328 lines
8.7 KiB
Fortran
328 lines
8.7 KiB
Fortran
*> \brief \b SLA_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 SLA_PORCOND + dependencies
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sla_porcond.f">
|
|
*> [TGZ]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sla_porcond.f">
|
|
*> [ZIP]</a>
|
|
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sla_porcond.f">
|
|
*> [TXT]</a>
|
|
*> \endhtmlonly
|
|
*
|
|
* Definition:
|
|
* ===========
|
|
*
|
|
* REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
|
|
* INFO, WORK, IWORK )
|
|
*
|
|
* .. Scalar Arguments ..
|
|
* CHARACTER UPLO
|
|
* INTEGER N, LDA, LDAF, INFO, CMODE
|
|
* REAL A( LDA, * ), AF( LDAF, * ), WORK( * ),
|
|
* $ C( * )
|
|
* ..
|
|
* .. Array Arguments ..
|
|
* INTEGER IWORK( * )
|
|
* ..
|
|
*
|
|
*
|
|
*> \par Purpose:
|
|
* =============
|
|
*>
|
|
*> \verbatim
|
|
*>
|
|
*> SLA_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 REAL 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 REAL 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 SPOTRF.
|
|
*> \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 REAL 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 REAL 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 September 2012
|
|
*
|
|
*> \ingroup realPOcomputational
|
|
*
|
|
* =====================================================================
|
|
REAL FUNCTION SLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, CMODE, C,
|
|
$ INFO, WORK, IWORK )
|
|
*
|
|
* -- LAPACK computational routine (version 3.4.2) --
|
|
* -- LAPACK is a software package provided by Univ. of Tennessee, --
|
|
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
|
|
* September 2012
|
|
*
|
|
* .. Scalar Arguments ..
|
|
CHARACTER UPLO
|
|
INTEGER N, LDA, LDAF, INFO, CMODE
|
|
REAL A( LDA, * ), AF( LDAF, * ), WORK( * ),
|
|
$ C( * )
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER IWORK( * )
|
|
* ..
|
|
*
|
|
* =====================================================================
|
|
*
|
|
* .. Local Scalars ..
|
|
INTEGER KASE, I, J
|
|
REAL AINVNM, TMP
|
|
LOGICAL UP
|
|
* ..
|
|
* .. Array Arguments ..
|
|
INTEGER ISAVE( 3 )
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
INTEGER ISAMAX
|
|
EXTERNAL LSAME, ISAMAX
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL SLACN2, SPOTRS, XERBLA
|
|
* ..
|
|
* .. Intrinsic Functions ..
|
|
INTRINSIC ABS, MAX
|
|
* ..
|
|
* .. Executable Statements ..
|
|
*
|
|
SLA_PORCOND = 0.0
|
|
*
|
|
INFO = 0
|
|
IF( N.LT.0 ) THEN
|
|
INFO = -2
|
|
END IF
|
|
IF( INFO.NE.0 ) THEN
|
|
CALL XERBLA( 'SLA_PORCOND', -INFO )
|
|
RETURN
|
|
END IF
|
|
|
|
IF( N.EQ.0 ) THEN
|
|
SLA_PORCOND = 1.0
|
|
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 = 0.0
|
|
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 = 0.0
|
|
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 = 0.0
|
|
|
|
KASE = 0
|
|
10 CONTINUE
|
|
CALL SLACN2( 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 SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
|
|
ELSE
|
|
CALL SPOTRS( '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 SPOTRS( 'Upper', N, 1, AF, LDAF, WORK, N, INFO )
|
|
ELSE
|
|
CALL SPOTRS( '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. 0.0 )
|
|
$ SLA_PORCOND = ( 1.0 / AINVNM )
|
|
*
|
|
RETURN
|
|
*
|
|
END
|