*> \brief \b CSYT01_3 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CSYT01_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 *> *> CSYT01_3 reconstructs a symmetric indefinite matrix A from its *> block L*D*L' or U*D*U' factorization computed by CSYTRF_RK *> (or CSYTRF_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 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 array, dimension (LDAFAC,N) *> Diagonal of the block diagonal matrix D and factors U or L *> as computed by CSYTRF_RK and CSYTRF_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 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 CSYTRF_RK (or CSYTRF_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 November 2016 * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CSYT01_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..-- * November 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 SLAMCH, CLANSY EXTERNAL LSAME, SLAMCH, CLANSY * .. * .. External Subroutines .. EXTERNAL CLASET, CLAVSY_ROOK, CSYCONVF_ROOK * .. * .. Intrinsic Functions .. INTRINSIC 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 = CLANSY( '1', UPLO, N, A, LDA, RWORK ) * * 2) Initialize C to the identity matrix. * CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) * * 3) Call ZLAVSY_ROOK to form the product D * U' (or D * L' ). * CALL CLAVSY_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 CLAVSY_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 = CLANSY( '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 CSYT01_3 * END