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// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_LAPACk_GEEV_Hh_
#define DLIB_LAPACk_GEEV_Hh_
#include "fortran_id.h"
#include "../matrix.h"
namespace dlib
{
namespace lapack
{
namespace binding
{
extern "C"
{
void DLIB_FORTRAN_ID(dgeev) (char *jobvl, char *jobvr, integer *n, double * a,
integer *lda, double *wr, double *wi, double *vl,
integer *ldvl, double *vr, integer *ldvr, double *work,
integer *lwork, integer *info);
void DLIB_FORTRAN_ID(sgeev) (char *jobvl, char *jobvr, integer *n, float * a,
integer *lda, float *wr, float *wi, float *vl,
integer *ldvl, float *vr, integer *ldvr, float *work,
integer *lwork, integer *info);
}
inline int geev (char jobvl, char jobvr, integer n, double *a,
integer lda, double *wr, double *wi, double *vl,
integer ldvl, double *vr, integer ldvr, double *work,
integer lwork)
{
integer info = 0;
DLIB_FORTRAN_ID(dgeev)(&jobvl, &jobvr, &n, a,
&lda, wr, wi, vl,
&ldvl, vr, &ldvr, work,
&lwork, &info);
return info;
}
inline int geev (char jobvl, char jobvr, integer n, float *a,
integer lda, float *wr, float *wi, float *vl,
integer ldvl, float *vr, integer ldvr, float *work,
integer lwork)
{
integer info = 0;
DLIB_FORTRAN_ID(sgeev)(&jobvl, &jobvr, &n, a,
&lda, wr, wi, vl,
&ldvl, vr, &ldvr, work,
&lwork, &info);
return info;
}
}
// ------------------------------------------------------------------------------------
/* -- LAPACK driver routine (version 3.1) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DGEEV computes for an N-by-N real 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)**H * A = lambda(j) * u(j)**H */
/* where u(j)**H denotes the conjugate transpose of u(j). */
/* The computed eigenvectors are normalized to have Euclidean norm */
/* equal to 1 and largest component real. */
/* Arguments */
/* ========= */
/* JOBVL (input) CHARACTER*1 */
/* = 'N': left eigenvectors of A are not computed; */
/* = 'V': left eigenvectors of A are computed. */
/* JOBVR (input) CHARACTER*1 */
/* = 'N': right eigenvectors of A are not computed; */
/* = 'V': right eigenvectors of A are computed. */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the N-by-N matrix A. */
/* On exit, A has been overwritten. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,N). */
/* WR (output) DOUBLE PRECISION array, dimension (N) */
/* WI (output) DOUBLE PRECISION 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) 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 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) INTEGER */
/* The leading dimension of the array VL. LDVL >= 1; 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 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) INTEGER */
/* The leading dimension of the array VR. LDVR >= 1; 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(1,3*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) INTEGER */
/* = 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. */
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2, long NR3, long NR4, long NR5,
long NC1, long NC2, long NC3, long NC4, long NC5,
typename MM,
typename layout
>
int geev (
const char jobvl,
const char jobvr,
matrix<T,NR1,NC1,MM,column_major_layout>& a,
matrix<T,NR2,NC2,MM,layout>& wr,
matrix<T,NR3,NC3,MM,layout>& wi,
matrix<T,NR4,NC4,MM,column_major_layout>& vl,
matrix<T,NR5,NC5,MM,column_major_layout>& vr
)
{
matrix<T,0,1,MM,column_major_layout> work;
const long n = a.nr();
wr.set_size(n,1);
wi.set_size(n,1);
if (jobvl == 'V')
vl.set_size(n,n);
else
vl.set_size(NR4?NR4:1, NC4?NC4:1);
if (jobvr == 'V')
vr.set_size(n,n);
else
vr.set_size(NR5?NR5:1, NC5?NC5:1);
// figure out how big the workspace needs to be.
T work_size = 1;
int info = binding::geev(jobvl, jobvr, n, &a(0,0),
a.nr(), &wr(0,0), &wi(0,0), &vl(0,0),
vl.nr(), &vr(0,0), vr.nr(), &work_size,
-1);
if (info != 0)
return info;
if (work.size() < work_size)
work.set_size(static_cast<long>(work_size), 1);
// compute the actual decomposition
info = binding::geev(jobvl, jobvr, n, &a(0,0),
a.nr(), &wr(0,0), &wi(0,0), &vl(0,0),
vl.nr(), &vr(0,0), vr.nr(), &work(0,0),
work.size());
return info;
}
// ------------------------------------------------------------------------------------
}
}
// ----------------------------------------------------------------------------------------
#endif // DLIB_LAPACk_GEEV_Hh_
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