*> \brief \b CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CLA_PORCOND_C + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, * INFO, WORK, RWORK ) * * .. Scalar Arguments .. * CHARACTER UPLO * LOGICAL CAPPLY * INTEGER N, LDA, LDAF, INFO * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) * REAL C( * ), RWORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CLA_PORCOND_C Computes the infinity norm condition number of *> op(A) * inv(diag(C)) where C is a REAL vector *> \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 COMPLEX 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 COMPLEX array, dimension (LDAF,N) *> The triangular factor U or L from the Cholesky factorization *> A = U**H*U or A = L*L**H, as computed by CPOTRF. *> \endverbatim *> *> \param[in] LDAF *> \verbatim *> LDAF is INTEGER *> The leading dimension of the array AF. LDAF >= max(1,N). *> \endverbatim *> *> \param[in] C *> \verbatim *> C is REAL array, dimension (N) *> The vector C in the formula op(A) * inv(diag(C)). *> \endverbatim *> *> \param[in] CAPPLY *> \verbatim *> CAPPLY is LOGICAL *> If .TRUE. then access the vector C in the formula above. *> \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 COMPLEX array, dimension (2*N). *> Workspace. *> \endverbatim *> *> \param[in] RWORK *> \verbatim *> RWORK is REAL 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 complexPOcomputational * * ===================================================================== REAL FUNCTION CLA_PORCOND_C( UPLO, N, A, LDA, AF, LDAF, C, CAPPLY, $ INFO, WORK, RWORK ) * * -- 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 LOGICAL CAPPLY INTEGER N, LDA, LDAF, INFO * .. * .. Array Arguments .. COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ) REAL C( * ), RWORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER KASE REAL AINVNM, ANORM, TMP INTEGER I, J LOGICAL UP, UPPER COMPLEX ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CLACN2, CPOTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL, AIMAG * .. * .. Statement Functions .. REAL CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) * .. * .. Executable Statements .. * CLA_PORCOND_C = 0.0E+0 * INFO = 0 UPPER = LSAME( UPLO, 'U' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -4 ELSE IF( LDAF.LT.MAX( 1, N ) ) THEN INFO = -6 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CLA_PORCOND_C', -INFO ) RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute norm of op(A)*op2(C). * ANORM = 0.0E+0 IF ( UP ) THEN DO I = 1, N TMP = 0.0E+0 IF ( CAPPLY ) THEN DO J = 1, I TMP = TMP + CABS1( A( J, I ) ) / C( J ) END DO DO J = I+1, N TMP = TMP + CABS1( A( I, J ) ) / C( J ) END DO ELSE DO J = 1, I TMP = TMP + CABS1( A( J, I ) ) END DO DO J = I+1, N TMP = TMP + CABS1( A( I, J ) ) END DO END IF RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO ELSE DO I = 1, N TMP = 0.0E+0 IF ( CAPPLY ) THEN DO J = 1, I TMP = TMP + CABS1( A( I, J ) ) / C( J ) END DO DO J = I+1, N TMP = TMP + CABS1( A( J, I ) ) / C( J ) END DO ELSE DO J = 1, I TMP = TMP + CABS1( A( I, J ) ) END DO DO J = I+1, N TMP = TMP + CABS1( A( J, I ) ) END DO END IF RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO END IF * * Quick return if possible. * IF( N.EQ.0 ) THEN CLA_PORCOND_C = 1.0E+0 RETURN ELSE IF( ANORM .EQ. 0.0E+0 ) THEN RETURN END IF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0E+0 * KASE = 0 10 CONTINUE CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.2 ) THEN * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * RWORK( I ) END DO * IF ( UP ) THEN CALL CPOTRS( 'U', N, 1, AF, LDAF, $ WORK, N, INFO ) ELSE CALL CPOTRS( 'L', N, 1, AF, LDAF, $ WORK, N, INFO ) ENDIF * * Multiply by inv(C). * IF ( CAPPLY ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF ELSE * * Multiply by inv(C**H). * IF ( CAPPLY ) THEN DO I = 1, N WORK( I ) = WORK( I ) * C( I ) END DO END IF * IF ( UP ) THEN CALL CPOTRS( 'U', N, 1, AF, LDAF, $ WORK, N, INFO ) ELSE CALL CPOTRS( 'L', N, 1, AF, LDAF, $ WORK, N, INFO ) END IF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * RWORK( I ) END DO END IF GO TO 10 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM .NE. 0.0E+0 ) $ CLA_PORCOND_C = 1.0E+0 / AINVNM * RETURN * END