zgeqrt3.f(3)

NAME
zgeqrt3.f -

SYNOPSIS

  Functions/Subroutines

recursive subroutine zgeqrt3 (M, N, A, LDA, T, LDT, INFO)
ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Function/Subroutine Documentation

  recursive subroutine zgeqrt3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, integerINFO)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

     ZGEQRT3 recursively computes a QR factorization of a complex 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 COMPLEX*16 array, dimension (LDA,N)
              On entry, the complex M-by-N matrix A.  On exit, the elements on
              and above the diagonal contain the N-by-N upper triangular matrix R;
              the elements below the diagonal are the columns 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 COMPLEX*16 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:
    September 2012

Further Details:

      The matrix V stores the elementary reflectors H(i) in the i-th column
      below the diagonal. For example, if M=5 and N=3, the matrix V is

                   V = (  1       )
                       ( v1  1    )
                       ( v1 v2  1 )
                       ( v1 v2 v3 )
                       ( v1 v2 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**H

      where V**H is the conjugate transpose of V.

      For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 133 of file zgeqrt3.f.

Author

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