// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_LAPACk_SVD_Hh_
#define DLIB_LAPACk_SVD_Hh_
#include "fortran_id.h"
#include "../matrix.h"
namespace dlib
{
namespace lapack
{
namespace binding
{
extern "C"
{
void DLIB_FORTRAN_ID(dgesvd) (const char* jobu, const char* jobvt,
const integer* m, const integer* n, double* a, const integer* lda,
double* s, double* u, const integer* ldu,
double* vt, const integer* ldvt,
double* work, const integer* lwork, integer* info);
void DLIB_FORTRAN_ID(sgesvd) (const char* jobu, const char* jobvt,
const integer* m, const integer* n, float* a, const integer* lda,
float* s, float* u, const integer* ldu,
float* vt, const integer* ldvt,
float* work, const integer* lwork, integer* info);
}
inline integer gesvd (const char jobu, const char jobvt,
const integer m, const integer n, double* a, const integer lda,
double* s, double* u, const integer ldu,
double* vt, const integer ldvt,
double* work, const integer lwork)
{
integer info = 0;
DLIB_FORTRAN_ID(dgesvd)(&jobu, &jobvt, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, &info);
return info;
}
inline integer gesvd (const char jobu, const char jobvt,
const integer m, const integer n, float* a, const integer lda,
float* s, float* u, const integer ldu,
float* vt, const integer ldvt,
float* work, const integer lwork)
{
integer info = 0;
DLIB_FORTRAN_ID(sgesvd)(&jobu, &jobvt, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, 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 */
/* ======= */
/* DGESVD computes the singular value decomposition (SVD) of a real */
/* M-by-N matrix A, optionally computing the left and/or right singular */
/* vectors. The SVD is written */
/* A = U * SIGMA * transpose(V) */
/* where SIGMA is an M-by-N matrix which is zero except for its */
/* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
/* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
/* are the singular values of A; they are real and non-negative, and */
/* are returned in descending order. The first min(m,n) columns of */
/* U and V are the left and right singular vectors of A. */
/* Note that the routine returns V**T, not V. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* Specifies options for computing all or part of the matrix U: */
/* = 'A': all M columns of U are returned in array U: */
/* = 'S': the first min(m,n) columns of U (the left singular */
/* vectors) are returned in the array U; */
/* = 'O': the first min(m,n) columns of U (the left singular */
/* vectors) are overwritten on the array A; */
/* = 'N': no columns of U (no left singular vectors) are */
/* computed. */
/* JOBVT (input) CHARACTER*1 */
/* Specifies options for computing all or part of the matrix */
/* V**T: */
/* = 'A': all N rows of V**T are returned in the array VT; */
/* = 'S': the first min(m,n) rows of V**T (the right singular */
/* vectors) are returned in the array VT; */
/* = 'O': the first min(m,n) rows of V**T (the right singular */
/* vectors) are overwritten on the array A; */
/* = 'N': no rows of V**T (no right singular vectors) are */
/* computed. */
/* JOBVT and JOBU cannot both be 'O'. */
/* M (input) INTEGER */
/* The number of rows of the input matrix A. M >= 0. */
/* N (input) INTEGER */
/* The number of columns of the input matrix A. N >= 0. */
/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, */
/* if JOBU = 'O', A is overwritten with the first min(m,n) */
/* columns of U (the left singular vectors, */
/* stored columnwise); */
/* if JOBVT = 'O', A is overwritten with the first min(m,n) */
/* rows of V**T (the right singular vectors, */
/* stored rowwise); */
/* if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A */
/* are destroyed. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* S (output) DOUBLE PRECISION array, dimension (min(M,N)) */
/* The singular values of A, sorted so that S(i) >= S(i+1). */
/* U (output) DOUBLE PRECISION array, dimension (LDU,UCOL) */
/* (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'. */
/* If JOBU = 'A', U contains the M-by-M orthogonal matrix U; */
/* if JOBU = 'S', U contains the first min(m,n) columns of U */
