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package org.nd4j.linalg.eigen;
import org.nd4j.linalg.api.complex.IComplexNDArray;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.factory.Nd4j;
/**
* Compute eigen values
*
* @author Adam Gibson
*/
public class Eigen {
public static INDArray dummy = Nd4j.scalar(1);
/**
* Computes the eigenvalues of a general matrix.
*/
public static IComplexNDArray eigenvalues(INDArray A) {
assert A.rows() == A.columns();
INDArray WR = Nd4j.create(A.rows(),A.rows());
INDArray WI = WR.dup();
Nd4j.getBlasWrapper().geev(
'N',
'N',
A.dup(),
WR,
WI,
dummy,
dummy);
return Nd4j.createComplex(WR, WI);
}
/**
* Compute generalized eigenvalues of the problem A x = L B x.
*
* @param A symmetric Matrix A. Only the upper triangle will be considered.
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A) {
INDArray eigenvalues = Nd4j.create(A.rows());
int isuppz[] = new int[2 * A.rows()];
Nd4j.getBlasWrapper().syevr(
'N',
'A',
'U',
A.dup(),
0,
0,
0,
0,
0,
eigenvalues,
Nd4j.ones(1),
isuppz);
return eigenvalues;
}
/**
* Computes the eigenvalues and eigenvectors of a general matrix.
*
* For matlab users note the following from their documentation:
* The columns of V present eigenvectors of A. The diagonal matrix D contains eigenvalues.
*
* This is in reverse order of the matlab eig(A) call.
*
* @param A the ndarray to getFloat the eigen vectors for
* @return 2 arrays representing W (eigen vectors) and V (normalized eigen vectors)
*/
public static IComplexNDArray[] eigenvectors(INDArray A) {
assert A.columns() == A.rows();
// setting up result arrays
INDArray WR = Nd4j.create(A.rows());
INDArray WI = WR.dup();
INDArray VR = Nd4j.create(A.rows(), A.rows());
INDArray VL = Nd4j.create(A.rows(),A.rows());
Nd4j.getBlasWrapper().geev(
'v',
'v',
A.dup(),
WR,
WI,
VL,
VR);
// transferring the result
IComplexNDArray E = Nd4j.createComplex(WR, WI);
IComplexNDArray V = Nd4j.createComplex(A.rows(), A.rows());
for (int i = 0; i < A.rows(); i++) {
if (E.getComplex(i).isReal()) {
IComplexNDArray column = Nd4j.createComplex(VR.getColumn(i));
V.putColumn(i,column);
}
else {
IComplexNDArray v = Nd4j.createComplex(VR.getColumn(i), VR.getColumn(i + 1));
V.putColumn(i, v);
V.putColumn(i + 1, v.conji());
i += 1;
}
}
return new IComplexNDArray[]{ Nd4j.diag(E),V};
}
/**
* Compute generalized eigenvalues of the problem A x = L B x.
*
* @param A symmetric Matrix A. Only the upper triangle will be considered.
* @param B symmetric Matrix B. Only the upper triangle will be considered.
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A, INDArray B) {
assert A.rows() == A.columns();
assert B.rows() == B.columns();
INDArray W = Nd4j.create(A.rows());
Nd4j.getBlasWrapper().sygvd(1, 'N', 'U', A.dup(), B.dup(), W);
return W;
}
}
