stzrqf.f (3)

Functions/Subroutines

subroutine stzrqf (M, N, A, LDA, TAU, INFO)

STZRQF

subroutine stzrqf (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, integerINFO)

STZRQF

Purpose:

 This routine is deprecated and has been replaced by routine STZRZF.

 STZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A
 to upper triangular form by means of orthogonal transformations.

 The upper trapezoidal matrix A is factored as

    A = ( R  0 ) * Z,

 where Z is an N-by-N orthogonal 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 REAL 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
          orthogonal 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 REAL 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 ), which 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 )**T,   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 stzrqf.f.

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