version 1.1, 2010/01/26 15:22:46
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version 1.11, 2012/12/14 14:22:40
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*> \brief \b DSTEBZ |
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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 DSTEDC + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstedc.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/dstedc.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/dstedc.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 DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, |
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* LIWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER COMPZ |
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* INTEGER INFO, LDZ, LIWORK, LWORK, N |
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* .. |
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* .. Array Arguments .. |
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* INTEGER IWORK( * ) |
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* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) |
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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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*> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a |
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*> symmetric tridiagonal matrix using the divide and conquer method. |
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*> The eigenvectors of a full or band real symmetric matrix can also be |
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*> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this |
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*> matrix to tridiagonal form. |
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*> |
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*> This code makes very mild assumptions about floating point |
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*> arithmetic. It will work on machines with a guard digit in |
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*> add/subtract, or on those binary machines without guard digits |
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*> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. |
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*> It could conceivably fail on hexadecimal or decimal machines |
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*> without guard digits, but we know of none. See DLAED3 for details. |
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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] COMPZ |
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*> \verbatim |
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*> COMPZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only. |
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*> = 'I': Compute eigenvectors of tridiagonal matrix also. |
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*> = 'V': Compute eigenvectors of original dense symmetric |
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*> matrix also. On entry, Z contains the orthogonal |
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*> matrix used to reduce the original matrix to |
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*> tridiagonal form. |
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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, if INFO = 0, 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 subdiagonal 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] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension (LDZ,N) |
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*> On entry, if COMPZ = 'V', then Z contains the orthogonal |
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*> matrix used in the reduction to tridiagonal form. |
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*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the |
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*> orthonormal eigenvectors of the original symmetric matrix, |
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*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors |
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*> of the symmetric tridiagonal matrix. |
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*> If COMPZ = 'N', then Z is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDZ >= 1. |
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*> If eigenvectors are desired, then LDZ >= max(1,N). |
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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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*> dimension (LWORK) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The dimension of the array WORK. |
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*> If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. |
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*> If COMPZ = 'V' and N > 1 then LWORK must be at least |
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*> ( 1 + 3*N + 2*N*lg N + 4*N**2 ), |
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*> where lg( N ) = smallest integer k such |
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*> that 2**k >= N. |
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*> If COMPZ = 'I' and N > 1 then LWORK must be at least |
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*> ( 1 + 4*N + N**2 ). |
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*> Note that for COMPZ = 'I' or 'V', then if N is less than or |
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*> equal to the minimum divide size, usually 25, then LWORK need |
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*> only be max(1,2*(N-1)). |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK is issued by XERBLA. |
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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, dimension (MAX(1,LIWORK)) |
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*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LIWORK |
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*> \verbatim |
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*> LIWORK is INTEGER |
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*> The dimension of the array IWORK. |
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*> If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. |
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*> If COMPZ = 'V' and N > 1 then LIWORK must be at least |
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*> ( 6 + 6*N + 5*N*lg N ). |
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*> If COMPZ = 'I' and N > 1 then LIWORK must be at least |
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*> ( 3 + 5*N ). |
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*> Note that for COMPZ = 'I' or 'V', then if N is less than or |
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*> equal to the minimum divide size, usually 25, then LIWORK |
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*> need only be 1. |
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*> |
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*> If LIWORK = -1, then a workspace query is assumed; the |
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*> routine only calculates the optimal size of the IWORK array, |
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*> returns this value as the first entry of the IWORK array, and |
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*> no error message related to LIWORK is issued by XERBLA. |
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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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*> \date November 2011 |
