sorgtsqr()

subroutine sorgtsqr	(	integer	M,
		integer	N,
		integer	MB,
		integer	NB,
		real, dimension( lda, * )	A,
		integer	LDA,
		real, dimension( ldt, * )	T,
		integer	LDT,
		real, dimension( * )	WORK,
		integer	LWORK,
		integer	INFO
	)

SORGTSQR

Download SORGTSQR + dependencies [TGZ] [ZIP] [TXT] \par Purpose: @verbatim SORGTSQR generates an M-by-N real matrix Q_out with orthonormal columns, which are the first N columns of a product of real orthogonal matrices of order M which are returned by SLATSQR Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ). See the documentation for SLATSQR. \endverbatim @param [in] M @verbatim M is INTEGER The number of rows of the matrix A. M >= 0. \endverbatim @param [in] N @verbatim N is INTEGER The number of columns of the matrix A. M >= N >= 0. \endverbatim @param [in] MB @verbatim MB is INTEGER The row block size used by SLATSQR to return arrays A and T. MB > N. (Note that if MB > M, then M is used instead of MB as the row block size). \endverbatim @param [in] NB @verbatim NB is INTEGER The column block size used by SLATSQR to return arrays A and T. NB >= 1. (Note that if NB > N, then N is used instead of NB as the column block size). \endverbatim @param [in,out] A @verbatim A is REAL array, dimension (LDA,N) On entry: The elements on and above the diagonal are not accessed. The elements below the diagonal represent the unit lower-trapezoidal blocked matrix V computed by SLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored) (same format as the output A below the diagonal in SLATSQR). On exit: The array A contains an M-by-N orthonormal matrix Q_out, i.e the columns of A are orthogonal unit vectors. \endverbatim @param [in] LDA @verbatim LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M). \endverbatim @param [in] T @verbatim T is REAL array, dimension (LDT, N * NIRB) where NIRB = Number_of_input_row_blocks = MAX( 1, CEIL((M-N)/(MB-N)) ) Let NICB = Number_of_input_col_blocks = CEIL(N/NB) The upper-triangular block reflectors used to define the input matrices Q_in(k), k=(1:NIRB*NICB). The block reflectors are stored in compact form in NIRB block reflector sequences. Each of NIRB block reflector sequences is stored in a larger NB-by-N column block of T and consists of NICB smaller NB-by-NB upper-triangular column blocks. (same format as the output T in SLATSQR). \endverbatim @param [in] LDT @verbatim LDT is INTEGER The leading dimension of the array T. LDT >= max(1,min(NB1,N)). \endverbatim @param [out] WORK @verbatim (workspace) REAL array, dimension (MAX(2,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. \endverbatim @param [in] LWORK @verbatim The dimension of the array WORK. LWORK >= (M+NB)*N. 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. \endverbatim @param [out] INFO @verbatim INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2019 \par Contributors: @verbatim November 2019, Igor Kozachenko, Computer Science Division, University of California, Berkeley \endverbatim

Definition at line 176 of file sorgtsqr.f.

      IMPLICIT NONE
*
*  -- LAPACK computational routine (version 3.9.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2019
*
*     .. Scalar Arguments ..
      INTEGER           INFO, LDA, LDT, LWORK, M, N, MB, NB
*     ..
*     .. Array Arguments ..
      REAL              A( LDA, * ), T( LDT, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY
      INTEGER            IINFO, LDC, LWORKOPT, LC, LW, NBLOCAL, J
*     ..
*     .. External Subroutines ..
      EXTERNAL           scopy, slamtsqr, slaset, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          real, max, min
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters
*
      lquery  = lwork.EQ.-1
      info = 0
      IF( m.LT.0 ) THEN
         info = -1
      ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
         info = -2
      ELSE IF( mb.LE.n ) THEN
         info = -3
      ELSE IF( nb.LT.1 ) THEN
         info = -4
      ELSE IF( lda.LT.max( 1, m ) ) THEN
         info = -6
      ELSE IF( ldt.LT.max( 1, min( nb, n ) ) ) THEN
         info = -8
      ELSE
*
*        Test the input LWORK for the dimension of the array WORK.
*        This workspace is used to store array C(LDC, N) and WORK(LWORK)
*        in the call to DLAMTSQR. See the documentation for DLAMTSQR.
*
         IF( lwork.LT.2 .AND. (.NOT.lquery) ) THEN
            info = -10
         ELSE
*
*           Set block size for column blocks
*
            nblocal = min( nb, n )
*
*           LWORK = -1, then set the size for the array C(LDC,N)
*           in DLAMTSQR call and set the optimal size of the work array
*           WORK(LWORK) in DLAMTSQR call.
*
            ldc = m
            lc = ldc*n
            lw = n * nblocal
*
            lworkopt = lc+lw
*
            IF( ( lwork.LT.max( 1, lworkopt ) ).AND.(.NOT.lquery) ) THEN
               info = -10
            END IF
         END IF
*
      END IF
*
*     Handle error in the input parameters and return workspace query.
*
      IF( info.NE.0 ) THEN
         CALL xerbla( 'SORGTSQR', -info )
         RETURN
      ELSE IF ( lquery ) THEN
         work( 1 ) = real( lworkopt )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( min( m, n ).EQ.0 ) THEN
         work( 1 ) = real( lworkopt )
         RETURN
      END IF
*
*     (1) Form explicitly the tall-skinny M-by-N left submatrix Q1_in
*     of M-by-M orthogonal matrix Q_in, which is implicitly stored in
*     the subdiagonal part of input array A and in the input array T.
*     Perform by the following operation using the routine DLAMTSQR.
*
*         Q1_in = Q_in * ( I ), where I is a N-by-N identity matrix,
*                        ( 0 )        0 is a (M-N)-by-N zero matrix.
*
*     (1a) Form M-by-N matrix in the array WORK(1:LDC*N) with ones
*     on the diagonal and zeros elsewhere.
*
      CALL slaset( 'F', m, n, zero, one, work, ldc )
*
*     (1b)  On input, WORK(1:LDC*N) stores ( I );
*                                          ( 0 )
*
*           On output, WORK(1:LDC*N) stores Q1_in.
*
      CALL slamtsqr( 'L', 'N', m, n, n, mb, nblocal, a, lda, t, ldt,
     $               work, ldc, work( lc+1 ), lw, iinfo )
*
*     (2) Copy the result from the part of the work array (1:M,1:N)
*     with the leading dimension LDC that starts at WORK(1) into
*     the output array A(1:M,1:N) column-by-column.
*
      DO j = 1, n
         CALL scopy( m, work( (j-1)*ldc + 1 ), 1, a( 1, j ), 1 )
      END DO
*
      work( 1 ) = real( lworkopt )
      RETURN
*
*     End of SORGTSQR
*

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