Examples of EigenDecomposition

org.apache.commons.math.linear.EigenDecomposition
nist.gov/javanumerics/jama/">JAMA library, with the following changes:
- a {@link #getVT() getVt} method has been added,
- two {@link #getRealEigenvalue(int) getRealEigenvalue} and {@link #getImagEigenvalue(int) getImagEigenvalue} methods to pick up a single eigenvalue have been added,
- a {@link #getEigenvector(int) getEigenvector} method to pick up a singleeigenvector has been added,
- a {@link #getDeterminant() getDeterminant} method has been added.
- a {@link #getSolver() getSolver} method has been added.
@see MathWorld @see Wikipedia @version $Revision: 997726 $ $Date: 2010-09-16 14:39:51 +0200 (jeu. 16 sept. 2010) $ @since 2.0
org.apache.commons.math3.linear.EigenDecomposition
nist.gov/javanumerics/jama/">JAMA library, with the following changes:
- a {@link #getVT() getVt} method has been added,
- two {@link #getRealEigenvalue(int) getRealEigenvalue} and {@link #getImagEigenvalue(int) getImagEigenvalue} methods to pick up a single eigenvalue have been added,
- a {@link #getEigenvector(int) getEigenvector} method to pick up a singleeigenvector has been added,
- a {@link #getDeterminant() getDeterminant} method has been added.
- a {@link #getSolver() getSolver} method has been added.
As of 3.1, this class supports general real matrices (both symmetric and non-symmetric):

If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal, i.e. A = V.multiply(D.multiply(V.transpose())) and V.multiply(V.transpose()) equals the identity matrix.

If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks:
```
 [lambda, mu    ] [   -mu, lambda] 
```
The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.multiply(V) equals V.multiply(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon the condition of V.

This implementation is based on the paper by A. Drubrulle, R.S. Martin and J.H. Wilkinson "The Implicit QL Algorithm" in Wilksinson and Reinsch (1971) Handbook for automatic computation, vol. 2, Linear algebra, Springer-Verlag, New-York
@see MathWorld @see Wikipedia @since 2.0 (changed to concrete class in 3.0)
org.apache.mahout.math.solver.EigenDecomposition
Eigenvalues and eigenvectors of a real matrix.
If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is diagonal and the eigenvector matrix V is orthogonal. I.e. A = V.times(D.times(V.transpose())) and V.times(V.transpose()) equals the identity matrix.
If A is not symmetric, then the eigenvalue matrix D is block diagonal with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues, lambda + i*mu, in 2-by-2 blocks, [lambda, mu; -mu, lambda]. The columns of V represent the eigenvectors in the sense that A*V = V*D, i.e. A.times(V) equals V.times(D). The matrix V may be badly conditioned, or even singular, so the validity of the equation A = V*D*inverse(V) depends upon V.cond().
org.ejml.factory.EigenDecomposition

This is a generic interface for computing the eigenvalues and eigenvectors of a matrix. Eigenvalues and eigenvectors have the following property:

A*v=λ*v

where A is a square matrix and v is an eigenvector associated with the eigenvalue λ.

In general, both eigenvalues and eigenvectors can be complex numbers. For symmetric matrices the eigenvalues and eigenvectors are always real numbers. EJML does not support complex matrices but it does have minimal support for complex numbers. As a result complex eigenvalues are found, but only the real eigenvectors are computed.

To create a new instance of {@link EigenDecomposition} use {@link DecompositionFactory}. If the matrix is known to be symmetric be sure to use the symmetric decomposition, which is much faster and more accurate than the general purpose one.
@author Peter Abeles

Examples of org.apache.commons.math3.linear.EigenDecomposition

        this.means = MathArrays.copyOf(means);


        covarianceMatrix = new Array2DRowRealMatrix(covariances);


        // Covariance matrix eigen decomposition.
        final EigenDecomposition covMatDec = new EigenDecomposition(covarianceMatrix);


        // Compute and store the inverse.
        covarianceMatrixInverse = covMatDec.getSolver().getInverse();
        // Compute and store the determinant.
        covarianceMatrixDeterminant = covMatDec.getDeterminant();


        // Eigenvalues of the covariance matrix.
        final double[] covMatEigenvalues = covMatDec.getRealEigenvalues();


        for (int i = 0; i < covMatEigenvalues.length; i++) {
            if (covMatEigenvalues[i] < 0) {
                throw new NonPositiveDefiniteMatrixException(covMatEigenvalues[i], i, 0);
            }
        }


