{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Numerically solving differential equations with R\n", "\n", "*This is a brief description of what numerical integration is and a practical tutorial on how to do it in R.*" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## Software required\n", "### R\n", "*In order to run the R codes in this notebook in your own computer, you need to install the following software:*\n", "\n", "* [R](http://www.r-project.org/), along with the packages from [CRAN](http://cran.r-project.org/):\n", " * [deSolve](http://www.vps.fmvz.usp.br/CRAN/web/packages/deSolve/index.html), a library for solving differential equations\n", " * [ggplot2](http://www.vps.fmvz.usp.br/CRAN/web/packages/ggplot2/index.html), a library for plotting\n", " * [reshape2](http://cran.r-project.org/web/packages/reshape2/index.html), for manipulating data.frames\n", "\n", "To install R, download it from its homepage (Windows or Mac): http://www.r-project.org/. On Linux, you can install it using your distribution's prefered way, e.g.:\n", "\n", "* Debian/Ubuntu: `sudo apt-get install r-base`\n", "* Fedora: `sudo yum install R`\n", "* Arch: `sudo pacman -S r`\n", "\n", "To install the packages, all you have to do is run the following in the `R` prompt\n", "\n", " install.packages(c(\"deSolve\", \"ggplot2\", \"reshape2\"))\n", " \n", "The R code presented here and some additional examples are available at https://github.com/diogro/ode_examples (thanks, [Diogro](https://github.com/diogro)!).\n", "\n", "### Running commands in R\n", "You can also follow the instructions in this notebook and run the commands in R in two ways:\n", "* Copy the R codes snippets in this notebook and paste them in the R promt. Alternatively you can save them in a pure text file with .r or .R extension and run directly in an R shell.\n", "* Download the [R script](https://github.com/diogro/ode_examples) and run the commands in a R shell.\n", "\n", "### Running R commands from Jupyter\n", "*To run the R commands in this notebook from IP[y] you need also:*\n", "\n", "* the [Jupyter notebook](http://jupyter.readthedocs.org/en/latest/install.html) and\n", "* the [R Kernel for Jupyter](http://irkernel.github.io/).\n", "\n", "To install the notebook on Windows and Mac, we recommend installing the [Anaconda distribution](https://store.continuum.io/cshop/anaconda/), available at http://continuum.io/downloads. On Linux it should be available from your distro's repositories.\n", "\n", "The R kernel can be installed running, on the R shell:\n", "\n", " install.packages(c('rzmq','repr','IRkernel','IRdisplay'),\n", " repos = c('http://irkernel.github.io/', getOption('repos')))\n", " IRkernel::installspec()\n", "\n", "### Running from the web\n", "If you for some reason don' want to install anything on your computer, you can use a service that runs notebooks on the cloud, e.g. [SageMathCloud](https://cloud.sagemath.com/) or [wakari](https://www.wakari.io/). It is possible to visualize publicly-available notebooks on http://nbviewer.ipython.org, but no computation can be performed (it just shows saved pre-calculated results).\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## How numerical integration works\n", "\n", "Let's say we have a differential equation that we don't know how (or don't want) to derive its (analytical) solution. We can still find out what the solutions are through **numerical integration**. So, how does that work?\n", "\n", "The idea is to approximate the solution at successive small time intervals, extrapolating the value of the derivative over each interval. For example, let's take the differential equation\n", "\n", "$$ \\frac{dx}{dt} = f(x) = x (1 - x) $$\n", "\n", "with an initial value $x_0 = 0.1$ at an initial time $t=0$ (that is, $x(0) = 0.1$). At $t=0$, the derivative $\\frac{dx}{dt}$ values $f(0.1) = 0.1 \\times (1-0.1) = 0.09$. We pick a small interval step, say, $\\Delta t = 0.5$, and assume that the derivative value is a good approximation to the function over the whole interval from $t=0$ up to $t=0.5$. This means that in this time $x$ is going to