lapack_dggev_interface.h

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/*
 * MAST: Multidisciplinary-design Adaptation and Sensitivity Toolkit
 * Copyright (C) 2013-2020  Manav Bhatia and MAST authors
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */

#ifndef __mast__lapack_dggev_interface_h__
#define __mast__lapack_dggev_interface_h__


// MAST includes
#include "base/mast_data_types.h"


extern "C" {
    
    /*
     *  =====================================================================
     *  Purpose
     *  =======
     *
     *  DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
     *  the generalized eigenvalues, and optionally, the left and/or right
     *  generalized eigenvectors.
     *
     *  A generalized eigenvalue for a pair of matrices (A,B) is a scalar
     *  lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
     *  singular. It is usually represented as the pair (alpha,beta), as
     *  there is a reasonable interpretation for beta=0, and even for both
     *  being zero.
     *
     *  The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
     *  of (A,B) satisfies
     *
     *                   A * v(j) = lambda(j) * B * v(j).
     *
     *  The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
     *  of (A,B) satisfies
     *
     *                   u(j)**H * A  = lambda(j) * u(j)**H * B .
     *
     *  where u(j)**H is the conjugate-transpose of u(j).
     *
     *
     *  Arguments
     *  =========
     *
     *  JOBVL   (input) CHARACTER*1
     *          = 'N':  do not compute the left generalized eigenvectors;
     *          = 'V':  compute the left generalized eigenvectors.
     *
     *  JOBVR   (input) CHARACTER*1
     *          = 'N':  do not compute the right generalized eigenvectors;
     *          = 'V':  compute the right generalized eigenvectors.
     *
     *  N       (input) INTEGER
     *          The order of the matrices A, B, VL, and VR.  N >= 0.
     *
     *  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)
     *          On entry, the matrix A in the pair (A,B).
     *          On exit, A has been overwritten.
     *
     *  LDA     (input) INTEGER
     *          The leading dimension of A.  LDA >= max(1,N).
     *
     *  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)
     *          On entry, the matrix B in the pair (A,B).
     *          On exit, B has been overwritten.
     *
     *  LDB     (input) INTEGER
     *          The leading dimension of B.  LDB >= max(1,N).
     *
     *  ALPHAR  (output) DOUBLE PRECISION array, dimension (N)
     *  ALPHAI  (output) DOUBLE PRECISION array, dimension (N)
     *  BETA    (output) DOUBLE PRECISION array, dimension (N)
     *          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
     *          be the generalized eigenvalues.  If ALPHAI(j) is zero, then
     *          the j-th eigenvalue is real; if positive, then the j-th and
     *          (j+1)-st eigenvalues are a complex conjugate pair, with
     *          ALPHAI(j+1) negative.
     *
     *          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
     *          may easily over- or underflow, and BETA(j) may even be zero.
     *          Thus, the user should avoid naively computing the ratio
     *          alpha/beta.  However, ALPHAR and ALPHAI will be always less
     *          than and usually comparable with norm(A) in magnitude, and
     *          BETA always less than and usually comparable with norm(B).
     *
     *  VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)
     *          If JOBVL = 'V', the left eigenvectors u(j) are stored one
     *          after another in the columns of VL, in the same order as
     *          their eigenvalues. If the j-th eigenvalue is real, then
     *          u(j) = VL(:,j), the j-th column of VL. If the j-th and
     *          (j+1)-th eigenvalues form a complex conjugate pair, then
     *          u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
     *          Each eigenvector is scaled so the largest component has
     *          abs(real part)+abs(imag. part)=1.
     *          Not referenced if JOBVL = 'N'.
     *
     *  LDVL    (input) INTEGER
     *          The leading dimension of the matrix VL. LDVL >= 1, and
     *          if JOBVL = 'V', LDVL >= N.
     *
     *  VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)
     *          If JOBVR = 'V', the right eigenvectors v(j) are stored one
     *          after another in the columns of VR, in the same order as
     *          their eigenvalues. If the j-th eigenvalue is real, then
     *          v(j) = VR(:,j), the j-th column of VR. If the j-th and
     *          (j+1)-th eigenvalues form a complex conjugate pair, then
     *          v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
     *          Each eigenvector is scaled so the largest component has
     *          abs(real part)+abs(imag. part)=1.
     *          Not referenced if JOBVR = 'N'.
     *
     *  LDVR    (input) INTEGER
     *          The leading dimension of the matrix VR. LDVR >= 1, and
     *          if JOBVR = 'V', LDVR >= N.
     *
     *  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
     *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
     *
     *  LWORK   (input) INTEGER
     *          The dimension of the array WORK.  LWORK >= max(1,8*N).
     *          For good performance, LWORK must generally be larger.
     *
     *          If LWORK = -1, then a workspace query is assumed; the routine
     *          only calculates the optimal size of the WORK array, returns
     *          this value as the first entry of the WORK array, and no error
     *          message related to LWORK is issued by XERBLA.
     *
     *  INFO    (output) INTEGER
     *          = 0:  successful exit
     *          < 0:  if INFO = -i, the i-th argument had an illegal value.
     *          = 1,...,N:
     *                The QZ iteration failed.  No eigenvectors have been
     *                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
     *                should be correct for j=INFO+1,...,N.
     *          > N:  =N+1: other than QZ iteration failed in DHGEQZ.
     *                =N+2: error return from DTGEVC.
     *
     *  =====================================================================
     */
    extern int dggev_(char*    jobvl,
                      char*    jobvr,
                      int*     n,
                      double*  a,
                      int*     lda,
                      double*  b,
                      int*     ldb,
                      double*  alpha_r,
                      double*  alpha_i,
                      double*  beta,
                      double*  vl,
                      int*     ldvl,
                      double*  vr,
                      int*     ldvr,
                      double*  work,
                      int*     lwork,
                      int*     info);
    
