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*> \brief \b DPTT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DPTT01( N, D, E, DF, EF, WORK, RESID )
*
* .. Scalar Arguments ..
* INTEGER N
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * ), DF( * ), E( * ), EF( * ), WORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DPTT01 reconstructs a tridiagonal matrix A from its L*D*L'
*> factorization and computes the residual
*> norm(L*D*L' - A) / ( n * norm(A) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGTER
*> The order of the matrix A.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> The n diagonal elements of the tridiagonal matrix A.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) subdiagonal elements of the tridiagonal matrix A.
*> \endverbatim
*>
*> \param[in] DF
*> \verbatim
*> DF is DOUBLE PRECISION array, dimension (N)
*> The n diagonal elements of the factor L from the L*D*L'
*> factorization of A.
*> \endverbatim
*>
*> \param[in] EF
*> \verbatim
*> EF is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) subdiagonal elements of the factor L from the
*> L*D*L' factorization of A.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> norm(L*D*L' - 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 DPTT01( N, D, E, DF, EF, WORK, 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 N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * ), DF( * ), E( * ), EF( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I
DOUBLE PRECISION ANORM, DE, EPS
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
EPS = DLAMCH( 'Epsilon' )
*
* Construct the difference L*D*L' - A.
*
WORK( 1 ) = DF( 1 ) - D( 1 )
DO 10 I = 1, N - 1
DE = DF( I )*EF( I )
WORK( N+I ) = DE - E( I )
WORK( 1+I ) = DE*EF( I ) + DF( I+1 ) - D( I+1 )
10 CONTINUE
*
* Compute the 1-norms of the tridiagonal matrices A and WORK.
*
IF( N.EQ.1 ) THEN
ANORM = D( 1 )
RESID = ABS( WORK( 1 ) )
ELSE
ANORM = MAX( D( 1 )+ABS( E( 1 ) ), D( N )+ABS( E( N-1 ) ) )
RESID = MAX( ABS( WORK( 1 ) )+ABS( WORK( N+1 ) ),
$ ABS( WORK( N ) )+ABS( WORK( 2*N-1 ) ) )
DO 20 I = 2, N - 1
ANORM = MAX( ANORM, D( I )+ABS( E( I ) )+ABS( E( I-1 ) ) )
RESID = MAX( RESID, ABS( WORK( I ) )+ABS( WORK( N+I-1 ) )+
$ ABS( WORK( N+I ) ) )
20 CONTINUE
END IF
*
* Compute norm(L*D*L' - A) / (n * norm(A) * EPS)
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID / DBLE( N ) ) / ANORM ) / EPS
END IF
*
RETURN
*
* End of DPTT01
*
END
|
