version 1.2, 2010/04/21 13:45:25
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version 1.12, 2012/12/14 12:30:27
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*> \brief <b> DSYEVR computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b> |
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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 DSYEVR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevr.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/dsyevr.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/dsyevr.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 DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, |
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* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, |
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* IWORK, LIWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER JOBZ, RANGE, UPLO |
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* INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LWORK, M, N |
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* DOUBLE PRECISION ABSTOL, VL, VU |
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* .. |
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* .. Array Arguments .. |
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* INTEGER ISUPPZ( * ), IWORK( * ) |
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* DOUBLE PRECISION A( LDA, * ), W( * ), 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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*> DSYEVR computes selected eigenvalues and, optionally, eigenvectors |
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*> of a real symmetric matrix A. Eigenvalues and eigenvectors can be |
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*> selected by specifying either a range of values or a range of |
|
*> indices for the desired eigenvalues. |
|
*> |
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*> DSYEVR first reduces the matrix A to tridiagonal form T with a call |
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*> to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute |
|
*> the eigenspectrum using Relatively Robust Representations. DSTEMR |
|
*> computes eigenvalues by the dqds algorithm, while orthogonal |
|
*> eigenvectors are computed from various "good" L D L^T representations |
|
*> (also known as Relatively Robust Representations). Gram-Schmidt |
|
*> orthogonalization is avoided as far as possible. More specifically, |
|
*> the various steps of the algorithm are as follows. |
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*> |
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*> For each unreduced block (submatrix) of T, |
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*> (a) Compute T - sigma I = L D L^T, so that L and D |
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*> define all the wanted eigenvalues to high relative accuracy. |
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*> This means that small relative changes in the entries of D and L |
|
*> cause only small relative changes in the eigenvalues and |
|
*> eigenvectors. The standard (unfactored) representation of the |
|
*> tridiagonal matrix T does not have this property in general. |
|
*> (b) Compute the eigenvalues to suitable accuracy. |
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*> If the eigenvectors are desired, the algorithm attains full |
|
*> accuracy of the computed eigenvalues only right before |
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*> the corresponding vectors have to be computed, see steps c) and d). |
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*> (c) For each cluster of close eigenvalues, select a new |
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*> shift close to the cluster, find a new factorization, and refine |
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*> the shifted eigenvalues to suitable accuracy. |
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*> (d) For each eigenvalue with a large enough relative separation compute |
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*> the corresponding eigenvector by forming a rank revealing twisted |
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*> factorization. Go back to (c) for any clusters that remain. |
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*> |
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*> The desired accuracy of the output can be specified by the input |
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*> parameter ABSTOL. |
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*> |
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*> For more details, see DSTEMR's documentation and: |
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*> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations |
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*> to compute orthogonal eigenvectors of symmetric tridiagonal matrices," |
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*> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. |
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*> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and |
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*> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, |
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*> 2004. Also LAPACK Working Note 154. |
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*> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric |
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*> tridiagonal eigenvalue/eigenvector problem", |
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*> Computer Science Division Technical Report No. UCB/CSD-97-971, |
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*> UC Berkeley, May 1997. |
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*> |
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*> |
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*> Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested |
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*> on machines which conform to the ieee-754 floating point standard. |
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*> DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and |
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*> when partial spectrum requests are made. |
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*> |
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*> Normal execution of DSTEMR may create NaNs and infinities and |
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*> hence may abort due to a floating point exception in environments |
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*> which do not handle NaNs and infinities in the ieee standard default |
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*> manner. |
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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] JOBZ |
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*> \verbatim |
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*> JOBZ is CHARACTER*1 |
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*> = 'N': Compute eigenvalues only; |
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*> = 'V': Compute eigenvalues and eigenvectors. |
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*> \endverbatim |
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*> |
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*> \param[in] RANGE |
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*> \verbatim |
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*> RANGE is CHARACTER*1 |
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*> = 'A': all eigenvalues will be found. |
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*> = 'V': all eigenvalues in the half-open interval (VL,VU] |
