{ "cells": [ { "cell_type": "markdown", "id": "90cc9c0f-f165-4482-a73f-05ade131f9d0", "metadata": {}, "source": [ "# Problem-Algorithm-Solver pattern\n", "\n", "* Gen Kuroki\n", "* 2021-07-11, 2022-06-08\n", "* https://discourse.julialang.org/t/function-depending-on-the-global-variable-inside-module/64322/10\n", "\n", "A code will be more readable and efficient if the global variables that store the parameters of a problem are passed as arguments to functions _everytime_.\n", "\n", "However, many people find it troublesome to pass the parameters as arguments to the function _everytime_.\n", "\n", "In order to resolve this misunderstanding, they can try the problem-algorithm-solver pattern explained below.\n", "\n", "In order to use the `(; a, b, c) = p` syntax, require VERSION ≥ v\"1.7.0-beta\" [#39285](https://github.com/JuliaLang/julia/pull/39285)." ] }, { "cell_type": "code", "execution_count": 1, "id": "0cb4648f-18e7-49fa-bcb6-9b0e1af58ea7", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "VERSION ≥ v\"1.7.0-beta\" #> true" ] }, { "cell_type": "markdown", "id": "151a3532-073e-498a-80ee-96a9b22da9bc", "metadata": {}, "source": [ "`@kwdef` macro is exported as of Julia v1.9." ] }, { "cell_type": "code", "execution_count": 2, "id": "915637a1-6748-48b1-9c20-58db365a317e", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "true" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "VERSION ≥ v\"1.9.0\" #> true" ] }, { "cell_type": "markdown", "id": "773dff20-c6f0-48c5-9f3a-c737dfe43a08", "metadata": {}, "source": [ "## A minimal working example of the problem-algorithm-solver pattern" ] }, { "cell_type": "code", "execution_count": 3, "id": "24d79d80-56a5-4daa-ab6e-817c5f68453b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Main.FreeFall" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "module FreeFall\n", "\n", "\"\"\"Problem type\"\"\"\n", "@kwdef struct Problem{G, Y0, V0, TS}\n", " g::G = 9.80665\n", " y0::Y0 = 0.0\n", " v0::V0 = 30.0\n", " tspan::TS = (0.0, 8.0)\n", "end\n", "\n", "\"\"\"Algorithm types\"\"\"\n", "@kwdef struct EulerMethod{T}\n", " dt::T = 0.1\n", "end\n", "@kwdef struct ExactFormula{T}\n", " dt::T = 0.1\n", "end\n", "default_algorithm(::Problem) = EulerMethod()\n", "\n", "\"\"\"Solution type\"\"\"\n", "struct Solution{Y, V, T, P<:Problem, A}\n", " y::Y\n", " v::V\n", " t::T\n", " prob::P\n", " alg::A\n", "end\n", "\n", "\"\"\"Solver function\"\"\"\n", "solve(prob::Problem) = solve(prob, default_algorithm(prob))\n", "\n", "function solve(prob::Problem, alg::ExactFormula)\n", " (; g, y0, v0, tspan) = prob\n", " (; dt) = alg\n", " t0, t1 = tspan\n", " t = range(t0, t1 + dt/2; step = dt) \n", " y(t) = y0 + v0*(t - t0) - g*(t - t0)^2/2\n", " v(t) = v0 - g*(t - t0)\n", " Solution(y.(t), v.(t), t, prob, alg)\n", "end\n", "\n", "function solve(prob::Problem, alg::EulerMethod)\n", " (; g, y0, v0, tspan) = prob\n", " (; dt) = alg\n", " t0, t1 = tspan\n", " t = range(t0, t1 + dt/2; step = dt) \n", " n = length(t) \n", " y = Vector{typeof(y0)}(undef, n)\n", " v = Vector{typeof(v0)}(undef, n)\n", " y[1] = y0\n", " v[1] = v0\n", " for i in 1:n-1\n", " v[i+1] = v[i] - g*dt\n", " y[i+1] = y[i] + v[i]*dt\n", " end\n", " Solution(y, v, t, prob, alg)\n", "end\n", "\n", "end" ] }, { "cell_type": "markdown", "id": "1e068974-4de7-47ab-b0bb-ad6a4ec20b78", "metadata": {}, "source": [ "This module will calculate the free-fall motion under a uniform gravity potential.