dget01.f

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*> \brief \b DGET01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGET01( M, N, A, LDA, AFAC, LDAFAC, IPIV, RWORK,
*                          RESID )
*
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDAFAC, M, N
*       DOUBLE PRECISION   RESID
*       ..
*       .. Array Arguments ..
*       INTEGER            IPIV( * )
*       DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGET01 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DGETRF.
*>          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 DGETRF.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          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 double_lin
*
*  =====================================================================
      SUBROUTINE dget01( 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
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   A( LDA, * ), AFAC( LDAFAC, * ), RWORK( * )
*     ..
*
*  =====================================================================
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, J, K
      DOUBLE PRECISION   ANORM, EPS, T
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DDOT, DLAMCH, DLANGE
      EXTERNAL           ddot, dlamch, dlange
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemv, dlaswp, dscal, dtrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, min
*     ..
*     .. 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 = dlamch( 'Epsilon' )
      anorm = dlange( '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 dtrmv( '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 dscal( m-k, t, afac( k+1, k ), 1 )
               CALL dgemv( 'No transpose', m-k, k-1, one,
     $                     afac( k+1, 1 ), ldafac, afac( 1, k ), 1, one,
     $                     afac( k+1, k ), 1 )
            END IF
*
*           Compute the (K,K) element
*
            afac( k, k ) = t + ddot( k-1, afac( k, 1 ), ldafac,
     $                     afac( 1, k ), 1 )
*
*           Compute elements (1:K-1,K)
*
            CALL dtrmv( 'Lower', 'No transpose', 'Unit', k-1, afac,
     $                  ldafac, afac( 1, k ), 1 )
         END IF
   10 CONTINUE
      CALL dlaswp( 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 = dlange( '1', m, n, afac, ldafac, rwork )
*
      IF( anorm.LE.zero ) THEN
         IF( resid.NE.zero )
     $      resid = one / eps
      ELSE
         resid = ( ( resid / dble( n ) ) / anorm ) / eps
      END IF
*
      RETURN
*
*     End of DGET01
*
      END