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Add numba parallel example
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‎source-code/numba/README.md‎

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1. `Primes`: code to compute the first n prime numbers comparing a pure Python
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implementation with numba JIT and eager JIT.
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1. `Ufunc`: defining a numpy ufunc using numba.
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1. `numba_parallel.ipynb`: jupyter notebook experimenting with numba's
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parallel capabilities.

‎source-code/numba/numba_parallel.ipynb‎

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{
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"cells": [
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{
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"cell_type": "markdown",
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"id": "647ec939-d34d-4a92-8a8d-60e0078fee69",
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"metadata": {},
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"source": [
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"# Requirements"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "98749cd7-43b1-45b4-8ad8-c68006996d22",
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"metadata": {},
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"outputs": [],
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"source": [
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"from numba import njit\n",
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"import numpy as np\n",
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"import random"
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]
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},
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{
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"cell_type": "markdown",
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"id": "3e3a9b00-2e46-4b57-9951-3d649a9ed193",
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"metadata": {},
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"source": [
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"# Random $\\pi$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1c79e332-5fb5-4103-8a02-74ef83972464",
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"metadata": {},
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"source": [
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"Compute $\\pi$ by generating random points in a square and counting how many there are in the circle inscribed in the square."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "75bbae32-14d6-44f4-b83d-3dda129355d2",
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"metadata": {},
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"outputs": [],
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"source": [
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"def compute_pi(nr_tries):\n",
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" hits = 0\n",
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" for _ in range(nr_tries):\n",
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" x = random.random()\n",
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" y = random.random()\n",
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" if x**2 + y**2 < 1.0:\n",
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" hits += 1\n",
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" return 4.0*hits/nr_tries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "f96298c8-d477-4da6-a19f-0de852c81329",
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"metadata": {},
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"outputs": [],
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"source": [
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"@njit\n",
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"def compute_pi_jit(nr_tries):\n",
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" hits = 0\n",
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" for _ in range(nr_tries):\n",
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" x = random.random()\n",
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" y = random.random()\n",
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" if x**2 + y**2 < 1.0:\n",
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" hits += 1\n",
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" return 4.0*hits/nr_tries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"id": "a0d922f3-13ba-4c6d-beeb-c8292b1baf67",
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"metadata": {},
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"outputs": [],
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"source": [
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"@njit(['float64(int64)'])\n",
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"def compute_pi_jit_sign(nr_tries):\n",
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" hits = 0\n",
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" for _ in range(nr_tries):\n",
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" x = random.random()\n",
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" y = random.random()\n",
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" if x**2 + y**2 < 1.0:\n",
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" hits += 1\n",
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" return 4.0*hits/nr_tries"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "b830e45b-bc46-42f6-9b40-2f636c9989cd",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"27.1 ms ± 277 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)\n"
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]
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}
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],
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"source": [
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"%timeit compute_pi(100_000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "b98f5c18-a5fb-468c-8f96-ca25782ebac8",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"687 µs ± 9.53 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
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]
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}
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],
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"source": [
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"%timeit compute_pi_jit(100_000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 34,
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"id": "78c37a87-dd0c-49c6-ac8d-85e6f21832c2",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"685 µs ± 8.96 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
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]
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}
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],
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"source": [
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"%timeit compute_pi_jit_sign(np.int64(100_000))"
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]
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},
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{
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"cell_type": "markdown",
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"id": "18e84532-48d9-4aa0-8218-709888e3162e",
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"metadata": {},
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"source": [
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"Using numba's just-in-time compiler significantly speeds up the computations."
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]
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},
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{
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"cell_type": "markdown",
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"id": "8fc275a6-8ac6-4481-beed-41896c5b39e9",
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"metadata": {},
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"source": [
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"# Quadrature $\\pi$"
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]
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},
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{
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"cell_type": "markdown",
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"id": "32312a15-8070-4a8a-a198-170252d8efde",
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"metadata": {},
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"source": [
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"Another method to compute $\\pi$ is to compute the definite integral\n",
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"$$\n",
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"\\frac{\\pi}{2} = \\int_{-1}^{1} \\sqrt{1 - x^2} dx\n",
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"$$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 38,
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"id": "17597694-cb80-4e2a-aa4c-c4c9e6d6de84",
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"metadata": {},
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"outputs": [],
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"source": [
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"@njit\n",
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"def quad_pi_jit(nr_steps):\n",
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" delta = 2.0/nr_steps\n",
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" x = np.linspace(-1.0, 1.0, nr_steps)\n",
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" f = np.empty_like(x)\n",
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" for i in range(x.size):\n",
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" f[i] = np.sqrt(1.0 - x[i]**2)\n",
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" return 2.0*f.sum()*delta"
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]
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},
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{
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"cell_type": "markdown",
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"id": "89b96c0e-78bf-4d89-b962-a3dd1cc9e92a",
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"metadata": {},
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"source": [
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"We can implement this so that the loop can be parallelized (numba cannot deal with reductions)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 35,
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"id": "39a14289-55a9-4775-b902-3d1f1b7f58ec",
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"metadata": {},
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"outputs": [],
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"source": [
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"@njit(parallel=True)\n",
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"def quad_pi_par(nr_steps):\n",
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" delta = 2.0/nr_steps\n",
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" x = np.linspace(-1.0, 1.0, nr_steps)\n",
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" f = np.empty_like(x)\n",
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" for i in range(x.size):\n",
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" f[i] = np.sqrt(1.0 - x[i]**2)\n",
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" return 2.0*f.sum()*delta"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4ea90942-284e-454d-a750-bd9d08ff057e",
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"metadata": {},
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"source": [
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"The pure numpy implementation for comparison."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 44,
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"id": "f1949a6a-8230-4c9d-b642-ce82e17fede7",
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"metadata": {},
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"outputs": [],
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"source": [
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"def quad_pi_np(nr_steps):\n",
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" delta = 2.0/nr_steps\n",
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" x = np.linspace(-1.0, 1.0, nr_steps)\n",
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" return 2.0*np.sqrt(1.0 - x**2).sum()*delta"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 50,
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"id": "2492cd21-68d8-4b9a-9a0b-656cfb2c9e2d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"328 ms ± 34.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
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]
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}
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],
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"source": [
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"%timeit quad_pi_jit(100_000_000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"id": "2acb30d2-92cf-4082-8572-675b7694747b",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"202 ms ± 1.19 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
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]
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}
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],
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"source": [
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"%timeit quad_pi_par(100_000_000)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 52,
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"id": "be932fa1-f46a-4e8b-a301-384adf777364",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"676 ms ± 43.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
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]
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}
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],
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"source": [
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"%timeit quad_pi_np(100_000_000)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a402e83f-ccb7-4518-b8de-b14e499f994a",
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"metadata": {},
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"source": [
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"The parallized version is faster, but the parallel efficiency is far from great."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.9.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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