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version 1.14, 2016/08/27 15:34:40
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*> \brief \b DSYTRI |
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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 DSYTRI + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsytri.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/dsytri.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/dsytri.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 DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, LDA, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* DOUBLE PRECISION A( LDA, * ), 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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*> DSYTRI computes the inverse of a real symmetric indefinite matrix |
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*> A using the factorization A = U*D*U**T or A = L*D*L**T computed by |
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*> DSYTRF. |
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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] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> Specifies whether the details of the factorization are stored |
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*> as an upper or lower triangular matrix. |
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*> = 'U': Upper triangular, form is A = U*D*U**T; |
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*> = 'L': Lower triangular, form is A = L*D*L**T. |
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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,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the block diagonal matrix D and the multipliers |
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*> used to obtain the factor U or L as computed by DSYTRF. |
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*> |
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*> On exit, if INFO = 0, the (symmetric) inverse of the original |
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*> matrix. If UPLO = 'U', the upper triangular part of the |
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*> inverse is formed and the part of A below the diagonal is not |
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*> referenced; if UPLO = 'L' the lower triangular part of the |
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*> inverse is formed and the part of A above the diagonal is |
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*> not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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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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*> Details of the interchanges and the block structure of D |
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*> as determined by DSYTRF. |
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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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*> > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its |
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*> inverse could not be computed. |
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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 doubleSYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, INFO ) |
SUBROUTINE DSYTRI( UPLO, N, A, LDA, IPIV, WORK, 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 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION A( LDA, * ), WORK( * ) |
DOUBLE PRECISION A( LDA, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSYTRI computes the inverse of a real symmetric indefinite matrix |
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* A using the factorization A = U*D*U**T or A = L*D*L**T computed by |
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* DSYTRF. |
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* |
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* Arguments |
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* ========= |
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* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the details of the factorization are stored |
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* as an upper or lower triangular matrix. |
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* = 'U': Upper triangular, form is A = U*D*U**T; |
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* = 'L': Lower triangular, form is A = L*D*L**T. |
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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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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the block diagonal matrix D and the multipliers |
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* used to obtain the factor U or L as computed by DSYTRF. |
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* |
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* On exit, if INFO = 0, the (symmetric) inverse of the original |
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* matrix. If UPLO = 'U', the upper triangular part of the |
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* inverse is formed and the part of A below the diagonal is not |
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* referenced; if UPLO = 'L' the lower triangular part of the |
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* inverse is formed and the part of A above the diagonal is |
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* not referenced. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* IPIV (input) INTEGER array, dimension (N) |
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* Details of the interchanges and the block structure of D |
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* as determined by DSYTRF. |
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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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* > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its |
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* inverse could not be computed. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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* |
* |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute inv(A) from the factorization A = U*D*U'. |
* Compute inv(A) from the factorization A = U*D*U**T. |
* |
* |
* K is the main loop index, increasing from 1 to N in steps of |
* K is the main loop index, increasing from 1 to N in steps of |
* 1 or 2, depending on the size of the diagonal blocks. |
* 1 or 2, depending on the size of the diagonal blocks. |
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* |
* |
ELSE |
ELSE |
* |
* |
* Compute inv(A) from the factorization A = L*D*L'. |
* Compute inv(A) from the factorization A = L*D*L**T. |
* |
* |
* K is the main loop index, increasing from 1 to N in steps of |
* K is the main loop index, increasing from 1 to N in steps of |
* 1 or 2, depending on the size of the diagonal blocks. |
* 1 or 2, depending on the size of the diagonal blocks. |