*> \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 *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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 December 2016 * *> \ingroup doublePOcomputational * * ===================================================================== DOUBLE PRECISION FUNCTION DLA_PORCOND( UPLO, N, A, LDA, AF, LDAF, \$ CMODE, C, INFO, WORK, \$ IWORK ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. 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 EXTERNAL LSAME * .. * .. 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