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version 1.18, 2023/08/07 08:39:28
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*> \brief \b ZLAED0 used by ZSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method. |
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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 ZLAED0 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaed0.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/zlaed0.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/zlaed0.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 ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, |
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* IWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER INFO, LDQ, LDQS, N, QSIZ |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION D( * ), E( * ), RWORK( * ) |
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* COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) |
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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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*> Using the divide and conquer method, ZLAED0 computes all eigenvalues |
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*> of a symmetric tridiagonal matrix which is one diagonal block of |
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*> those from reducing a dense or band Hermitian matrix and |
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*> corresponding eigenvectors of the dense or band matrix. |
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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] QSIZ |
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*> \verbatim |
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*> QSIZ is INTEGER |
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*> The dimension of the unitary matrix used to reduce |
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*> the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. |
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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 dimension of the symmetric tridiagonal matrix. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] D |
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*> \verbatim |
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*> D is DOUBLE PRECISION array, dimension (N) |
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*> On entry, the diagonal elements of the tridiagonal matrix. |
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*> On exit, the eigenvalues in ascending order. |
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*> \endverbatim |
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*> |
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*> \param[in,out] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> On entry, the off-diagonal elements of the tridiagonal matrix. |
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*> On exit, E has been destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Q |
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*> \verbatim |
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*> Q is COMPLEX*16 array, dimension (LDQ,N) |
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*> On entry, Q must contain an QSIZ x N matrix whose columns |
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*> unitarily orthonormal. It is a part of the unitary matrix |
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*> that reduces the full dense Hermitian matrix to a |
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*> (reducible) symmetric tridiagonal matrix. |
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*> \endverbatim |
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*> |
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*> \param[in] LDQ |
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*> \verbatim |
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*> LDQ is INTEGER |
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*> The leading dimension of the array Q. LDQ >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] IWORK |
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*> \verbatim |
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*> IWORK is INTEGER array, |
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*> the dimension of IWORK must be at least |
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*> 6 + 6*N + 5*N*lg N |
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*> ( lg( N ) = smallest integer k |
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*> such that 2^k >= N ) |
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*> \endverbatim |
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*> |
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*> \param[out] RWORK |
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*> \verbatim |
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*> RWORK is DOUBLE PRECISION array, |
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*> dimension (1 + 3*N + 2*N*lg N + 3*N**2) |
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*> ( lg( N ) = smallest integer k |
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*> such that 2^k >= N ) |
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*> \endverbatim |
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*> |
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*> \param[out] QSTORE |
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*> \verbatim |
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*> QSTORE is COMPLEX*16 array, dimension (LDQS, N) |
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*> Used to store parts of |
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*> the eigenvector matrix when the updating matrix multiplies |
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*> take place. |
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*> \endverbatim |
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*> |
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*> \param[in] LDQS |
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*> \verbatim |
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*> LDQS is INTEGER |
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*> The leading dimension of the array QSTORE. |
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*> LDQS >= 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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*> > 0: The algorithm failed to compute an eigenvalue while |
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*> working on the submatrix lying in rows and columns |
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*> INFO/(N+1) through mod(INFO,N+1). |
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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 ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, |
SUBROUTINE ZLAED0( QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, RWORK, |
$ IWORK, INFO ) |
$ IWORK, 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 .. |
INTEGER INFO, LDQ, LDQS, N, QSIZ |
INTEGER INFO, LDQ, LDQS, N, QSIZ |
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COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) |
COMPLEX*16 Q( LDQ, * ), QSTORE( LDQS, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
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* Using the divide and conquer method, ZLAED0 computes all eigenvalues |
|
* of a symmetric tridiagonal matrix which is one diagonal block of |
|
* those from reducing a dense or band Hermitian matrix and |
|
* corresponding eigenvectors of the dense or band matrix. |
|
* |
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* Arguments |
|
* ========= |
|
* |
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* QSIZ (input) INTEGER |
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* The dimension of the unitary matrix used to reduce |
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* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. |
|
* |
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* N (input) INTEGER |
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* The dimension of the symmetric tridiagonal matrix. N >= 0. |
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* |
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* D (input/output) DOUBLE PRECISION array, dimension (N) |
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* On entry, the diagonal elements of the tridiagonal matrix. |
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* On exit, the eigenvalues in ascending order. |
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* |
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* E (input/output) DOUBLE PRECISION array, dimension (N-1) |
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* On entry, the off-diagonal elements of the tridiagonal matrix. |
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* On exit, E has been destroyed. |
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* |
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* Q (input/output) COMPLEX*16 array, dimension (LDQ,N) |
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* On entry, Q must contain an QSIZ x N matrix whose columns |
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* unitarily orthonormal. It is a part of the unitary matrix |
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* that reduces the full dense Hermitian matrix to a |
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* (reducible) symmetric tridiagonal matrix. |
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* |
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* LDQ (input) INTEGER |
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* The leading dimension of the array Q. LDQ >= max(1,N). |
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* |
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* IWORK (workspace) INTEGER array, |
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* the dimension of IWORK must be at least |
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* 6 + 6*N + 5*N*lg N |
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* ( lg( N ) = smallest integer k |
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* such that 2^k >= N ) |
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* |
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* RWORK (workspace) DOUBLE PRECISION array, |
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* dimension (1 + 3*N + 2*N*lg N + 3*N**2) |
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* ( lg( N ) = smallest integer k |
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* such that 2^k >= N ) |
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* |
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* QSTORE (workspace) COMPLEX*16 array, dimension (LDQS, N) |
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* Used to store parts of |
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* the eigenvector matrix when the updating matrix multiplies |
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* take place. |
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* |
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* LDQS (input) INTEGER |
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* The leading dimension of the array QSTORE. |
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* LDQS >= 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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* > 0: The algorithm failed to compute an eigenvalue while |
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* working on the submatrix lying in rows and columns |
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* INFO/(N+1) through mod(INFO,N+1). |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* Warning: N could be as big as QSIZ! |
* Warning: N could be as big as QSIZ! |