This routine is deprecated and has been replaced by routine STZRZF.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

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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 ).