251 lines
6.7 KiB
Fortran
251 lines
6.7 KiB
Fortran
*> \brief \b CGTCON
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download CGTCON + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtcon.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtcon.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtcon.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
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* WORK, INFO )
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*
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* .. Scalar Arguments ..
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* CHARACTER NORM
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* INTEGER INFO, N
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* REAL ANORM, RCOND
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* ..
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* .. Array Arguments ..
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* INTEGER IPIV( * )
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* COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CGTCON estimates the reciprocal of the condition number of a complex
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*> tridiagonal matrix A using the LU factorization as computed by
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*> CGTTRF.
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*>
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*> An estimate is obtained for norm(inv(A)), and the reciprocal of the
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*> condition number is computed as RCOND = 1 / (ANORM * norm(inv(A))).
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] NORM
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*> \verbatim
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*> NORM is CHARACTER*1
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*> Specifies whether the 1-norm condition number or the
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*> infinity-norm condition number is required:
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*> = '1' or 'O': 1-norm;
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*> = 'I': Infinity-norm.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The order of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] DL
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*> \verbatim
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*> DL is COMPLEX array, dimension (N-1)
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*> The (n-1) multipliers that define the matrix L from the
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*> LU factorization of A as computed by CGTTRF.
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is COMPLEX array, dimension (N)
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*> The n diagonal elements of the upper triangular matrix U from
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*> the LU factorization of A.
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*> \endverbatim
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*>
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*> \param[in] DU
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*> \verbatim
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*> DU is COMPLEX array, dimension (N-1)
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*> The (n-1) elements of the first superdiagonal of U.
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*> \endverbatim
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*>
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*> \param[in] DU2
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*> \verbatim
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*> DU2 is COMPLEX array, dimension (N-2)
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*> The (n-2) elements of the second superdiagonal of U.
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*> \endverbatim
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*>
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*> \param[in] IPIV
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*> \verbatim
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*> IPIV is INTEGER array, dimension (N)
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*> The pivot indices; for 1 <= i <= n, row i of the matrix was
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*> interchanged with row IPIV(i). IPIV(i) will always be either
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*> i or i+1; IPIV(i) = i indicates a row interchange was not
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*> required.
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*> \endverbatim
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*>
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*> \param[in] ANORM
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*> \verbatim
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*> ANORM is REAL
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*> If NORM = '1' or 'O', the 1-norm of the original matrix A.
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*> If NORM = 'I', the infinity-norm of the original matrix A.
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*> \endverbatim
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*>
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*> \param[out] RCOND
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*> \verbatim
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*> RCOND is REAL
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*> The reciprocal of the condition number of the matrix A,
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*> computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
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*> estimate of the 1-norm of inv(A) computed in this routine.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (2*N)
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*> \endverbatim
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*>
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*> \param[out] INFO
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*> \verbatim
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*> INFO is INTEGER
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*> = 0: successful exit
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*> < 0: if INFO = -i, the i-th argument had an illegal value
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complexGTcomputational
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*
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* =====================================================================
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SUBROUTINE CGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND,
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$ WORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER NORM
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INTEGER INFO, N
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REAL ANORM, RCOND
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* ..
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* .. Array Arguments ..
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INTEGER IPIV( * )
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COMPLEX D( * ), DL( * ), DU( * ), DU2( * ), WORK( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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* ..
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* .. Local Scalars ..
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LOGICAL ONENRM
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INTEGER I, KASE, KASE1
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REAL AINVNM
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* ..
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* .. Local Arrays ..
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INTEGER ISAVE( 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL CGTTRS, CLACN2, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments.
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*
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INFO = 0
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ONENRM = NORM.EQ.'1' .OR. LSAME( NORM, 'O' )
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IF( .NOT.ONENRM .AND. .NOT.LSAME( NORM, 'I' ) ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( ANORM.LT.ZERO ) THEN
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INFO = -8
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'CGTCON', -INFO )
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RETURN
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END IF
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*
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* Quick return if possible
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*
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RCOND = ZERO
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IF( N.EQ.0 ) THEN
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RCOND = ONE
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RETURN
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ELSE IF( ANORM.EQ.ZERO ) THEN
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RETURN
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END IF
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*
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* Check that D(1:N) is non-zero.
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*
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DO 10 I = 1, N
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IF( D( I ).EQ.CMPLX( ZERO ) )
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$ RETURN
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10 CONTINUE
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*
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AINVNM = ZERO
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IF( ONENRM ) THEN
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KASE1 = 1
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ELSE
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KASE1 = 2
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END IF
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KASE = 0
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20 CONTINUE
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CALL CLACN2( N, WORK( N+1 ), WORK, AINVNM, KASE, ISAVE )
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IF( KASE.NE.0 ) THEN
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IF( KASE.EQ.KASE1 ) THEN
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*
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* Multiply by inv(U)*inv(L).
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*
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CALL CGTTRS( 'No transpose', N, 1, DL, D, DU, DU2, IPIV,
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$ WORK, N, INFO )
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ELSE
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*
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* Multiply by inv(L**H)*inv(U**H).
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*
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CALL CGTTRS( 'Conjugate transpose', N, 1, DL, D, DU, DU2,
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$ IPIV, WORK, N, INFO )
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END IF
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GO TO 20
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END IF
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*
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* Compute the estimate of the reciprocal condition number.
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*
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IF( AINVNM.NE.ZERO )
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$ RCOND = ( ONE / AINVNM ) / ANORM
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*
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RETURN
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*
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* End of CGTCON
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*
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END
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