Develop Reference

Oj-Algo - Matrix exponential

I resolve the following equation :
To solve it, I would like to use matrix exponential :
I thought about 3 ways to do it :
I could have missed it but Oj-Algo could have a simple way to compute exp(A) (I did not find it in MatrixStore javadoc)
I get matrix D and V from EigenValue methods ([A] = [V][D][V]-1) and then I compute
Then the question that comes first is how I apply x->exp(x*t) function to all diagonal elements of D ?
Last idea is basically the same as 2. but I previously store the scalar-matrix product in a new matrix ([X] = [D]*(-t)) and then I compute :
Can you help me find the best way/methods/class I should use ? Thank you
NB : This question is a "follow up question" : initial question
EDIT :
This is what i have tried for now, Is it the best way to do it ? :
import static org.ojalgo.function.PrimitiveFunction.EXP;
public class SolveDifferentialEquationTest
{
private static final PhysicalStore.Factory<Double, PrimitiveDenseStore> matrixFactory = PrimitiveDenseStore.FACTORY;
public static void main(String[] args)
{
SparseStore<Double> matrix;
final PhysicalStore<Double> diagMatrix;
final PhysicalStore<Double> eigenVectorMatrix;
final PhysicalStore<Double> inverseEigenVectorMatrix;
final Eigenvalue<Double> eigenvalue;
final int time = 100;
PhysicalStore<Double> initialVector;
final PhysicalStore<Double> finalVector;
int dim = 2000;
matrix = SparseStore.PRIMITIVE.make(dim, dim);
initialVector = matrixFactory.makeZero(dim,1);
// fill matrix and initialVector
//...
//Decompose matrix
eigenvalue = Eigenvalue.PRIMITIVE.make(matrix);
eigenvalue.decompose(matrix);
diagMatrix = eigenvalue.getD().copy();
eigenVectorMatrix = eigenvalue.getV().copy();
InverterTask<Double> inverter = InverterTask.PRIMITIVE.make(eigenVectorMatrix);
try {
inverseEigenVectorMatrix = inverter.invert(eigenVectorMatrix).copy();
} catch (RecoverableCondition e) {
throw new RuntimeException(e);
}
// Construct exp(Dt)
diagMatrix.multiply(time);
diagMatrix.modifyDiagonal(EXP);
// Compute
finalVector = inverseEigenVectorMatrix.multiply(diagMatrix)
.multiply(eigenVectorMatrix)
.multiply(initialVector)
.copy();
}
}

Finding all complex roots of cubic function by using Newton's Method in Java

I've looked everywhere for code I can understand which could help me on my way. I've found one but I'm struggling, so I hope someone could help me.
This is what I want to achieve:
Solve a cubic function (ax^3+bx^2+cx+d) where a,b,c and d are filled
in by the command line when you run it.
I need the roots and complex roots to be found using the Newton's Method. The code I'm struggling with is this, but I don't know if this works and I don't know how I can calculate all 3 roots (even knowing if it has multiplicity 1, 2 or 3).
Any help is appreciated.
import java.util.function.Function;
public class Newton {
static double a = Polynom.geta(); // these are to get the input from the class you run from calling this class to solve the roots
static double b = Polynom.getb();
static double c = Polynom.getc();
static double d = Polynom.getd();
public static void main(String args[]) {
}
private Complex[] sqrt(double x, double y) {
Complex com = new Complex(x,y); // Complex is my class that deals with Complexnumbers, com is supposed to get the value of the root in the end
double tolerance = 1e-11; // tolerance for the error
int iterations = 1, max = 512;
Complex aa = com.pow(3).multiply(a); // These put in the values from input to complex values and fill in the cubic function of ax^3+bx^2+cx+d
Complex bb = com.pow(2).multiply(b);
Complex cc = com.multiply(c);
Complex dd = com.pow(2).multiply(a).multiply(3.0);
Complex ee = com.multiply(2.0).add(com);
Complex function = aa.add(bb).add(cc).add(d,0);
Complex derivative = dd.add(ee);
for(int k = 0; k<3; k++) {
while(iterations<max) {
Complex difference = function.divide(derivative); //difference=fx/dx
com = com.subtract(difference);
if (Math.abs(difference.getReal()) < tolerance && Math.abs(difference.getImaginary()) < tolerance)
return com; // this is where i get an error atm "Cannot convert from Complex to Complex
iterations++;
}
}
}

How can I get full-ranged random float values?

I found that Random#nextFloat returns a value between 0.0 and 1.0.
How can I get a random float value such as -72.0F or 126.232F?
I currently doing like this.
float randomFloat() {
final ThreadLocalRandom random = ThreadLocalRandom.current();
float value = random.nextFloat() * Float.MAX_VALUE;
if (random.nextBoolean()) {
value = 0 - value;
}
return value;
}
Is this right? Is there any other way to do this?

