cget01.f

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*> \brief \b CGET01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
*                          RESID )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDAFAC, M, N
*       REAL               RESID
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       REAL               RWORK( * )
*       COMPLEX            A( LDA, * ), AFAC( LDAFAC, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CGET01 reconstructs a matrix A from its L*U factorization and
*> computes the residual
*>    norm(L*U - A) / ( N * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          The original M x N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] AFAC
*> \verbatim
*>          AFAC is COMPLEX array, dimension (LDAFAC,N)
*>          The factored form of the matrix A.  AFAC contains the factors
*>          L and U from the L*U factorization as computed by CGETRF.
*>          Overwritten with the reconstructed matrix, and then with the
*>          difference L*U - A.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*>          LDAFAC is INTEGER
*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,M).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices from CGETRF.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is REAL
*>          norm(L*U - A) / ( N * norm(A) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex_lin
*
*  =====================================================================
      SUBROUTINE cget01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
     $                   RESID )
*
*  -- LAPACK test routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      INTEGER            LDA, LDAFAC, M, N
      REAL               RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      REAL               RWORK( * )
      COMPLEX            A( lda, * ), AFAC( ldafac, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( zero = 0.0e+0, one = 1.0e+0 )
      COMPLEX            CONE
      parameter( cone = ( 1.0e+0, 0.0e+0 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, K
      REAL               ANORM, EPS
      COMPLEX            T
*     ..
*     .. External Functions ..
      REAL               CLANGE, SLAMCH
      COMPLEX            CDOTU
      EXTERNAL           clange, slamch, cdotu
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemv, claswp, cscal, ctrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          min, real
*     ..
*     .. Executable Statements ..
*
*     Quick exit if M = 0 or N = 0.
*
      IF( m.LE.0 .OR. n.LE.0 ) THEN
         resid = zero
         RETURN
      END IF
*
*     Determine EPS and the norm of A.
*
      eps = slamch( 'Epsilon' )
      anorm = clange( '1', m, n, a, lda, rwork )
*
*     Compute the product L*U and overwrite AFAC with the result.
*     A column at a time of the product is obtained, starting with
*     column N.
*
      DO 10 k = n, 1, -1
         IF( k.GT.m ) THEN
            CALL ctrmv( 'Lower', 'No transpose', 'Unit', m, afac,
     $                  ldafac, afac( 1, k ), 1 )
         ELSE
*
*           Compute elements (K+1:M,K)
*
            t = afac( k, k )
            IF( k+1.LE.m ) THEN
               CALL cscal( m-k, t, afac( k+1, k ), 1 )
               CALL cgemv( 'No transpose', m-k, k-1, cone,
     $                     afac( k+1, 1 ), ldafac, afac( 1, k ), 1,
     $                     cone, afac( k+1, k ), 1 )
            END IF
*
*           Compute the (K,K) element
*
            afac( k, k ) = t + cdotu( k-1, afac( k, 1 ), ldafac,
     $                     afac( 1, k ), 1 )
*
*           Compute elements (1:K-1,K)
*
            CALL ctrmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
     $                  ldafac, afac( 1, k ), 1 )
         END IF
   10 CONTINUE
      CALL claswp( n, afac, ldafac, 1, min( m, n ), ipiv, -1 )
*
*     Compute the difference  L*U - A  and store in AFAC.
*
      DO 30 j = 1, n
         DO 20 i = 1, m
            afac( i, j ) = afac( i, j ) - a( i, j )
   20    CONTINUE
   30 CONTINUE
*
*     Compute norm( L*U - A ) / ( N * norm(A) * EPS )
*
      resid = clange( '1', m, n, afac, ldafac, rwork )
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         resid = ( ( resid/REAL( N ) )/anorm ) / eps
      END IF
*
      RETURN
*
*     End of CGET01
*
      END