version 1.3, 2010/08/06 15:29:01
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version 1.10, 2012/08/22 09:48:40
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*> \brief \b ZSTEDC |
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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 ZSTEDC + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zstedc.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/zstedc.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/zstedc.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 ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, |
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* LRWORK, IWORK, 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, LRWORK, 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( * ), RWORK( * ) |
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* COMPLEX*16 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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*> ZSTEDC 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 complex Hermitian matrix can also |
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*> be found if ZHETRD or ZHPTRD or ZHBTRD 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 Hermitian matrix |
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*> also. On entry, Z contains the unitary matrix used |
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*> to reduce the original matrix to 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 COMPLEX*16 array, dimension (LDZ,N) |
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*> On entry, if COMPZ = 'V', then Z contains the unitary |
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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 Hermitian 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 COMPLEX*16 array, dimension (MAX(1,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 'I', or N <= 1, LWORK must be at least 1. |
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*> If COMPZ = 'V' and N > 1, LWORK must be at least N*N. |
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*> Note that for COMPZ = '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 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 sizes of the WORK, RWORK and |
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*> IWORK arrays, returns these values as the first entries of |
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*> the WORK, RWORK and IWORK arrays, and no error message |
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*> related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
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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 (LRWORK) |
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*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LRWORK |
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*> \verbatim |
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*> LRWORK is INTEGER |
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*> The dimension of the array RWORK. |
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*> If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. |
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*> If COMPZ = 'V' and N > 1, LRWORK 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, LRWORK must be at least |
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*> 1 + 4*N + 2*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 LRWORK |
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*> need only be max(1,2*(N-1)). |
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*> |
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*> If LRWORK = -1, then a workspace query is assumed; the |
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*> routine only calculates the optimal sizes of the WORK, RWORK |
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*> and IWORK arrays, returns these values as the first entries |
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*> of the WORK, RWORK and IWORK arrays, and no error message |
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*> related to LWORK or LRWORK or LIWORK 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, LIWORK must be at least 1. |
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*> If COMPZ = 'V' or N > 1, LIWORK must be at least |
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*> 6 + 6*N + 5*N*lg N. |
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*> If COMPZ = 'I' or N > 1, 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 sizes of the WORK, RWORK |
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*> and IWORK arrays, returns these values as the first entries |
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*> of the WORK, RWORK and IWORK arrays, and no error message |
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*> related to LWORK or LRWORK or 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 complex16OTHERcomputational |
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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 ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, |
SUBROUTINE ZSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, |
$ LRWORK, IWORK, LIWORK, INFO ) |
$ LRWORK, IWORK, LIWORK, 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 COMPZ |
CHARACTER COMPZ |
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COMPLEX*16 WORK( * ), Z( LDZ, * ) |
COMPLEX*16 WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* ZSTEDC computes all eigenvalues and, optionally, eigenvectors of a |
|
* symmetric tridiagonal matrix using the divide and conquer method. |
|
* The eigenvectors of a full or band complex Hermitian matrix can also |
|
* be found if ZHETRD or ZHPTRD or ZHBTRD has been used to reduce this |
|
* matrix to tridiagonal form. |
|
* |
|
* 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 Hermitian matrix |
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* also. On entry, Z contains the unitary matrix used |
|
* to reduce the original matrix to 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) COMPLEX*16 array, dimension (LDZ,N) |
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* On entry, if COMPZ = 'V', then Z contains the unitary |
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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 Hermitian 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) COMPLEX*16 array, dimension (MAX(1,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 'I', or N <= 1, LWORK must be at least 1. |
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* If COMPZ = 'V' and N > 1, LWORK must be at least N*N. |
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* Note that for COMPZ = '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 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 sizes of the WORK, RWORK and |
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* IWORK arrays, returns these values as the first entries of |
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* the WORK, RWORK and IWORK arrays, and no error message |
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* related to LWORK or LRWORK or LIWORK is issued by XERBLA. |
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* |
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* RWORK (workspace/output) DOUBLE PRECISION array, |
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* dimension (LRWORK) |
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* On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK. |
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* |
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* LRWORK (input) INTEGER |
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* The dimension of the array RWORK. |
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* If COMPZ = 'N' or N <= 1, LRWORK must be at least 1. |
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* If COMPZ = 'V' and N > 1, LRWORK 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, LRWORK must be at least |
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* 1 + 4*N + 2*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 LRWORK |
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* need only be max(1,2*(N-1)). |
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* |
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* If LRWORK = -1, then a workspace query is assumed; the |
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* routine only calculates the optimal sizes of the WORK, RWORK |
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* and IWORK arrays, returns these values as the first entries |
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* of the WORK, RWORK and IWORK arrays, and no error message |
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* related to LWORK or LRWORK or LIWORK 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, LIWORK must be at least 1. |
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* If COMPZ = 'V' or N > 1, LIWORK must be at least |
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* 6 + 6*N + 5*N*lg N. |
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* If COMPZ = 'I' or N > 1, 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 sizes of the WORK, RWORK |
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* and IWORK arrays, returns these values as the first entries |
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* of the WORK, RWORK and IWORK arrays, and no error message |
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* related to LWORK or LRWORK or 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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* |
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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 |
LWMIN = N*N |
LWMIN = N*N |
LRWMIN = 1 + 3*N + 2*N*LGN + 3*N**2 |
LRWMIN = 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 |
LWMIN = 1 |