coco
365 lines
14 KiB
C++
365 lines
14 KiB
C++
// Copyright (C) 2010 Davis E. King (davis@dlib.net)
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// License: Boost Software License See LICENSE.txt for the full license.
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#ifndef DLIB_LAPACk_SDD_Hh_
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#define DLIB_LAPACk_SDD_Hh_
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#include "fortran_id.h"
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#include "../matrix.h"
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namespace dlib
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{
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namespace lapack
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{
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namespace binding
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{
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extern "C"
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{
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void DLIB_FORTRAN_ID(dgesdd) (char const* jobz,
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const integer* m, const integer* n, double* a, const integer* lda,
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double* s, double* u, const integer* ldu,
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double* vt, const integer* ldvt,
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double* work, const integer* lwork, integer* iwork, integer* info);
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void DLIB_FORTRAN_ID(sgesdd) (char const* jobz,
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const integer* m, const integer* n, float* a, const integer* lda,
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float* s, float* u, const integer* ldu,
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float* vt, const integer* ldvt,
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float* work, const integer* lwork, integer* iwork, integer* info);
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}
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inline integer gesdd (const char jobz,
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const integer m, const integer n, double* a, const integer lda,
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double* s, double* u, const integer ldu,
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double* vt, const integer ldvt,
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double* work, const integer lwork, integer* iwork)
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{
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integer info = 0;
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DLIB_FORTRAN_ID(dgesdd)(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &info);
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return info;
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}
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inline integer gesdd (const char jobz,
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const integer m, const integer n, float* a, const integer lda,
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float* s, float* u, const integer ldu,
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float* vt, const integer ldvt,
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float* work, const integer lwork, integer* iwork)
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{
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integer info = 0;
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DLIB_FORTRAN_ID(sgesdd)(&jobz, &m, &n, a, &lda, s, u, &ldu, vt, &ldvt, work, &lwork, iwork, &info);
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return info;
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}
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}
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// ------------------------------------------------------------------------------------
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/* -- LAPACK driver routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DGESDD computes the singular value decomposition (SVD) of a real */
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/* M-by-N matrix A, optionally computing the left and right singular */
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/* vectors. If singular vectors are desired, it uses a */
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/* divide-and-conquer algorithm. */
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/* The SVD is written */
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/* A = U * SIGMA * transpose(V) */
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/* where SIGMA is an M-by-N matrix which is zero except for its */
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/* min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and */
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/* V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA */
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/* are the singular values of A; they are real and non-negative, and */
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/* are returned in descending order. The first min(m,n) columns of */
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/* U and V are the left and right singular vectors of A. */
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/* Note that the routine returns VT = V**T, not V. */
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/* The divide and conquer algorithm makes very mild assumptions about */
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/* floating point arithmetic. It will work on machines with a guard */
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/* digit in add/subtract, or on those binary machines without guard */
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/* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */
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/* Cray-2. It could conceivably fail on hexadecimal or decimal machines */
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/* without guard digits, but we know of none. */
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/* Arguments */
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/* ========= */
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/* JOBZ (input) CHARACTER*1 */
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/* Specifies options for computing all or part of the matrix U: */
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/* = 'A': all M columns of U and all N rows of V**T are */
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/* returned in the arrays U and VT; */
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/* = 'S': the first min(M,N) columns of U and the first */
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/* min(M,N) rows of V**T are returned in the arrays U */
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/* and VT; */
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/* = 'O': If M >= N, the first N columns of U are overwritten */
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/* on the array A and all rows of V**T are returned in */
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/* the array VT; */
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/* otherwise, all columns of U are returned in the */
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/* array U and the first M rows of V**T are overwritten */
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/* in the array A; */
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/* = 'N': no columns of U or rows of V**T are computed. */
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/* M (input) INTEGER */
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/* The number of rows of the input matrix A. M >= 0. */
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/* N (input) INTEGER */
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/* The number of columns of the input matrix A. N >= 0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the M-by-N matrix A. */
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/* On exit, */
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/* if JOBZ = 'O', A is overwritten with the first N columns */
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/* of U (the left singular vectors, stored */
