: {(t1-t0)*1000:.2f} milliseconds\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c15d93fa",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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