*> \brief \b ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZLA_HERCOND_X + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF, * LDAF, IPIV, X, INFO, * WORK, RWORK ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER N, LDA, LDAF, INFO * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) * DOUBLE PRECISION RWORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLA_HERCOND_X computes the infinity norm condition number of *> op(A) * diag(X) where X is a COMPLEX*16 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*16 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*16 array, dimension (LDAF,N) *> The block diagonal matrix D and the multipliers used to *> obtain the factor U or L as computed by ZHETRF. *> \endverbatim *> *> \param[in] LDAF *> \verbatim *> LDAF is INTEGER *> The leading dimension of the array AF. LDAF >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> Details of the interchanges and the block structure of D *> as determined by CHETRF. *> \endverbatim *> *> \param[in] X *> \verbatim *> X is COMPLEX*16 array, dimension (N) *> The vector X in the formula op(A) * diag(X). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: Successful exit. *> i > 0: The ith argument is invalid. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (2*N). *> Workspace. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION 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 complex16HEcomputational * * ===================================================================== DOUBLE PRECISION FUNCTION ZLA_HERCOND_X( UPLO, N, A, LDA, AF, $ LDAF, IPIV, X, INFO, $ WORK, RWORK ) * * -- 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 * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) * .. * * ===================================================================== * * .. Local Scalars .. INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP LOGICAL UP, UPPER COMPLEX*16 ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL ZLACN2, ZHETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) * .. * .. Executable Statements .. * ZLA_HERCOND_X = 0.0D+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( 'ZLA_HERCOND_X', -INFO ) RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute norm of op(A)*op2(C). * ANORM = 0.0D+0 IF ( UP ) THEN DO I = 1, N TMP = 0.0D+0 DO J = 1, I TMP = TMP + CABS1( A( J, I ) * X( J ) ) END DO DO J = I+1, N TMP = TMP + CABS1( A( I, J ) * X( J ) ) END DO RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO ELSE DO I = 1, N TMP = 0.0D+0 DO J = 1, I TMP = TMP + CABS1( A( I, J ) * X( J ) ) END DO DO J = I+1, N TMP = TMP + CABS1( A( J, I ) * X( J ) ) END DO RWORK( I ) = TMP ANORM = MAX( ANORM, TMP ) END DO END IF * * Quick return if possible. * IF( N.EQ.0 ) THEN ZLA_HERCOND_X = 1.0D+0 RETURN ELSE IF( ANORM .EQ. 0.0D+0 ) THEN RETURN END IF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0D+0 * KASE = 0 10 CONTINUE CALL ZLACN2( 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 ZHETRS( 'U', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ENDIF * * Multiply by inv(X). * DO I = 1, N WORK( I ) = WORK( I ) / X( I ) END DO ELSE * * Multiply by inv(X**H). * DO I = 1, N WORK( I ) = WORK( I ) / X( I ) END DO * IF ( UP ) THEN CALL ZHETRS( 'U', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL ZHETRS( 'L', N, 1, AF, LDAF, IPIV, $ 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. 0.0D+0 ) $ ZLA_HERCOND_X = 1.0D+0 / AINVNM * RETURN * END