numeric-linalg

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*> \brief \b CRZT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       REAL             FUNCTION CRZT01( M, N, A, AF, LDA, TAU, WORK,
*                        LWORK )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), AF( LDA, * ), TAU( * ),
*      $                   WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CRZT01 returns
*>      || A - R*Q || / ( M * eps * ||A|| )
*> for an upper trapezoidal A that was factored with CTZRZF.
*> \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 COMPLEX array, dimension (LDA,N)
*>          The original upper trapezoidal M by N matrix A.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is COMPLEX array, dimension (LDA,N)
*>          The output of CTZRZF 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 COMPLEX array, dimension (M)
*>          Details of the  Householder transformations as returned by
*>          CTZRZF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The length of the array WORK.  LWORK >= m*n + m.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex_lin
*
*  =====================================================================
      REAL             FUNCTION CRZT01( M, N, A, AF, LDA, TAU, WORK,
     $                 LWORK )
*
*  -- LAPACK test routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      COMPLEX            A( LDA, * ), AF( LDA, * ), TAU( * ),
     $                   WORK( LWORK )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      PARAMETER          ( ZERO = 0.0E0, ONE = 1.0E0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, INFO, J
      REAL               NORMA
*     ..
*     .. Local Arrays ..
      REAL               RWORK( 1 )
*     ..
*     .. External Functions ..
      REAL               CLANGE, SLAMCH
      EXTERNAL           CLANGE, SLAMCH
*     ..
*     .. External Subroutines ..
      EXTERNAL           CAXPY, CLASET, CUNMRZ, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          CMPLX, MAX, REAL
*     ..
*     .. Executable Statements ..
*
      CRZT01 = ZERO
*
      IF( LWORK.LT.M*N+M ) THEN
         CALL XERBLA( 'CRZT01', 8 )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( M.LE.0 .OR. N.LE.0 )
     $   RETURN
*
      NORMA = CLANGE( 'One-norm', M, N, A, LDA, RWORK )
*
*     Copy upper triangle R
*
      CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( 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 CUNMRZ( 'Right', 'No transpose', 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 CAXPY( M, CMPLX( -ONE ), A( 1, I ), 1,
     $               WORK( ( I-1 )*M+1 ), 1 )
   30 CONTINUE
*
      CRZT01 = CLANGE( 'One-norm', M, N, WORK, M, RWORK )
*
      CRZT01 = CRZT01 / ( SLAMCH( 'Epsilon' )*REAL( MAX( M, N ) ) )
      IF( NORMA.NE.ZERO )
     $   CRZT01 = CRZT01 / NORMA
*
      RETURN
*
*     End of CRZT01
*
      END