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|
*> \brief \b ZHPT01
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER LDC, N
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZHPT01 reconstructs a Hermitian indefinite packed matrix A from its
*> block L*D*L' or U*D*U' factorization and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix, EPS is the machine epsilon,
*> L' is the conjugate transpose of L, and U' is the conjugate transpose
*> of U.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> Hermitian matrix A is stored:
*> = 'U': Upper triangular
*> = 'L': Lower triangular
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows and columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (N*(N+1)/2)
*> The original Hermitian matrix A, stored as a packed
*> triangular matrix.
*> \endverbatim
*>
*> \param[in] AFAC
*> \verbatim
*> AFAC is COMPLEX*16 array, dimension (N*(N+1)/2)
*> The factored form of the matrix A, stored as a packed
*> triangular matrix. AFAC contains the block diagonal matrix D
*> and the multipliers used to obtain the factor L or U from the
*> block L*D*L' or U*D*U' factorization as computed by ZHPTRF.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from ZHPTRF.
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is COMPLEX*16 array, dimension (LDC,N)
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*> LDC is INTEGER
*> The leading dimension of the array C. LDC >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
*> If UPLO = 'U', norm(U*D*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.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZHPT01( UPLO, N, A, AFAC, IPIV, C, LDC, RWORK, RESID )
*
* -- 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 UPLO
INTEGER LDC, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( * ), AFAC( * ), C( LDC, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
COMPLEX*16 CZERO, CONE
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
$ CONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J, JC
DOUBLE PRECISION ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANHE, ZLANHP
EXTERNAL LSAME, DLAMCH, ZLANHE, ZLANHP
* ..
* .. External Subroutines ..
EXTERNAL ZLASET, ZLAVHP
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DIMAG
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* Determine EPS and the norm of A.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
*
* Check the imaginary parts of the diagonal elements and return with
* an error code if any are nonzero.
*
JC = 1
IF( LSAME( UPLO, 'U' ) ) THEN
DO 10 J = 1, N
IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
JC = JC + J + 1
10 CONTINUE
ELSE
DO 20 J = 1, N
IF( DIMAG( AFAC( JC ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
JC = JC + N - J + 1
20 CONTINUE
END IF
*
* Initialize C to the identity matrix.
*
CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
*
* Call ZLAVHP to form the product D * U' (or D * L' ).
*
CALL ZLAVHP( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Call ZLAVHP again to multiply by U ( or L ).
*
CALL ZLAVHP( UPLO, 'No transpose', 'Unit', N, N, AFAC, IPIV, C,
$ LDC, INFO )
*
* Compute the difference C - A .
*
IF( LSAME( UPLO, 'U' ) ) THEN
JC = 0
DO 40 J = 1, N
DO 30 I = 1, J - 1
C( I, J ) = C( I, J ) - A( JC+I )
30 CONTINUE
C( J, J ) = C( J, J ) - DBLE( A( JC+J ) )
JC = JC + J
40 CONTINUE
ELSE
JC = 1
DO 60 J = 1, N
C( J, J ) = C( J, J ) - DBLE( A( JC ) )
DO 50 I = J + 1, N
C( I, J ) = C( I, J ) - A( JC+I-J )
50 CONTINUE
JC = JC + N - J + 1
60 CONTINUE
END IF
*
* Compute norm( C - A ) / ( N * norm(A) * EPS )
*
RESID = ZLANHE( '1', UPLO, N, C, LDC, 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 ZHPT01
*
END
|
