version 1.7, 2010/12/21 13:53:27
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version 1.10, 2011/11/21 22:19:29
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*> \brief \b DGTCON |
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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 DGTCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgtcon.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/dgtcon.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/dgtcon.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 DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, |
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* WORK, IWORK, 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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* DOUBLE PRECISION ANORM, RCOND |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ), IWORK( * ) |
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* DOUBLE PRECISION 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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*> DGTCON estimates the reciprocal of the condition number of a real |
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*> tridiagonal matrix A using the LU factorization as computed by |
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*> DGTTRF. |
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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 DOUBLE PRECISION 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 DGTTRF. |
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION |
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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 DOUBLE PRECISION |
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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 DOUBLE PRECISION array, dimension (2*N) |
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*> \endverbatim |
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*> |
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*> \param[out] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER array, dimension (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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*> \date November 2011 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, |
SUBROUTINE DGTCON( NORM, N, DL, D, DU, DU2, IPIV, ANORM, RCOND, |
$ WORK, IWORK, INFO ) |
$ WORK, IWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
* November 2011 |
* |
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* Modified to call DLACN2 in place of DLACON, 5 Feb 03, SJH. |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER NORM |
CHARACTER NORM |
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DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) |
DOUBLE PRECISION D( * ), DL( * ), DU( * ), DU2( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DGTCON estimates the reciprocal of the condition number of a real |
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* tridiagonal matrix A using the LU factorization as computed by |
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* DGTTRF. |
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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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* |
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* Arguments |
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* ========= |
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* |
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* NORM (input) 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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* |
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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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* |
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* DL (input) DOUBLE PRECISION 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 DGTTRF. |
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* |
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* D (input) DOUBLE PRECISION 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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* |
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* DU (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) elements of the first superdiagonal of U. |
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* |
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* DU2 (input) DOUBLE PRECISION array, dimension (N-2) |
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* The (n-2) elements of the second superdiagonal of U. |
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* |
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* IPIV (input) 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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* |
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* ANORM (input) DOUBLE PRECISION |
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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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* |
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* RCOND (output) DOUBLE PRECISION |
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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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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) |
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* |
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* IWORK (workspace) INTEGER array, dimension (N) |
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* |
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* INFO (output) 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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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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$ WORK, N, INFO ) |
$ WORK, N, INFO ) |
ELSE |
ELSE |
* |
* |
* Multiply by inv(L')*inv(U'). |
* Multiply by inv(L**T)*inv(U**T). |
* |
* |
CALL DGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK, |
CALL DGTTRS( 'Transpose', N, 1, DL, D, DU, DU2, IPIV, WORK, |
$ N, INFO ) |
$ N, INFO ) |