250 lines
6.6 KiB
Fortran
250 lines
6.6 KiB
Fortran
*> \brief \b ZPPT03
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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 ZPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
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* RESID )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER LDWORK, N
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* DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( * ), AINV( * ), WORK( LDWORK, * )
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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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*> ZPPT03 computes the residual for a Hermitian packed matrix times its
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*> inverse:
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*> norm( I - A*AINV ) / ( N * norm(A) * norm(AINV) * EPS ),
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*> where 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 (N*(N+1)/2)
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*> The original Hermitian matrix A, stored as a packed
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*> triangular matrix.
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*> \endverbatim
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*>
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*> \param[in] AINV
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*> \verbatim
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*> AINV is COMPLEX*16 array, dimension (N*(N+1)/2)
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*> The (Hermitian) inverse of the matrix A, stored as a packed
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*> triangular matrix.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (LDWORK,N)
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*> \endverbatim
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*>
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*> \param[in] LDWORK
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*> \verbatim
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*> LDWORK is INTEGER
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*> The leading dimension of the array WORK. LDWORK >= 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] RCOND
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*> \verbatim
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*> RCOND is DOUBLE PRECISION
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*> The reciprocal of the condition number of A, computed as
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*> ( 1/norm(A) ) / norm(AINV).
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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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*> norm(I - A*AINV) / ( N * norm(A) * norm(AINV) * 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 ZPPT03( UPLO, N, A, AINV, WORK, LDWORK, RWORK, RCOND,
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$ 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 LDWORK, N
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DOUBLE PRECISION RCOND, RESID
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( * ), AINV( * ), WORK( LDWORK, * )
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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, J, JJ
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DOUBLE PRECISION AINVNM, ANORM, EPS
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, ZLANGE, ZLANHP
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EXTERNAL LSAME, DLAMCH, ZLANGE, ZLANHP
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, DCONJG
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* ..
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* .. External Subroutines ..
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EXTERNAL ZCOPY, ZHPMV
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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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RCOND = ONE
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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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* Exit with RESID = 1/EPS if ANORM = 0 or AINVNM = 0.
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*
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EPS = DLAMCH( 'Epsilon' )
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ANORM = ZLANHP( '1', UPLO, N, A, RWORK )
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AINVNM = ZLANHP( '1', UPLO, N, AINV, RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCOND = ZERO
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RESID = ONE / EPS
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RETURN
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END IF
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RCOND = ( ONE / ANORM ) / AINVNM
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*
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* UPLO = 'U':
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* Copy the leading N-1 x N-1 submatrix of AINV to WORK(1:N,2:N) and
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* expand it to a full matrix, then multiply by A one column at a
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* time, moving the result one column to the left.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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* Copy AINV
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*
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JJ = 1
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DO 20 J = 1, N - 1
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CALL ZCOPY( J, AINV( JJ ), 1, WORK( 1, J+1 ), 1 )
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DO 10 I = 1, J - 1
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WORK( J, I+1 ) = DCONJG( AINV( JJ+I-1 ) )
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10 CONTINUE
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JJ = JJ + J
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20 CONTINUE
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JJ = ( ( N-1 )*N ) / 2 + 1
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DO 30 I = 1, N - 1
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WORK( N, I+1 ) = DCONJG( AINV( JJ+I-1 ) )
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30 CONTINUE
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*
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* Multiply by A
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*
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DO 40 J = 1, N - 1
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CALL ZHPMV( 'Upper', N, -CONE, A, WORK( 1, J+1 ), 1, CZERO,
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$ WORK( 1, J ), 1 )
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40 CONTINUE
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CALL ZHPMV( 'Upper', N, -CONE, A, AINV( JJ ), 1, CZERO,
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$ WORK( 1, N ), 1 )
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*
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* UPLO = 'L':
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* Copy the trailing N-1 x N-1 submatrix of AINV to WORK(1:N,1:N-1)
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* and multiply by A, moving each column to the right.
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*
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ELSE
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*
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* Copy AINV
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*
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DO 50 I = 1, N - 1
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WORK( 1, I ) = DCONJG( AINV( I+1 ) )
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50 CONTINUE
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JJ = N + 1
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DO 70 J = 2, N
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CALL ZCOPY( N-J+1, AINV( JJ ), 1, WORK( J, J-1 ), 1 )
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DO 60 I = 1, N - J
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WORK( J, J+I-1 ) = DCONJG( AINV( JJ+I ) )
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60 CONTINUE
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JJ = JJ + N - J + 1
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70 CONTINUE
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*
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* Multiply by A
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*
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DO 80 J = N, 2, -1
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CALL ZHPMV( 'Lower', N, -CONE, A, WORK( 1, J-1 ), 1, CZERO,
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$ WORK( 1, J ), 1 )
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80 CONTINUE
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CALL ZHPMV( 'Lower', N, -CONE, A, AINV( 1 ), 1, CZERO,
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$ WORK( 1, 1 ), 1 )
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*
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END IF
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*
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* Add the identity matrix to WORK .
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*
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DO 90 I = 1, N
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WORK( I, I ) = WORK( I, I ) + CONE
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90 CONTINUE
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*
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* Compute norm(I - A*AINV) / (N * norm(A) * norm(AINV) * EPS)
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*
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RESID = ZLANGE( '1', N, N, WORK, LDWORK, RWORK )
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*
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RESID = ( ( RESID*RCOND ) / EPS ) / DBLE( N )
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*
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RETURN
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*
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* End of ZPPT03
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*
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END
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