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246 lines
6.7 KiB
246 lines
6.7 KiB
2 years ago
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*> \brief \b SPPCON
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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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*> \htmlonly
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*> Download SPPCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sppcon.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sppcon.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sppcon.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, N
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* REAL ANORM, RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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* REAL AP( * ), WORK( * )
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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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*> SPPCON estimates the reciprocal of the condition number (in the
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*> 1-norm) of a real symmetric positive definite packed matrix using
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*> the Cholesky factorization A = U**T*U or A = L*L**T computed by
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*> SPPTRF.
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*>
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*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
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*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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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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*> = 'U': Upper triangle of A is stored;
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*> = 'L': Lower triangle of A is stored.
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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 order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] AP
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*> \verbatim
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*> AP is REAL array, dimension (N*(N+1)/2)
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*> The triangular factor U or L from the Cholesky factorization
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*> A = U**T*U or A = L*L**T, packed columnwise in a linear
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*> array. The j-th column of U or L is stored in the array AP
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*> as follows:
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
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*> \endverbatim
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*>
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*> \param[in] ANORM
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*> \verbatim
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*> ANORM is REAL
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*> The 1-norm (or infinity-norm) of the symmetric matrix A.
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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 REAL
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*> The reciprocal of the condition number of the matrix A,
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*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
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*> estimate of the 1-norm of inv(A) computed in this routine.
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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 REAL array, dimension (3*N)
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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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 realOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE SPPCON( UPLO, N, AP, ANORM, RCOND, WORK, IWORK, INFO )
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*
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* -- LAPACK computational 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 INFO, N
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REAL ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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REAL AP( * ), WORK( * )
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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 ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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CHARACTER NORMIN
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INTEGER IX, KASE
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REAL AINVNM, SCALE, SCALEL, SCALEU, SMLNUM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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INTEGER ISAMAX
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REAL SLAMCH
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EXTERNAL LSAME, ISAMAX, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SLACN2, SLATPS, SRSCL, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS
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* ..
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* .. Executable Statements ..
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*
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* Test the input parameters.
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*
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INFO = 0
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UPPER = LSAME( UPLO, 'U' )
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IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -4
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SPPCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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RCOND = ZERO
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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ELSE IF( ANORM.EQ.ZERO ) THEN
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RETURN
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END IF
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*
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SMLNUM = SLAMCH( 'Safe minimum' )
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*
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* Estimate the 1-norm of the inverse.
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*
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KASE = 0
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NORMIN = 'N'
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10 CONTINUE
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CALL SLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( UPPER ) THEN
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*
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* Multiply by inv(U**T).
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*
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CALL SLATPS( 'Upper', 'Transpose', 'Non-unit', NORMIN, N,
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$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
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NORMIN = 'Y'
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*
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* Multiply by inv(U).
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*
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CALL SLATPS( 'Upper', 'No transpose', 'Non-unit', NORMIN, N,
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$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
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ELSE
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*
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* Multiply by inv(L).
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*
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CALL SLATPS( 'Lower', 'No transpose', 'Non-unit', NORMIN, N,
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$ AP, WORK, SCALEL, WORK( 2*N+1 ), INFO )
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NORMIN = 'Y'
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*
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* Multiply by inv(L**T).
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*
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CALL SLATPS( 'Lower', 'Transpose', 'Non-unit', NORMIN, N,
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$ AP, WORK, SCALEU, WORK( 2*N+1 ), INFO )
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END IF
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*
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* Multiply by 1/SCALE if doing so will not cause overflow.
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*
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SCALE = SCALEL*SCALEU
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IF( SCALE.NE.ONE ) THEN
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IX = ISAMAX( N, WORK, 1 )
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IF( SCALE.LT.ABS( WORK( IX ) )*SMLNUM .OR. SCALE.EQ.ZERO )
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$ GO TO 20
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CALL SRSCL( N, SCALE, WORK, 1 )
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END IF
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GO TO 10
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / AINVNM ) / ANORM
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*
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20 CONTINUE
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RETURN
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*
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* End of SPPCON
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*
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END
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