Contents

• NAME
• SYNOPSIS
  • F95 INTERFACE
  • C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

     dtzrqf - routine is deprecated and has been replaced by rou-
     tine STZRZF

SYNOPSIS

     SUBROUTINE DTZRQF(M, N, A, LDA, TAU, INFO)

     INTEGER M, N, LDA, INFO
     DOUBLE PRECISION A(LDA,*), TAU(*)

     SUBROUTINE DTZRQF_64(M, N, A, LDA, TAU, INFO)

     INTEGER*8 M, N, LDA, INFO
     DOUBLE PRECISION A(LDA,*), TAU(*)

  F95 INTERFACE
     SUBROUTINE TZRQF(M, N, A, [LDA], TAU, [INFO])

     INTEGER :: M, N, LDA, INFO
     REAL(8), DIMENSION(:) :: TAU
     REAL(8), DIMENSION(:,:) :: A

     SUBROUTINE TZRQF_64(M, N, A, [LDA], TAU, [INFO])

     INTEGER(8) :: M, N, LDA, INFO
     REAL(8), DIMENSION(:) :: TAU
     REAL(8), DIMENSION(:,:) :: A

  C INTERFACE
     #include <sunperf.h>

     void dtzrqf(int m, int n, double *a, int lda,  double  *tau,
               int *info);

     void dtzrqf_64(long m, long n, double *a, long  lda,  double
               *tau, long *info);

PURPOSE

     dtzrqf routine is deprecated and has been replaced  by  rou-
     tine 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) The number of rows of the matrix A.  M >= 0.

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

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

     TAU (output)
               The scalar factors of the elementary reflectors.

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

FURTHER DETAILS

     The factorization is obtained by Householder's method.   The
     kth  transformation  matrix, Z( k ), which is used to intro-
     duce 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 ).