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*> \brief \b DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLA_PORCOND + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_porcond.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_porcond.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_porcond.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
* CMODE, C, INFO, WORK,
* IWORK )
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* INTEGER N, LDA, LDAF, INFO, CMODE
* DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
* $ C( * )
* ..
* .. Array Arguments ..
* INTEGER IWORK( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLA_PORCOND Estimates the Skeel condition number of op(A) * op2(C)
*> where op2 is determined by CMODE as follows
*> CMODE = 1 op2(C) = C
*> CMODE = 0 op2(C) = I
*> CMODE = -1 op2(C) = inv(C)
*> The Skeel condition number cond(A) = norminf( |inv(A)||A| )
*> is computed by computing scaling factors R such that
*> diag(R)*A*op2(C) is row equilibrated and computing the standard
*> infinity-norm condition number.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of linear equations, i.e., the order of the
*> matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> On entry, the N-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*> AF is DOUBLE PRECISION array, dimension (LDAF,N)
*> The triangular factor U or L from the Cholesky factorization
*> A = U**T*U or A = L*L**T, as computed by DPOTRF.
*> \endverbatim
*>
*> \param[in] LDAF
*> \verbatim
*> LDAF is INTEGER
*> The leading dimension of the array AF. LDAF >= max(1,N).
*> \endverbatim
*>
*> \param[in] CMODE
*> \verbatim
*> CMODE is INTEGER
*> Determines op2(C) in the formula op(A) * op2(C) as follows:
*> CMODE = 1 op2(C) = C
*> CMODE = 0 op2(C) = I
*> CMODE = -1 op2(C) = inv(C)
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is DOUBLE PRECISION array, dimension (N)
*> The vector C in the formula op(A) * op2(C).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: Successful exit.
*> i > 0: The ith argument is invalid.
*> \endverbatim
*>
*> \param[in] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (3*N).
*> Workspace.
*> \endverbatim
*>
*> \param[in] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (N).
*> Workspace.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup doublePOcomputational
*
* =====================================================================
DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF,
$ CMODE, C, INFO, WORK,
$ IWORK )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER N, LDA, LDAF, INFO, CMODE
DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), WORK( * ),
$ C( * )
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER KASE, I, J
DOUBLE PRECISION AINVNM, TMP
LOGICAL UP
* ..
* .. Array Arguments ..
INTEGER ISAVE( 3 )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER IDAMAX
EXTERNAL LSAME, IDAMAX
* ..
* .. External Subroutines ..
EXTERNAL DLACN2, DPOTRS, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
DLA_PORCOND = 0.0D+0
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -2
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLA_PORCOND', -INFO )
RETURN
END IF
IF( N.EQ.0 ) THEN
DLA_PORCOND = 1.0D+0
RETURN
END IF
UP = .FALSE.
IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE.
*
* Compute the equilibration matrix R such that
* inv(R)*A*C has unit 1-norm.
*
IF ( UP ) THEN
DO I = 1, N
TMP = 0.0D+0
IF ( CMODE .EQ. 1 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( J, I ) * C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) * C( J ) )
END DO
ELSE IF ( CMODE .EQ. 0 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( J, I ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) )
END DO
ELSE
DO J = 1, I
TMP = TMP + ABS( A( J ,I ) / C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( I, J ) / C( J ) )
END DO
END IF
WORK( 2*N+I ) = TMP
END DO
ELSE
DO I = 1, N
TMP = 0.0D+0
IF ( CMODE .EQ. 1 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( I, J ) * C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I ) * C( J ) )
END DO
ELSE IF ( CMODE .EQ. 0 ) THEN
DO J = 1, I
TMP = TMP + ABS( A( I, J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I ) )
END DO
ELSE
DO J = 1, I
TMP = TMP + ABS( A( I, J ) / C( J ) )
END DO
DO J = I+1, N
TMP = TMP + ABS( A( J, I ) / C( J ) )
END DO
END IF
WORK( 2*N+I ) = TMP
END DO
ENDIF
*
* Estimate the norm of inv(op(A)).
*
AINVNM = 0.0D+0
KASE = 0
10 CONTINUE
CALL DLACN2( N, WORK( N+1 ), WORK, IWORK, AINVNM, KASE, ISAVE )
IF( KASE.NE.0 ) THEN
IF( KASE.EQ.2 ) THEN
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * WORK( 2*N+I )
END DO
IF (UP) THEN
CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
ELSE
CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
ENDIF
*
* Multiply by inv(C).
*
IF ( CMODE .EQ. 1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) / C( I )
END DO
ELSE IF ( CMODE .EQ. -1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
ELSE
*
* Multiply by inv(C**T).
*
IF ( CMODE .EQ. 1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) / C( I )
END DO
ELSE IF ( CMODE .EQ. -1 ) THEN
DO I = 1, N
WORK( I ) = WORK( I ) * C( I )
END DO
END IF
IF ( UP ) THEN
CALL DPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
ELSE
CALL DPOTRS( 'Lower', N, 1, AF, LDAF, WORK, N, INFO )
ENDIF
*
* Multiply by R.
*
DO I = 1, N
WORK( I ) = WORK( I ) * WORK( 2*N+I )
END DO
END IF
GO TO 10
END IF
*
* Compute the estimate of the reciprocal condition number.
*
IF( AINVNM .NE. 0.0D+0 )
$ DLA_PORCOND = ( 1.0D+0 / AINVNM )
*
RETURN
*
END
|
