zsyt01.f

Go to the documentation of this file.

*> \brief \b ZSYT01
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZSYT01( UPLO, N, A, LDA, AFAC, LDAFAC, 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, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZSYT01 reconstructs a complex symmetric indefinite 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 transpose of L, and U' is the transpose of U.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] UPLO
*> \verbatim
*>          UPLO is CHARACTER*1
*>          Specifies whether the upper or lower triangular part of the
*>          complex 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 complex 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)
*>          The factored form of the matrix A.  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 ZSYTRF.
*> \endverbatim
*>
*> \param[in] LDAFAC
*> \verbatim
*>          LDAFAC is INTEGER
*>          The leading dimension of the array AFAC.  LDAFAC >= max(1,N).
*> \endverbatim
*>
*> \param[in] IPIV
*> \verbatim
*>          IPIV is INTEGER array, dimension (N)
*>          The pivot indices from ZSYTRF.
*> \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 zsyt01( UPLO, N, A, LDA, AFAC, LDAFAC, 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            LDA, LDAFAC, LDC, N
      DOUBLE PRECISION   RESID
*     ..
*     .. Array Arguments ..
      INTEGER            IPIV( * )
      DOUBLE PRECISION   RWORK( * )
      COMPLEX*16         A( LDA, * ), AFAC( LDAFAC, * ), 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
      DOUBLE PRECISION   ANORM, EPS
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, ZLANSY
      EXTERNAL           lsame, dlamch, zlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           zlaset, zlavsy
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble
*     ..
*     .. 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 = zlansy( '1', uplo, n, a, lda, rwork )
*
*     Initialize C to the identity matrix.
*
      CALL zlaset( 'Full', n, n, czero, cone, c, ldc )
*
*     Call ZLAVSY to form the product D * U' (or D * L' ).
*
      CALL zlavsy( uplo, 'Transpose', 'Non-unit', n, n, afac, ldafac,
     $             ipiv, c, ldc, info )
*
*     Call ZLAVSY again to multiply by U (or L ).
*
      CALL zlavsy( uplo, 'No transpose', 'Unit', n, n, afac, ldafac,
     $             ipiv, c, ldc, info )
*
*     Compute the difference  C - A .
*
      IF( lsame( uplo, 'U' ) ) THEN
         DO 20 j = 1, n
            DO 10 i = 1, j
               c( i, j ) = c( i, j ) - a( i, j )
   10       CONTINUE
   20    CONTINUE
      ELSE
         DO 40 j = 1, n
            DO 30 i = j, n
               c( i, j ) = c( i, j ) - a( i, j )
   30       CONTINUE
   40    CONTINUE
      END IF
*
*     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
*
      RETURN
*
*     End of ZSYT01
*
      SUBROUTINE zsyt01( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, …
      END