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329 lines
8.9 KiB
329 lines
8.9 KiB
2 years ago
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*> \brief \b DLA_GERCOND estimates the Skeel condition number for a general 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 DLA_GERCOND + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gercond.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/dla_gercond.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/dla_gercond.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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* DOUBLE PRECISION FUNCTION DLA_GERCOND( TRANS, N, A, LDA, AF,
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* LDAF, IPIV, CMODE, C,
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* INFO, WORK, IWORK )
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*
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* .. Scalar Arguments ..
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* CHARACTER TRANS
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* INTEGER N, LDA, LDAF, INFO, CMODE
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * ), IWORK( * )
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* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
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* $ C( * )
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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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*> DLA_GERCOND 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] TRANS
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*> \verbatim
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*> TRANS is CHARACTER*1
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*> Specifies the form of the system of equations:
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*> = 'N': A * X = B (No transpose)
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*> = 'T': A**T * X = B (Transpose)
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*> = 'C': A**H * X = B (Conjugate Transpose = Transpose)
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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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N)
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*> The factors L and U from the factorization
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*> A = P*L*U as computed by DGETRF.
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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] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices from the factorization A = P*L*U
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*> as computed by DGETRF; row i of the matrix was interchanged
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*> with row IPIV(i).
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleGEcomputational
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*
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* =====================================================================
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DOUBLE PRECISION FUNCTION DLA_GERCOND( TRANS, N, A, LDA, AF,
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$ LDAF, IPIV, 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 TRANS
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INTEGER N, LDA, LDAF, INFO, CMODE
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * ), IWORK( * )
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DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
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$ C( * )
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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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LOGICAL NOTRANS
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INTEGER KASE, I, J
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DOUBLE PRECISION AINVNM, TMP
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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, DGETRS, 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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DLA_GERCOND = 0.0D+0
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*
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INFO = 0
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NOTRANS = LSAME( TRANS, 'N' )
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IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T')
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$ .AND. .NOT. LSAME(TRANS, 'C') ) 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( LDAF.LT.MAX( 1, N ) ) THEN
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INFO = -6
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DLA_GERCOND', -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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DLA_GERCOND = 1.0D+0
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RETURN
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END IF
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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 (NOTRANS) THEN
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DO I = 1, N
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TMP = 0.0D+0
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IF ( CMODE .EQ. 1 ) THEN
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DO J = 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, 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, 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 = 0.0D+0
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IF ( CMODE .EQ. 1 ) THEN
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DO J = 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, 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, 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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END IF
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*
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* Estimate the norm of inv(op(A)).
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*
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AINVNM = 0.0D+0
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KASE = 0
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10 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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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 (NOTRANS) THEN
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CALL DGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
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$ WORK, N, INFO )
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ELSE
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CALL DGETRS( 'Transpose', N, 1, AF, LDAF, IPIV,
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$ WORK, N, INFO )
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END IF
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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 (NOTRANS) THEN
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CALL DGETRS( 'Transpose', N, 1, AF, LDAF, IPIV,
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$ WORK, N, INFO )
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ELSE
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CALL DGETRS( 'No transpose', N, 1, AF, LDAF, IPIV,
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$ WORK, N, INFO )
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END IF
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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. 0.0D+0 )
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$ DLA_GERCOND = ( 1.0D+0 / AINVNM )
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*
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RETURN
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*
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* End of DLA_GERCOND
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*
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END
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