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236 lines
6.2 KiB
236 lines
6.2 KiB
2 years ago
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*> \brief \b DSPCON
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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 DSPCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dspcon.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/dspcon.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/dspcon.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 DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
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* 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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* DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * ), IWORK( * )
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* DOUBLE PRECISION 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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*> DSPCON estimates the reciprocal of the condition number (in the
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*> 1-norm) of a real symmetric packed matrix A using the factorization
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*> A = U*D*U**T or A = L*D*L**T computed by DSPTRF.
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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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*> Specifies whether the details of the factorization are stored
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*> as an upper or lower triangular matrix.
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*> = 'U': Upper triangular, form is A = U*D*U**T;
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*> = 'L': Lower triangular, form is A = L*D*L**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] AP
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*> \verbatim
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
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*> The block diagonal matrix D and the multipliers used to
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*> obtain the factor U or L as computed by DSPTRF, stored as a
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*> packed triangular matrix.
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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 DSPTRF.
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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 DOUBLE PRECISION array, dimension (2*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 doubleOTHERcomputational
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*
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* =====================================================================
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SUBROUTINE DSPCON( UPLO, N, AP, IPIV, ANORM, RCOND, WORK, IWORK,
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$ 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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DOUBLE PRECISION ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * ), IWORK( * )
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DOUBLE PRECISION 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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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 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, IP, 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 DLACN2, DSPTRS, XERBLA
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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 = -5
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DSPCON', -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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IP = N*( N+1 ) / 2
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DO 10 I = N, 1, -1
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IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
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$ RETURN
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IP = IP - I
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10 CONTINUE
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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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IP = 1
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DO 20 I = 1, N
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IF( IPIV( I ).GT.0 .AND. AP( IP ).EQ.ZERO )
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$ RETURN
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IP = IP + N - I + 1
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20 CONTINUE
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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 DLACN2( N, WORK( N+1 ), WORK, IWORK, 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 DSPTRS( UPLO, N, 1, AP, 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 DSPCON
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*
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END
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