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DOUBLE PRECISION FUNCTION ZLA_GBRCOND_X( TRANS, N, KL, KU, AB,
$ LDAB, AFB, LDAFB, 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, KL, KU, KD, KE, LDAB, LDAFB, INFO * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * ), WORK( * ), $ X( * ) DOUBLE PRECISION RWORK( * ) * * * Purpose * ======= * * ZLA_GBRCOND_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. * * KL (input) INTEGER * The number of subdiagonals within the band of A. KL >= 0. * * KU (input) INTEGER * The number of superdiagonals within the band of A. KU >= 0. * * AB (input) COMPLEX*16 array, dimension (LDAB,N) * On entry, the matrix A in band storage, in rows 1 to KL+KU+1. * The j-th column of A is stored in the j-th column of the * array AB as follows: * AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl) * * LDAB (input) INTEGER * The leading dimension of the array AB. LDAB >= KL+KU+1. * * AFB (input) COMPLEX*16 array, dimension (LDAFB,N) * Details of the LU factorization of the band matrix A, as * computed by ZGBTRF. U is stored as an upper triangular * band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, * and the multipliers used during the factorization are stored * in rows KL+KU+2 to 2*KL+KU+1. * * LDAFB (input) INTEGER * The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. * * IPIV (input) INTEGER array, dimension (N) * The pivot indices from the factorization A = P*L*U * as computed by ZGBTRF; 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, 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 ELSE IF( KL.LT.0 .OR. KL.GT.N-1 ) THEN INFO = -3 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN INFO = -4 ELSE IF( LDAB.LT.KL+KU+1 ) THEN INFO = -6 ELSE IF( LDAFB.LT.2*KL+KU+1 ) THEN INFO = -8 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 KE = KL + 1 ANORM = 0.0D+0 IF ( NOTRANS ) THEN DO I = 1, N TMP = 0.0D+0 DO J = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + CABS1( AB( KD+I-J, 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 = MAX( I-KL, 1 ), MIN( I+KU, N ) TMP = TMP + CABS1( AB( KE-I+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_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( 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**H). * 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( 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 |