DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB, $ LDAB, AFB, LDAFB, 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 TRANS INTEGER N, KL, KU, KD, LDAB, LDAFB, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ X( * ) DOUBLE PRECISION RWORK( * ) * * ZLA_GBRCOND_X Computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. * WORK is a COMPLEX*16 workspace of size 2*N, and * RWORK is a DOUBLE PRECISION workspace of size 3*N. * .. * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J DOUBLE PRECISION AINVNM, ANORM, TMP COMPLEX*16 ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL ZLACN2, ZGBTRS, 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_GBRCOND_X = 0.0D+0 * INFO = 0 NOTRANS = LSAME( TRANS, 'N' ) IF ( .NOT. NOTRANS .AND. .NOT. LSAME(TRANS, 'T') .AND. .NOT. $ LSAME( TRANS, 'C' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZLA_GBRCOND_X', -INFO ) RETURN END IF * * Compute norm of op(A)*op2(C). * KD = KU + 1 ANORM = 0.0D+0 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0D+0 DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + CABS1( AB( KD+I-J, J) * X( J ) ) END IF END DO RWORK( 2*N+I ) = TMP ANORM = MAX( ANORM, TMP ) END DO ELSE DO I = 1, N TMP = 0.0D+0 DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + CABS1( AB( J, KD+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 ZLA_GBRCOND_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( 2*N+I ) END DO * IF ( NOTRANS ) THEN CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, $ IPIV, WORK, N, INFO ) ELSE CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB, $ LDAFB, 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 ( NOTRANS ) THEN CALL ZGBTRS( 'Conjugate transpose', N, KL, KU, 1, AFB, $ LDAFB, IPIV, WORK, N, INFO ) ELSE CALL ZGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, $ 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. 0.0D+0 ) $ ZLA_GBRCOND_X = 1.0D+0 / AINVNM * RETURN * END