dlib C++ Library - gesvd.h

    // 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_