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326 lines
8.7 KiB
326 lines
8.7 KiB
2 years ago
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*> \brief \b SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
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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 SLA_PORCOND + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_porcond.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/sla_porcond.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/sla_porcond.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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* REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
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* INFO, WORK, IWORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER UPLO
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* INTEGER N, LDA, LDAF, INFO, CMODE
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* REAL A( LDA, * ), AF( LDAF, * ), WORK( * ),
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* $ C( * )
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* ..
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* .. Array Arguments ..
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* INTEGER IWORK( * )
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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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*> SLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C)
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*> where op2 is determined by CMODE as follows
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*> CMODE = 1 op2(C) = C
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*> CMODE = 0 op2(C) = I
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*> CMODE = -1 op2(C) = inv(C)
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*> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
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*> is computed by computing scaling factors R such that
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*> diag(R)*A*op2(C) is row equilibrated and computing the standard
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*> infinity-norm condition number.
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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 number of linear equations, i.e., the order of the
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*> 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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*> On entry, the N-by-N 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] AF
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*> \verbatim
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*> AF is REAL array, dimension (LDAF,N)
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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, as computed by SPOTRF.
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*> \endverbatim
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*>
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*> \param[in] LDAF
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*> \verbatim
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*> LDAF is INTEGER
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*> The leading dimension of the array AF. LDAF >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] CMODE
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*> \verbatim
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*> CMODE is INTEGER
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*> Determines op2(C) in the formula op(A) * op2(C) as follows:
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*> CMODE = 1 op2(C) = C
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*> CMODE = 0 op2(C) = I
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*> CMODE = -1 op2(C) = inv(C)
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is REAL array, dimension (N)
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*> The vector C in the formula op(A) * op2(C).
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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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*> i > 0: The ith argument is invalid.
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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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*> Workspace.
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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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*> Workspace.
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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 realPOcomputational
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*
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* =====================================================================
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REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
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$ INFO, WORK, IWORK )
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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 N, LDA, LDAF, INFO, CMODE
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REAL A( LDA, * ), AF( LDAF, * ), WORK( * ),
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$ C( * )
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* ..
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* .. Array Arguments ..
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INTEGER IWORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Local Scalars ..
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INTEGER KASE, I, J
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REAL AINVNM, TMP
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LOGICAL UP
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* ..
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* .. Array Arguments ..
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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 SLACN2, SPOTRS, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Executable Statements ..
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*
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SLA_PORCOND = 0.0
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*
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INFO = 0
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IF( N.LT.0 ) THEN
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INFO = -2
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'SLA_PORCOND', -INFO )
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RETURN
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END IF
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IF( N.EQ.0 ) THEN
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SLA_PORCOND = 1.0
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RETURN
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END IF
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UP = .FALSE.
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IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
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*
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* Compute the equilibration matrix R such that
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* inv(R)*A*C has unit 1-norm.
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*
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IF ( UP ) THEN
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DO I = 1, N
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TMP = 0.0
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IF ( CMODE .EQ. 1 ) THEN
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DO J = 1, I
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TMP = TMP + ABS( A( J, I ) * C( J ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( I, J ) * C( J ) )
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END DO
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ELSE IF ( CMODE .EQ. 0 ) THEN
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DO J = 1, I
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TMP = TMP + ABS( A( J, I ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( I, J ) )
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END DO
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ELSE
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DO J = 1, I
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TMP = TMP + ABS( A( J ,I ) / C( J ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( I, J ) / C( J ) )
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END DO
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END IF
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WORK( 2*N+I ) = TMP
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END DO
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ELSE
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DO I = 1, N
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TMP = 0.0
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IF ( CMODE .EQ. 1 ) THEN
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DO J = 1, I
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TMP = TMP + ABS( A( I, J ) * C( J ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( J, I ) * C( J ) )
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END DO
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ELSE IF ( CMODE .EQ. 0 ) THEN
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DO J = 1, I
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TMP = TMP + ABS( A( I, J ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( J, I ) )
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END DO
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ELSE
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DO J = 1, I
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TMP = TMP + ABS( A( I, J ) / C( J ) )
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END DO
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DO J = I+1, N
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TMP = TMP + ABS( A( J, I ) / C( J ) )
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END DO
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END IF
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WORK( 2*N+I ) = TMP
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END DO
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ENDIF
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*
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* Estimate the norm of inv(op(A)).
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*
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AINVNM = 0.0
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KASE = 0
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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( KASE.EQ.2 ) THEN
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*
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* Multiply by R.
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*
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DO I = 1, N
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WORK( I ) = WORK( I ) * WORK( 2*N+I )
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END DO
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IF (UP) THEN
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CALL SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
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ELSE
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CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
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ENDIF
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*
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* Multiply by inv(C).
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*
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IF ( CMODE .EQ. 1 ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) / C( I )
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END DO
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ELSE IF ( CMODE .EQ. -1 ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) * C( I )
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END DO
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END IF
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ELSE
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*
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* Multiply by inv(C**T).
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*
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IF ( CMODE .EQ. 1 ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) / C( I )
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END DO
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ELSE IF ( CMODE .EQ. -1 ) THEN
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DO I = 1, N
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WORK( I ) = WORK( I ) * C( I )
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END DO
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END IF
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IF ( UP ) THEN
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CALL SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
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ELSE
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CALL SPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
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ENDIF
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*
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* Multiply by R.
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*
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DO I = 1, N
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WORK( I ) = WORK( I ) * WORK( 2*N+I )
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END DO
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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. 0.0 )
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$ SLA_PORCOND = ( 1.0 / AINVNM )
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*
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RETURN
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*
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* End of SLA_PORCOND
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*
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END
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