2021-02-01 13:31:45 +01:00
/* ******************************************************************************
*
2020-05-14 17:06:13 +02:00
*
* 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.
*
2021-02-01 13:31:45 +01:00
* See the NOTICE file distributed with this work for additional
* information regarding copyright ownership .
2020-05-14 17:06:13 +02:00
* 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
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * */
//
// @author Yurii Shyrma (iuriish@yahoo.com)
//
# ifndef LIBND4J_EIGENVALSANDVECS_H
# define LIBND4J_EIGENVALSANDVECS_H
# include <array/NDArray.h>
namespace sd {
namespace ops {
namespace helpers {
// this class calculates eigenvalues and eigenvectors of given input matrix
template < typename T >
class EigenValsAndVecs {
public :
// suppose we got input square NxN matrix
NDArray _Vals ; // {N,2} matrix of eigenvalues, 2 means real and imaginary part
NDArray _Vecs ; // {N,N,2} matrix, whose columns are the eigenvectors (complex), 2 means real and imaginary part
explicit EigenValsAndVecs ( const NDArray & matrix ) ;
//////////////////////////////////////////////////////////////////////////
FORCEINLINE static void divideComplexNums ( const T & a1 , const T & b1 , const T & a2 , const T & b2 , T & a3 , T & b3 ) {
T norm2 = a2 * a2 + b2 * b2 ;
a3 = ( a1 * a2 + b1 * b2 ) / norm2 ;
b3 = ( a2 * b1 - a1 * b2 ) / norm2 ;
}
//////////////////////////////////////////////////////////////////////////
FORCEINLINE static void multiplyComplexNums ( const T & a1 , const T & b1 , const T & a2 , const T & b2 , T & a3 , T & b3 ) {
a3 = ( a1 * a2 - b1 * b2 ) ;
b3 = ( a1 * b2 + b1 * a2 ) ;
}
//////////////////////////////////////////////////////////////////////////
FORCEINLINE static void sqrtComplexNum ( T & a , T & b ) {
T norm = math : : nd4j_sqrt < T , T > ( a * a + b * b ) ;
if ( b < ( T ) 0 )
b = - math : : nd4j_sqrt < T , T > ( ( T ) 0.5 * ( norm - a ) ) ;
else
b = math : : nd4j_sqrt < T , T > ( ( T ) 0.5 * ( norm - a ) ) ;
a = math : : nd4j_sqrt < T , T > ( ( T ) 0.5 * ( norm + a ) ) ;
}
private :
void calcEigenVals ( const NDArray & schurMatrixT ) ; // calculates _Vals
void calcPseudoEigenVecs ( NDArray & schurMatrixT , NDArray & schurMatrixU ) ; // makes changes both in schurMatrixT(NxN) and schurMatrixU(NxN), also calculates and stores pseudo-eigenvectors (real) in schurMatrixU columns
void calcEigenVecs ( const NDArray & schurMatrixU ) ; // calculates _Vecs
} ;
}
}
}
# endif //LIBND4J_EIGENVALSANDVECS_H
