version 1.2, 2010/12/21 13:53:56
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version 1.5, 2011/11/21 22:19:58
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*> \brief \b ZSYTRI2X |
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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 ZSYTRI2X + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zsytri2x.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/zsytri2x.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/zsytri2x.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 ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, 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, NB |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IPIV( * ) |
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* COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* ) |
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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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*> ZSYTRI2X computes the inverse of a complex 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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*> ZSYTRF. |
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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 COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the NNB diagonal matrix D and the multipliers |
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*> used to obtain the factor U or L as computed by ZSYTRF. |
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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 NNB structure of D |
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*> as determined by ZSYTRF. |
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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+NNB+1,NNB+3) |
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*> \endverbatim |
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*> |
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*> \param[in] NB |
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*> \verbatim |
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*> NB is INTEGER |
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*> Block size |
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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 complex16SYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) |
SUBROUTINE ZSYTRI2X( UPLO, N, A, LDA, IPIV, WORK, NB, INFO ) |
* |
* |
* -- LAPACK routine (version 3.3.0) -- |
* -- 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 2010 |
* November 2011 |
* |
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* -- Written by Julie Langou of the Univ. of TN -- |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
INTEGER IPIV( * ) |
INTEGER IPIV( * ) |
DOUBLE COMPLEX A( LDA, * ), WORK( N+NB+1,* ) |
COMPLEX*16 A( LDA, * ), WORK( N+NB+1,* ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZSYTRI2X computes the inverse of a complex 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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* ZSYTRF. |
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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 COMPLEX array, dimension (LDA,N) |
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* On entry, the NNB diagonal matrix D and the multipliers |
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* used to obtain the factor U or L as computed by ZSYTRF. |
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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 NNB structure of D |
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* as determined by ZSYTRF. |
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* |
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* WORK (workspace) DOUBLE COMPLEX array, dimension (N+NNB+1,NNB+3) |
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* |
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* NB (input) INTEGER |
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* Block size |
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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 .. |
DOUBLE COMPLEX ONE, ZERO |
COMPLEX*16 ONE, ZERO |
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), |
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), |
$ ZERO = ( 0.0D+0, 0.0D+0 ) ) |
$ ZERO = ( 0.0D+0, 0.0D+0 ) ) |
* .. |
* .. |
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INTEGER COUNT |
INTEGER COUNT |
INTEGER J, U11, INVD |
INTEGER J, U11, INVD |
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DOUBLE COMPLEX AK, AKKP1, AKP1, D, T |
COMPLEX*16 AK, AKKP1, AKP1, D, T |
DOUBLE COMPLEX U01_I_J, U01_IP1_J |
COMPLEX*16 U01_I_J, U01_IP1_J |
DOUBLE COMPLEX U11_I_J, U11_IP1_J |
COMPLEX*16 U11_I_J, U11_IP1_J |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME |
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IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* invA = P * inv(U')*inv(D)*inv(U)*P'. |
* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. |
* |
* |
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO ) |
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO ) |
* |
* |
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END IF |
END IF |
END DO |
END DO |
* |
* |
* inv(U') = (inv(U))' |
* inv(U**T) = (inv(U))**T |
* |
* |
* inv(U')*inv(D)*inv(U) |
* inv(U**T)*inv(D)*inv(U) |
* |
* |
CUT=N |
CUT=N |
DO WHILE (CUT .GT. 0) |
DO WHILE (CUT .GT. 0) |
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END IF |
END IF |
END DO |
END DO |
* |
* |
* U11T*invD1*U11->U11 |
* U11**T*invD1*U11->U11 |
* |
* |
CALL ZTRMM('L','U','T','U',NNB, NNB, |
CALL ZTRMM('L','U','T','U',NNB, NNB, |
$ ONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1) |
$ ONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1) |
* |
* |
* U01'invD*U01->A(CUT+I,CUT+J) |
DO I=1,NNB |
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DO J=I,NNB |
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A(CUT+I,CUT+J)=WORK(U11+I,J) |
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END DO |
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END DO |
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* |
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* U01**T*invD*U01->A(CUT+I,CUT+J) |
* |
* |
CALL ZGEMM('T','N',NNB,NNB,CUT,ONE,A(1,CUT+1),LDA, |
CALL ZGEMM('T','N',NNB,NNB,CUT,ONE,A(1,CUT+1),LDA, |
$ WORK,N+NB+1, ZERO, A(CUT+1,CUT+1), LDA) |
$ WORK,N+NB+1, ZERO, WORK(U11+1,1), N+NB+1) |
* |
* |
* U11 = U11T*invD1*U11 + U01'invD*U01 |
* U11 = U11**T*invD1*U11 + U01**T*invD*U01 |
* |
* |
DO I=1,NNB |
DO I=1,NNB |
DO J=I,NNB |
DO J=I,NNB |
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END DO |
END DO |
END DO |
END DO |
* |
* |
* U01 = U00T*invD0*U01 |
* U01 = U00**T*invD0*U01 |
* |
* |
CALL ZTRMM('L',UPLO,'T','U',CUT, NNB, |
CALL ZTRMM('L',UPLO,'T','U',CUT, NNB, |
$ ONE,A,LDA,WORK,N+NB+1) |
$ ONE,A,LDA,WORK,N+NB+1) |
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* |
* |
END DO |
END DO |
* |
* |
* Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P' |
* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T |
* |
* |
I=1 |
I=1 |
DO WHILE ( I .LE. N ) |
DO WHILE ( I .LE. N ) |
IF( IPIV(I) .GT. 0 ) THEN |
IF( IPIV(I) .GT. 0 ) THEN |
IP=IPIV(I) |
IP=IPIV(I) |
IF (I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, I ,IP ) |
IF (I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, I ,IP ) |
IF (I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, IP ,I ) |
IF (I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, IP ,I ) |
ELSE |
ELSE |
IP=-IPIV(I) |
IP=-IPIV(I) |
I=I+1 |
I=I+1 |
IF ( (I-1) .LT. IP) |
IF ( (I-1) .LT. IP) |
$ CALL ZSYSWAPR( UPLO, N, A, I-1 ,IP ) |
$ CALL ZSYSWAPR( UPLO, N, A, LDA, I-1 ,IP ) |
IF ( (I-1) .GT. IP) |
IF ( (I-1) .GT. IP) |
$ CALL ZSYSWAPR( UPLO, N, A, IP ,I-1 ) |
$ CALL ZSYSWAPR( UPLO, N, A, LDA, IP ,I-1 ) |
ENDIF |
ENDIF |
I=I+1 |
I=I+1 |
END DO |
END DO |
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* |
* |
* LOWER... |
* LOWER... |
* |
* |
* invA = P * inv(U')*inv(D)*inv(U)*P'. |
* invA = P * inv(U**T)*inv(D)*inv(U)*P**T. |
* |
* |
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO ) |
CALL ZTRTRI( UPLO, 'U', N, A, LDA, INFO ) |
* |
* |
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END IF |
END IF |
END DO |
END DO |
* |
* |
* inv(U') = (inv(U))' |
* inv(U**T) = (inv(U))**T |
* |
* |
* inv(U')*inv(D)*inv(U) |
* inv(U**T)*inv(D)*inv(U) |
* |
* |
CUT=0 |
CUT=0 |
DO WHILE (CUT .LT. N) |
DO WHILE (CUT .LT. N) |
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END IF |
END IF |
END DO |
END DO |
* |
* |
* L11T*invD1*L11->L11 |
* L11**T*invD1*L11->L11 |
* |
* |
CALL ZTRMM('L',UPLO,'T','U',NNB, NNB, |
CALL ZTRMM('L',UPLO,'T','U',NNB, NNB, |
$ ONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1) |
$ ONE,A(CUT+1,CUT+1),LDA,WORK(U11+1,1),N+NB+1) |
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* |
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DO I=1,NNB |
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DO J=1,I |
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A(CUT+I,CUT+J)=WORK(U11+I,J) |
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END DO |
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END DO |
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* |
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IF ( (CUT+NNB) .LT. N ) THEN |
IF ( (CUT+NNB) .LT. N ) THEN |
* |
* |
* L21T*invD2*L21->A(CUT+I,CUT+J) |
* L21**T*invD2*L21->A(CUT+I,CUT+J) |
* |
* |
CALL ZGEMM('T','N',NNB,NNB,N-NNB-CUT,ONE,A(CUT+NNB+1,CUT+1) |
CALL ZGEMM('T','N',NNB,NNB,N-NNB-CUT,ONE,A(CUT+NNB+1,CUT+1) |
$ ,LDA,WORK,N+NB+1, ZERO, A(CUT+1,CUT+1), LDA) |
$ ,LDA,WORK,N+NB+1, ZERO, WORK(U11+1,1), N+NB+1) |
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* |
* |
* L11 = L11T*invD1*L11 + U01'invD*U01 |
* L11 = L11**T*invD1*L11 + U01**T*invD*U01 |
* |
* |
DO I=1,NNB |
DO I=1,NNB |
DO J=1,I |
DO J=1,I |
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END DO |
END DO |
END DO |
END DO |
* |
* |
* U01 = L22T*invD2*L21 |
* U01 = L22**T*invD2*L21 |
* |
* |
CALL ZTRMM('L',UPLO,'T','U', N-NNB-CUT, NNB, |
CALL ZTRMM('L',UPLO,'T','U', N-NNB-CUT, NNB, |
$ ONE,A(CUT+NNB+1,CUT+NNB+1),LDA,WORK,N+NB+1) |
$ ONE,A(CUT+NNB+1,CUT+NNB+1),LDA,WORK,N+NB+1) |
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END DO |
END DO |
ELSE |
ELSE |
* |
* |
* L11 = L11T*invD1*L11 |
* L11 = L11**T*invD1*L11 |
* |
* |
DO I=1,NNB |
DO I=1,NNB |
DO J=1,I |
DO J=1,I |
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CUT=CUT+NNB |
CUT=CUT+NNB |
END DO |
END DO |
* |
* |
* Apply PERMUTATIONS P and P': P * inv(U')*inv(D)*inv(U) *P' |
* Apply PERMUTATIONS P and P**T: P * inv(U**T)*inv(D)*inv(U) *P**T |
* |
* |
I=N |
I=N |
DO WHILE ( I .GE. 1 ) |
DO WHILE ( I .GE. 1 ) |
IF( IPIV(I) .GT. 0 ) THEN |
IF( IPIV(I) .GT. 0 ) THEN |
IP=IPIV(I) |
IP=IPIV(I) |
IF (I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, I ,IP ) |
IF (I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, I ,IP ) |
IF (I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, IP ,I ) |
IF (I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, IP ,I ) |
ELSE |
ELSE |
IP=-IPIV(I) |
IP=-IPIV(I) |
IF ( I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, I ,IP ) |
IF ( I .LT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, I ,IP ) |
IF ( I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, IP ,I ) |
IF ( I .GT. IP) CALL ZSYSWAPR( UPLO, N, A, LDA, IP ,I ) |
I=I-1 |
I=I-1 |
ENDIF |
ENDIF |
I=I-1 |
I=I-1 |