*> \brief \b ZGTCON
*
* =========== DOCUMENTATION ===========
*
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* http://www.netlib.org/lapack/explore-html/
*
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*
* 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.
*
*> \ingroup complex16GTcomputational
*
* =====================================================================
SUBROUTINE ZGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
$ WORK, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. 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