version 1.3, 2010/08/06 15:28:46
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version 1.18, 2018/05/29 07:18:05
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*> \brief \b DPTCON |
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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 DPTCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dptcon.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/dptcon.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/dptcon.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 DPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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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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* DOUBLE PRECISION D( * ), E( * ), 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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*> DPTCON computes the reciprocal of the condition number (in the |
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*> 1-norm) of a real symmetric positive definite tridiagonal matrix |
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*> using the factorization A = L*D*L**T or A = U**T*D*U computed by |
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*> DPTTRF. |
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*> |
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*> Norm(inv(A)) is computed by a direct method, and the reciprocal of |
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*> the condition number is computed as |
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*> 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] 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] 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 diagonal matrix D from the |
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*> factorization of A, as computed by DPTTRF. |
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*> \endverbatim |
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*> |
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*> \param[in] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> The (n-1) off-diagonal elements of the unit bidiagonal factor |
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*> U or L from the factorization of A, as computed by DPTTRF. |
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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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*> The 1-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 the |
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*> 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 (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 December 2016 |
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* |
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*> \ingroup doublePTcomputational |
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* |
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*> \par Further Details: |
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* ===================== |
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*> |
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*> \verbatim |
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*> |
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*> The method used is described in Nicholas J. Higham, "Efficient |
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*> Algorithms for Computing the Condition Number of a Tridiagonal |
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*> Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. |
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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) |
SUBROUTINE DPTCON( N, D, E, ANORM, RCOND, WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER INFO, N |
INTEGER INFO, N |
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DOUBLE PRECISION D( * ), E( * ), WORK( * ) |
DOUBLE PRECISION D( * ), E( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DPTCON computes the reciprocal of the condition number (in the |
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* 1-norm) of a real symmetric positive definite tridiagonal matrix |
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* using the factorization A = L*D*L**T or A = U**T*D*U computed by |
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* DPTTRF. |
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* |
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* Norm(inv(A)) is computed by a direct method, and the reciprocal of |
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* the condition number is computed as |
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* 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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* N (input) INTEGER |
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* The order of the matrix A. N >= 0. |
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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 diagonal matrix D from the |
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* factorization of A, as computed by DPTTRF. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (N-1) |
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* The (n-1) off-diagonal elements of the unit bidiagonal factor |
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* U or L from the factorization of A, as computed by DPTTRF. |
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* |
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* ANORM (input) DOUBLE PRECISION |
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* The 1-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 the |
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* 1-norm of inv(A) computed in this routine. |
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* |
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* WORK (workspace) DOUBLE PRECISION 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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* Further Details |
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* =============== |
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* |
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* The method used is described in Nicholas J. Higham, "Efficient |
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* Algorithms for Computing the Condition Number of a Tridiagonal |
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* Matrix", SIAM J. Sci. Stat. Comput., Vol. 7, No. 1, January 1986. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* m(i,j) = abs(A(i,j)), i = j, |
* m(i,j) = abs(A(i,j)), i = j, |
* m(i,j) = -abs(A(i,j)), i .ne. j, |
* m(i,j) = -abs(A(i,j)), i .ne. j, |
* |
* |
* and e = [ 1, 1, ..., 1 ]'. Note M(A) = M(L)*D*M(L)'. |
* and e = [ 1, 1, ..., 1 ]**T. Note M(A) = M(L)*D*M(L)**T. |
* |
* |
* Solve M(L) * x = e. |
* Solve M(L) * x = e. |
* |
* |
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WORK( I ) = ONE + WORK( I-1 )*ABS( E( I-1 ) ) |
WORK( I ) = ONE + WORK( I-1 )*ABS( E( I-1 ) ) |
20 CONTINUE |
20 CONTINUE |
* |
* |
* Solve D * M(L)' * x = b. |
* Solve D * M(L)**T * x = b. |
* |
* |
WORK( N ) = WORK( N ) / D( N ) |
WORK( N ) = WORK( N ) / D( N ) |
DO 30 I = N - 1, 1, -1 |
DO 30 I = N - 1, 1, -1 |