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version 1.13, 2014/01/27 09:28:35
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*> \brief \b ZHPGST |
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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 ZHPGST + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhpgst.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/zhpgst.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/zhpgst.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 ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, ITYPE, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 AP( * ), BP( * ) |
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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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*> ZHPGST reduces a complex Hermitian-definite generalized |
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*> eigenproblem to standard form, using packed storage. |
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*> |
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*> If ITYPE = 1, the problem is A*x = lambda*B*x, |
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*> and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) |
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*> |
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*> If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or |
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*> B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. |
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*> |
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*> B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. |
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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] ITYPE |
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*> \verbatim |
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*> ITYPE is INTEGER |
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*> = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); |
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*> = 2 or 3: compute U*A*U**H or L**H*A*L. |
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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': Upper triangle of A is stored and B is factored as |
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*> U**H*U; |
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*> = 'L': Lower triangle of A is stored and B is factored as |
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*> L*L**H. |
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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 matrices A and B. 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 upper or lower triangle of the Hermitian matrix |
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*> A, packed columnwise in a linear array. The j-th column of A |
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*> is stored in the array 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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*> |
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*> On exit, if INFO = 0, the transformed matrix, stored in the |
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*> same format as A. |
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*> \endverbatim |
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*> |
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*> \param[in] BP |
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*> \verbatim |
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*> BP is COMPLEX*16 array, dimension (N*(N+1)/2) |
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*> The triangular factor from the Cholesky factorization of B, |
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*> stored in the same format as A, as returned by ZPPTRF. |
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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 November 2011 |
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* |
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*> \ingroup complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, INFO ) |
SUBROUTINE ZHPGST( ITYPE, UPLO, N, AP, BP, 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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COMPLEX*16 AP( * ), BP( * ) |
COMPLEX*16 AP( * ), BP( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZHPGST reduces a complex Hermitian-definite generalized |
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* eigenproblem to standard form, using packed storage. |
|
* |
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* If ITYPE = 1, the problem is A*x = lambda*B*x, |
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* and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H) |
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* |
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* If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or |
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* B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H*A*L. |
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* |
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* B must have been previously factorized as U**H*U or L*L**H by ZPPTRF. |
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* |
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* Arguments |
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* ========= |
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* |
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* ITYPE (input) INTEGER |
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* = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); |
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* = 2 or 3: compute U*A*U**H or L**H*A*L. |
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* |
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* UPLO (input) CHARACTER*1 |
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* = 'U': Upper triangle of A is stored and B is factored as |
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* U**H*U; |
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* = 'L': Lower triangle of A is stored and B is factored as |
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* L*L**H. |
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* |
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* N (input) INTEGER |
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* The order of the matrices A and B. 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 upper or lower triangle of the Hermitian matrix |
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* A, packed columnwise in a linear array. The j-th column of A |
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* is stored in the array 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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* |
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* On exit, if INFO = 0, the transformed matrix, stored in the |
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* same format as A. |
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* |
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* BP (input) COMPLEX*16 array, dimension (N*(N+1)/2) |
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* The triangular factor from the Cholesky factorization of B, |
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* stored in the same format as A, as returned by ZPPTRF. |
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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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IF( ITYPE.EQ.1 ) THEN |
IF( ITYPE.EQ.1 ) THEN |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute inv(U')*A*inv(U) |
* Compute inv(U**H)*A*inv(U) |
* |
* |
* J1 and JJ are the indices of A(1,j) and A(j,j) |
* J1 and JJ are the indices of A(1,j) and A(j,j) |
* |
* |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
* |
* |
* Compute inv(L)*A*inv(L') |
* Compute inv(L)*A*inv(L**H) |
* |
* |
* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) |
* KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) |
* |
* |
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ELSE |
ELSE |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute U*A*U' |
* Compute U*A*U**H |
* |
* |
* K1 and KK are the indices of A(1,k) and A(k,k) |
* K1 and KK are the indices of A(1,k) and A(k,k) |
* |
* |
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30 CONTINUE |
30 CONTINUE |
ELSE |
ELSE |
* |
* |
* Compute L'*A*L |
* Compute L**H *A*L |
* |
* |
* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) |
* JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) |
* |
* |