// Copyright (C) 2010 Davis E. King (davis@dlib.net)
// License: Boost Software License See LICENSE.txt for the full license.
#ifndef DLIB_LAPACk_SDD_Hh_
#define DLIB_LAPACk_SDD_Hh_
#include "fortran_id.h"
#include "../matrix.h"
namespace dlib
{
namespace lapack
{
namespace binding
{
extern "C"
{
void DLIB_FORTRAN_ID(dgesdd) (char const* jobz,
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* iwork, integer* info);
void DLIB_FORTRAN_ID(sgesdd) (char const* jobz,
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* iwork, integer* info);
}
inline integer gesdd (const char jobz,
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* iwork)
{
integer info = 0;
DLIB_FORTRAN_ID(dgesdd)(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &info);
return info;
}
inline integer gesdd (const char jobz,
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* iwork)
{
integer info = 0;
DLIB_FORTRAN_ID(sgesdd)(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &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 */
/* ======= */
/* DGESDD computes the singular value decomposition (SVD) of a real */
/* M-by-N matrix A, optionally computing the left and right singular */
/* vectors. If singular vectors are desired, it uses a */
/* divide-and-conquer algorithm. */
/* 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 VT = V**T, not V. */
/* The divide and conquer algorithm makes very mild assumptions about */
/* floating point arithmetic. It will work on machines with a guard */
/* digit in add/subtract, or on those binary machines without guard */
/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
/* without guard digits, but we know of none. */
/* Arguments */
/* ========= */
/* JOBZ (input) CHARACTER*1 */
/* Specifies options for computing all or part of the matrix U: */
/* = 'A': all M columns of U and all N rows of V**T are */
/* returned in the arrays U and VT; */
/* = 'S': the first min(M,N) columns of U and the first */
/* min(M,N) rows of V**T are returned in the arrays U */
/* and VT; */
/* = 'O': If M >= N, the first N columns of U are overwritten */
/* on the array A and all rows of V**T are returned in */
/* the array VT; */
/* otherwise, all columns of U are returned in the */
/* array U and the first M rows of V**T are overwritten */
/* in the array A; */
/* = 'N': no columns of U or rows of V**T are computed. */
/* 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 JOBZ = 'O', A is overwritten with the first N columns */
/* of U (the left singular vectors, stored */
/* columnwise) if M >= N; */
/* A is overwritten with the first M rows */
/* of V**T (the right singular vectors, stored */
/* rowwise) otherwise. */
/* if JOBZ .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) */
/* UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
/* UCOL = min(M,N) if JOBZ = 'S'. */
/* If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
/* orthogonal matrix U; */
/* if JOBZ = 'S', U contains the first min(M,N) columns of U */
/* (the left singular vectors, stored columnwise); */
/* if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= 1; if */
/* JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
/* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) */
/* If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
/* N-by-N orthogonal matrix V**T; */
/* if JOBZ = 'S', VT contains the first min(M,N) rows of */
/* V**T (the right singular vectors, stored rowwise); */
/* if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
/* LDVT (input) INTEGER */
/* The leading dimension of the array VT. LDVT >= 1; if */
/* JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
/* if JOBZ = '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; */
/* LWORK (input) INTEGER */
/* The dimension of the array WORK. LWORK >= 1. */
/* If JOBZ = 'N', */
/* LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)). */
/* If JOBZ = 'O', */
/* LWORK >= 3*min(M,N)*min(M,N) + */
/* max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). */
/* If JOBZ = 'S' or 'A' */
/* LWORK >= 3*min(M,N)*min(M,N) + */
/* max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)). */
/* For good performance, LWORK should generally be larger. */
/* If LWORK = -1 but other input arguments are legal, WORK(1) */
/* returns the optimal LWORK. */
/* IWORK (workspace) INTEGER array, dimension (8*min(M,N)) */
/* INFO (output) INTEGER */
/* = 0: successful exit. */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* > 0: DBDSDC did not converge, updating process failed. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Ming Gu and Huan Ren, Computer Science Division, University of */
/* California at Berkeley, USA */
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2, long NR3, long NR4,
long NC1, long NC2, long NC3, long NC4,
typename MM
>
int gesdd (
const char jobz,
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;
matrix<integer,0,1,MM,column_major_layout> iwork;
const long m = a.nr();
const long n = a.nc();
s.set_size(std::min(m,n), 1);
// make sure the iwork memory block is big enough
if (iwork.size() < 8*std::min(m,n))
iwork.set_size(8*std::min(m,n), 1);
if (jobz == 'A')
{
u.set_size(m,m);
vt.set_size(n,n);
}
else if (jobz == 'S')
{
u.set_size(m, std::min(m,n));
vt.set_size(std::min(m,n), n);
}
else if (jobz == 'O')
{
DLIB_CASSERT(false, "jobz == 'O' not supported");
}
else
{
u.set_size(NR3?NR3:1, NC3?NC3:1);
vt.set_size(NR4?NR4:1, NC4?NC4:1);
}
// figure out how big the workspace needs to be.
