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// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
// vi: set et ts=4 sw=2 sts=2:
// SPDX-FileCopyrightInfo: Copyright © DUNE Project contributors, see file LICENSE.md in module root
// SPDX-License-Identifier: LicenseRef-GPL-2.0-only-with-DUNE-exception
#ifndef DUNE_FMATRIXEIGENVALUES_CC
#define DUNE_FMATRIXEIGENVALUES_CC
#include <iostream>
#include <cmath>
#include <cassert>
#include <dune-common-config.hh> // HAVE_LAPACK, LAPACK_NEEDS_UNDERLINE
#include <dune/common/exceptions.hh>
#include <dune/common/fmatrixev.hh>
#if HAVE_LAPACK
#ifdef LAPACK_NEEDS_UNDERLINE
#define LAPACK_MANGLE(name,NAME) name##_
#else
#define LAPACK_MANGLE(name,NAME) name
#endif
#define FC_FUNC LAPACK_MANGLE
// symmetric matrices
#define DSYEV_FORTRAN FC_FUNC (dsyev, DSYEV)
#define SSYEV_FORTRAN FC_FUNC (ssyev, SSYEV)
// nonsymmetric matrices
#define DGEEV_FORTRAN FC_FUNC (dgeev, DGEEV)
#define SGEEV_FORTRAN FC_FUNC (sgeev, SGEEV)
// dsyev declaration (in liblapack)
extern "C" {
/*
*
** purpose
** =======
**
** xsyev computes all eigenvalues and, optionally, eigenvectors of a
** BASE DATA TYPE symmetric matrix a.
**
** arguments
** =========
**
** jobz (input) char
** = 'n': compute eigenvalues only;
** = 'v': compute eigenvalues and eigenvectors.
**
** uplo (input) char
** = 'u': upper triangle of a is stored;
** = 'l': lower triangle of a is stored.
**
** n (input) long int
** the order of the matrix a. n >= 0.
**
** a (input/output) BASE DATA TYPE array, dimension (lda, n)
** on entry, the symmetric matrix a. if uplo = 'u', the
** leading n-by-n upper triangular part of a contains the
** upper triangular part of the matrix a. if uplo = 'l',
** the leading n-by-n lower triangular part of a contains
** the lower triangular part of the matrix a.
** on exit, if jobz = 'v', then if info = 0, a contains the
** orthonormal eigenvectors of the matrix a.
** if jobz = 'n', then on exit the lower triangle (if uplo='l')
** or the upper triangle (if uplo='u') of a, including the
** diagonal, is destroyed.
**
** lda (input) long int
** the leading dimension of the array a. lda >= max(1,n).
**
** w (output) BASE DATA TYPE array, dimension (n)
** if info = 0, the eigenvalues in ascending order.
**
** 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 length of the array WORK. LWORK >= max(1,3*N-1).
** For optimal efficiency, LWORK >= (NB+2)*N,
** where NB is the blocksize for DSYTRD returned by ILAENV.
**
** 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) long int
** = 0: successful exit
** < 0: if info = -i, the i-th argument had an illegal value
** > 0: if info = i, the algorithm failed to converge; i
** off-diagonal elements of an intermediate tridiagonal
** form did not converge to zero.
**
**/
extern void DSYEV_FORTRAN(const char* jobz, const char* uplo, const long
int* n, double* a, const long int* lda, double* w,
double* work, const long int* lwork, long int* info);
extern void SSYEV_FORTRAN(const char* jobz, const char* uplo, const long
int* n, float* a, const long int* lda, float* w,
float* work, const long int* lwork, long int* info);
