*> \brief \b ZSYT01_3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZSYT01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
* LDC, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER LDA, LDAFAC, LDC, N
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* DOUBLE PRECISION RWORK( * )
* COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
* E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZSYT01_3 reconstructs a symmetric indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization computed by ZSYTRF_RK
*> (or ZSYTRF_BK) and computes the residual
*> norm( C - A ) / ( N * norm(A) * EPS ),
*> where C is the reconstructed matrix and EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> Specifies whether the upper or lower triangular part of the
*> symmetric 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 (LDA,N)
*> The original symmetric matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N)
*> \endverbatim
*>
*> \param[in] AFAC
*> \verbatim
*> AFAC is COMPLEX*16 array, dimension (LDAFAC,N)
*> Diagonal of the block diagonal matrix D and factors U or L
*> as computed by ZSYTRF_RK and ZSYTRF_BK:
*> a) ONLY diagonal elements of the symmetric block diagonal
*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
*> (superdiagonal (or subdiagonal) elements of D
*> should be provided on entry in array E), and
*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
*> If UPLO = 'L': factor L in the subdiagonal part of A.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*> LDAFAC is INTEGER
*> The leading dimension of the array AFAC.
*> LDAFAC >= max(1,N).
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is COMPLEX*16 array, dimension (N)
*> On entry, contains the superdiagonal (or subdiagonal)
*> elements of the symmetric block diagonal matrix D
*> with 1-by-1 or 2-by-2 diagonal blocks, where
*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not refernced;
*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*> IPIV is INTEGER array, dimension (N)
*> The pivot indices from ZSYTRF_RK (or ZSYTRF_BK).
*> \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.
*
*> \date December 2016
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZSYT01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
$ LDC, RWORK, 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 ..
CHARACTER UPLO
INTEGER LDA, LDAFAC, LDC, N
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
$ E( * )
* ..
*
* =====================================================================
*
* .. 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
DOUBLE PRECISION ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANSY
EXTERNAL LSAME, DLAMCH, ZLANSY
* ..
* .. External Subroutines ..
EXTERNAL ZLASET, ZLAVSY_ROOK, ZSYCONVF_ROOK
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* a) Revert to multiplyers of L
*
CALL ZSYCONVF_ROOK( UPLO, 'R', N, AFAC, LDAFAC, E, IPIV, INFO )
*
* 1) Determine EPS and the norm of A.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
*
* 2) Initialize C to the identity matrix.
*
CALL ZLASET( 'Full', N, N, CZERO, CONE, C, LDC )
*
* 3) Call ZLAVSY_ROOK to form the product D * U' (or D * L' ).
*
CALL ZLAVSY_ROOK( UPLO, 'Transpose', 'Non-unit', N, N, AFAC,
$ LDAFAC, IPIV, C, LDC, INFO )
*
* 4) Call ZLAVSY_ROOK again to multiply by U (or L ).
*
CALL ZLAVSY_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC,
$ LDAFAC, IPIV, C, LDC, INFO )
*
* 5) Compute the difference C - A .
*
IF( LSAME( UPLO, 'U' ) ) THEN
DO J = 1, N
DO I = 1, J
C( I, J ) = C( I, J ) - A( I, J )
END DO
END DO
ELSE
DO J = 1, N
DO I = J, N
C( I, J ) = C( I, J ) - A( I, J )
END DO
END DO
END IF
*
* 6) Compute norm( C - A ) / ( N * norm(A) * EPS )
*
RESID = ZLANSY( '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
*
* b) Convert to factor of L (or U)
*
CALL ZSYCONVF_ROOK( UPLO, 'C', N, AFAC, LDAFAC, E, IPIV, INFO )
*
RETURN
*
* End of ZSYT01_3
*
END