REAL FUNCTION CLA_HERCOND_X( UPLO, N, A, LDA, AF, LDAF, IPIV, X, $ INFO, WORK, RWORK ) * * -- LAPACK routine (version 3.2) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- November 2008 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley and NAG Ltd. -- * IMPLICIT NONE * .. * .. Scalar Arguments .. CHARACTER UPLO INTEGER N, LDA, LDAF, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) REAL RWORK( * ) * * CLA_HERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX vector. * WORK is a COMPLEX workspace of size 2*N, and * RWORK is a REAL workspace of size 3*N. * .. * .. Local Scalars .. INTEGER KASE, I, J REAL AINVNM, ANORM, TMP LOGICAL UP COMPLEX ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL CLACN2, CHETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Statement Functions .. REAL CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) ) * .. * .. Executable Statements .. * CLA_HERCOND_X = 0.0E+0 * INFO = 0 IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'CLA_HERCOND_X', -INFO ) RETURN END IF UP = .FALSE. IF ( LSAME( UPLO, 'U' ) ) UP = .TRUE. * * Compute norm of op(A)*op2(C). * ANORM = 0.0 IF ( UP ) THEN DO I = 1, N TMP = 0.0E+0 DO J = 1, N IF ( I.GT.J ) THEN TMP = TMP + CABS1( A( J, I ) * X( J ) ) ELSE TMP = TMP + CABS1( A( I, J ) * X( J ) ) END IF END DO RWORK( 2*N+I ) = TMP ANORM = MAX( ANORM, TMP ) END DO ELSE DO I = 1, N TMP = 0.0E+0 DO J = 1, N IF ( I.LT.J ) THEN TMP = TMP + CABS1( A( J, I ) * X( J ) ) ELSE TMP = TMP + CABS1( A( I, J ) * X( J ) ) END IF END DO RWORK( 2*N+I ) = TMP ANORM = MAX( ANORM, TMP ) END DO END IF * * Quick return if possible. * IF( N.EQ.0 ) THEN CLA_HERCOND_X = 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( 2*N+I ) END DO * IF ( UP ) THEN CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL CHETRS( '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'). * DO I = 1, N WORK( I ) = WORK( I ) / X( I ) END DO * IF ( UP ) THEN CALL CHETRS( 'U', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) ELSE CALL CHETRS( 'L', N, 1, AF, LDAF, IPIV, $ WORK, N, INFO ) END IF * * Multiply by R. * DO I = 1, N WORK( I ) = WORK( I ) * RWORK( 2*N+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_HERCOND_X = 1.0E+0 / AINVNM * RETURN * END