version 1.6, 2010/08/13 21:04:00
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version 1.16, 2017/06/17 11:06:37
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*> \brief \b DTPCON |
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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 DTPCON + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtpcon.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/dtpcon.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/dtpcon.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 DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, |
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* INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER DIAG, NORM, UPLO |
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* INTEGER INFO, N |
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* DOUBLE PRECISION RCOND |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION AP( * ), 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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*> DTPCON estimates the reciprocal of the condition number of a packed |
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*> triangular matrix A, in either the 1-norm or the infinity-norm. |
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*> |
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*> The norm of A is computed and an estimate is obtained for |
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*> norm(inv(A)), then the reciprocal of the condition number is |
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*> computed as |
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*> RCOND = 1 / ( norm(A) * 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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': A is upper triangular; |
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*> = 'L': A is lower triangular. |
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*> \endverbatim |
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*> |
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*> \param[in] DIAG |
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*> \verbatim |
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*> DIAG is CHARACTER*1 |
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*> = 'N': A is non-unit triangular; |
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*> = 'U': A is unit triangular. |
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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] AP |
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*> \verbatim |
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*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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*> The upper or lower triangular matrix A, packed columnwise in |
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*> a linear array. The j-th column of A is stored in the array |
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*> AP as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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*> If DIAG = 'U', the diagonal elements of A are not referenced |
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*> and are assumed to be 1. |
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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/(norm(A) * norm(inv(A))). |
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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 (3*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 December 2016 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, |
SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, AP, RCOND, WORK, IWORK, |
$ INFO ) |
$ 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 |
* |
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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 DIAG, NORM, UPLO |
CHARACTER DIAG, NORM, UPLO |
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DOUBLE PRECISION AP( * ), WORK( * ) |
DOUBLE PRECISION AP( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DTPCON estimates the reciprocal of the condition number of a packed |
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* triangular matrix A, in either the 1-norm or the infinity-norm. |
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* |
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* The norm of A is computed and an estimate is obtained for |
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* norm(inv(A)), then the reciprocal of the condition number is |
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* computed as |
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* RCOND = 1 / ( norm(A) * 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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* UPLO (input) CHARACTER*1 |
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* = 'U': A is upper triangular; |
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* = 'L': A is lower triangular. |
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* |
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* DIAG (input) CHARACTER*1 |
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* = 'N': A is non-unit triangular; |
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* = 'U': A is unit triangular. |
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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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* AP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2) |
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* The upper or lower triangular matrix A, packed columnwise in |
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* a linear array. The j-th column of A is stored in the array |
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* AP as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; |
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* if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. |
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* If DIAG = 'U', the diagonal elements of A are not referenced |
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* and are assumed to be 1. |
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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/(norm(A) * norm(inv(A))). |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (3*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, SCALE, WORK( 2*N+1 ), INFO ) |
$ WORK, SCALE, WORK( 2*N+1 ), INFO ) |
ELSE |
ELSE |
* |
* |
* Multiply by inv(A'). |
* Multiply by inv(A**T). |
* |
* |
CALL DLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP, |
CALL DLATPS( UPLO, 'Transpose', DIAG, NORMIN, N, AP, |
$ WORK, SCALE, WORK( 2*N+1 ), INFO ) |
$ WORK, SCALE, WORK( 2*N+1 ), INFO ) |