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303 lines
7.8 KiB
303 lines
7.8 KiB
*> \brief \b SPST01
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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 SPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
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* PIV, RWORK, RESID, RANK )
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*
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* .. Scalar Arguments ..
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* REAL RESID
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* INTEGER LDA, LDAFAC, LDPERM, N, RANK
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* CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AFAC( LDAFAC, * ),
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* $ PERM( LDPERM, * ), RWORK( * )
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* INTEGER PIV( * )
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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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*> SPST01 reconstructs a symmetric positive semidefinite matrix A
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*> from its L or U factors and the permutation matrix P and computes
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*> the residual
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*> norm( P*L*L'*P' - A ) / ( N * norm(A) * EPS ) or
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*> norm( P*U'*U*P' - A ) / ( N * norm(A) * 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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*> 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 REAL array, dimension (LDA,N)
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*> The original symmetric matrix A.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,N)
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*> \endverbatim
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*>
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*> \param[in] AFAC
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*> \verbatim
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*> AFAC is REAL array, dimension (LDAFAC,N)
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*> The factor L or U from the L*L' or U'*U
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*> factorization of A.
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*> \endverbatim
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*>
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*> \param[in] LDAFAC
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*> \verbatim
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*> LDAFAC is INTEGER
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*> The leading dimension of the array AFAC. LDAFAC >= max(1,N).
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*> \endverbatim
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*>
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*> \param[out] PERM
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*> \verbatim
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*> PERM is REAL array, dimension (LDPERM,N)
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*> Overwritten with the reconstructed matrix, and then with the
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*> difference P*L*L'*P' - A (or P*U'*U*P' - A)
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*> \endverbatim
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*>
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*> \param[in] LDPERM
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*> \verbatim
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*> LDPERM is INTEGER
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*> The leading dimension of the array PERM.
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*> LDAPERM >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] PIV
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*> \verbatim
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*> PIV is INTEGER array, dimension (N)
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*> PIV is such that the nonzero entries are
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*> P( PIV( K ), K ) = 1.
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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 REAL array, dimension (N)
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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 REAL
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*> If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS )
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*> If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS )
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*> \endverbatim
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*>
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*> \param[in] RANK
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*> \verbatim
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*> RANK is INTEGER
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*> number of nonzero singular values of A.
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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 single_lin
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*
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* =====================================================================
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SUBROUTINE SPST01( UPLO, N, A, LDA, AFAC, LDAFAC, PERM, LDPERM,
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$ PIV, RWORK, RESID, RANK )
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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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REAL RESID
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INTEGER LDA, LDAFAC, LDPERM, N, RANK
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CHARACTER UPLO
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AFAC( LDAFAC, * ),
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$ PERM( LDPERM, * ), RWORK( * )
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INTEGER PIV( * )
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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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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REAL ANORM, EPS, T
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INTEGER I, J, K
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* ..
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* .. External Functions ..
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REAL SDOT, SLAMCH, SLANSY
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LOGICAL LSAME
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EXTERNAL SDOT, SLAMCH, SLANSY, LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL SSCAL, SSYR, STRMV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC REAL
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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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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.
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*
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EPS = SLAMCH( 'Epsilon' )
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ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
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IF( ANORM.LE.ZERO ) THEN
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RESID = ONE / EPS
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RETURN
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END IF
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*
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* Compute the product U'*U, overwriting U.
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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IF( RANK.LT.N ) THEN
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DO 110 J = RANK + 1, N
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DO 100 I = RANK + 1, J
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AFAC( I, J ) = ZERO
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100 CONTINUE
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110 CONTINUE
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END IF
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*
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DO 120 K = N, 1, -1
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*
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* Compute the (K,K) element of the result.
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*
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T = SDOT( K, AFAC( 1, K ), 1, AFAC( 1, K ), 1 )
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AFAC( K, K ) = T
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*
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* Compute the rest of column K.
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*
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CALL STRMV( 'Upper', 'Transpose', 'Non-unit', K-1, AFAC,
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$ LDAFAC, AFAC( 1, K ), 1 )
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*
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120 CONTINUE
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*
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* Compute the product L*L', overwriting L.
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*
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ELSE
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*
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IF( RANK.LT.N ) THEN
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DO 140 J = RANK + 1, N
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DO 130 I = J, N
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AFAC( I, J ) = ZERO
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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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DO 150 K = N, 1, -1
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* Add a multiple of column K of the factor L to each of
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* columns K+1 through N.
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*
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IF( K+1.LE.N )
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$ CALL SSYR( 'Lower', N-K, ONE, AFAC( K+1, K ), 1,
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$ AFAC( K+1, K+1 ), LDAFAC )
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*
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* Scale column K by the diagonal element.
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*
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T = AFAC( K, K )
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CALL SSCAL( N-K+1, T, AFAC( K, K ), 1 )
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150 CONTINUE
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*
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END IF
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*
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* Form P*L*L'*P' or P*U'*U*P'
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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*
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DO 170 J = 1, N
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DO 160 I = 1, N
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IF( PIV( I ).LE.PIV( J ) ) THEN
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IF( I.LE.J ) THEN
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PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
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ELSE
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PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
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END IF
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END IF
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160 CONTINUE
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170 CONTINUE
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*
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*
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ELSE
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*
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DO 190 J = 1, N
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DO 180 I = 1, N
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IF( PIV( I ).GE.PIV( J ) ) THEN
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IF( I.GE.J ) THEN
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PERM( PIV( I ), PIV( J ) ) = AFAC( I, J )
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ELSE
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PERM( PIV( I ), PIV( J ) ) = AFAC( J, I )
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END IF
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END IF
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180 CONTINUE
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190 CONTINUE
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*
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END IF
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*
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* Compute the difference P*L*L'*P' - A (or P*U'*U*P' - A).
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*
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 210 J = 1, N
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DO 200 I = 1, J
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PERM( I, J ) = PERM( I, J ) - A( I, J )
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200 CONTINUE
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210 CONTINUE
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ELSE
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DO 230 J = 1, N
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DO 220 I = J, N
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PERM( I, J ) = PERM( I, J ) - A( I, J )
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220 CONTINUE
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230 CONTINUE
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END IF
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*
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* Compute norm( P*L*L'P - A ) / ( N * norm(A) * EPS ), or
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* ( P*U'*U*P' - A )/ ( N * norm(A) * EPS ).
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*
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RESID = SLANSY( '1', UPLO, N, PERM, LDAFAC, RWORK )
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*
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RESID = ( ( RESID / REAL( N ) ) / ANORM ) / EPS
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*
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RETURN
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*
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* End of SPST01
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*
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END
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