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283 lines
7.8 KiB
283 lines
7.8 KiB
2 years ago
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*> \brief \b ZSPT03
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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 ZSPT03( UPLO, N, A, AINV, WORK, LDW, 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 LDW, 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( LDW, * )
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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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*> ZSPT03 computes the residual for a complex symmetric packed matrix
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*> times its 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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*> complex symmetric 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 complex symmetric 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 (symmetric) 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 (LDW,N)
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*> \endverbatim
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*>
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*> \param[in] LDW
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*> \verbatim
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*> LDW is INTEGER
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*> The leading dimension of the array WORK. LDW >= 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 ZSPT03( UPLO, N, A, AINV, WORK, LDW, 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 LDW, 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( LDW, * )
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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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* ..
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* .. Local Scalars ..
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INTEGER I, ICOL, J, JCOL, K, KCOL, NALL
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DOUBLE PRECISION AINVNM, ANORM, EPS
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COMPLEX*16 T
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSP
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COMPLEX*16 ZDOTU
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EXTERNAL LSAME, DLAMCH, ZLANGE, ZLANSP, ZDOTU
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE
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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 = ZLANSP( '1', UPLO, N, A, RWORK )
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AINVNM = ZLANSP( '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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* Case where both A and AINV are upper triangular:
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* Each element of - A * AINV is computed by taking the dot product
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* of a row of A with a column of AINV.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 70 I = 1, N
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ICOL = ( ( I-1 )*I ) / 2 + 1
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*
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* Code when J <= I
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*
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DO 30 J = 1, I
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JCOL = ( ( J-1 )*J ) / 2 + 1
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T = ZDOTU( J, A( ICOL ), 1, AINV( JCOL ), 1 )
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JCOL = JCOL + 2*J - 1
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KCOL = ICOL - 1
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DO 10 K = J + 1, I
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T = T + A( KCOL+K )*AINV( JCOL )
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JCOL = JCOL + K
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10 CONTINUE
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KCOL = KCOL + 2*I
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DO 20 K = I + 1, N
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T = T + A( KCOL )*AINV( JCOL )
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KCOL = KCOL + K
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JCOL = JCOL + K
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20 CONTINUE
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WORK( I, J ) = -T
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30 CONTINUE
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*
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* Code when J > I
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*
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DO 60 J = I + 1, N
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JCOL = ( ( J-1 )*J ) / 2 + 1
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T = ZDOTU( I, A( ICOL ), 1, AINV( JCOL ), 1 )
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JCOL = JCOL - 1
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KCOL = ICOL + 2*I - 1
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DO 40 K = I + 1, J
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T = T + A( KCOL )*AINV( JCOL+K )
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KCOL = KCOL + K
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40 CONTINUE
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JCOL = JCOL + 2*J
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DO 50 K = J + 1, N
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T = T + A( KCOL )*AINV( JCOL )
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KCOL = KCOL + K
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JCOL = JCOL + K
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50 CONTINUE
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WORK( I, J ) = -T
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60 CONTINUE
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70 CONTINUE
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ELSE
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*
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* Case where both A and AINV are lower triangular
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*
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NALL = ( N*( N+1 ) ) / 2
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DO 140 I = 1, N
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*
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* Code when J <= I
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*
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ICOL = NALL - ( ( N-I+1 )*( N-I+2 ) ) / 2 + 1
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DO 100 J = 1, I
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JCOL = NALL - ( ( N-J )*( N-J+1 ) ) / 2 - ( N-I )
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T = ZDOTU( N-I+1, A( ICOL ), 1, AINV( JCOL ), 1 )
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KCOL = I
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JCOL = J
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DO 80 K = 1, J - 1
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T = T + A( KCOL )*AINV( JCOL )
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JCOL = JCOL + N - K
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KCOL = KCOL + N - K
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80 CONTINUE
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JCOL = JCOL - J
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DO 90 K = J, I - 1
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T = T + A( KCOL )*AINV( JCOL+K )
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KCOL = KCOL + N - K
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90 CONTINUE
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WORK( I, J ) = -T
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100 CONTINUE
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*
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* Code when J > I
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*
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ICOL = NALL - ( ( N-I )*( N-I+1 ) ) / 2
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DO 130 J = I + 1, N
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JCOL = NALL - ( ( N-J+1 )*( N-J+2 ) ) / 2 + 1
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T = ZDOTU( N-J+1, A( ICOL-N+J ), 1, AINV( JCOL ), 1 )
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KCOL = I
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JCOL = J
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DO 110 K = 1, I - 1
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T = T + A( KCOL )*AINV( JCOL )
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JCOL = JCOL + N - K
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KCOL = KCOL + N - K
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110 CONTINUE
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KCOL = KCOL - I
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DO 120 K = I, J - 1
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T = T + A( KCOL+K )*AINV( JCOL )
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JCOL = JCOL + N - K
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120 CONTINUE
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WORK( I, J ) = -T
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130 CONTINUE
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140 CONTINUE
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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 150 I = 1, N
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WORK( I, I ) = WORK( I, I ) + ONE
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150 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, LDW, 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 ZSPT03
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*
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END
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