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/* columnwise) if M >= N; */
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/* A is overwritten with the first M rows */
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/* of V**T (the right singular vectors, stored */
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/* rowwise) otherwise. */
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/* if JOBZ .ne. 'O', the contents of A are destroyed. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,M). */
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/* S (output) DOUBLE PRECISION array, dimension (min(M,N)) */
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/* The singular values of A, sorted so that S(i) >= S(i+1). */
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/* U (output) DOUBLE PRECISION array, dimension (LDU,UCOL) */
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/* UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N; */
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/* UCOL = min(M,N) if JOBZ = 'S'. */
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/* If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M */
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/* orthogonal matrix U; */
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/* if JOBZ = 'S', U contains the first min(M,N) columns of U */
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/* (the left singular vectors, stored columnwise); */
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/* if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced. */
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/* LDU (input) INTEGER */
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/* The leading dimension of the array U. LDU >= 1; if */
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/* JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M. */
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/* VT (output) DOUBLE PRECISION array, dimension (LDVT,N) */
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/* If JOBZ = 'A' or JOBZ = 'O' and M >= N, VT contains the */
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/* N-by-N orthogonal matrix V**T; */
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/* if JOBZ = 'S', VT contains the first min(M,N) rows of */
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/* V**T (the right singular vectors, stored rowwise); */
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/* if JOBZ = 'O' and M < N, or JOBZ = 'N', VT is not referenced. */
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/* LDVT (input) INTEGER */
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/* The leading dimension of the array VT. LDVT >= 1; if */
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/* JOBZ = 'A' or JOBZ = 'O' and M >= N, LDVT >= N; */
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/* if JOBZ = 'S', LDVT >= min(M,N). */
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* On exit, if INFO = 0, WORK(1) returns the optimal LWORK; */
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/* LWORK (input) INTEGER */
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/* The dimension of the array WORK. LWORK >= 1. */
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/* If JOBZ = 'N', */
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/* LWORK >= 3*min(M,N) + max(max(M,N),7*min(M,N)). */
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/* If JOBZ = 'O', */
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/* LWORK >= 3*min(M,N)*min(M,N) + */
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/* max(max(M,N),5*min(M,N)*min(M,N)+4*min(M,N)). */
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/* If JOBZ = 'S' or 'A' */
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/* LWORK >= 3*min(M,N)*min(M,N) + */
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/* max(max(M,N),4*min(M,N)*min(M,N)+4*min(M,N)). */
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/* For good performance, LWORK should generally be larger. */
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/* If LWORK = -1 but other input arguments are legal, WORK(1) */
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/* returns the optimal LWORK. */
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/* IWORK (workspace) INTEGER array, dimension (8*min(M,N)) */
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/* INFO (output) INTEGER */
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/* = 0: successful exit. */
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */
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/* > 0: DBDSDC did not converge, updating process failed. */
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/* Further Details */
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/* =============== */
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/* Based on contributions by */
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/* Ming Gu and Huan Ren, Computer Science Division, University of */
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/* California at Berkeley, USA */
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// ------------------------------------------------------------------------------------
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template <
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typename T,
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long NR1, long NR2, long NR3, long NR4,
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long NC1, long NC2, long NC3, long NC4,
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typename MM
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>
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int gesdd (
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const char jobz,
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matrix<T,NR1,NC1,MM,column_major_layout>& a,
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matrix<T,NR2,NC2,MM,column_major_layout>& s,
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matrix<T,NR3,NC3,MM,column_major_layout>& u,
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matrix<T,NR4,NC4,MM,column_major_layout>& vt
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)
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{
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matrix<T,0,1,MM,column_major_layout> work;
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matrix<integer,0,1,MM,column_major_layout> iwork;
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const long m = a.nr();
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const long n = a.nc();
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s.set_size(std::min(m,n), 1);
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// make sure the iwork memory block is big enough
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if (iwork.size() < 8*std::min(m,n))
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iwork.set_size(8*std::min(m,n), 1);
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if (jobz == 'A')
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{
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u.set_size(m,m);
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vt.set_size(n,n);
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}
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else if (jobz == 'S')
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{
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u.set_size(m, std::min(m,n));
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vt.set_size(std::min(m,n), n);
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}
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else if (jobz == 'O')
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{
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DLIB_CASSERT(false, "jobz == 'O' not supported");
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}
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else
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{
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u.set_size(NR3?NR3:1, NC3?NC3:1);
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vt.set_size(NR4?NR4:1, NC4?NC4:1);
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}
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// figure out how big the workspace needs to be.
