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261 lines
7.3 KiB
261 lines
7.3 KiB
*> \brief \b ZHET01_3
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZHET01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
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* LDC, RWORK, RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDA, LDAFAC, LDC, N
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* DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
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* E( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZHET01_3 reconstructs a Hermitian indefinite matrix A from its
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*> block L*D*L' or U*D*U' factorization computed by ZHETRF_RK
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*> (or ZHETRF_BK) and computes the residual
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*> norm( C - A ) / ( N * norm(A) * EPS ),
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*> where C is the reconstructed matrix and EPS is the machine epsilon.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] UPLO
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*> \verbatim
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*> UPLO is CHARACTER*1
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*> Specifies whether the upper or lower triangular part of the
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*> Hermitian matrix A is stored:
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*> = 'U': Upper triangular
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*> = 'L': Lower triangular
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows and columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> The original Hermitian matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N)
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*> \endverbatim
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*>
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*> \param[in] AFAC
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*> \verbatim
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*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
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*> Diagonal of the block diagonal matrix D and factors U or L
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*> as computed by ZHETRF_RK and ZHETRF_BK:
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*> a) ONLY diagonal elements of the Hermitian block diagonal
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*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
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*> (superdiagonal (or subdiagonal) elements of D
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*> should be provided on entry in array E), and
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*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
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*> If UPLO = 'L': factor L in the subdiagonal part of A.
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*> \endverbatim
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*>
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*> \param[in] LDAFAC
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*> \verbatim
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*> LDAFAC is INTEGER
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*> The leading dimension of the array AFAC.
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*> LDAFAC >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (N)
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*> On entry, contains the superdiagonal (or subdiagonal)
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*> elements of the Hermitian block diagonal matrix D
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*> with 1-by-1 or 2-by-2 diagonal blocks, where
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*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
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*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from ZHETRF_RK (or ZHETRF_BK).
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*> \endverbatim
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*>
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*> \param[out] C
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*> \verbatim
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*> C is COMPLEX*16 array, dimension (LDC,N)
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*> \endverbatim
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*>
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*> \param[in] LDC
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*> \verbatim
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*> LDC is INTEGER
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*> The leading dimension of the array C. LDC >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] RESID
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*> \verbatim
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*> RESID is DOUBLE PRECISION
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*> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS )
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*> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZHET01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
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$ LDC, RWORK, RESID )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER UPLO
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INTEGER LDA, LDAFAC, LDC, N
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DOUBLE PRECISION RESID
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
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$ E( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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COMPLEX*16 CZERO, CONE
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ),
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$ CONE = ( 1.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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INTEGER I, INFO, J
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DOUBLE PRECISION ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION ZLANHE, DLAMCH
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EXTERNAL LSAME, ZLANHE, DLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLASET, ZLAVHE_ROOK, ZSYCONVF_ROOK
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DIMAG, DBLE
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* ..
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* .. Executable Statements ..
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*
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* Quick exit if N = 0.
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*
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IF( N.LE.0 ) THEN
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RESID = ZERO
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RETURN
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END IF
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*
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* a) Revert to multipliers of L
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*
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CALL ZSYCONVF_ROOK( UPLO, 'R', N, AFAC, LDAFAC, E, IPIV, INFO )
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*
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* 1) Determine EPS and the norm of A.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
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*
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* Check the imaginary parts of the diagonal elements and return with
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* an error code if any are nonzero.
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*
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DO J = 1, N
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IF( DIMAG( AFAC( J, J ) ).NE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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END DO
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*
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* 2) Initialize C to the identity matrix.
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*
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CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
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*
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* 3) Call ZLAVHE_ROOK to form the product D * U' (or D * L' ).
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*
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CALL ZLAVHE_ROOK( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC,
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$ LDAFAC, IPIV, C, LDC, INFO )
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*
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* 4) Call ZLAVHE_RK again to multiply by U (or L ).
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*
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CALL ZLAVHE_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC,
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$ LDAFAC, IPIV, C, LDC, INFO )
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*
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* 5) Compute the difference C - A .
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO J = 1, N
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DO I = 1, J - 1
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C( I, J ) = C( I, J ) - A( I, J )
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END DO
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C( J, J ) = C( J, J ) - DBLE( A( J, J ) )
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END DO
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ELSE
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DO J = 1, N
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C( J, J ) = C( J, J ) - DBLE( A( J, J ) )
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DO I = J + 1, N
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C( I, J ) = C( I, J ) - A( I, J )
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END DO
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END DO
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END IF
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*
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* 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
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*
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RESID = ZLANHE( '1', UPLO, N, C, LDC, RWORK )
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*
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IF( ANORM.LE.ZERO ) THEN
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IF( RESID.NE.ZERO )
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$ RESID = ONE / EPS
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ELSE
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RESID = ( ( RESID/DBLE( N ) )/ANORM ) / EPS
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END IF
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*
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* b) Convert to factor of L (or U)
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*
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CALL ZSYCONVF_ROOK( UPLO, 'C', N, AFAC, LDAFAC, E, IPIV, INFO )
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*
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RETURN
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*
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* End of ZHET01_3
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*
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END
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