dlib C++ Library - gesdd.h

    // 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_