SRC/sorgtsqr.f(3)

NAME
SRC/sorgtsqr.f

SYNOPSIS

  Functions/Subroutines
subroutine sorgtsqr (m, n, mb, nb, a, lda, t, ldt, work, lwork, info)
SORGTSQR

Function/Subroutine Documentation

  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

Purpose:

    !>
    !> 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.
    !>

Parameters
    M

    !>          M is INTEGER
    !>          The number of rows of the matrix A.  M >= 0.
    !>

    N

    !>          N is INTEGER
    !>          The number of columns of the matrix A. M >= N >= 0.
    !>

    MB

    !>          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).
    !>

    NB

    !>          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).
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,M).
    !>

    T

    !>          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).
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.
    !>          LDT >= max(1,min(NB1,N)).
    !>

    WORK

    !>          (workspace) REAL array, dimension (MAX(2,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          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.
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !> November 2019, Igor Kozachenko,
    !>                Computer Science Division,
    !>                University of California, Berkeley
    !>
    !>

Definition at line 174 of file sorgtsqr.f.

Author

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