ztzrqf.f(3)

NAME
ztzrqf.f -

SYNOPSIS

  Functions/Subroutines
subroutine ztzrqf (M, N, A, LDA, TAU, INFO)
ZTZRQF

Function/Subroutine Documentation

  subroutine ztzrqf (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, integerINFO)

ZTZRQF

Purpose:

     This routine is deprecated and has been replaced by routine ZTZRZF.
     ZTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A
     to upper triangular form by means of unitary transformations.
     The upper trapezoidal matrix A is factored as
        A = ( R  0 ) * Z,
     where Z is an N-by-N unitary matrix and R is an M-by-M upper
     triangular matrix.

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 >= M.

    A

              A is COMPLEX*16 array, dimension (LDA,N)
              On entry, the leading M-by-N upper trapezoidal part of the
              array A must contain the matrix to be factorized.
              On exit, the leading M-by-M upper triangular part of A
              contains the upper triangular matrix R, and elements M+1 to
              N of the first M rows of A, with the array TAU, represent the
              unitary matrix Z as a product of M elementary reflectors.

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension (M)
              The scalar factors of the elementary reflectors.

    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 2011

Further Details:

      The  factorization is obtained by Householder's method.  The kth
      transformation matrix, Z( k ), whose conjugate transpose is used to
      introduce zeros into the (m - k + 1)th row of A, is given in the form
         Z( k ) = ( I     0   ),
                  ( 0  T( k ) )
      where
         T( k ) = I - tau*u( k )*u( k )**H,   u( k ) = (   1    ),
                                                       (   0    )
                                                       ( z( k ) )
      tau is a scalar and z( k ) is an ( n - m ) element vector.
      tau and z( k ) are chosen to annihilate the elements of the kth row
      of X.
      The scalar tau is returned in the kth element of TAU and the vector
      u( k ) in the kth row of A, such that the elements of z( k ) are
      in  a( k, m + 1 ), ..., a( k, n ). The elements of R are returned in
      the upper triangular part of A.
      Z is given by
         Z =  Z( 1 ) * Z( 2 ) * ... * Z( m ).

Definition at line 139 of file ztzrqf.f.

Author

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