increase by $\\frac{dx}{dt} \\times \\Delta t = 0.09 \\times 0.5 = 0.045$. So our approximate solution for $x$ at $t=0.5$ is $x(0) + 0.045 = 0.145$. We can then use this value of $x(0.5)$ to calculate the next point in time, $t=1$. We calculate the derivative at each step, multiply by the time step and add to the previous value of the solution, as in the table below:\n", "\n", "| $t$ | $x$ | $\\frac{dx}{dt}$ |\n", "| ---:|---------:|----------:|\n", "| 0 | 0.1 | 0.09 |\n", "| 0.5 | 0.145 | 0.123975 |\n", "| 1.0 | 0.206987 | 0.164144 |\n", "| 1.5 | 0.289059 | 0.205504 |\n", "| 2.0 | 0.391811 | 0.238295 |\n", "\n", "Of course, this is terribly tedious to do by hand, so we can write a simple program to do it and plot the solution. Below we compare it to the known analytical solution of this differential equation (the *logistic equation*). **Don't worry about the code just yet**: there are better and simpler ways to do it!" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "image/png": 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I7Z66vGjAUSkIILaXG9o7waCyQgBRfSA+per8YCCUjBhfTbugu9GgskIAUW0nR1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\nkN5Vf/V0KpAESBJASOertz2dCiQBkgQP0sJ6hxV7OhVIAiQJHqS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"text/plain": [ "plot without title" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# time intervals: a sequence from zero to ten at 0.5 steps\n", "dt = 0.5\n", "time <- seq(0, 10, by = dt)\n", "# initial condition\n", "x0 <- 0.1\n", "## The function to be integrated (right-hand expression of the derivative above)\n", "f <- function(x){x * (1.-x)}\n", "\n", "## An empty R vector to store the results\n", "x <- c()\n", "## Store the initial condition in the first position of the vector\n", "x[1] <- x0\n", "\n", "\n", "# loop over time: approximate the function at each time step\n", "for (i in 1:(length(time)-1)){\n", " x[i+1] = x[i] + dt * f(x[i])\n", "}\n", "\n", "## plotting with ggplot2\n", "library(ggplot2)#load each library once per R session\n", "p <- ggplot(data = data.frame(x = x, t = time), aes(t, x)) + geom_point()\n", "analytic <- stat_function(fun=function(t){0.1 * exp(t)/(1+0.1*(exp(t)-1.))})\n", "print(p+analytic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Why use scientific libraries?\n", "\n", "The method we just used above is called the *Euler method*, and is the simplest one available. The problem is that, although it works reasonably well for the differential equation above, in many cases it doesn't perform very well. There are many ways to improve it: in fact, there are many books entirely dedicated to this. Although many math or physics students do learn how to implement more sophisticated methods, the topic is really deep. Luckily, we can rely on the expertise of lots of people to come up with good algorithms that work well in most situations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Then, how... ?\n", "\n", "We are going to demonstrate how to use scientific libraries to integrate differential equations. Although the specific commands depend on the software, the general procedure is usually the same:\n", "\n", "* define the derivative function (the right hand side of the differential equation)\n", "* choose a time step or a sequence of times where you want the solution\n", "* provide the parameters and the initial condition\n", "* pass the function, time sequence, parameters and initial conditions to a computer routine that runs the integration.\n", "\n", "### A single equation\n", "\n", "So, let's start with the same equation as above, the logistic equation, now with any parameters for growth rate and carrying capacity:\n", "\n", "$$ \\frac{dx}{dt} = f(x) = r x \\left(1 - \\frac{x}{K} \\right) $$\n", "\n", "with $r=2$, $K=10$ and $x(0) = 0.1$. We show how to integrate it using the desolve package below, introducing key language syntax as necessary. We'll use the [deSolve](http://desolve.r-forge.r-project.org/), the most popular R library to run numerical integration. The basic workflow recommended by the authors of the package is\n", "\n", "#### 1. Declare initial conditions, parameters, time interval" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "library(deSolve)# loads the library\n", "\n", "## time sequence\n", "time <- seq(from=0, to=10, by = 1.)