{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameter space exploration with Latin Hypercube in R\n",
    "\n",
    "*This tutorial assumes you have read the [tutorial on numerical integration](http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/Numerical%20Integration%20Tutorial%20-%20R.ipynb?create=1). and the [tutorial on bifurcation analysis](http://nbviewer.ipython.org/github/diogro/ode_examples/blob/master/Qualitative%20analysis%20and%20Bifurcation%20diagram%20Tutorial%20-%20R.ipynb)\n",
    "\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",
    "* [rootsolve](https://cran.r-project.org/web/packages/rootSolve/index.html): root finding and equilibrium and steady-state analyses.\n",
    "* [pse](http://cran.r-project.org/web/packages/pse/), a library to run parameter space exploration of models\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\", \"rootSolve, \"\"ggplot2\", \"pse\"))\n",
    "\n",
    "And then load the packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "library(ggplot2)\n",
    "library(pse)\n",
    "library(deSolve)\n",
    "library(rootSolve)\n",
    "\n",
    "#### For jupyter notebook only\n",
    "options(jupyter.plot_mimetypes = 'image/png')\n",
    "####"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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",
    "\n",
    "## Exploring the parameter space with the Latin Hypercube\n",
    "\n",
    "### First example: two competitors in a Lotka-Volterra System\n",
    "\n",
    "#### 1. Create a R function that runs the model once\n",
    "Create a function that gets the model parameters and time sequence\n",
    "and outputs the final size of populations, by numerical integration. \n",
    "If argument `runsteady=TRUE` the function uses the `runsteady` function of package *rootSolve*\n",
    "to run numerical integration till a stationary point (hopefully, please see help of the function).\n",
    "If `runsteady=FALSE` the function uses the `ode` function to do the integration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "oneRun <- function(X0, Y0, a, b,  times, runsteady=TRUE){\n",
    "    ## parameters: initial sizes and competition coefficients\n",
    "    parameters <- c(a = a, b = b)\n",
    "    state <- c(X = X0, Y = Y0)\n",
    "    ## The function to be integrated\n",
    "    LV <- function(t, state, parameters){\n",
    "        with(as.list(c(state, parameters)), {\n",
    "            dX = X*(1 - X - a*Y)\n",
    "            dY = Y*(1 - Y - b*X)\n",
    "            list(c(dX, dY))\n",
    "        })\n",
    "    }\n",
    "    ## Integrating: runsteady to run untill convergence (be carefull using that!)\n",
    "    ## Or the usual integration with the function ode\n",
    "    if(runsteady){\n",
    "        out <- runsteady(y = state, times = times, func = LV, parms = parameters)\n",
    "        return(out$y) # runsteady returns only final states\n",
    "    }\n",
    "    else{\n",
    "        out <- ode(y = state, times = times, func = LV, parms = parameters)\n",
    "        return(out[nrow(out),-1]) # indexing to get final state values\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. Create a R function for running the model for each combination of parameters\n",
    "Create a function with `mapply` that gets a matrix of parameter combinations\n",
    "(combinations are lines and parameters are columns)\n",
    "and returns the output of the function above for each parameter combination.\n",
    "Use argument `MoreArgs` to input the values for additional arguments that are not in the matrix of parameter\n",
    "(arguments `runsteady` and `times` in this case)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "modelRun <- function (my.pars) {\n",
    "    return(mapply(oneRun, my.pars[,1], my.pars[,2], my.pars[,3], my.pars[,4],\n",
    "                  MoreArgs=list(times=c(0,Inf), runsteady=TRUE)))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Set the hypercube\n",
    "Now prepare the hypercube. You have to specify:\n",
    "\n",
    "* A character vector to name the parameters. In this case the initial conditions and the two competition coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "factors <- c(\"X0\", \"Y0\", \"a\", \"b\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The probability quantile function used to draw values of each parameter. If you do not information on the distribution of parameters use uniform distribution to have equiprobable values in a range from `min` to `max`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q <- c(\"qunif\", \"qunif\", \"qunif\", \"qunif\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* A list of the parameters of the above probability distributions. For the uniform the parameters are minimum and maximun values. So in this case each element of the list is another listwith the `max` and `min` of the corresponding model parameter, in the same order as above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q.arg <- list(list(min=0, max=1), list(min=0, max=1), list(min=0, max=2), list(min=0, max=2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.  Run the hypercube\n",
