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*> \brief \b CHET01_3
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE CHET01_3( UPLO, N, A, LDA, AFAC, LDAFAC, E, IPIV, C,
* LDC, RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER LDA, LDAFAC, LDC, N
* REAL RESID
* ..
* .. Array Arguments ..
* INTEGER IPIV( * )
* REAL RWORK( * )
* COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
* E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHET01_3 reconstructs a Hermitian indefinite matrix A from its
*> block L*D*L' or U*D*U' factorization computed by CHETRF_RK
*> (or CHETRF_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
*> 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 (LDA,N)
*> The original Hermitian 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 array, dimension (LDAFAC,N)
*> Diagonal of the block diagonal matrix D and factors U or L
*> as computed by CHETRF_RK and CHETRF_BK:
*> a) ONLY diagonal elements of the Hermitian 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 array, dimension (N)
*> On entry, contains the superdiagonal (or subdiagonal)
*> elements of the Hermitian 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 referenced;
*> 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 CHETRF_RK (or CHETRF_BK).
*> \endverbatim
*>
*> \param[out] C
*> \verbatim
*> C is COMPLEX 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 REAL array, dimension (N)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is REAL
*> 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 complex_lin
*
* =====================================================================
SUBROUTINE CHET01_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
REAL RESID
* ..
* .. Array Arguments ..
INTEGER IPIV( * )
REAL RWORK( * )
COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ),
$ E( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ),
$ CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
REAL ANORM, EPS
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHE, SLAMCH
EXTERNAL LSAME, CLANHE, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CLASET, CLAVHE_ROOK, CSYCONVF_ROOK
* ..
* .. Intrinsic Functions ..
INTRINSIC AIMAG, REAL
* ..
* .. Executable Statements ..
*
* Quick exit if N = 0.
*
IF( N.LE.0 ) THEN
RESID = ZERO
RETURN
END IF
*
* a) Revert to multiplyers of L
*
CALL CSYCONVF_ROOK( UPLO, 'R', N, AFAC, LDAFAC, E, IPIV, INFO )
*
* 1) Determine EPS and the norm of A.
*
EPS = SLAMCH( 'Epsilon' )
ANORM = CLANHE( '1', UPLO, N, A, LDA, RWORK )
*
* Check the imaginary parts of the diagonal elements and return with
* an error code if any are nonzero.
*
DO J = 1, N
IF( AIMAG( AFAC( J, J ) ).NE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
END DO
*
* 2) Initialize C to the identity matrix.
*
CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC )
*
* 3) Call CLAVHE_ROOK to form the product D * U' (or D * L' ).
*
CALL CLAVHE_ROOK( UPLO, 'Conjugate', 'Non-unit', N, N, AFAC,
$ LDAFAC, IPIV, C, LDC, INFO )
*
* 4) Call ZLAVHE_RK again to multiply by U (or L ).
*
CALL CLAVHE_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 - 1
C( I, J ) = C( I, J ) - A( I, J )
END DO
C( J, J ) = C( J, J ) - REAL( A( J, J ) )
END DO
ELSE
DO J = 1, N
C( J, J ) = C( J, J ) - REAL( A( J, J ) )
DO I = J + 1, 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 = CLANHE( '1', UPLO, N, C, LDC, RWORK )
*
IF( ANORM.LE.ZERO ) THEN
IF( RESID.NE.ZERO )
$ RESID = ONE / EPS
ELSE
RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS
END IF
*
* b) Convert to factor of L (or U)
*
CALL CSYCONVF_ROOK( UPLO, 'C', N, AFAC, LDAFAC, E, IPIV, INFO )
*
RETURN
*
* End of CHET01_3
*
END
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