I would suggest generating a bound double and then converting to float:
return Double.valueOf(random.nextDouble(Float.MIN_VALUE, Float.MAX_VALUE)).floatValue();
The nextDouble method has been replaced in Java 8 with a method to produce a stream of doubles. So in Java 8 you would use the following equivalent:
DoubleStream randomDoubles = new Random().doubles(Float.MIN_VALUE, Float.MAX_VALUE);
Double.valueOf(randomDoubles.findAny().getAsDouble()).floatValue();

This is based on a the general idea in the prior answer, but fixes a small bug and shows how to actually write the method using JDK 1.8:
import java.util.Iterator;
import java.util.concurrent.ThreadLocalRandom;
public class Test {
public static void main(String[] args) {
Test t = new Test();
for (int i = 0; i < 100; i++) {
System.out.println(t.randomFloat());
}
}
final ThreadLocalRandom random = ThreadLocalRandom.current();
Iterator<Double> randomDoubles = random.doubles(-Float.MAX_VALUE,
Math.nextUp((double) Float.MAX_VALUE)).iterator();
float randomFloat() {
return randomDoubles.next().floatValue();
}
}
The code in the question used ThreadLocalRandom, so I did the same. The Random doubles method excludes the upper limit. In order to get the required full range, use as limit the smallest double that is greater than all finite float values. Getting an iterator<Double> seemed simpler and more direct than using findAny etc.

Random numbers shared between canvases

I am new to Java, and I am also new to posting a question online. So please bear with me.
I am currently constructing a Java program which displays several canvases, and I require the different canvases to use shared and/or inherited information. Let's assume for simplicity that canvas C1 displays a polygon with random vertices on a circle. Currently these vertices are created in a coordinate class and are then instantiated by a drawing class. I am now trying to store these values in a way which allows the second canvas C2 (via drawing class) to use them, but without instantiating it, as I need the same sequence of random numbers.
Let this be a simplified example of my coordinate class:
public class Coord {
public Complex[] z = new Complex[5];
public Coord() {}
// create n random vertices (length of a and z will match)
public Complex[] randCoord(Complex[] a) {
for(int i = 0; i < a.length; i++){
z[i] = new Complex(200 * Math.random(), 200 * Math.random());
}
return z;
}
// public static Complex[] getCoord() {
// return z;
// }
}
The commented out section is one of my million attempts to generate a static version of the coordinate list, but I am not allowed to return z as it is not a static variable (in this case). I am probably missing something painfully obvious in regard to transferring between static and non-static methods, but any insight on how to store the random sequence (and likewise, how to call it) would be appreciated.

It sounds like the Singleton pattern would be helpful :
public class Coord {
private static final Complex[] z = fixedRandomPoints(5);
private Coord() {}
//this is the method you call from both canvases
public static Complex[] getInstance() {
return z;
}
private static Complex[] fixedRandomPoints(int n) {
final Complex[] results = new Complex[n];
for(int i = 0; i < n.length; i++){
results[i] = new Complex(200 * Math.random(), 200 * Math.random());
}
return results;
}
}
The only thing thats unclear is the relationship of this class to the 'a' variable, which I think you need to explain a little better.

First of all, you should read up on the MVC-pattern: Model-View-Controller.
Secondly, it looks like what you're currently trying to do can simply be done by declaring z to be static:
public static Complex[] z = new Complex[5];

PCA pca = new PCA

How can we apply PCA to a one dimensional array ?
double[][] data = new double [1][600];
PCA pca = new PCA(data, 20);
data = pca.getPCATransformedDataAsDoubleArray();
When a print the values in data array, the features in the data array decrease 600 to 20, but all values zero.
Why?
package VoiceRecognation;
import Jama.Matrix;
import comirva.data.DataMatrix;
import comirva.util.PCA;
import javax.print.attribute.standard.Finishings;
import java.io.File;
/**
* Created by IntelliJ IDEA.
* User: SAHIN
* Date: 11.06.2011
* Time: 19:33
* To change this template use File | Settings | File Templates.
*/
public class Deneme {
public static void main(String[] args) {
int[] group = Groups.getGroups();
File[] files = Files.getFiles();
double[][] data = FindMfccOfFiles.findMFCCValuesOfFiles(files);
PCA pca = new PCA(data, 20);
data = pca.getPCATransformedDataAsDoubleArray();
File file = new File("src/main/resources/Karisik/E-Mail/(1).wav");
double[] testdata = MFCC.getMFCC(file);
double[][] result = new double[1][600];
result[0] = testdata;
PCA p = new PCA(result, 20);
double [][] sum = p.getPCATransformedDataAsDoubleArray();
for (int i = 0; i < sum[0].length; i++) {
System.out.print(sum[0][i] + " ");
}
}
}

Principal component analysis is used for reducing the dimensionality of your problem. The dimensions of the audio file are the channels (e.g. left speaker, right speaker), not the individual samples. In that case, you really have only one dimension for a mono audio stream. So, you're not going to reduce the number of samples using PCA, but you could reduce the number of channels in the audio. But you could do that without PCA just by averaging the samples on each channel. So unless you're trying to convert stereo audio into mono, I think you need a different approach to your problem.

You overwrite the data array with the result of the method getPCATransformedDataAsDoubleArray. I assume, this is an array with 20 entries because of the constructor arg. I don't know, why all values are zero, i think, because it's defined in the class PCA.