    "Now create the hypercube and run the model for each combination of parameters with `LHS`,\n",
    "the working horse function of *pse* package.\n",
    "The argument `N=200` sets 200 combinations of parameters, please see help for further information"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "myLHS <- LHS(model=modelRun, factors=factors, \n",
    "             N=200, q=q, q.arg=q.arg, nboot=100) # use nboot=0 if do not need partial correlations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Explore your results\n",
    "And now use exploratory statistics to identify interesting regions of the parameter space. The *pse* package provides some options like:\n",
    "\n",
    "###### Cumulative distribution of outputs. \n",
    "Shows that about 40% of the population sizes are $\\simeq 0$, so coexistence is not granted:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotecdf(myLHS, stack=TRUE, xlab=\"Population relative size\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Scatterplots of response x parameter values\n",
    "Again we see that many runs resulted in exclusion of one of the species.\n",
    "We see also that initial conditions do not affect the final result, but\n",
    "competition coefficients do:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotscatter(myLHS, add.lm=FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Partial correlation plots\n",
    "Partial correlations are the non-parametric correlation of each output with each parameter,\n",
    "with the effects of the other variables partialed out.\n",
    "Confidence bars crossing the zero horizontal line indicate no-significant partial correlation.\n",
    "These plots show that final population sizes have a strong correlation with competition coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plotprcc(myLHS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Non-standard analyses\n",
    "The package *pse* allows to extract a table with the outputs for each combination of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## get.data export a table with parameter values\n",
    "hypercube <- get.data(myLHS)\n",
    "\n",
    "## get.results exports the outputs\n",
    "hypercube <- cbind(hypercube, get.results(myLHS)) # appending columns of outputs to the hypercube matrix\n",
    "names(hypercube)[5:6] <- c(\"X\", \"Y\") # cosmetic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now you are free to use any exploratory tool to identify interesting regions of the parameter space\n",
    "There is not a single recipe, but a first guess is to try univariate and then bivariate and multivariate analyses.\n",
    "In some case you can also use linear models such as multiple regressions to identify patterns.\n",
    "\n",
    "For instance, we already know that there is coexistence in this parameter space.\n",
    "But in how many runs?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "52"
      ],
      "text/latex": [
       "52"
      ],
      "text/markdown": [
       "52"
      ],
      "text/plain": [
       "[1] 52"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(hypercube$X>1e-6&hypercube$Y>1e-6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which parameter combinations ensue coexistence?\n",
    "Univariate exploration with boxplot shows that\n",
    "there is an upper bound of coefficients to have coexistence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Create a logical variable to flag coexistence\n",
    "hypercube$coexistence <- hypercube$X>1e-6&hypercube$Y>1e-6\n",
    "## boxplots\n",
    "par(mfrow=c(2,2))\n",
    "boxplot(X0~coexistence, data=hypercube, xlab=\"Coexistence\", main=\"X0\")\n",
    "boxplot(Y0~coexistence, data=hypercube, xlab=\"Coexistence\", main=\"Y0\")\n",
    "boxplot(a~coexistence, data=hypercube, xlab=\"Coexistence\", main=\"a\")\n",
    "boxplot(b~coexistence, data=hypercube, xlab=\"Coexistence\", main=\"b\")\n",
    "par(mfrow=c(1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bivariate plots shows that coexistence is possible only if both  coeficients are less than one, roughly (blue dots):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(a~b, data=hypercube, type=\"n\") ## to scale the plot for the whole parameter space\n",
    "points(a~b, data=hypercube, subset=hypercube$X>1e-6&hypercube$Y>1e-6, col=\"blue\")\n",
    "points(a~b, data=hypercube, subset=!(hypercube$X>1e-6&hypercube$Y>1e-6), col=\"red\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Further exploration can  reveal more!\n",