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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 \n |
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*> Modified by Francoise Tisseur, University of Tennessee |
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*> |
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* ===================================================================== |
SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, |
SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, |
$ LIWORK, INFO ) |
$ LIWORK, INFO ) |
* |
* |
* -- LAPACK driver 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 COMPZ |
CHARACTER COMPZ |
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DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) |
DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DSTEDC computes all eigenvalues and, optionally, eigenvectors of a |
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* symmetric tridiagonal matrix using the divide and conquer method. |
|
* The eigenvectors of a full or band real symmetric matrix can also be |
|
* found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this |
|
* matrix to tridiagonal form. |
|
* |
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* This code makes very mild assumptions about floating point |
|
* arithmetic. It will work on machines with a guard digit in |
|
* add/subtract, or on those binary machines without guard digits |
|
* which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. |
|
* It could conceivably fail on hexadecimal or decimal machines |
|
* without guard digits, but we know of none. See DLAED3 for details. |
|
* |
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* Arguments |
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* ========= |
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* |
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* COMPZ (input) CHARACTER*1 |
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* = 'N': Compute eigenvalues only. |
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* = 'I': Compute eigenvectors of tridiagonal matrix also. |
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* = 'V': Compute eigenvectors of original dense symmetric |
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* matrix also. On entry, Z contains the orthogonal |
|
* matrix used to reduce the original matrix to |
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* tridiagonal form. |
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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 diagonal elements of the tridiagonal matrix. |
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* On exit, if INFO = 0, 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 subdiagonal elements of the tridiagonal matrix. |
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* On exit, E has been destroyed. |
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* |
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* Z (input/output) DOUBLE PRECISION array, dimension (LDZ,N) |
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* On entry, if COMPZ = 'V', then Z contains the orthogonal |
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* matrix used in the reduction to tridiagonal form. |
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* On exit, if INFO = 0, then if COMPZ = 'V', Z contains the |
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* orthonormal eigenvectors of the original symmetric matrix, |
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* and if COMPZ = 'I', Z contains the orthonormal eigenvectors |
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* of the symmetric tridiagonal matrix. |
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* If COMPZ = 'N', then Z is not referenced. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1. |
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* If eigenvectors are desired, then LDZ >= max(1,N). |
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* |
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* WORK (workspace/output) DOUBLE PRECISION array, |
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* dimension (LWORK) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. |
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* If COMPZ = 'N' or N <= 1 then LWORK must be at least 1. |
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* If COMPZ = 'V' and N > 1 then LWORK must be at least |
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* ( 1 + 3*N + 2*N*lg N + 3*N**2 ), |
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* where lg( N ) = smallest integer k such |
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* that 2**k >= N. |
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* If COMPZ = 'I' and N > 1 then LWORK must be at least |
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* ( 1 + 4*N + N**2 ). |
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* Note that for COMPZ = 'I' or 'V', then if N is less than or |
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* equal to the minimum divide size, usually 25, then LWORK need |
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* only be max(1,2*(N-1)). |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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* |
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* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) |
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* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. |
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* |
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* LIWORK (input) INTEGER |
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* The dimension of the array IWORK. |
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* If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1. |
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* If COMPZ = 'V' and N > 1 then LIWORK must be at least |
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* ( 6 + 6*N + 5*N*lg N ). |
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* If COMPZ = 'I' and N > 1 then LIWORK must be at least |
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* ( 3 + 5*N ). |
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* Note that for COMPZ = 'I' or 'V', then if N is less than or |
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* equal to the minimum divide size, usually 25, then LIWORK |
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* need only be 1. |
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* |
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* If LIWORK = -1, then a workspace query is assumed; the |
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* routine only calculates the optimal size of the IWORK array, |
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* returns this value as the first entry of the IWORK array, and |
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* no error message related to LIWORK is issued by XERBLA. |
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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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* Modified by Francoise Tisseur, University of Tennessee. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
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IF( 2**LGN.LT.N ) |
IF( 2**LGN.LT.N ) |
$ LGN = LGN + 1 |
$ LGN = LGN + 1 |
IF( ICOMPZ.EQ.1 ) THEN |
IF( ICOMPZ.EQ.1 ) THEN |
LWMIN = 1 + 3*N + 2*N*LGN + 3*N**2 |
LWMIN = 1 + 3*N + 2*N*LGN + 4*N**2 |
LIWMIN = 6 + 6*N + 5*N*LGN |
LIWMIN = 6 + 6*N + 5*N*LGN |
ELSE IF( ICOMPZ.EQ.2 ) THEN |
ELSE IF( ICOMPZ.EQ.2 ) THEN |
LWMIN = 1 + 4*N + N**2 |
LWMIN = 1 + 4*N + N**2 |