177 lines
4.4 KiB
Fortran
177 lines
4.4 KiB
Fortran
*> \brief \b ZPTT01
|
|
*
|
|
* =========== DOCUMENTATION ===========
|
|
*
|
|
* Online html documentation available at
|
|
* http://www.netlib.org/lapack/explore-html/
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* SUBROUTINE ZPTT01( N, D, E, DF, EF, WORK, RESID )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* INTEGER N
|
|
* DOUBLE PRECISION RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* DOUBLE PRECISION D( * ), DF( * )
|
|
* COMPLEX*16 E( * ), EF( * ), WORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> ZPTT01 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 November 2011
|
|
*
|
|
*> \ingroup complex16_lin
|
|
*
|
|
* =====================================================================
|
|
SUBROUTINE ZPTT01( N, D, E, DF, EF, 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 ..
|
|
INTEGER N
|
|
DOUBLE PRECISION RESID
|
|
* ..
|
|
* .. Array Arguments ..
|
|
DOUBLE PRECISION D( * ), DF( * )
|
|
COMPLEX*16 E( * ), EF( * ), WORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Parameters ..
|
|
DOUBLE PRECISION ONE, ZERO
|
|
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
|
|
* ..
|
|
* .. Local Scalars ..
|
|
INTEGER I
|
|
DOUBLE PRECISION ANORM, EPS
|
|
COMPLEX*16 DE
|
|
* ..
|
|
* .. External Functions ..
|
|
DOUBLE PRECISION DLAMCH
|
|
EXTERNAL DLAMCH
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, DBLE, DCONJG, 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*DCONJG( 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 ZPTT01
|
|
*
|
|
END
|