version 1.7, 2010/12/21 13:53:55
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version 1.18, 2023/08/07 08:39:37
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*> \brief \b ZSPTRI |
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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 ZSPTRI + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsptri.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/zsptri.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/zsptri.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 ZSPTRI( UPLO, N, AP, 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, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 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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*> ZSPTRI computes the inverse of a complex symmetric indefinite matrix |
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*> A in packed storage using the factorization A = U*D*U**T or |
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*> A = L*D*L**T computed by ZSPTRF. |
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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] AP |
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*> \verbatim |
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*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) |
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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 ZSPTRF, |
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*> stored as a packed triangular matrix. |
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*> |
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*> On exit, if INFO = 0, the (symmetric) inverse of the original |
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*> matrix, stored as a packed triangular matrix. The j-th column |
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*> of inv(A) is stored in the array AP as follows: |
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*> if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; |
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*> if UPLO = 'L', |
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*> AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 ZSPTRF. |
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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*16 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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*> \ingroup complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO ) |
SUBROUTINE ZSPTRI( UPLO, N, AP, IPIV, WORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine -- |
* -- 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 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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COMPLEX*16 AP( * ), WORK( * ) |
COMPLEX*16 AP( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSPTRI computes the inverse of a complex symmetric indefinite matrix |
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* A in packed storage using the factorization A = U*D*U**T or |
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* A = L*D*L**T computed by ZSPTRF. |
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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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* AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) |
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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 ZSPTRF, |
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* stored as a packed triangular matrix. |
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* |
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* On exit, if INFO = 0, the (symmetric) inverse of the original |
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* matrix, stored as a packed triangular matrix. The j-th column |
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* of inv(A) is stored in the array AP as follows: |
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* if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j; |
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* if UPLO = 'L', |
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* AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=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 ZSPTRF. |
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* |
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* WORK (workspace) COMPLEX*16 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. |