dgelqt3.f(3)

NAME
dgelqt3.f

SYNOPSIS

  Functions/Subroutines
recursive subroutine dgelqt3 (M, N, A, LDA, T, LDT, INFO)
DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

  recursive subroutine dgelqt3 (integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( ldt, * ) T, integer LDT, integer INFO)

DGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

     DGELQT3 recursively computes a LQ factorization of a real M-by-N
     matrix A, using the compact WY representation of Q.
     Based on the algorithm of Elmroth and Gustavson,
     IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters:
    M

              M is INTEGER
              The number of rows of the matrix A.  M =< N.

    N

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

    A

              A is DOUBLE PRECISION array, dimension (LDA,N)
              On entry, the real M-by-N matrix A.  On exit, the elements on and
              below the diagonal contain the N-by-N lower triangular matrix L; the
              elements above the diagonal are the rows of V.  See below for
              further details.

    LDA

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

    T

              T is DOUBLE PRECISION array, dimension (LDT,N)
              The N-by-N upper triangular factor of the block reflector.
              The elements on and above the diagonal contain the block
              reflector T; the elements below the diagonal are not used.
              See below for further details.

    LDT

              LDT is INTEGER
              The leading dimension of the array T.  LDT >= max(1,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.

Date:
    November 2017

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 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.  The
      block reflector H is then given by
                   H = I - V * T * V**T
      where V**T is the transpose of V.
      For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 133 of file dgelqt3.f.

Author

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