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/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://www.apache.org/licenses/LICENSE-2.0.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
package org.nd4j.linalg.eigen;
import org.nd4j.common.base.Preconditions;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.factory.Nd4j;
import org.nd4j.linalg.inverse.InvertMatrix;
/**
* Compute eigen values
*
* @author Adam Gibson
*/
public class Eigen {
public static INDArray dummy = Nd4j.scalar(1);
/**
* Compute generalized eigenvalues of the problem A x = L x.
* Matrix A is modified in the process, holding eigenvectors after execution.
*
* @param A symmetric Matrix A. After execution, A will contain the eigenvectors as columns
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A) {
INDArray eigenvalues = Nd4j.create(A.dataType(), A.rows());
Nd4j.getBlasWrapper().syev('V', 'L', A, eigenvalues);
return eigenvalues;
}
/**
* Compute generalized eigenvalues of the problem A x = L x.
* Matrix A is modified in the process, holding eigenvectors as columns after execution.
*
* @param A symmetric Matrix A. After execution, A will contain the eigenvectors as columns
* @param calculateVectors if false, it will not modify A and calculate eigenvectors
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A, boolean calculateVectors) {
INDArray eigenvalues = Nd4j.create(A.dataType(), A.rows());
Nd4j.getBlasWrapper().syev('V', 'L', (calculateVectors ? A : A.dup()), eigenvalues);
return eigenvalues;
}
/**
* Compute generalized eigenvalues of the problem A x = L B x.
* The data will be unchanged, no eigenvectors returned.
*
* @param A symmetric Matrix A.
* @param B symmetric Matrix B.
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A, INDArray B) {
Preconditions.checkArgument(A.isMatrix() && A.isSquare(), "Argument A must be a square matrix: has shape %s", A.shape());
Preconditions.checkArgument(B.isMatrix() && B.isSquare(), "Argument B must be a square matrix: has shape %s", B.shape());
INDArray W = Nd4j.create(A.rows());
A = InvertMatrix.invert(B, false).mmuli(A);
Nd4j.getBlasWrapper().syev('V', 'L', A, W);
return W;
}
/**
* Compute generalized eigenvalues of the problem A x = L B x.
* The data will be unchanged, no eigenvectors returned unless calculateVectors is true.
* If calculateVectors == true, A will contain a matrix with the eigenvectors as columns.
*
* @param A symmetric Matrix A.
* @param B symmetric Matrix B.
* @return a vector of eigenvalues L.
*/
public static INDArray symmetricGeneralizedEigenvalues(INDArray A, INDArray B, boolean calculateVectors) {
Preconditions.checkArgument(A.isMatrix() && A.isSquare(), "Argument A must be a square matrix: has shape %s", A.shape());
Preconditions.checkArgument(B.isMatrix() && B.isSquare(), "Argument B must be a square matrix: has shape %s", B.shape());
INDArray W = Nd4j.create(A.dataType(), A.rows());
if (calculateVectors)
A.assign(InvertMatrix.invert(B, false).mmuli(A));
else
A = InvertMatrix.invert(B, false).mmuli(A);
Nd4j.getBlasWrapper().syev('V', 'L', A, W);
return W;
}
}