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*> will be found. |
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*> = 'I': the IL-th through IU-th eigenvalues will be found. |
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*> For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and |
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*> DSTEIN are called |
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*> \endverbatim |
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*> |
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*> \param[in] UPLO |
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*> \verbatim |
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*> UPLO is CHARACTER*1 |
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*> = 'U': Upper triangle of A is stored; |
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*> = 'L': Lower triangle of A is stored. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrix A. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is DOUBLE PRECISION array, dimension (LDA, N) |
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*> On entry, the symmetric matrix A. If UPLO = 'U', the |
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*> leading N-by-N upper triangular part of A contains the |
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*> upper triangular part of the matrix A. If UPLO = 'L', |
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*> the leading N-by-N lower triangular part of A contains |
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*> the lower triangular part of the matrix A. |
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*> On exit, the lower triangle (if UPLO='L') or the upper |
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*> triangle (if UPLO='U') of A, including the diagonal, is |
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*> destroyed. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in] VL |
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*> \verbatim |
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*> VL is DOUBLE PRECISION |
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*> \endverbatim |
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*> |
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*> \param[in] VU |
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*> \verbatim |
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*> VU is DOUBLE PRECISION |
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*> If RANGE='V', the lower and upper bounds of the interval to |
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*> be searched for eigenvalues. VL < VU. |
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*> Not referenced if RANGE = 'A' or 'I'. |
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*> \endverbatim |
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*> |
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*> \param[in] IL |
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*> \verbatim |
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*> IL is INTEGER |
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*> \endverbatim |
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*> |
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*> \param[in] IU |
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*> \verbatim |
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*> IU is INTEGER |
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*> If RANGE='I', the indices (in ascending order) of the |
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*> smallest and largest eigenvalues to be returned. |
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*> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. |
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*> Not referenced if RANGE = 'A' or 'V'. |
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*> \endverbatim |
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*> |
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*> \param[in] ABSTOL |
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*> \verbatim |
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*> ABSTOL is DOUBLE PRECISION |
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*> The absolute error tolerance for the eigenvalues. |
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*> An approximate eigenvalue is accepted as converged |
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*> when it is determined to lie in an interval [a,b] |
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*> of width less than or equal to |
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*> |
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*> ABSTOL + EPS * max( |a|,|b| ) , |
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*> |
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*> where EPS is the machine precision. If ABSTOL is less than |
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*> or equal to zero, then EPS*|T| will be used in its place, |
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*> where |T| is the 1-norm of the tridiagonal matrix obtained |
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*> by reducing A to tridiagonal form. |
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*> |
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*> See "Computing Small Singular Values of Bidiagonal Matrices |
|
*> with Guaranteed High Relative Accuracy," by Demmel and |
|
*> Kahan, LAPACK Working Note #3. |
|
*> |
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*> If high relative accuracy is important, set ABSTOL to |
|
*> DLAMCH( 'Safe minimum' ). Doing so will guarantee that |
|
*> eigenvalues are computed to high relative accuracy when |
|
*> possible in future releases. The current code does not |
|
*> make any guarantees about high relative accuracy, but |
|
*> future releases will. See J. Barlow and J. Demmel, |
|
*> "Computing Accurate Eigensystems of Scaled Diagonally |
|
*> Dominant Matrices", LAPACK Working Note #7, for a discussion |
|
*> of which matrices define their eigenvalues to high relative |
|
*> accuracy. |
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*> \endverbatim |
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*> |
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*> \param[out] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The total number of eigenvalues found. 0 <= M <= N. |
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*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. |
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*> \endverbatim |
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*> |
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*> \param[out] W |
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*> \verbatim |
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*> W is DOUBLE PRECISION array, dimension (N) |
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*> The first M elements contain the selected eigenvalues in |
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*> ascending order. |
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*> \endverbatim |
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*> |
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*> \param[out] Z |
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*> \verbatim |
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*> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M)) |
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*> If JOBZ = 'V', then if INFO = 0, the first M columns of Z |
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*> contain the orthonormal eigenvectors of the matrix A |
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*> corresponding to the selected eigenvalues, with the i-th |