T work_size = 1;
int info = binding::gesdd(jobz, 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, &iwork(0,0));
if (info != 0)
return info;
// There is a bug in an older version of LAPACK in Debian etch
// that causes the gesdd to return the wrong value for work_size
// when jobz == 'N'. So verify the value of work_size.
if (jobz == 'N')
{
using std::min;
using std::max;
const T min_work_size = 3*min(m,n) + max(max(m,n),7*min(m,n));
if (work_size < min_work_size)
work_size = min_work_size;
}
if (work.size() < work_size)
work.set_size(static_cast<long>(work_size), 1);
// compute the actual SVD
info = binding::gesdd(jobz, 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(), &iwork(0,0));
return info;
}
// ------------------------------------------------------------------------------------
template <
typename T,
long NR1, long NR2, long NR3, long NR4,
long NC1, long NC2, long NC3, long NC4,
typename MM
>
int gesdd (
const char jobz,
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;
matrix<integer,0,1,MM,row_major_layout> iwork;
// 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_;
const long m = a.nc();
const long n = a.nr();
s.set_size(std::min(m,n), 1);
// make sure the iwork memory block is big enough
if (iwork.size() < 8*std::min(m,n))
iwork.set_size(8*std::min(m,n), 1);
if (jobz == 'A')
{
u.set_size(m,m);
vt.set_size(n,n);
}
else if (jobz == 'S')
{
u.set_size(std::min(m,n), m);
vt.set_size(n, std::min(m,n));
}
else if (jobz == 'O')
{
DLIB_CASSERT(false, "jobz == 'O' not supported");
}
else
{
u.set_size(NR4?NR4:1, NC4?NC4:1);
vt.set_size(NR3?NR3:1, NC3?NC3:1);
}
// figure out how big the workspace needs to be.
T work_size = 1;
int info = binding::gesdd(jobz, m, n, &a(0,0), a.nc(),
&s(0,0), &u(0,0), u.nc(), &vt(0,0), vt.nc(),
&work_size, -1, &iwork(0,0));
if (info != 0)
return info;
// There is a bug in an older version of LAPACK in Debian etch
// that causes the gesdd to return the wrong value for work_size
// when jobz == 'N'. So verify the value of work_size.
if (jobz == 'N')
{
using std::min;
using std::max;
const T min_work_size = 3*min(m,n) + max(max(m,n),7*min(m,n));
if (work_size < min_work_size)
work_size = min_work_size;
}
if (work.size() < work_size)
work.set_size(static_cast<long>(work_size), 1);
// compute the actual SVD
info = binding::gesdd(jobz, 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(), &iwork(0,0));
return info;
}
// ------------------------------------------------------------------------------------
}
}
// ----------------------------------------------------------------------------------------
#endif // DLIB_LAPACk_SDD_Hh_