SRC/sgelqt.f(3)

NAME
SRC/sgelqt.f

SYNOPSIS

  Functions/Subroutines
subroutine sgelqt (m, n, mb, a, lda, t, ldt, work, info)
SGELQT

Function/Subroutine Documentation

  subroutine sgelqt (integer m, integer n, integer mb, real, dimension( lda, * ) a, integer lda, real, dimension( ldt, * ) t, integer ldt, real, dimension( * ) work, integer info)

SGELQT

Purpose:

    !>
    !> SGELQT computes a blocked LQ factorization of a real M-by-N matrix A
    !> using the compact WY representation of Q.
    !>

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.  N >= 0.
    !>

    MB

    !>          MB is INTEGER
    !>          The block size to be used in the blocked QR.  MIN(M,N) >= MB >= 1.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the M-by-N matrix A.
    !>          On exit, the elements on and below the diagonal of the array
    !>          contain the M-by-MIN(M,N) lower trapezoidal matrix L (L is
    !>          lower triangular if M <= N); the elements above the diagonal
    !>          are the rows of V.
    !>

    LDA

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

    T

    !>          T is REAL array, dimension (LDT,MIN(M,N))
    !>          The upper triangular block reflectors stored in compact form
    !>          as a sequence of upper triangular blocks.  See below
    !>          for further details.
    !>

    LDT

    !>          LDT is INTEGER
    !>          The leading dimension of the array T.  LDT >= MB.
    !>

    WORK

    !>          WORK is REAL array, dimension (MB*N)
    !>

    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.

Further Details:

    !>
    !>  The matrix V stores the elementary reflectors H(i) in the i-th row
    !>  above the diagonal. For example, if M=5 and N=3, the matrix V is
    !>
    !>               V = (  1  v1 v1 v1 v1 )
    !>                   (     1  v2 v2 v2 )
    !>                   (         1 v3 v3 )
    !>
    !>
    !>  where the vi's represent the vectors which define H(i), which are returned
    !>  in the matrix A.  The 1's along the diagonal of V are not stored in A.
    !>  Let K=MIN(M,N).  The number of blocks is B = ceiling(K/MB), where each
    !>  block is of order MB except for the last block, which is of order
    !>  IB = K - (B-1)*MB.  For each of the B blocks, a upper triangular block
    !>  reflector factor is computed: T1, T2, ..., TB.  The MB-by-MB (and IB-by-IB
    !>  for the last block) T's are stored in the MB-by-K matrix T as
    !>
    !>               T = (T1 T2 ... TB).
    !>

Definition at line 123 of file sgelqt.f.

Author

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