\n", "\n", "* Problem: The parameters of problems are stored in objects of type `FreeFall.Problem`.\n", "\n", "* Algorithm: The parameters of algorithms are stored in objects of types `FreeFall.EulerMethod` and of `FreeFall.ExactFormula`.\n", "\n", "* Solver function: The function `FreeFall.solve(prob::FreeFall.Problem, alg)` returns the object of type `FreeFall.Solution` obtained by solving the problem `prob` with the algorithm `alg`.\n", "\n", "Note that the `(; a, b, c) = p` syntax of Julia ≥ v1.7, is very useful for extracting the contents of the object that contains parameters. (You can also do the same thing with `@unpack` in the exellent well-known package [Parameters.jl](https://github.com/mauro3/Parameters.jl).)" ] }, { "cell_type": "markdown", "id": "195baa24-8e8b-47d1-9b7a-cc0a443e3455", "metadata": {}, "source": [ "### Example 1: Compare a numerical solution and an exact one" ] }, { "cell_type": "code", "execution_count": 4, "id": "5669ac37-9025-42c5-b8f5-25657bcdbf61", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Plots\n", "default(fmt=:png)\n", "\n", "earth = FreeFall.Problem()\n", "sol_euler = FreeFall.solve(earth)\n", "sol_exact = FreeFall.solve(earth, FreeFall.ExactFormula())\n", "\n", "plot(sol_euler.t, sol_euler.y; label=\"Euler's method (dt = $(sol_euler.alg.dt))\", ls=:auto)\n", "plot!(sol_exact.t, sol_exact.y; label=\"exact solution\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft)" ] }, { "cell_type": "markdown", "id": "e815fae5-421d-4c73-9a0f-d230514d251f", "metadata": {}, "source": [ "Since the time step `dt = 0.1` is not enough small, the error of the Euler method is rather large." ] }, { "cell_type": "markdown", "id": "d1cb8a2c-825e-484f-b7cb-1ab1741e6c60", "metadata": {}, "source": [ "### Example 2: Change the algorithm parameter `dt` smaller" ] }, { "cell_type": "code", "execution_count": 5, "id": "8a9091d9-9604-47a1-aca5-5a073113819d", "metadata": {}, "outputs": [ { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "earth = FreeFall.Problem()\n", "sol_euler = FreeFall.solve(earth, FreeFall.EulerMethod(dt = 0.01))\n", "sol_exact = FreeFall.solve(earth, FreeFall.ExactFormula())\n", "\n", "plot(sol_euler.t, sol_euler.y; label=\"Euler's method (dt = $(sol_euler.alg.dt))\", ls=:auto)\n", "plot!(sol_exact.t, sol_exact.y; label=\"exact solution\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft)" ] }, { "cell_type": "markdown", "id": "1c998b2d-d0e8-4dde-b847-b1c6b333b59c", "metadata": {}, "source": [ "### Example 3: Change the problem parameter `g` to the gravitational acceleration on the moon" ] }, { "cell_type": "code", "execution_count": 6, "id": "780da4d3-9cfb-4a88-a25a-459d4dac5060", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "moon = FreeFall.Problem(g = 1.62, tspan = (0.0, 40.0))\n", "sol_euler = FreeFall.solve(moon)\n", "sol_exact = FreeFall.solve(moon, FreeFall.ExactFormula(dt = sol_euler.alg.dt))\n", "\n", "plot(sol_euler.t, sol_euler.y; label=\"Euler's method (dt = $(sol_euler.alg.dt))\", ls=:auto)\n", "plot!(sol_exact.t, sol_exact.y; label=\"exact solution\", ls=:auto)\n", "title!