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version 1.18, 2023/08/07 08:38:53
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*> \brief \b DLAED0 used by DSTEDC. 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 DLAED0 + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed0.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/dlaed0.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/dlaed0.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 DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, |
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* WORK, IWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* INTEGER ICOMPQ, 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( * ), Q( LDQ, * ), QSTORE( LDQS, * ), |
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* $ 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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*> DLAED0 computes all eigenvalues and corresponding eigenvectors of a |
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*> symmetric tridiagonal matrix using the divide and conquer method. |
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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] ICOMPQ |
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*> \verbatim |
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*> ICOMPQ is INTEGER |
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*> = 0: Compute eigenvalues only. |
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*> = 1: Compute eigenvectors of original dense symmetric matrix |
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*> also. On entry, Q contains the orthogonal matrix used |
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*> to reduce the original matrix to tridiagonal form. |
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*> = 2: Compute eigenvalues and eigenvectors of tridiagonal |
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*> matrix. |
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*> \endverbatim |
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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 orthogonal 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 main diagonal of the tridiagonal matrix. |
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*> On exit, its eigenvalues. |
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*> \endverbatim |
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*> |
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*> \param[in] E |
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*> \verbatim |
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*> E is DOUBLE PRECISION array, dimension (N-1) |
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*> 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 DOUBLE PRECISION array, dimension (LDQ, N) |
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*> On entry, Q must contain an N-by-N orthogonal matrix. |
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*> If ICOMPQ = 0 Q is not referenced. |
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*> If ICOMPQ = 1 On entry, Q is a subset of the columns of the |
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*> orthogonal matrix used to reduce the full |
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*> matrix to tridiagonal form corresponding to |
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*> the subset of the full matrix which is being |
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*> decomposed at this time. |
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*> If ICOMPQ = 2 On entry, Q will be the identity matrix. |
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*> On exit, Q contains the eigenvectors of the |
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*> 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. If eigenvectors are |
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*> desired, then LDQ >= max(1,N). In any case, LDQ >= 1. |
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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 DOUBLE PRECISION array, dimension (LDQS, N) |
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*> Referenced only when ICOMPQ = 1. 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. If ICOMPQ = 1, |
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*> then LDQS >= max(1,N). In any case, LDQS >= 1. |
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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 DOUBLE PRECISION array, |
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*> If ICOMPQ = 0 or 1, the dimension of WORK must be at least |
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*> 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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*> If ICOMPQ = 2, the dimension of WORK must be at least |
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*> 4*N + N**2. |
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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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*> If ICOMPQ = 0 or 1, 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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*> If ICOMPQ = 2, the dimension of IWORK must be at least |
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*> 3 + 5*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 auxOTHERcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Jeff Rutter, Computer Science Division, University of California |
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*> at Berkeley, USA |
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* |
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* ===================================================================== |
SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, |
SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS, |
$ WORK, IWORK, INFO ) |
$ WORK, 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 ICOMPQ, INFO, LDQ, LDQS, N, QSIZ |
INTEGER ICOMPQ, INFO, LDQ, LDQS, N, QSIZ |
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$ WORK( * ) |
$ WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DLAED0 computes all eigenvalues and corresponding eigenvectors of a |
|
* symmetric tridiagonal matrix using the divide and conquer method. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
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* ICOMPQ (input) INTEGER |
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* = 0: Compute eigenvalues only. |
|
* = 1: Compute eigenvectors of original dense symmetric matrix |
|
* also. On entry, Q contains the orthogonal matrix used |
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* to reduce the original matrix to tridiagonal form. |
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* = 2: Compute eigenvalues and eigenvectors of tridiagonal |
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* matrix. |
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* |
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* QSIZ (input) INTEGER |
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* The dimension of the orthogonal matrix used to reduce |
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* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. |
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* |
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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 main diagonal of the tridiagonal matrix. |
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* On exit, its eigenvalues. |
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* |
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* E (input) DOUBLE PRECISION array, dimension (N-1) |
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* 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) DOUBLE PRECISION array, dimension (LDQ, N) |
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* On entry, Q must contain an N-by-N orthogonal matrix. |
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* If ICOMPQ = 0 Q is not referenced. |
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* If ICOMPQ = 1 On entry, Q is a subset of the columns of the |
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* orthogonal matrix used to reduce the full |
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* matrix to tridiagonal form corresponding to |
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* the subset of the full matrix which is being |
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* decomposed at this time. |
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* If ICOMPQ = 2 On entry, Q will be the identity matrix. |
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* On exit, Q contains the eigenvectors of the |
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* tridiagonal matrix. |
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* |
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* LDQ (input) INTEGER |
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* The leading dimension of the array Q. If eigenvectors are |
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* desired, then LDQ >= max(1,N). In any case, LDQ >= 1. |
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* |
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* QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N) |
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* Referenced only when ICOMPQ = 1. 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. If ICOMPQ = 1, |
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* then LDQS >= max(1,N). In any case, LDQS >= 1. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, |
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* If ICOMPQ = 0 or 1, the dimension of WORK must be at least |
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* 1 + 3*N + 2*N*lg N + 2*N**2 |
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* ( lg( N ) = smallest integer k |
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* such that 2^k >= N ) |
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* If ICOMPQ = 2, the dimension of WORK must be at least |
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* 4*N + N**2. |
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* |
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* IWORK (workspace) INTEGER array, |
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* If ICOMPQ = 0 or 1, 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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* If ICOMPQ = 2, the dimension of IWORK must be at least |
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* 3 + 5*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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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Jeff Rutter, Computer Science Division, University of California |
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* at Berkeley, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |