/* * LVroutines.java * @author Michael Anderson * * Common and useful routines for use with the * Lotka Volterra Model. Like the java Math class, * this class is non-instantiable. * * Created on July 29, 2004, 6:53 PM * Last Updated on January 16, 2005 */ package LotkaVolterra; import Jama.*; public final class LVroutines { // A private constructor will make this // class non-instantiable private LVroutines() {} // Initialize each species in the animal array // animal is the array of species. // numberOfConnections is the number of species each species is // connected to. // p ranges from 0 to 1. p = 0 is a perfectly ordered network // p = 1 is a totally random network. public static void initializeAnimals(Animal[] animal, int numberOfConnections, double p) { int numberOfSpecies = animal.length; double[][] alphaMatrix = LVmatrix.createAlphaMatrix(numberOfSpecies, numberOfConnections, p); for (int i = 0; i < numberOfSpecies; i++) { animal[i] = new Animal(alphaMatrix[i]); } } // End of the initializeAnimals method // Initialize the animals with the paramaters from a file public static Animal[] createAnimals(String paramFile) { Animal[] animal = LVfileIO.createAnimalsFromFile(paramFile); return animal; } // Create a copy of an Animal array public static Animal[] createCopy(Animal[] animal) { int numberOfSpecies = animal.length; Animal[] copy = new Animal[numberOfSpecies]; for (int i = 0; i < numberOfSpecies; i++) { copy[i] = new Animal(animal[i].r, animal[i].getX(), (int[])animal[i].connection.clone(), (double[])animal[i].conStrength.clone()); } return copy; } // Create an ordered ring of animals with specified: // size, initial populations, number of connections and connection strengths public static Animal[] createOrderedAnimals(int size, double[] initialPopulations, int numConnections, double connectionStrengths) { Animal[] orderedAnimals = new Animal[size]; double[][] orderedAlphaMatrix = LVmatrix.createOrderedMatrix(size, numConnections, connectionStrengths); for (int i = 0; i < size; i++) { orderedAnimals[i] = new Animal(1.0, initialPopulations[i], orderedAlphaMatrix[i]); } return orderedAnimals; } // End createOrderedAnimals // Set the populations near some fixed point // by some value +- d public static void setPopulationsNearPoint(Animal[] animal, double d, double[] point) { for (int i = 0; i < animal.length; i++) { animal[i].setX(Math.random() * 2 * d + (point[i] - d)); } } // End setPopulationsNearPoint // Mix up the populations of the animals // (Usually done in the initialization process) public static void randomizePopulations(Animal[] animal) { for (int i = 0; i < animal.length; i++) { animal[i].setX(Math.random()); } } // End of randomizePopulations // Given an Animal array, mix up a specific number, p // of the links and return that new array public static Animal[] createAnimals(Animal[] animal, int p) { int numberOfSpecies = animal.length; Animal[] mixedUpAnimal = createCopy(animal); // Change p number of links for (int i = 0; i < p; i++) { // pick a species at random 0 thru N-1 int q = (int)(Math.random() * numberOfSpecies); int linkToMove; int moveHere; // now pick one of that species // links, but don't move a self link do { linkToMove = (int)(Math.random() * animal[q].connection.length); } while (animal[q].connection[linkToMove] == q); // now find somewhere else to put that link // but don't move it to an occupied spot boolean occupied = false; do { occupied = false; //pick a place to move it to moveHere = (int)(Math.random() * numberOfSpecies); //look through q's links and see //if that place is occupied already for (int j = 0; j < animal[q].connection.length; j++) { if (animal[q].connection[j] == moveHere) { occupied = true; } } } while (occupied == true); mixedUpAnimal[q].connection[linkToMove] = moveHere; } // end of change number of p links return mixedUpAnimal; } // Given an Animal array, mix up a percentage, p // of the links and return that new array public static Animal[] createAnimals(Animal[] animal, double p) { int numberOfSpecies = animal.length; Animal[] mixedUpAnimal = createCopy(animal); int newLocation = 0; boolean LinkThereAlready = false; int i, j, k; // counters for (i = 0; i < numberOfSpecies; i++) { for (j = 0; j < animal[i].connection.length; j++) { if ((i != animal[i].connection[j]) && (Math.random() < p)) { // Don't change an animal's connection to itself // and only change a percentage, p, of the links do { newLocation = (int)(numberOfSpecies * Math.random()); LinkThereAlready = false; for (k = 0; k < animal[i].connection.length; k++) { if (animal[i].connection[k] == newLocation) { LinkThereAlready = true; } } } while (LinkThereAlready == true); mixedUpAnimal[i].connection[j] = newLocation; } } // end of j loop } // end of i loop return mixedUpAnimal; } // End of the mixUpConnections method // Given an Animal array, a percentage, p // of the links and return that new array public static Animal[] deleteConnections(Animal[] animal, double p) { int numberOfSpecies = animal.length; Animal[] smallerAnimal = createCopy(animal); for (int i = 0; i < numberOfSpecies; i++) { for (int j = 0; j < animal[i].connection.length; j++) { if ((i != animal[i].connection[j]) && (Math.random() < p)) { // Don't delete an animal's connection to itself // and only delete a percentage, p, of the links smallerAnimal[i].conStrength[j] = 0; //smallerAnimal[i].removeConnection(animal[i].connection[j]); } } // end of j loop } // end of i loop return smallerAnimal; } // End of the mixUpConnections method // Let the system play out through time. // Pass in an array of animals, // the number of time units to go through, and the time step size (dt) public static void evolveThruTime(Animal[] animal, double timeUnits, double dt) { int numberOfSpecies = animal.length; int i = 0; // counter // Create the storage area for an array of populations double[] x = new double[numberOfSpecies]; for (double t = 0; t < timeUnits; t = t + dt) { //Copy all the populations into an array before //steping through time. for (i = 0; i < numberOfSpecies; i++) { x[i] = animal[i].getX(); } //Have each species step once through time dt. for (i = 0; i < numberOfSpecies; i++) { animal[i].stepOnce(x, dt); } } } // End of the evolveThruTime method // Let the system play out through time. // Change links if a species comes close to dying. // Pass in an array of animals, // the number of time units to go through, and the time step size (dt) public static void evolveLinks(Animal[] animal, double timeUnits, double dt) { int numberOfSpecies = animal.length; int i = 0; // counter // Create the storage area for an array of populations double[] x = new double[numberOfSpecies]; for (double t = 0; t < timeUnits; t = t + dt) { //Copy all the populations into an array before //steping through time. for (i = 0; i < numberOfSpecies; i++) { x[i] = animal[i].getX(); } //Have each species step once through time dt. for (i = 0; i < numberOfSpecies; i++) { animal[i].stepOnce(x, dt); } //Check populations and shift link if too low for (i = 0; i < numberOfSpecies; i++) { // check to see if population is too low if (animal[i].getX() < Math.pow(10, -7)) { System.out.println(t); // Move a random link one over moveRandomLinksByOne(animal, 1); // Reset populations near fixed point for (int j = 0; j < numberOfSpecies; j++) { animal[j].setX(Math.random() * 0.05 + 0.3083333); } } // end of IF pop is low } // end of i loop (for checking populations) } // end of t loop } // End of the evolveLinks method // Let the system play out through time. Find info // about it's distance from the All-Alive-Fixed-Point // Pass in an array of animals, // the number of time units to go through, and the time step size (dt) // and also the location of the All-Alive-Fixed-Point public static double[] findMinAveMaxDist(Animal[] animal, double timeUnits, double dt, double[] allAlivePoint) { //these variables are for determining size of attractor double[] minAveMax = new double[3]; double min = Integer.MAX_VALUE; double ave = 0; double max = Integer.MIN_VALUE; double currentDistance; long bigCount = 0; int numberOfSpecies = animal.length; int i = 0; // counter // Create the storage area for an array of populations double[] x = new double[numberOfSpecies]; for (double t = 0; t < timeUnits; t = t + dt) { //Copy all the populations into an array before //steping through time. for (i = 0; i < numberOfSpecies; i++) { x[i] = animal[i].getX(); } //Have each species step once through time dt. for (i = 0; i < numberOfSpecies; i++) { animal[i].stepOnce(x, dt); } //now determine distance currentDistance = 0; for (i = 0; i < numberOfSpecies; i++) { currentDistance = currentDistance + Math.pow(animal[i].getX() - allAlivePoint[i], 2); } currentDistance = Math.pow(currentDistance, 0.5); //check to see if that distance is a min or max if (currentDistance < min) { min = currentDistance; } if (currentDistance > max) { max = currentDistance; } ave = ave + currentDistance; bigCount = bigCount + 1; } ave = ave / bigCount; minAveMax[0] = min; minAveMax[1] = ave; minAveMax[2] = max; return minAveMax; } // End of the evolveThruTime method // Check to see if any species is dead public static boolean noneDead(Animal[] animal) { boolean noneDead = true; for (int i = 0; i < animal.length; i++) { if (animal[i].getX() < Math.pow(10, -7)) { noneDead = false; } } return noneDead; } // Calculate the Largest Lyapunov Exponent public static double calculateLE(Animal[] animal, int timeUnits, double dt) { int numberOfSpecies = animal.length; // First Create a copy of both animal systems Animal[] animalSet1 = createCopy(animal); Animal[] animalSet2 = createCopy(animal); // Now create the variables used in calculating LE double d0 = Math.pow(10, -10); double d1 = 0; long count = 0; double sum = 0; int i = 0; // counter // Move the location of Set 2 by some small d0 animalSet2[0].setX(animalSet2[0].getX() + d0); //int times = 0; * for calculating StDev of LLE for (double t = 0; t < timeUnits; t = t + dt) { // Have both systems move through one step dt allStepOnce(animalSet1, dt); allStepOnce(animalSet2, dt); //allStepOnceRK(animalSet1, dt); // RK has higher accuracy? //allStepOnceRK(animalSet2, dt); // Calculate new separation d1 = 0; for (i = 0; i < numberOfSpecies; i++) { d1 = d1 + Math.pow(animalSet2[i].getX() - animalSet1[i].getX(), 2); } d1 = Math.pow(d1, 0.5); sum = sum + Math.log(d1/d0); count++; // Re-adjust the orbit the orbit of Set 2 // to be only a distance d0 away for (i = 0; i < numberOfSpecies; i++) { animalSet2[i].setX(animalSet1[i].getX() + (d0/d1) * (animalSet2[i].getX() - animalSet1[i].getX())); } //maybe print off some of the LLE //if ((times % 20000) == 0) { // System.out.println(t + ";" + (1 / dt) * (sum / count)); //} //times++; } // end of t loop return (1 / dt) * (sum / count); } // end of the calculateLE method // Returns the location of the all-alive fixed point public static double[] allAliveFixedPoint(Animal[] animal) { int numberOfSpecies = animal.length; // Ax = 1 // is the location of the All-Alive fixed point Matrix alphaMatrix = new Matrix(LVmatrix.createAlphaMatrix(animal)); Matrix onesVector = new Matrix(numberOfSpecies, 1, 1.0); Matrix x = alphaMatrix.solve(onesVector); return x.transpose().getArray()[0]; } // Have all the animals step one timestep, dt, into the future. // pop is the array of populations before any took a step. // This method is using the "Improved Euler Method" // which is why it looks a little wacky. public static void allStepOnce(Animal[] animal, double dt) { int numberOfSpecies = animal.length; double[] xNow = new double[numberOfSpecies]; double[] xAfter = new double[numberOfSpecies]; //Copy all the populations into an array before //steping through time. for (int i = 0; i < numberOfSpecies; i++) { xNow[i] = animal[i].getX(); } // Get the dx/dt for all the species now double[] dxdtNow = new double[numberOfSpecies]; for (int i = 0; i < numberOfSpecies; i++) { dxdtNow[i] = animal[i].getdxdt(xNow); } // Find the population of each after for (int i = 0; i < numberOfSpecies; i++) { xAfter[i] = xNow[i] + dt * dxdtNow[i]; } // Get the dx/dt for all the species after the timestep double[] dxdtAfter = new double[numberOfSpecies]; for (int i = 0; i < numberOfSpecies; i++) { dxdtAfter[i] = animal[i].getdxdt(xAfter); } for (int i = 0; i < numberOfSpecies; i++) { animal[i].setX(animal[i].getX() + (dt/2) * (dxdtNow[i] + dxdtAfter[i])); } } // End of the allStepOnce method public static void allStepOnceRK(Animal[] animal, double dt) { int numberOfSpecies = animal.length; double[] x0 = new double[numberOfSpecies]; double[] x1 = new double[numberOfSpecies]; double[] x2 = new double[numberOfSpecies]; double[] x3 = new double[numberOfSpecies]; double[] dxdt0 = new double[numberOfSpecies]; double[] dxdt1 = new double[numberOfSpecies]; double[] dxdt2 = new double[numberOfSpecies]; double[] dxdt3 = new double[numberOfSpecies]; for (int i = 0; i < numberOfSpecies; i++) { x0[i] = animal[i].getX(); } // dxdt0 is dx/dt now for (int i = 0; i < numberOfSpecies; i++) { dxdt0[i] = animal[i].getdxdt(x0); } // dxdt1 is dx/dt now + 1/2*dt for (int i = 0; i < numberOfSpecies; i++) { x1[i] = x0[i] + 0.5 * dt * dxdt0[i]; } for (int i = 0; i< numberOfSpecies; i++) { dxdt1[i] = animal[i].getdxdt(x1); } // dxdt2 is dx/dt now + 1/2*dt for (int i = 0; i < numberOfSpecies; i++) { x2[i] = x0[i] + 0.5 * dt * dxdt1[i]; } for (int i = 0; i< numberOfSpecies; i++) { dxdt2[i] = animal[i].getdxdt(x2); } // dxdt3 is dx/dt now + dt for (int i = 0; i < numberOfSpecies; i++) { x3[i] = x0[i] + dt * dxdt2[i]; } for (int i = 0; i< numberOfSpecies; i++) { dxdt3[i] = animal[i].getdxdt(x3); } // now set the new population of each animal for (int i = 0; i < numberOfSpecies; i++) { animal[i].setX(x0[i] + dt / 6 * (dxdt0[i] + 2 * dxdt1[i] + 2 * dxdt2[i] + dxdt3[i])); } } //Count the total number of links public static int totalLinks(Animal[] animal) { int totalLinks = 0; for (int i = 0; i < animal.length; i++) { totalLinks = totalLinks + animal[i].connection.length; } return totalLinks; } // end of the countTotalLinks method //Find the species with the most links and return that number public static int maxLinks(Animal[] animal) { int max = 0; for (int i = 0; i < animal.length; i++) { if (animal[i].connection.length > max) { max = animal[i].connection.length; } } return max; } //Find the species with the least links and return that number public static int minLinks(Animal[] animal) { int min = animal[0].connection.length; for (int i = 1; i < animal.length; i++) { if (animal[i].connection.length < min) { min = animal[i].connection.length; } } return min; } // Randomly move link +-1 space public static Animal[] moveRandomLinksByOne(Animal[] template, int numLinksToMove) { int numberOfSpecies = template.length; Animal[] animal = LVroutines.createCopy(template); // Change a number of links for (int i = 0; i < numLinksToMove; i++) { // p