/*
*
** purpose
** =======
**
** xgeev computes for an N-by-N BASE DATA TYPE nonsymmetric matrix A, the
** eigenvalues and, optionally, the left and/or right eigenvectors.
**
** The right eigenvector v(j) of A satisfies
** A * v(j) = lambda(j) * v(j)
** where lambda(j) is its eigenvalue.
** The left eigenvector u(j) of A satisfies
** u(j)**T * A = lambda(j) * u(j)**T
** where u(j)**T denotes the transpose of u(j).
**
** The computed eigenvectors are normalized to have Euclidean norm
** equal to 1 and largest component real.
**
** arguments
** =========
**
** jobvl (input) char
** = 'n': left eigenvectors of a are not computed;
** = 'v': left eigenvectors of a are computed.
**
** jobvr (input) char
** = 'n': right eigenvectors of a are not computed;
** = 'v': right eigenvectors of a are computed.
**
** n (input) long int
** the order of the matrix v. v >= 0.
**
** a (input/output) BASE DATA TYPE array, dimension (lda,n)
** on entry, the n-by-n matrix a.
** on exit, a has been overwritten.
**
** lda (input) long int
** the leading dimension of the array a. lda >= max(1,n).
**
** wr (output) BASE DATA TYPE array, dimension (n)
** wi (output) BASE DATA TYPE array, dimension (n)
** wr and wi contain the real and imaginary parts,
** respectively, of the computed eigenvalues. complex
** conjugate pairs of eigenvalues appear consecutively
** with the eigenvalue having the positive imaginary part
** first.
**
** vl (output) COMPLEX DATA TYPE 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 jobvl = 'n', vl is not referenced.
** 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)-st 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).
**
** ldvl (input) long int
** the leading dimension of the array vl. ldvl >= 1; if
** jobvl = 'v', ldvl >= n.
**
** vr (output) COMPLEX DATA TYPE 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 jobvr = 'n', vr is not referenced.
** 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)-st 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).
**
** ldvr (input) long int
** the leading dimension of the array vr. ldvr >= 1; if
** jobvr = 'v', ldvr >= n.
**
** work (workspace/output) BASE DATA TYPE array, dimension (max(1,lwork))
** on exit, if info = 0, work(1) returns the optimal lwork.
**
** lwork (input) long int
** the dimension of the array work. lwork >= max(1,3*n), and
** if jobvl = 'v' or jobvr = 'v', lwork >= 4*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) long int
** = 0: successful exit
** < 0: if info = -i, the i-th argument had an illegal value.
** > 0: if info = i, the qr algorithm failed to compute all the
** eigenvalues, and no eigenvectors have been computed;
** elements i+1:n of wr and wi contain eigenvalues which
** have converged.
**
**/
extern void DGEEV_FORTRAN(const char* jobvl, const char* jobvr, const long
int* n, double* a, const long int* lda, double* wr, double* wi, double* vl,
const long int* ldvl, double* vr, const long int* ldvr, double* work,
const long int* lwork, long int* info);
extern void SGEEV_FORTRAN(const char* jobvl, const char* jobvr, const long
int* n, float* a, const long int* lda, float* wr, float* wi, float* vl,
const long int* ldvl, float* vr, const long int* ldvr, float* work,
const long int* lwork, long int* info);
} // end extern C
namespace Dune {
namespace FMatrixHelp {
void eigenValuesLapackCall(
const char* jobz, const char* uplo, const long
int* n, double* a, const long int* lda, double* w,
double* work, const long int* lwork, long int* info)
{
// call LAPACK dsyev
DSYEV_FORTRAN(jobz, uplo, n, a, lda, w, work, lwork, info);
}
void eigenValuesLapackCall(
const char* jobz, const char* uplo, const long
int* n, float* a, const long int* lda, float* w,
float* work, const long int* lwork, long int* info)
{
// call LAPACK dsyev
SSYEV_FORTRAN(jobz, uplo, n, a, lda, w, work, lwork, info);
}
void eigenValuesNonsymLapackCall(
const char* jobvl, const char* jobvr, const long
int* n, double* a, const long int* lda, double* wr, double* wi, double* vl,
const long int* ldvl, double* vr, const long int* ldvr, double* work,
const long int* lwork, long int* info)
{
// call LAPACK dgeev
DGEEV_FORTRAN(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr,
work, lwork, info);
}
void eigenValuesNonsymLapackCall(
const char* jobvl, const char* jobvr, const long
int* n, float* a, const long int* lda, float* wr, float* wi, float* vl,
const long int* ldvl, float* vr, const long int* ldvr, float* work,
const long int* lwork, long int* info)
{
// call LAPACK dgeev
SGEEV_FORTRAN(jobvl, jobvr, n, a, lda, wr, wi, vl, ldvl, vr, ldvr,
work, lwork, info);
}
} // end namespace FMatrixHelp
} // end namespace Dune
#endif // #if HAVE_LAPACK
#endif // #ifndef DUNE_FMATRIXEIGENVALUES_CC
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