/* (the left singular vectors, stored columnwise); */
/* if JOBU = 'N' or 'O', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= 1; if */
/* JOBU = 'S' or 'A', LDU >= M. */
/* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) */
/* If JOBVT = 'A', VT contains the N-by-N orthogonal matrix */
/* V**T; */
/* if JOBVT = 'S', VT contains the first min(m,n) rows of */
/* V**T (the right singular vectors, stored rowwise); */
/* if JOBVT = 'N' or 'O', VT is not referenced. */
/* LDVT (input) INTEGER */
/* The leading dimension of the array VT. LDVT >= 1; if */
/* JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N). */
/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
/* if INFO > 0, WORK(2:MIN(M,N)) contains the unconverged */
/* superdiagonal elements of an upper bidiagonal matrix B */
/* whose diagonal is in S (not necessarily sorted). B */
/* satisfies A = U * B * VT, so it has the same singular values */
/* as A, and singular vectors related by U and VT. */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. */
/* LWORK >= MAX(1,3*MIN(M,N)+MAX(M,N),5*MIN(M,N)). */
/* For good performance, LWORK should 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 DBDSQR did not converge, INFO specifies how many */
/* superdiagonals of an intermediate bidiagonal form B */
/* did not converge to zero. See the description of WORK */
/* above for details. */
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2, long NR3, long NR4,
long NC1, long NC2, long NC3, long NC4,
typename MM
>
int gesvd (
const char jobu,
const char jobvt,
matrix<T,NR1,NC1,MM,column_major_layout>& a,
matrix<T,NR2,NC2,MM,column_major_layout>& s,
matrix<T,NR3,NC3,MM,column_major_layout>& u,
matrix<T,NR4,NC4,MM,column_major_layout>& vt
)
{
matrix<T,0,1,MM,column_major_layout> work;
const long m = a.nr();
const long n = a.nc();
s.set_size(std::min(m,n), 1);
if (jobu == 'A')
u.set_size(m,m);
else if (jobu == 'S')
u.set_size(m, std::min(m,n));
else
u.set_size(NR3?NR3:1, NC3?NC3:1);
if (jobvt == 'A')
vt.set_size(n,n);
else if (jobvt == 'S')
vt.set_size(std::min(m,n), n);
else
vt.set_size(NR4?NR4:1, NC4?NC4:1);
if (jobu == 'O' || jobvt == 'O')
{
DLIB_CASSERT(false, "job == 'O' not supported");
}
// figure out how big the workspace needs to be.
T work_size = 1;
int info = binding::gesvd(jobu, jobvt, a.nr(), a.nc(), &a(0,0), a.nr(),
&s(0,0), &u(0,0), u.nr(), &vt(0,0), vt.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 SVD
info = binding::gesvd(jobu, jobvt, a.nr(), a.nc(), &a(0,0), a.nr(),
&s(0,0), &u(0,0), u.nr(), &vt(0,0), vt.nr(),
&work(0,0), work.size());
return info;
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2, long NR3, long NR4,
long NC1, long NC2, long NC3, long NC4,
typename MM
>
int gesvd (
char jobu,
char jobvt,
matrix<T,NR1,NC1,MM,row_major_layout>& a,
matrix<T,NR2,NC2,MM,row_major_layout>& s,
matrix<T,NR3,NC3,MM,row_major_layout>& u_,
matrix<T,NR4,NC4,MM,row_major_layout>& vt_
)
{
matrix<T,0,1,MM,row_major_layout> work;
// Row major order matrices are transposed from LAPACK's point of view.
matrix<T,NR4,NC4,MM,row_major_layout>& u = vt_;
matrix<T,NR3,NC3,MM,row_major_layout>& vt = u_;
std::swap(jobu, jobvt);
const long m = a.nc();
const long n = a.nr();
s.set_size(std::min(m,n), 1);
if (jobu == 'A')
u.set_size(m,m);
else if (jobu == 'S')
u.set_size(std::min(m,n), m);
else
u.set_size(NR4?NR4:1, NC4?NC4:1);
if (jobvt == 'A')
vt.set_size(n,n);
else if (jobvt == 'S')
vt.set_size(n, std::min(m,n));
else
vt.set_size(NR3?NR3:1, NC3?NC3:1);
if (jobu == 'O' || jobvt == 'O')
{
DLIB_CASSERT(false, "job == 'O' not supported");
}
// figure out how big the workspace needs to be.
T work_size = 1;
int info = binding::gesvd(jobu, jobvt, m, n, &a(0,0), a.nc(),
&s(0,0), &u(0,0), u.nc(), &vt(0,0), vt.nc(),
&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 SVD
info = binding::gesvd(jobu, jobvt, m, n, &a(0,0), a.nc(),
&s(0,0), &u(0,0), u.nc(), &vt(0,0), vt.nc(),
&work(0,0), work.size());
return info;
}
// ------------------------------------------------------------------------------------
}
}
// ----------------------------------------------------------------------------------------
#endif // DLIB_LAPACk_SVD_Hh_