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T work_size = 1;
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int info = binding::gesdd(jobz, a.nr(), a.nc(), &a(0,0), a.nr(),
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&s(0,0), &u(0,0), u.nr(), &vt(0,0), vt.nr(),
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&work_size, -1, &iwork(0,0));
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if (info != 0)
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return info;
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// There is a bug in an older version of LAPACK in Debian etch
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// that causes the gesdd to return the wrong value for work_size
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// when jobz == 'N'. So verify the value of work_size.
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if (jobz == 'N')
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{
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using std::min;
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using std::max;
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const T min_work_size = 3*min(m,n) + max(max(m,n),7*min(m,n));
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if (work_size < min_work_size)
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work_size = min_work_size;
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}
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if (work.size() < work_size)
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work.set_size(static_cast<long>(work_size), 1);
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// compute the actual SVD
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info = binding::gesdd(jobz, a.nr(), a.nc(), &a(0,0), a.nr(),
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&s(0,0), &u(0,0), u.nr(), &vt(0,0), vt.nr(),
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&work(0,0), work.size(), &iwork(0,0));
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return info;
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}
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// ------------------------------------------------------------------------------------
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template <
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typename T,
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long NR1, long NR2, long NR3, long NR4,
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long NC1, long NC2, long NC3, long NC4,
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typename MM
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>
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int gesdd (
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const char jobz,
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matrix<T,NR1,NC1,MM,row_major_layout>& a,
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matrix<T,NR2,NC2,MM,row_major_layout>& s,
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matrix<T,NR3,NC3,MM,row_major_layout>& u_,
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matrix<T,NR4,NC4,MM,row_major_layout>& vt_
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)
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{
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matrix<T,0,1,MM,row_major_layout> work;
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matrix<integer,0,1,MM,row_major_layout> iwork;
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// Row major order matrices are transposed from LAPACK's point of view.
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matrix<T,NR4,NC4,MM,row_major_layout>& u = vt_;
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matrix<T,NR3,NC3,MM,row_major_layout>& vt = u_;
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const long m = a.nc();
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const long n = a.nr();
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s.set_size(std::min(m,n), 1);
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// make sure the iwork memory block is big enough
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if (iwork.size() < 8*std::min(m,n))
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iwork.set_size(8*std::min(m,n), 1);
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if (jobz == 'A')
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{
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u.set_size(m,m);
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vt.set_size(n,n);
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}
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else if (jobz == 'S')
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{
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u.set_size(std::min(m,n), m);
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vt.set_size(n, std::min(m,n));
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}
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else if (jobz == 'O')
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{
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DLIB_CASSERT(false, "jobz == 'O' not supported");
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}
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else
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{
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u.set_size(NR4?NR4:1, NC4?NC4:1);
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vt.set_size(NR3?NR3:1, NC3?NC3:1);
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}
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// figure out how big the workspace needs to be.
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T work_size = 1;
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int info = binding::gesdd(jobz, m, n, &a(0,0), a.nc(),
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&s(0,0), &u(0,0), u.nc(), &vt(0,0), vt.nc(),
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&work_size, -1, &iwork(0,0));
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if (info != 0)
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return info;
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// There is a bug in an older version of LAPACK in Debian etch
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// that causes the gesdd to return the wrong value for work_size
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// when jobz == 'N'. So verify the value of work_size.
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if (jobz == 'N')
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{
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using std::min;
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using std::max;
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const T min_work_size = 3*min(m,n) + max(max(m,n),7*min(m,n));
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if (work_size < min_work_size)
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work_size = min_work_size;
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}
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if (work.size() < work_size)
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work.set_size(static_cast<long>(work_size), 1);
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// compute the actual SVD
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info = binding::gesdd(jobz, m, n, &a(0,0), a.nc(),
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&s(0,0), &u(0,0), u.nc(), &vt(0,0), vt.nc(),
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&work(0,0), work.size(), &iwork(0,0));
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return info;
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}
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// ------------------------------------------------------------------------------------
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}
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}
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// ----------------------------------------------------------------------------------------
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#endif // DLIB_LAPACk_SDD_Hh_
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