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280 lines
8.0 KiB
280 lines
8.0 KiB
2 years ago
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*> \brief \b ZSYCON_3
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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 ZSYCON_3 + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsycon_3.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/zsycon_3.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/zsycon_3.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 ZSYCON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
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* WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER INFO, LDA, N
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* DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX*16 A( LDA, * ), E ( * ), 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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*> ZSYCON_3 estimates the reciprocal of the condition number (in the
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*> 1-norm) of a complex symmetric matrix A using the factorization
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*> computed by ZSYTRF_RK or ZSYTRF_BK:
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*>
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*> A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
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*>
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*> where U (or L) is unit upper (or lower) triangular matrix,
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*> U**T (or L**T) is the transpose of U (or L), P is a permutation
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*> matrix, P**T is the transpose of P, and D is symmetric and block
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*> diagonal with 1-by-1 and 2-by-2 diagonal blocks.
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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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*> This routine uses BLAS3 solver ZSYTRS_3.
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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 details of the factorization are
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*> stored as an upper or lower triangular matrix:
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*> = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T);
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*> = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T).
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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] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,N)
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*> Diagonal of the block diagonal matrix D and factors U or L
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*> as computed by ZSYTRF_RK and ZSYTRF_BK:
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*> a) ONLY diagonal elements of the symmetric block diagonal
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*> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
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*> (superdiagonal (or subdiagonal) elements of D
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*> should be provided on entry in array E), and
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*> b) If UPLO = 'U': factor U in the superdiagonal part of A.
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*> If UPLO = 'L': factor L in the subdiagonal part of 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] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (N)
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*> On entry, contains the superdiagonal (or subdiagonal)
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*> elements of the symmetric block diagonal matrix D
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*> with 1-by-1 or 2-by-2 diagonal blocks, where
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*> If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
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*> If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
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*>
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*> NOTE: For 1-by-1 diagonal block D(k), where
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*> 1 <= k <= N, the element E(k) is not referenced in both
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*> UPLO = 'U' or UPLO = 'L' cases.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> Details of the interchanges and the block structure of D
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*> as determined by ZSYTRF_RK or ZSYTRF_BK.
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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 DOUBLE PRECISION
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*> The 1-norm of the original 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 DOUBLE PRECISION
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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 COMPLEX*16 array, dimension (2*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 complex16SYcomputational
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*
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*> \par Contributors:
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* ==================
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*> \verbatim
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*>
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*> June 2017, Igor Kozachenko,
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*> Computer Science Division,
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*> University of California, Berkeley
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*>
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*> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
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*> School of Mathematics,
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*> University of Manchester
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*>
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*> \endverbatim
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*
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* =====================================================================
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SUBROUTINE ZSYCON_3( UPLO, N, A, LDA, E, IPIV, ANORM, RCOND,
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$ WORK, 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, LDA, N
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DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX*16 A( LDA, * ), E( * ), 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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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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COMPLEX*16 CZERO
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL UPPER
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INTEGER I, KASE
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DOUBLE PRECISION AINVNM
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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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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL ZLACN2, ZSYTRS_3, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -4
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -7
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZSYCON_3', -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.LE.ZERO ) THEN
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RETURN
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END IF
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*
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* Check that the diagonal matrix D is nonsingular.
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*
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IF( UPPER ) THEN
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*
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* Upper triangular storage: examine D from bottom to top
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*
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DO I = N, 1, -1
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IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
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$ RETURN
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END DO
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ELSE
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*
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* Lower triangular storage: examine D from top to bottom.
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*
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DO I = 1, N
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IF( IPIV( I ).GT.0 .AND. A( I, I ).EQ.CZERO )
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$ RETURN
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END DO
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END IF
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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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30 CONTINUE
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CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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*
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* Multiply by inv(L*D*L**T) or inv(U*D*U**T).
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*
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CALL ZSYTRS_3( UPLO, N, 1, A, LDA, E, IPIV, WORK, N, INFO )
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GO TO 30
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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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RETURN
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*
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* End of ZSYCON_3
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*
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END
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