REAL FUNCTION SLA_GERCOND ( TRANS, N, A, LDA, AF, LDAF, IPIV, \$ CMODE, C, INFO, WORK, IWORK ) * * -- LAPACK routine (version 3.2.1) -- * -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and -- * -- Jason Riedy of Univ. of California Berkeley. -- * -- April 2009 -- * * -- 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, LDA, LDAF, INFO, CMODE * .. * .. Array Arguments .. INTEGER IPIV( * ), IWORK( * ) REAL A( LDA, * ), AF( LDAF, * ), WORK( * ), \$ C( * ) * .. * * Purpose * ======= * * SLA_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. * * Arguments * ========== * * TRANS (input) CHARACTER*1 * Specifies the form of the system of equations: * = 'N': A * X = B (No transpose) * = 'T': A**T * X = B (Transpose) * = 'C': A**H * X = B (Conjugate Transpose = Transpose) * * N (input) INTEGER * The number of linear equations, i.e., the order of the * matrix A. N >= 0. * * A (input) REAL array, dimension (LDA,N) * On entry, the N-by-N matrix A. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * AF (input) REAL array, dimension (LDAF,N) * The factors L and U from the factorization * A = P*L*U as computed by SGETRF. * * LDAF (input) INTEGER * The leading dimension of the array AF. LDAF >= max(1,N). * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from the factorization A = P*L*U * as computed by SGETRF; row i of the matrix was interchanged * with row IPIV(i). * * CMODE (input) INTEGER * Determines op2(C) in the formula op(A) * op2(C) as follows: * CMODE = 1 op2(C) = C * CMODE = 0 op2(C) = I * CMODE = -1 op2(C) = inv(C) * * C (input) REAL array, dimension (N) * The vector C in the formula op(A) * op2(C). * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) REAL array, dimension (3*N). * Workspace. * * IWORK (input) INTEGER array, dimension (N). * Workspace.2 * * ===================================================================== * * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE, I, J REAL AINVNM, TMP * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SLACN2, SGETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX * .. * .. Executable Statements .. * SLA_GERCOND = 0.0 * 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( 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( 'SLA_GERCOND', -INFO ) RETURN END IF IF( N.EQ.0 ) THEN SLA_GERCOND = 1.0 RETURN END IF * * Compute the equilibration matrix R such that * inv(R)*A*C has unit 1-norm. * IF (NOTRANS) THEN DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, N TMP = TMP + ABS( A( I, J ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, N TMP = TMP + ABS( A( I, J ) ) END DO ELSE DO J = 1, N TMP = TMP + ABS( A( I, J ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO ELSE DO I = 1, N TMP = 0.0 IF ( CMODE .EQ. 1 ) THEN DO J = 1, N TMP = TMP + ABS( A( J, I ) * C( J ) ) END DO ELSE IF ( CMODE .EQ. 0 ) THEN DO J = 1, N TMP = TMP + ABS( A( J, I ) ) END DO ELSE DO J = 1, N TMP = TMP + ABS( A( J, I ) / C( J ) ) END DO END IF WORK( 2*N+I ) = TMP END DO END IF * * Estimate the norm of inv(op(A)). * AINVNM = 0.0 KASE = 0 10 CONTINUE CALL SLACN2( 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 SGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, \$ WORK, N, INFO ) ELSE CALL SGETRS( 'Transpose', N, 1, AF, LDAF, 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 SGETRS( 'Transpose', N, 1, AF, LDAF, IPIV, \$ WORK, N, INFO ) ELSE CALL SGETRS( 'No transpose', N, 1, AF, LDAF, 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. 0.0 ) \$ SLA_GERCOND = ( 1.0 / AINVNM ) * RETURN * END