\n", "# parameters: a named vector\n", "parameters <- c(r = 1.5, K = 10)\n", "\n", "# initial conditions: also a named vector\n", "state <- c(x = 0.1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2. Define a function in R for the ODE to be integrated\n", "\n", "Let's define the right-hand side of the differential equation. \n", "To be recognized by the integration routines of *deSolve*\n", "it must be an R function that computes the values\n", "of the derivative on a time $t$. \n", "There are many ways to do this, but the recommended format is:\n", "* Make a function with three arguments: time sequence, state variables and parameters, in this order.\n", "* The function should return a list with results of the function to be integrated. \n", "To do this use `with(as.list(c(state, parameters){ ... }` inside the R function.\n", "Include between brackets the function(s) to be integrated\n", "and then close returning the list of the calculated values." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "## The logistic ODE to be integrated\n", "logistic <- function(t, state, parameters){\n", " with(\n", " as.list(c(state, parameters)),{\n", " dx <- r*x*(1-x/K)\n", " return(list(dx))\n", " }\n", " )\n", "}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3. Integrate the function\n", "\n", "Now call the R function `ode`, to perform the integration the basic arguments of 'ode' are\n", "* `y`: the vector of initial conditions\n", "* `times`: the vector with the time sequence\n", "* `func`: the R function as described above\n", "* `parms`: vector of parameter values (named)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "out <- ode(y = state, times = time, func = logistic, parms = parameters)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The resulting object has the values of the integration\n", "at each time point in the vector of times" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
timex
0 0.1000000
1 0.4330952
2 1.6866507
3 4.7624004
4 8.0295822
5 9.4808777
\n" ], "text/latex": [ "\\begin{tabular}{ll}\n", " time & x\\\\\n", "\\hline\n", "\t 0 & 0.1000000\\\\\n", "\t 1 & 0.4330952\\\\\n", "\t 2 & 1.6866507\\\\\n", "\t 3 & 4.7624004\\\\\n", "\t 4 & 8.0295822\\\\\n", "\t 5 & 9.4808777\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "| time | x |\n", "|---|---|\n", "| 0 | 0.1000000 |\n", "| 1 | 0.4330952 |\n", "| 2 | 1.6866507 |\n", "| 3 | 4.7624004 |\n", "| 4 | 8.0295822 |\n", "| 5 | 9.4808777 |\n", "\n" ], "text/plain": [ " time x \n", "[1,] 0 0.1000000\n", "[2,] 1 0.4330952\n", "[3,] 2 1.6866507\n", "[4,] 3 4.7624004\n", "[5,] 4 8.0295822\n", "[6,] 5 9.4808777" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "head(out) # first 6 lines" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "which you can plot with" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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ePGjQ0bNuT4EesCxWXKlGnXrl3W9rZt24aGhp45c2bGjBk6nc7mU7Vq1Tp16lS/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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### For jupyter notebook only\n", "options(jupyter.plot_mimetypes = 'image/png', repr.plot.height=5)\n", "####\n", "\n", "plot(out, lwd=6, col=\"lightblue\", main=\"\", ylab=\"N(t)\")\n", "curve(0.1*10*exp(1.5*x)/(10+0.1*(exp(1.5*x)-1)), add=TRUE)\n", "legend(\"topleft\", c(\"Numerical\", \"Analytical\"), lty=1, col=c(\"lightblue\", \"black\"), lwd=c(6,1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We get a much better approximation now, the two curves superimpose each other!