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version 1.18, 2018/05/29 07:18:08
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*> \brief \b DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). |
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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 DSYGS2 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsygs2.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/dsygs2.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/dsygs2.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 DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER UPLO |
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* INTEGER INFO, ITYPE, LDA, LDB, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
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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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*> DSYGS2 reduces a real symmetric-definite generalized eigenproblem |
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*> to standard form. |
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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**T)*A*inv(U) or inv(L)*A*inv(L**T) |
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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**T or L**T *A*L. |
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*> |
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*> B must have been previously factorized as U**T *U or L*L**T by DPOTRF. |
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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**T)*A*inv(U) or inv(L)*A*inv(L**T); |
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*> = 2 or 3: compute U*A*U**T or L**T *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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*> Specifies whether the upper or lower triangular part of the |
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*> symmetric matrix A is stored, and how B has been factorized. |
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*> = 'U': Upper triangular |
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*> = 'L': Lower 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 matrices A and B. 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 symmetric matrix A. If UPLO = 'U', the leading |
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*> n by n upper triangular part of A contains the upper |
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*> triangular part of the matrix A, and the strictly lower |
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*> triangular part of A is not referenced. If UPLO = 'L', the |
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*> leading n by n lower triangular part of A contains the lower |
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*> triangular part of the matrix A, and the strictly upper |
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*> triangular part of A is not referenced. |
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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] 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] B |
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*> \verbatim |
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*> B is DOUBLE PRECISION array, dimension (LDB,N) |
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*> The triangular factor from the Cholesky factorization of B, |
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*> as returned by DPOTRF. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,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 doubleSYcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, INFO ) |
SUBROUTINE DSYGS2( ITYPE, UPLO, N, A, LDA, B, LDB, 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 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER UPLO |
CHARACTER UPLO |
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DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
DOUBLE PRECISION A( LDA, * ), B( LDB, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSYGS2 reduces a real symmetric-definite generalized eigenproblem |
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* to standard form. |
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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')*A*inv(U) or inv(L)*A*inv(L') |
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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` or L'*A*L. |
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* |
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* B must have been previously factorized as U'*U or L*L' by DPOTRF. |
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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')*A*inv(U) or inv(L)*A*inv(L'); |
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* = 2 or 3: compute U*A*U' or L'*A*L. |
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* |
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* UPLO (input) CHARACTER*1 |
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* Specifies whether the upper or lower triangular part of the |
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* symmetric matrix A is stored, and how B has been factorized. |
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* = 'U': Upper triangular |
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* = 'L': Lower triangular |
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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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* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the symmetric matrix A. If UPLO = 'U', the leading |
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* n by n upper triangular part of A contains the upper |
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* triangular part of the matrix A, and the strictly lower |
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* triangular part of A is not referenced. If UPLO = 'L', the |
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* leading n by n lower triangular part of A contains the lower |
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* triangular part of the matrix A, and the strictly upper |
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* triangular part of A is not referenced. |
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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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* 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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* B (input) DOUBLE PRECISION array, dimension (LDB,N) |
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* The triangular factor from the Cholesky factorization of B, |
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* as returned by DPOTRF. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,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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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**T)*A*inv(U) |
* |
* |
DO 10 K = 1, N |
DO 10 K = 1, N |
* |
* |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
* |
* |
* Compute inv(L)*A*inv(L') |
* Compute inv(L)*A*inv(L**T) |
* |
* |
DO 20 K = 1, N |
DO 20 K = 1, N |
* |
* |
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ELSE |
ELSE |
IF( UPPER ) THEN |
IF( UPPER ) THEN |
* |
* |
* Compute U*A*U' |
* Compute U*A*U**T |
* |
* |
DO 30 K = 1, N |
DO 30 K = 1, N |
* |
* |
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30 CONTINUE |
30 CONTINUE |
ELSE |
ELSE |
* |
* |
* Compute L'*A*L |
* Compute L**T *A*L |
* |
* |
DO 40 K = 1, N |
DO 40 K = 1, N |
* |
* |