dlib C++ Library - geqrf.h

    // Copyright (C) 2010  Davis E. King (davis@dlib.net)
    // License: Boost Software License   See LICENSE.txt for the full license.
    #ifndef DLIB_LAPACk_GEQRF_Hh_
    #define DLIB_LAPACk_GEQRF_Hh_

    #include "fortran_id.h"
    #include "../matrix.h"

    namespace dlib
    {
        namespace lapack
        {
            namespace binding
            {
                extern "C"
                {
                    void DLIB_FORTRAN_ID(dgeqrf) (const integer *m, const integer *n, double *a, const integer*
                                                  lda, double *tau, double *work, const integer *lwork,
                                                  integer *info);

                    void DLIB_FORTRAN_ID(sgeqrf) (const integer *m, const integer *n, float *a, const integer*
                                                  lda, float *tau, float *work, const integer *lwork,
                                                  integer *info);
                }

                inline int geqrf (integer m, integer n, double *a, integer lda,
                                  double *tau, double *work, integer lwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(dgeqrf)(&m, &n, a, &lda,
                                            tau, work, &lwork, &info);
                    return info;
                }

                inline int geqrf (integer m, integer n, float *a, integer lda,
                                  float *tau, float *work, integer lwork)
                {
                    integer info = 0;
                    DLIB_FORTRAN_ID(sgeqrf)(&m, &n, a, &lda,
                                            tau, work, &lwork, &info);
                    return info;
                }

            }

        // ------------------------------------------------------------------------------------

    /*  -- LAPACK routine (version 3.1) -- */
    /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
    /*     November 2006 */

    /*     .. Scalar Arguments .. */
    /*     .. */
    /*     .. Array Arguments .. */
    /*     .. */

    /*  Purpose */
    /*  ======= */

    /*  DGEQRF computes a QR factorization of a real M-by-N matrix A: */
    /*  A = Q * R. */

    /*  Arguments */
    /*  ========= */

    /*  M       (input) INTEGER */
    /*          The number of rows of the matrix A.  M >= 0. */

    /*  N       (input) INTEGER */
    /*          The number of columns of the matrix A.  N >= 0. */

    /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
    /*          On entry, the M-by-N matrix A. */
    /*          On exit, the elements on and above the diagonal of the array */
    /*          contain the min(M,N)-by-N upper trapezoidal matrix R (R is */
    /*          upper triangular if m >= n); the elements below the diagonal, */
    /*          with the array TAU, represent the orthogonal matrix Q as a */
    /*          product of min(m,n) elementary reflectors (see Further */
    /*          Details). */

    /*  LDA     (input) INTEGER */
    /*          The leading dimension of the array A.  LDA >= max(1,M). */

    /*  TAU     (output) DOUBLE PRECISION array, dimension (min(M,N)) */
    /*          The scalar factors of the elementary reflectors (see Further */
    /*          Details). */

    /*  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 >= max(1,N). */
    /*          For optimum performance LWORK >= N*NB, where NB is */
    /*          the optimal blocksize. */

    /*          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 */

    /*  Further Details */
    /*  =============== */

    /*  The matrix Q is represented as a product of elementary reflectors */

    /*     Q = H(1) H(2) . . . H(k), where k = min(m,n). */

    /*  Each H(i) has the form */

    /*     H(i) = I - tau * v * v' */

    /*  where tau is a real scalar, and v is a real vector with */
    /*  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i), */
    /*  and tau in TAU(i). */

        // ------------------------------------------------------------------------------------

            template <
                typename T,
                long NR1, long NR2,
                long NC1, long NC2,
                typename MM
                >
            int geqrf (
                matrix<T,NR1,NC1,MM,column_major_layout>& a,
                matrix<T,NR2,NC2,MM,column_major_layout>& tau
            )
            {
                matrix<T,0,1,MM,column_major_layout> work;

                tau.set_size(std::min(a.nr(), a.nc()), 1);

                // figure out how big the workspace needs to be.
                T work_size = 1;
                int info = binding::geqrf(a.nr(), a.nc(), &a(0,0), a.nr(),
                                          &tau(0,0), &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 decomposition
                info = binding::geqrf(a.nr(), a.nc(), &a(0,0), a.nr(),
                                      &tau(0,0), &work(0,0), work.size());

                return info;
            }

        // ------------------------------------------------------------------------------------

        }

    }

    // ----------------------------------------------------------------------------------------

    #endif // DLIB_LAPACk_GEQRF_Hh_