    "\n",
    "### A more complicated example\n",
    "\n",
    "Let's check a well-known result: in which conditions disease spreads in a Suscetible-Infected-Recovered epidemic model (SIR). \n",
    "\n",
    "#### 1. R function for the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "oneRun.sir <- function(S0, I0, R0, r, a, time=seq(0, 50, by = 0.01)){\n",
    "    ## parameters: transmission and recovering rates\n",
    "    parameters <- c(r = r, a = a)\n",
    "    ## initial population sizes: start with a single infected individual to test invasibility\n",
    "    state <- c(S = S0, I = I0, R = R0)\n",
    "    ## The function to be integrated\n",
    "    sir <- function(t, state, parameters){\n",
    "        with(as.list(c(state, parameters)), {\n",
    "            dS = -r*S*I\n",
    "            dI = r*S*I - a*I\n",
    "            dR = a*I\n",
    "            list(c(dS, dI, dR))\n",
    "        })\n",
    "    }\n",
    "    ## Integrating\n",
    "    out <- ode(y = state, times = time, func = sir, parms = parameters)\n",
    "    return(any(out[,3]>I0)) # returns a logical: any infected number larger than initial number?\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2. R function to run the model for each parameter combinations\n",
    "As we are interested in disease spread we restrict I0 to one and R0 to zero."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "modelRun.sir <- function (my.pars) {\n",
    "    return(mapply(oneRun.sir, my.pars[,1], 1, 0, my.pars[,2], my.pars[,3]))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3. Set the hypercube"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## A string vector to name the parameters\n",
    "factors <- c(\"S0\", \"r\", \"a\")\n",
    "## The probability quantile function used to draw values of each parameter\n",
    "q <- c(\"qunif\", \"qunif\", \"qunif\")\n",
    "## A list of the parameters of the above probability distributions\n",
    "q.arg <- list(list(min=10, max=200), list(min=0.001, max=0.01), list(min=0, max=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4. Run the hypercube"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "myLHS <- LHS(model=modelRun.sir, factors=factors, N=200, q=q, q.arg=q.arg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 5. Explore the results\n",
    "Let's start looking at the effect of each parameter.\n",
    "with a boxplot of each parameter value in function of the occurrence of disease spread."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "##Table of parameter combinations with get.data\n",
    "hypercube <- get.data(myLHS)\n",
    "## adding the output for each combination with get.results\n",
    "hypercube$Spread <- get.results(myLHS)\n",
    "## box plots parameter ~ occurence of spread (logical)\n",
    "par(mfrow=c(1,3))\n",
    "boxplot(S0~Spread, data=hypercube, xlab=\"Disease spread\", ylab=\"Initial number of susceptibles\")\n",
    "boxplot(r~Spread, data=hypercube, xlab=\"Disease spread\", ylab=\"Transmission rate\")\n",
    "boxplot(a~Spread, data=hypercube, xlab=\"Disease spread\", ylab=\"Recovering rate\")\n",
    "par(mfrow=c(1,1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also explore relatioships between parameters conditioned\n",
    "to the output. This is relationship of parameter $a$ and $r$ when spread occured or not.\n",
    "We'll restrict our exploration to populations with initial size < median of all initial size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(a~r, data=hypercube, type=\"n\") # to show all ranges of the parameters\n",
    "points(a~r, data=hypercube, subset=S0<median(S0)&Spread==1, col=\"red\")\n",
    "points(a~r, data=hypercube, subset=S0<median(S0)&Spread==0, col=\"blue\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A next step is to explore relationships between ratios of two parameters\n",
    "in function of additional parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(I(a/r)~S0, data=hypercube, type=\"n\") # to show all ranges of the parameters\n",
    "points(I(a/r)~S0, subset=Spread==1, data=hypercube, col=\"red\")\n",
    "points(I(a/r)~S0, subset=Spread==0, data=hypercube, col=\"blue\")\n",
    "abline(0,1) ## equivalence line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "BINGO! Disease spreads (red dots) if $S_0 > \\frac{a}{r}$\n",
    "\n",
    "### For more info:\n",
    "\n",
    "* Chalom, A. & Prado, P.I., 2012. Parameter space exploration of ecological models. http://arxiv.org/abs/1210.6278\n",
    "* [Vignette of package pse](https://cran.r-project.org/web/packages/pse/vignettes/pse_tutorial.pdf)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "",
   "name": "r"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.2.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}