srzt01.f

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*> \brief \b SRZT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       REAL             FUNCTION SRZT01( M, N, A, AF, LDA, TAU, WORK,
*                        LWORK )
* 
*       .. Scalar Arguments ..
*       INTEGER            LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), AF( LDA, * ), TAU( * ),
*      $                   WORK( LWORK )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SRZT01 returns
*>      || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with STZRZF.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrices A and AF.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is REAL array, dimension (LDA,N)
*>          The original upper trapezoidal M by N matrix A.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is REAL array, dimension (LDA,N)
*>          The output of STZRZF for input matrix A.
*>          The lower triangle is not referenced.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the arrays A and AF.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is REAL array, dimension (M)
*>          Details of the Householder transformations as returned by
*>          STZRZF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK.  LWORK >= m*n + m*nb.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup single_lin
*
*  =====================================================================
      REAL             FUNCTION srzt01( M, N, A, AF, LDA, TAU, WORK,
     $                 lwork )
*
*  -- LAPACK test routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      REAL               A( lda, * ), AF( lda, * ), TAU( * ),
     $                   work( lwork )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter                ( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, J
      REAL               NORMA
*     ..
*     .. Local Arrays ..
      REAL               RWORK( 1 )
*     ..
*     .. External Functions ..
      REAL               SLAMCH, SLANGE
      EXTERNAL           slamch, slange
*     ..
*     .. External Subroutines ..
      EXTERNAL           saxpy, slaset, sormrz, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          max, real
*     ..
*     .. Executable Statements ..
*
      srzt01 = zero
*
      IF( lwork.LT.m*n+m ) THEN
         CALL xerbla( 'SRZT01', 8 )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( m.LE.0 .OR. n.LE.0 )
     $   RETURN
*
      norma = slange( 'One-norm', m, n, a, lda, rwork )
*
*     Copy upper triangle R
*
      CALL slaset( 'Full', m, n, zero, zero, work, m )
      DO 20 j = 1, m
         DO 10 i = 1, j
            work( ( j-1 )*m+i ) = af( i, j )
   10    CONTINUE
   20 CONTINUE
*
*     R = R * P(1) * ... *P(m)
*
      CALL sormrz( 'Right', 'No tranpose', m, n, m, n-m, af, lda, tau,
     $             work, m, work( m*n+1 ), lwork-m*n, info )
*
*     R = R - A
*
      DO 30 i = 1, n
         CALL saxpy( m, -one, a( 1, i ), 1, work( ( i-1 )*m+1 ), 1 )
   30 CONTINUE
*
      srzt01 = slange( 'One-norm', m, n, work, m, rwork )
*
      srzt01 = srzt01 / ( slamch( 'Epsilon' )*REAL( MAX( M, N ) ) )
      IF( norma.NE.zero )
     $   srzt01 = srzt01 / norma
*
      RETURN
*
*     End of SRZT01
*
      END