(\"On the Moon\"; xlabel=\"t\", legend=:bottomleft)" ] }, { "cell_type": "markdown", "id": "e01c24c5-9cfa-4d66-800d-027b9952c630", "metadata": {}, "source": [ "## Extensibility of the Julia ecosystem\n", "\n", "A different author of the `FreeFall` module can define , in the `SomeExtension` module, a new algorithm type and a new method of the `FreeFall.solve` function. Both a new type and a new method!" ] }, { "cell_type": "code", "execution_count": 7, "id": "7f257c50-bfa4-4593-a409-868891984563", "metadata": {}, "outputs": [ { "data": { "image/png": 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"image/svg+xml": [ "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", " \n", " \n", " \n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/html": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "module SomeExtension\n", "\n", "using ..FreeFall\n", "using ..FreeFall: Problem, Solution\n", "\n", "@kwdef struct Symplectic2ndOrder{T}\n", " dt::T = 0.1\n", "end\n", "\n", "function FreeFall.solve(prob::Problem, alg::Symplectic2ndOrder)\n", " (; g, y0, v0, tspan) = prob\n", " (; dt) = alg\n", " t0, t1 = tspan\n", " t = range(t0, t1 + dt/2; step = dt) \n", " n = length(t) \n", " y = Vector{typeof(y0)}(undef, n)\n", " v = Vector{typeof(v0)}(undef, n)\n", " y[1] = y0\n", " v[1] = v0\n", " for i in 1:n-1\n", " ytmp = y[i] + v[i]*dt/2\n", " v[i+1] = v[i] - g*dt\n", " y[i+1] = ytmp + v[i+1]*dt/2\n", " end\n", " Solution(y, v, t, prob, alg)\n", "end\n", "\n", "end\n", "\n", "earth = FreeFall.Problem()\n", "sol_sympl = FreeFall.solve(earth, SomeExtension.Symplectic2ndOrder(dt = 2.0))\n", "sol_exact = FreeFall.solve(earth, FreeFall.ExactFormula())\n", "\n", "plot(sol_sympl.t, sol_sympl.y; label=\"2nd order symplectic (dt = $(sol_sympl.alg.dt))\", ls=:auto)\n", "plot!(sol_exact.t, sol_exact.y; label=\"exact solution\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft)" ] }, { "cell_type": "markdown", "id": "876cf29b-a732-40de-b47f-dfb03ff4a0db", "metadata": {}, "source": [ "The second-order symplectic method gives exact discretizations of the free-fall motions under uniform gravity potentials." ] }, { "cell_type": "markdown", "id": "90696808-a7a9-4567-b345-2cde048c7566", "metadata": {}, "source": [ "## Composability of the Julia ecosystem\n", "\n", "By combining the MonteCarloMeasurements.jl package with the modules given above, we can plot the behavior of the system for perturbations of the initial value. We did not intend for them to be used in this way!" ] }, { "cell_type": "code", "execution_count": 8, "id": "e6a8adb3-60aa-40f1-903c-fa4365d7c6c7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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60)\n", "P = plot(sol_euler.t, sol_euler.y; label=\"Euler's method (dt = $(sol_euler.alg.dt))\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft, ylim)\n", "Q = plot(sol_sympl.t, sol_sympl.y; label=\"2nd order symplectic (dt = $(sol_sympl.alg.dt))\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft, ylim)\n", "R = plot(sol_exact.t, sol_exact.y; label=\"exact solution\", ls=:auto)\n", "title!(\"On the Earth\"; xlabel=\"t\", legend=:bottomleft, ylim)\n", "plot(P, Q, R; size=(720, 600))" ] }, { "cell_type": "code", "execution_count": null, "id": "8e29238e-76f4-43f1-98e6-697ce5b69e71", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "encoding": "# -*- coding: utf-8 -*-", "formats": "ipynb,jl:hydrogen" }, "kernelspec": { "display_name": "Julia 1.9.1", "language": "julia", "name": "julia-1.9" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.1" } }, "nbformat": 4, "nbformat_minor": 5 }