DOUBLE PRECISION FUNCTION ZLA_GERCOND_X( TRANS, N, A, LDA, AF, \$ LDAF, IPIV, X, INFO, \$ WORK, RWORK ) * * -- 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 * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) * .. * * Purpose * ======= * * ZLA_GERCOND_X computes the infinity norm condition number of * op(A) * diag(X) where X is a COMPLEX*16 vector. * * 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) COMPLEX*16 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) COMPLEX*16 array, dimension (LDAF,N) * The factors L and U from the factorization * A = P*L*U as computed by ZGETRF. * * 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 ZGETRF; row i of the matrix was interchanged * with row IPIV(i). * * X (input) COMPLEX*16 array, dimension (N) * The vector X in the formula op(A) * diag(X). * * INFO (output) INTEGER * = 0: Successful exit. * i > 0: The ith argument is invalid. * * WORK (input) COMPLEX*16 array, dimension (2*N). * Workspace. * * RWORK (input) DOUBLE PRECISION array, dimension (N). * Workspace. * * ===================================================================== * * .. Local Scalars .. LOGICAL NOTRANS INTEGER KASE DOUBLE PRECISION AINVNM, ANORM, TMP INTEGER I, J COMPLEX*16 ZDUM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL ZLACN2, ZGETRS, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL, DIMAG * .. * .. Statement Functions .. DOUBLE PRECISION CABS1 * .. * .. Statement Function Definitions .. CABS1( ZDUM ) = ABS( DBLE( ZDUM ) ) + ABS( DIMAG( ZDUM ) ) * .. * .. Executable Statements .. * ZLA_GERCOND_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_GERCOND_X', -INFO ) RETURN END IF * * Compute norm of op(A)*op2(C). * ANORM = 0.0D+0 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0D+0 DO J = 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, 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_GERCOND_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 ( NOTRANS ) THEN CALL ZGETRS( 'No transpose', N, 1, AF, LDAF, IPIV, \$ WORK, N, INFO ) ELSE CALL ZGETRS( 'Conjugate transpose', 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 ( NOTRANS ) THEN CALL ZGETRS( 'Conjugate transpose', N, 1, AF, LDAF, IPIV, \$ WORK, N, INFO ) ELSE CALL ZGETRS( 'No transpose', 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_GERCOND_X = 1.0D+0 / AINVNM * RETURN * END