dtrt01.f

Go to the documentation of this file.

*> \brief \b DTRT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
*                          WORK, RESID )
* 
*       .. Scalar Arguments ..
*       CHARACTER          DIAG, UPLO
*       INTEGER            LDA, LDAINV, N
*       DOUBLE PRECISION   RCOND, RESID
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), AINV( LDAINV, * ), WORK( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DTRT01 computes the residual for a triangular matrix A times its
*> inverse:
*>    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the matrix A is upper or lower triangular.
*>          = 'U':  Upper triangular
*>          = 'L':  Lower triangular
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*>          DIAG is CHARACTER*1
*>          Specifies whether or not the matrix A is unit triangular.
*>          = 'N':  Non-unit triangular
*>          = 'U':  Unit triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The triangular matrix A.  If UPLO = 'U', the leading n by n
*>          upper triangular part of the array A contains the upper
*>          triangular matrix, and the strictly lower triangular part of
*>          A is not referenced.  If UPLO = 'L', the leading n by n lower
*>          triangular part of the array A contains the lower triangular
*>          matrix, and the strictly upper triangular part of A is not
*>          referenced.  If DIAG = 'U', the diagonal elements of A are
*>          also not referenced and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] AINV
*> \verbatim
*>          AINV is DOUBLE PRECISION array, dimension (LDAINV,N)
*>          On entry, the (triangular) inverse of the matrix A, in the
*>          same storage format as A.
*>          On exit, the contents of AINV are destroyed.
*> \endverbatim
*>
*> \param[in] LDAINV
*> \verbatim
*>          LDAINV is INTEGER
*>          The leading dimension of the array AINV.  LDAINV >= max(1,N).
*> \endverbatim
*>
*> \param[out] RCOND
*> \verbatim
*>          RCOND is DOUBLE PRECISION
*>          The reciprocal condition number of A, computed as
*>          1/(norm(A) * norm(AINV)).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*>          RESID is DOUBLE PRECISION
*>          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dtrt01( UPLO, DIAG, N, A, LDA, AINV, LDAINV, RCOND,
     $                   work, resid )
*
*  -- 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 ..
      CHARACTER          DIAG, UPLO
      INTEGER            LDA, LDAINV, N
      DOUBLE PRECISION   RCOND, RESID
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( lda, * ), AINV( ldainv, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter                ( zero = 0.0d+0, one = 1.0d+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J
      DOUBLE PRECISION   AINVNM, ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANTR
      EXTERNAL           lsame, dlamch, dlantr
*     ..
*     .. External Subroutines ..
      EXTERNAL           dtrmv
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. Executable Statements ..
*
*     Quick exit if N = 0
*
      IF( n.LE.0 ) THEN
         rcond = one
         resid = zero
         RETURN
      END IF
*
*     Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
*
      eps = dlamch( 'Epsilon' )
      anorm = dlantr( '1', uplo, diag, n, n, a, lda, work )
      ainvnm = dlantr( '1', uplo, diag, n, n, ainv, ldainv, work )
      IF( anorm.LE.zero .OR. ainvnm.LE.zero ) THEN
         rcond = zero
         resid = one / eps
         RETURN
      END IF
      rcond = ( one / anorm ) / ainvnm
*
*     Set the diagonal of AINV to 1 if AINV has unit diagonal.
*
      IF( lsame( diag, 'U' ) ) THEN
         DO 10 j = 1, n
            ainv( j, j ) = one
   10    CONTINUE
      END IF
*
*     Compute A * AINV, overwriting AINV.
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 20 j = 1, n
            CALL dtrmv( 'Upper', 'No transpose', diag, j, a, lda,
     $                  ainv( 1, j ), 1 )
   20    CONTINUE
      ELSE
         DO 30 j = 1, n
            CALL dtrmv( 'Lower', 'No transpose', diag, n-j+1, a( j, j ),
     $                  lda, ainv( j, j ), 1 )
   30    CONTINUE
      END IF
*
*     Subtract 1 from each diagonal element to form A*AINV - I.
*
      DO 40 j = 1, n
         ainv( j, j ) = ainv( j, j ) - one
   40 CONTINUE
*
*     Compute norm(A*AINV - I) / (N * norm(A) * norm(AINV) * EPS)
*
      resid = dlantr( '1', uplo, 'Non-unit', n, n, ainv, ldainv, work )
*
      resid = ( ( resid*rcond ) / dble( n ) ) / eps
*
      RETURN
*
*     End of DTRT01
*
      END