}


namespace MAST {
    
    
    class LAPACK_DGGEV{
        
    public:
        
        LAPACK_DGGEV():
        info_val(-1)
        { }
        
        void compute(const RealMatrixX& A,
                     const RealMatrixX& B,
                     bool computeEigenvectors = true);
        
        ComputationInfo info() const;
        
        const RealMatrixX& A() const {
            libmesh_assert(info_val == 0);
            return this->_A;
        }
        
        
        const RealMatrixX& B() const {
            libmesh_assert(info_val == 0);
            return this->_B;
        }
        
        
        const ComplexVectorX& alphas() const {
            libmesh_assert(info_val == 0);
            return this->alpha;
        }
        
        const RealVectorX& betas() const {
            libmesh_assert(info_val == 0);
            return this->beta;
        }
        
        const ComplexMatrixX& left_eigenvectors() const {
            libmesh_assert(info_val == 0);
            return this->VL;
        }
        
        const ComplexMatrixX& right_eigenvectors() const {
            libmesh_assert(info_val == 0);
            return this->VR;
        }
        
        void scale_eigenvectors_to_identity_innerproduct() {
            libmesh_assert(info_val == 0);
            
            // this product should be an identity matrix
            ComplexMatrixX r = this->VL.conjugate().transpose() * _B * this->VR;
            
            // scale the right eigenvectors by the inverse of the inner-product
            // diagonal
            Complex val;
            for (unsigned int i=0; i<_B.cols(); i++) {
                val = r(i,i);
                if (std::abs(val) > 0.)
                    this->VR.col(i) *= (1./val);
            }
        }
        
        void print_inner_product(std::ostream& out) const {
            libmesh_assert(info_val == 0);
            ComplexMatrixX r;
            r = this->VL.conjugate().transpose() * _A * this->VR;
            out << "conj(VL)' * A * VR" << std::endl
            << r << std::endl;
            
            r = this->VL.conjugate().transpose() * _B * this->VR;
            out << "conj(VL)' * B * VR" << std::endl
            << r << std::endl;
            
        }
        
    protected:
        
        RealMatrixX    _A;
        
        RealMatrixX    _B;
        
        ComplexMatrixX VL;
        
        ComplexMatrixX VR;
        
        ComplexVectorX alpha;
        
        RealVectorX    beta;
        
        int info_val;
    };
    
}

#endif // __mast__lapack_dggev_interface_h__