dget07.f

Go to the documentation of this file.

*> \brief \b DGET07
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DGET07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
*                          LDXACT, FERR, CHKFERR, BERR, RESLTS )
*
*       .. Scalar Arguments ..
*       CHARACTER          TRANS
*       LOGICAL            CHKFERR
*       INTEGER            LDA, LDB, LDX, LDXACT, N, NRHS
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ),
*      $                   RESLTS( * ), X( LDX, * ), XACT( LDXACT, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DGET07 tests the error bounds from iterative refinement for the
*> computed solution to a system of equations op(A)*X = B, where A is a
*> general n by n matrix and op(A) = A or A**T, depending on TRANS.
*>
*> RESLTS(1) = test of the error bound
*>           = norm(X - XACT) / ( norm(X) * FERR )
*>
*> A large value is returned if this ratio is not less than one.
*>
*> RESLTS(2) = residual from the iterative refinement routine
*>           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
*>             (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] TRANS
*> \verbatim
*>          TRANS is CHARACTER*1
*>          Specifies the form of the system of equations.
*>          = 'N':  A * X = B     (No transpose)
*>          = 'T':  A**T * X = B  (Transpose)
*>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of rows of the matrices X and XACT.  N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*>          NRHS is INTEGER
*>          The number of columns of the matrices X and XACT.  NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The original n by n matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*>          The right hand side vectors for the system of linear
*>          equations.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*>          LDB is INTEGER
*>          The leading dimension of the array B.  LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*>          The computed solution vectors.  Each vector is stored as a
*>          column of the matrix X.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*>          LDX is INTEGER
*>          The leading dimension of the array X.  LDX >= max(1,N).
*> \endverbatim
*>
*> \param[in] XACT
*> \verbatim
*>          XACT is DOUBLE PRECISION array, dimension (LDX,NRHS)
*>          The exact solution vectors.  Each vector is stored as a
*>          column of the matrix XACT.
*> \endverbatim
*>
*> \param[in] LDXACT
*> \verbatim
*>          LDXACT is INTEGER
*>          The leading dimension of the array XACT.  LDXACT >= max(1,N).
*> \endverbatim
*>
*> \param[in] FERR
*> \verbatim
*>          FERR is DOUBLE PRECISION array, dimension (NRHS)
*>          The estimated forward error bounds for each solution vector
*>          X.  If XTRUE is the true solution, FERR bounds the magnitude
*>          of the largest entry in (X - XTRUE) divided by the magnitude
*>          of the largest entry in X.
*> \endverbatim
*>
*> \param[in] CHKFERR
*> \verbatim
*>          CHKFERR is LOGICAL
*>          Set to .TRUE. to check FERR, .FALSE. not to check FERR.
*>          When the test system is ill-conditioned, the "true"
*>          solution in XACT may be incorrect.
*> \endverbatim
*>
*> \param[in] BERR
*> \verbatim
*>          BERR is DOUBLE PRECISION array, dimension (NRHS)
*>          The componentwise relative backward error of each solution
*>          vector (i.e., the smallest relative change in any entry of A
*>          or B that makes X an exact solution).
*> \endverbatim
*>
*> \param[out] RESLTS
*> \verbatim
*>          RESLTS is DOUBLE PRECISION array, dimension (2)
*>          The maximum over the NRHS solution vectors of the ratios:
*>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
*>          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dget07( TRANS, N, NRHS, A, LDA, B, LDB, X, LDX, XACT,
     $                   LDXACT, FERR, CHKFERR, BERR, RESLTS )
*
*  -- 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 ..
      CHARACTER          TRANS
      LOGICAL            CHKFERR
      INTEGER            LDA, LDB, LDX, LDXACT, N, NRHS
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), BERR( * ), FERR( * ),
     $                   reslts( * ), x( ldx, * ), xact( ldxact, * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      LOGICAL            NOTRAN
      INTEGER            I, IMAX, J, K
      DOUBLE PRECISION   AXBI, DIFF, EPS, ERRBND, OVFL, TMP, UNFL, XNORM
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      INTEGER            IDAMAX
      DOUBLE PRECISION   DLAMCH
      EXTERNAL           lsame, idamax, dlamch
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, max, min
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0 or NRHS = 0.
*
      IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
         reslts( 1 ) = zero
         reslts( 2 ) = zero
         RETURN
      END IF
*
      eps = dlamch( 'Epsilon' )
      unfl = dlamch( 'Safe minimum' )
      ovfl = one / unfl
      notran = lsame( trans, 'n' )
*
*     Test 1:  Compute the maximum of
*        norm(X - XACT) / ( norm(X) * FERR )
*     over all the vectors X and XACT using the infinity-norm.
*
      ERRBND = ZERO
      IF( CHKFERR ) THEN
         DO 30 J = 1, NRHS
            IMAX = IDAMAX( N, X( 1, J ), 1 )
            XNORM = MAX( ABS( X( IMAX, J ) ), UNFL )
            DIFF = ZERO
            DO 10 I = 1, N
               DIFF = MAX( DIFF, ABS( X( I, J )-XACT( I, J ) ) )
 10         CONTINUE
*
.GT.            IF( XNORMONE ) THEN
               GO TO 20
.LE.            ELSE IF( DIFFOVFL*XNORM ) THEN
               GO TO 20
            ELSE
               ERRBND = ONE / EPS
               GO TO 30
            END IF
*
 20         CONTINUE
.LE.            IF( DIFF / XNORMFERR( J ) ) THEN
               ERRBND = MAX( ERRBND, ( DIFF / XNORM ) / FERR( J ) )
            ELSE
               ERRBND = ONE / EPS
            END IF
 30      CONTINUE
      END IF
      RESLTS( 1 ) = ERRBND
*
*     Test 2:  Compute the maximum of BERR / ( (n+1)*EPS + (*) ), where
*     (*) = (n+1)*UNFL / (min_i (abs(op(A))*abs(X) +abs(b))_i )
*
      DO 70 K = 1, NRHS
         DO 60 I = 1, N
            TMP = ABS( B( I, K ) )
            IF( NOTRAN ) THEN
               DO 40 J = 1, N
                  TMP = TMP + ABS( A( I, J ) )*ABS( X( J, K ) )
   40          CONTINUE
            ELSE
               DO 50 J = 1, N
                  TMP = TMP + ABS( A( J, I ) )*ABS( X( J, K ) )
   50          CONTINUE
            END IF
.EQ.            IF( I1 ) THEN
               AXBI = TMP
            ELSE
               AXBI = MIN( AXBI, TMP )
            END IF
   60    CONTINUE
         TMP = BERR( K ) / ( ( N+1 )*EPS+( N+1 )*UNFL /
     $         MAX( AXBI, ( N+1 )*UNFL ) )
.EQ.         IF( K1 ) THEN
            RESLTS( 2 ) = TMP
         ELSE
            RESLTS( 2 ) = MAX( RESLTS( 2 ), TMP )
         END IF
   70 CONTINUE
*
      RETURN
*
*     End of DGET07
*
      END