\n", "The get the same plot with *ggplot2* package use:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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vrH0uyppV0zfQlwHJc8WB\nlCNGfBrKwlNxk2MByXPFgbRXjNZf++3MgzV783wakDzXs6IwFiSt00mbNO3ola0DRgPkQkDy\nXBPEo0tjQVp93ElDnr4s5R81ffv8GZA819YODe+PBUnbeNtpTa9dUMO3zq8BiciBgETkQEAi\nciAgETkQkIgcCEhEDgQkIgcCEpEDAYnIgYBE5EBAInIgIBE5EJCIHAhIRA70/5dP/c0oZ9Rm\nAAAAAElFTkSuQmCC" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "## Ploting with ggplot2\n", "p <- ggplot(data = as.data.frame(out), aes(time, x)) + geom_point()\n", "analytic <- stat_function(fun=function(t){0.1*10*exp(1.5*t)/(10+0.1*(exp(1.5*t)-1))})\n", "print(p+analytic)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "### A system of equations\n", "Now, what if we wanted to integrate a system of differential equations? Let's take the Lotka-Volterra equations:\n", "\n", "$$ \\begin{aligned}\n", "\\frac{dV}{dt} &= r V - c V P\\\\\n", "\\frac{dP}{dt} &= ec V P - dP\n", "\\end{aligned}$$\n", "\n", "All that you have to do is to write an R function that returns the values of both derivatives at each time, and to define the values of the parameters and of the initial conditions:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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hQ0cLf7rF7DUPd+RLjaGhFHPaCpb4xFqrSVa3w2qUS8t6Z0bnPq6ed9M0YwG3Dz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UJZUSO/JgigoYY+u/D+j/DwBQWQNen03Q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\nHoJYyuK67i5e7htw4dGYM29hCYMbPahE4pv09UD2nIeHHe2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9N8GynHkLl15ldQAAIABJREFUSxfhaIH677GqKjyr4zzy4fZh2SBeXZN8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\nqHbfOsiEEzqdNe6WgZOkGSL57zOEcZTmbyGkoWvQk8mS8YTzxkcBRC2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Ys89lDx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\n3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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# time sequence \n", "time <- seq(0, 50, by = 0.01)\n", "\n", "# parameters: a named vector\n", "parameters <- c(r = 2, k = 0.5, e = 0.1, d = 1)\n", "\n", "# initial condition: a named vector\n", "state <- c(V = 1, P = 3)\n", "\n", "# R function to calculate the value of the derivatives at each time value\n", "# Use the names of the variables as defined in the vectors above\n", "lotkaVolterra <- function(t, state, parameters){\n", " with(as.list(c(state, parameters)), {\n", " dV = r * V - k * V * P\n", " dP = e * k * V * P - d * P\n", " return(list(c(dV, dP)))\n", " })\n", "}\n", "## Integration with 'ode'\n", "out <- ode(y = state, times = time, func = lotkaVolterra, parms = parameters)\n", "\n", "## Ploting\n", "out.df = as.data.frame(out) # required by ggplot: data object must be a data frame\n", "library(reshape2)\n", "out.m = melt(out.df, id.vars='time') # this makes plotting easier by puting all variables in a single column\n", "\n", "p <- ggplot(out.m, aes(time, value, color = variable)) + geom_point()\n", "print(p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An interesting thing to do here is take a look at the *phase space*, that is, plot only the dependent variables, without respect to time:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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t5eWVm5dOlS/1UUxfMWNq4cazKdbDGHxicXpgifDACEz/Ip2QaVdP2hs+0WV7JG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\nPffcQ0T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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "p2 <- ggplot(data = out.df[1:567,], aes(x = P, V, color = time)) + geom_point()\n", "print(p2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Congratulations**: you are now ready to integrate any system of differential equations!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### For more info:\n", "\n", "* [Introduction to R](http://cran.r-project.org/doc/manuals/R-intro.html)\n", "* [Crash course in R](http://www.r-bloggers.com/a-crash-course-in-r/)\n", "* [ode package](http://desolve.r-forge.r-project.org/)\n", "* [Some additional example codes](https://github.com/diogro/ode_examples)\n", "* [ggplot2 package](https://ggplot2.tidyverse.org/)\n", "* [A R graph gallery](http://www.sr.bham.ac.uk/~ajrs/R/r-gallery.html)\n", "* [Another tutorial on numerical integration in R](http://www.r-bloggers.com/learning-r-parameter-fitting-for-models-involving-differential-equations/)" ] } ], 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