        // Matrix where each column is an eigenvector of the covariance matrix.
        final Array2DRowRealMatrix covMatEigenvectors = new Array2DRowRealMatrix(dim, dim);
        for (int v = 0; v < dim; v++) {
            final double[] evec = covMatDec.getEigenvector(v).toArray();
            covMatEigenvectors.setColumn(v, evec);
        }


        final RealMatrix tmpMatrix = covMatEigenvectors.transpose();

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Examples of org.apache.commons.math3.linear.EigenDecomposition

            for (int i = 0; i < dim; i++) {
               sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();
        }
    }

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Examples of org.apache.commons.math3.linear.EigenDecomposition

        if (ccov1 + ccovmu + negccov > 0 &&
            (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1) {
            // to achieve O(N^2)
            C = triu(C, 0).add(triu(C, 1).transpose());
            // enforce symmetry to prevent complex numbers
            final EigenDecomposition eig = new EigenDecomposition(C);
            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
            D = eig.getD();
            diagD = diag(D);
            if (min(diagD) <= 0) {
                for (int i = 0; i < dimension; i++) {
                    if (diagD.getEntry(i, 0) < 0) {
                        diagD.setEntry(i, 0, 0);

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Examples of org.apache.commons.math3.linear.EigenDecomposition

        if (ccov1 + ccovmu + negccov > 0 &&
            (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1) {
            // to achieve O(N^2)
            C = triu(C, 0).add(triu(C, 1).transpose());
            // enforce symmetry to prevent complex numbers
            final EigenDecomposition eig = new EigenDecomposition(C);
            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
            D = eig.getD();
            diagD = diag(D);
            if (min(diagD) <= 0) {
                for (int i = 0; i < dimension; i++) {
                    if (diagD.getEntry(i, 0) < 0) {
                        diagD.setEntry(i, 0, 0);

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Examples of org.apache.commons.math3.linear.EigenDecomposition

        if (ccov1 + ccovmu + negccov > 0 &&
                (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1.) {
            // to achieve O(N^2)
            C = triu(C, 0).add(triu(C, 1).transpose());
            // enforce symmetry to prevent complex numbers
            EigenDecomposition eig = new EigenDecomposition(C, 1.0);
            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
            D = eig.getD();
            diagD = diag(D);
            if (min(diagD) <= 0) {
                for (int i = 0; i < dimension; i++) {
                    if (diagD.getEntry(i, 0) < 0) {
                        diagD.setEntry(i, 0, 0.);

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Examples of org.apache.commons.math3.linear.EigenDecomposition

        if (ccov1 + ccovmu + negccov > 0 &&
            (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1) {
            // to achieve O(N^2)
            C = triu(C, 0).add(triu(C, 1).transpose());
            // enforce symmetry to prevent complex numbers
            final EigenDecomposition eig = new EigenDecomposition(C);
            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
            D = eig.getD();
            diagD = diag(D);
            if (min(diagD) <= 0) {
                for (int i = 0; i < dimension; i++) {
                    if (diagD.getEntry(i, 0) < 0) {
                        diagD.setEntry(i, 0, 0);

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Examples of org.apache.commons.math3.linear.EigenDecomposition

            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();
        }
    }

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Examples of org.apache.commons.math3.linear.EigenDecomposition

        if (ccov1 + ccovmu + negccov > 0 &&
            (iterations % 1. / (ccov1 + ccovmu + negccov) / dimension / 10.) < 1) {
            // to achieve O(N^2)
            C = triu(C, 0).add(triu(C, 1).transpose());
            // enforce symmetry to prevent complex numbers
            final EigenDecomposition eig = new EigenDecomposition(C);
            B = eig.getV(); // eigen decomposition, B==normalized eigenvectors
            D = eig.getD();
            diagD = diag(D);
            if (min(diagD) <= 0) {
                for (int i = 0; i < dimension; i++) {
                    if (diagD.getEntry(i, 0) < 0) {
                        diagD.setEntry(i, 0, 0);

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Examples of org.apache.commons.math3.linear.EigenDecomposition

            for (int i = 0; i < dim; i++) {
                sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();
        }
    }

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Examples of org.apache.commons.math3.linear.EigenDecomposition

            for (int i = 0; i < dim; i++) {
               sqrtM.setEntry(i, i, FastMath.sqrt(m.getEntry(i, i)));
            }
            return sqrtM;
        } else {
            final EigenDecomposition dec = new EigenDecomposition(m);
            return dec.getSquareRoot();
        }
    }

View Full Code Here

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