DOUBLE PRECISION FUNCTION DLA_GBRCOND( TRANS, N, KL, KU, AB, LDAB, $ AFB, LDAFB, IPIV, CMODE, C, INFO, $ WORK, IWORK ) * * -- 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, LDAB, LDAFB, INFO, KL, KU, CMODE * .. * .. Array Arguments .. INTEGER IWORK( * ), IPIV( * ) DOUBLE PRECISION AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ C( * ) * * DLA_GERCOND 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. * WORK is a double precision workspace of size 5*N, and * IWORK is an integer workspace of size N. * .. * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J, KD DOUBLE PRECISION AINVNM, TMP * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL DLACN2, DGBTRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * DLA_GBRCOND = 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 ELSE IF( KL.LT.0 ) THEN INFO = -4 ELSE IF( KU.LT.0 ) THEN INFO = -5 ELSE IF( LDAB.LT.KL+KU+1 ) THEN INFO = -8 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN INFO = -10 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DLA_GBRCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN DLA_GBRCOND = 1.0D+0 RETURN END IF * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * KD = KU + 1 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0D+0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS( AB( KD+I-J, J ) * C( J ) ) END IF END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS( AB( KD+I-J, J ) ) END IF END DO ELSE DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS( AB( KD+I-J, J ) / C( J ) ) END IF 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, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS( AB( J, KD+I-J ) * C( J ) ) END IF END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS(AB(J,KD+I-J)) END IF END DO ELSE DO J = 1, N IF ( I.GE.MAX( 1, J-KU ) $ .AND. I.LE.MIN( N, J+KL ) ) THEN TMP = TMP + ABS( AB( J, KD+I-J ) / C( J ) ) END IF END DO END IF WORK( 2*N+I ) = TMP END DO END IF * * 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 ( NOTRANS ) THEN CALL DGBTRS( 'No transpose', N, KL, KU, 1, AFB, LDAFB, $ IPIV, WORK, N, INFO ) ELSE CALL DGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV, $ WORK, N, INFO ) END IF * * 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'). * 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 ( NOTRANS ) THEN CALL DGBTRS( 'Transpose', N, KL, KU, 1, AFB, LDAFB, IPIV, $ WORK, N, INFO ) ELSE CALL DGBTRS( '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 ) * 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_GBRCOND = ( 1.0D+0 / AINVNM ) * RETURN * END