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LAPACK version 3.0
stzrqf(3)

PURPOSE
  STZRQF - routine is deprecated and has been replaced by routine STZRZF

SYNTAX
  SUBROUTINE STZRQF( M, N, A, LDA, TAU, INFO )

      INTEGER	     INFO, LDA, M, N

      REAL	     A( LDA, * ), TAU( * )

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  This routine is deprecated and has been replaced by routine STZRZF.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

ARGUMENTS
  M	  (input) INTEGER
	  The number of rows of the matrix A.  M >= 0.

  N	  (input) INTEGER
	  The number of columns of the matrix A.  N >= M.

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

  TAU	  (output) REAL array, dimension (M)
	  The scalar factors of the elementary reflectors.

  INFO	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value

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 )',	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 ).