*> \brief \b ZGTCON * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download ZGTCON + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, * WORK, INFO ) * * .. Scalar Arguments .. * CHARACTER NORM * INTEGER INFO, N * DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. * INTEGER IPIV( * ) * COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGTCON estimates the reciprocal of the condition number of a complex *> tridiagonal matrix A using the LU factorization as computed by *> ZGTTRF. *> *> An estimate is obtained for norm(inv(A)), and the reciprocal of the *> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))). *> \endverbatim * * Arguments: * ========== * *> \param[in] NORM *> \verbatim *> NORM is CHARACTER*1 *> Specifies whether the 1-norm condition number or the *> infinity-norm condition number is required: *> = '1' or 'O': 1-norm; *> = 'I': Infinity-norm. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] DL *> \verbatim *> DL is COMPLEX*16 array, dimension (N-1) *> The (n-1) multipliers that define the matrix L from the *> LU factorization of A as computed by ZGTTRF. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is COMPLEX*16 array, dimension (N) *> The n diagonal elements of the upper triangular matrix U from *> the LU factorization of A. *> \endverbatim *> *> \param[in] DU *> \verbatim *> DU is COMPLEX*16 array, dimension (N-1) *> The (n-1) elements of the first superdiagonal of U. *> \endverbatim *> *> \param[in] DU2 *> \verbatim *> DU2 is COMPLEX*16 array, dimension (N-2) *> The (n-2) elements of the second superdiagonal of U. *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices; for 1 <= i <= n, row i of the matrix was *> interchanged with row IPIV(i). IPIV(i) will always be either *> i or i+1; IPIV(i) = i indicates a row interchange was not *> required. *> \endverbatim *> *> \param[in] ANORM *> \verbatim *> ANORM is DOUBLE PRECISION *> If NORM = '1' or 'O', the 1-norm of the original matrix A. *> If NORM = 'I', the infinity-norm of the original matrix A. *> \endverbatim *> *> \param[out] RCOND *> \verbatim *> RCOND is DOUBLE PRECISION *> The reciprocal of the condition number of the matrix A, *> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an *> estimate of the 1-norm of inv(A) computed in this routine. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (2*N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup complex16GTcomputational * * ===================================================================== SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, \$ WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER NORM INTEGER INFO, N DOUBLE PRECISION ANORM, RCOND * .. * .. Array Arguments .. INTEGER IPIV( * ) COMPLEX*16 D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. LOGICAL ONENRM INTEGER I, KASE, KASE1 DOUBLE PRECISION AINVNM * .. * .. Local Arrays .. INTEGER ISAVE( 3 ) * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGTTRS, ZLACN2 * .. * .. Intrinsic Functions .. INTRINSIC DCMPLX * .. * .. Executable Statements .. * * Test the input arguments. * INFO = 0 ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' ) IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( ANORM.LT.ZERO ) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'ZGTCON', -INFO ) RETURN END IF * * Quick return if possible * RCOND = ZERO IF( N.EQ.0 ) THEN RCOND = ONE RETURN ELSE IF( ANORM.EQ.ZERO ) THEN RETURN END IF * * Check that D(1:N) is non-zero. * DO 10 I = 1, N IF( D( I ).EQ.DCMPLX( ZERO ) ) \$ RETURN 10 CONTINUE * AINVNM = ZERO IF( ONENRM ) THEN KASE1 = 1 ELSE KASE1 = 2 END IF KASE = 0 20 CONTINUE CALL ZLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE ) IF( KASE.NE.0 ) THEN IF( KASE.EQ.KASE1 ) THEN * * Multiply by inv(U)*inv(L). * CALL ZGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV, \$ WORK, N, INFO ) ELSE * * Multiply by inv(L**H)*inv(U**H). * CALL ZGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2, \$ IPIV, WORK, N, INFO ) END IF GO TO 20 END IF * * Compute the estimate of the reciprocal condition number. * IF( AINVNM.NE.ZERO ) \$ RCOND = ( ONE / AINVNM ) / ANORM * RETURN * * End of ZGTCON * END