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*> column of Z holding the eigenvector associated with W(i). |
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*> If JOBZ = 'N', then Z is not referenced. |
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*> Note: the user must ensure that at least max(1,M) columns are |
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*> supplied in the array Z; if RANGE = 'V', the exact value of M |
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*> is not known in advance and an upper bound must be used. |
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*> Supplying N columns is always safe. |
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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, and if |
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*> JOBZ = 'V', LDZ >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[out] ISUPPZ |
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*> \verbatim |
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*> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) ) |
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*> The support of the eigenvectors in Z, i.e., the indices |
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*> indicating the nonzero elements in Z. The i-th eigenvector |
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*> is nonzero only in elements ISUPPZ( 2*i-1 ) through |
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*> ISUPPZ( 2*i ). |
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*> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 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, 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. LWORK >= max(1,26*N). |
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*> For optimal efficiency, LWORK >= (NB+6)*N, |
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*> where NB is the max of the blocksize for DSYTRD and DORMTR |
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*> returned by ILAENV. |
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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 LWORK. |
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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. LIWORK >= max(1,10*N). |
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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: Internal error |
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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 September 2012 |
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* |
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*> \ingroup doubleSYeigen |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Inderjit Dhillon, IBM Almaden, USA \n |
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*> Osni Marques, LBNL/NERSC, USA \n |
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*> Ken Stanley, Computer Science Division, University of |
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*> California at Berkeley, USA \n |
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*> Jason Riedy, Computer Science Division, University of |
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*> California at Berkeley, USA \n |
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*> |
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* ===================================================================== |
SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, |
SUBROUTINE DSYEVR( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, |
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, |
$ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, |
$ IWORK, LIWORK, INFO ) |
$ IWORK, LIWORK, INFO ) |
* |
* |
* -- LAPACK driver routine (version 3.2) -- |
* -- LAPACK driver routine (version 3.4.2) -- |
* -- 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 |
* September 2012 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER JOBZ, RANGE, UPLO |
CHARACTER JOBZ, RANGE, UPLO |
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Line 340
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DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) |
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
|
* ======= |
|
* |
|
* DSYEVR computes selected eigenvalues and, optionally, eigenvectors |
|
* of a real symmetric matrix A. Eigenvalues and eigenvectors can be |
|
* selected by specifying either a range of values or a range of |
|
* indices for the desired eigenvalues. |
|
* |
|
* DSYEVR first reduces the matrix A to tridiagonal form T with a call |
|
* to DSYTRD. Then, whenever possible, DSYEVR calls DSTEMR to compute |
|
* the eigenspectrum using Relatively Robust Representations. DSTEMR |
|
* computes eigenvalues by the dqds algorithm, while orthogonal |
|
* eigenvectors are computed from various "good" L D L^T representations |
|
* (also known as Relatively Robust Representations). Gram-Schmidt |
|
* orthogonalization is avoided as far as possible. More specifically, |
|
* the various steps of the algorithm are as follows. |
|
* |
|
* For each unreduced block (submatrix) of T, |
|
* (a) Compute T - sigma I = L D L^T, so that L and D |
|
* define all the wanted eigenvalues to high relative accuracy. |
|
* This means that small relative changes in the entries of D and L |
|
* cause only small relative changes in the eigenvalues and |
|
* eigenvectors. The standard (unfactored) representation of the |
|
* tridiagonal matrix T does not have this property in general. |
|
* (b) Compute the eigenvalues to suitable accuracy. |
|
* If the eigenvectors are desired, the algorithm attains full |
|
* accuracy of the computed eigenvalues only right before |
|
* the corresponding vectors have to be computed, see steps c) and d). |
|
* (c) For each cluster of close eigenvalues, select a new |
|
* shift close to the cluster, find a new factorization, and refine |
|
* the shifted eigenvalues to suitable accuracy. |
|
* (d) For each eigenvalue with a large enough relative separation compute |
|
* the corresponding eigenvector by forming a rank revealing twisted |
|
* factorization. Go back to (c) for any clusters that remain. |
|
* |
|
* The desired accuracy of the output can be specified by the input |
|
* parameter ABSTOL. |
|
* |
|
* For more details, see DSTEMR's documentation and: |
|
* - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations |
|
* to compute orthogonal eigenvectors of symmetric tridiagonal matrices," |
|
* Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. |
|
* - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and |
|
* Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, |
|
* 2004. Also LAPACK Working Note 154. |
|
* - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric |
|
* tridiagonal eigenvalue/eigenvector problem", |
|
* Computer Science Division Technical Report No. UCB/CSD-97-971, |
|
* UC Berkeley, May 1997. |
|
* |
|
* |
|
* Note 1 : DSYEVR calls DSTEMR when the full spectrum is requested |
|
* on machines which conform to the ieee-754 floating point standard. |
|
* DSYEVR calls DSTEBZ and SSTEIN on non-ieee machines and |
|
* when partial spectrum requests are made. |
|
* |
|
* Normal execution of DSTEMR may create NaNs and infinities and |
|
* hence may abort due to a floating point exception in environments |
|
* which do not handle NaNs and infinities in the ieee standard default |
|
* manner. |
|
* |
|
* Arguments |
|
* ========= |
|
* |
|
* JOBZ (input) CHARACTER*1 |
|
* = 'N': Compute eigenvalues only; |
|
* = 'V': Compute eigenvalues and eigenvectors. |
|
* |
|
* RANGE (input) CHARACTER*1 |
|
* = 'A': all eigenvalues will be found. |
|
* = 'V': all eigenvalues in the half-open interval (VL,VU] |
|
* will be found. |
|
* = 'I': the IL-th through IU-th eigenvalues will be found. |
|
********** For RANGE = 'V' or 'I' and IU - IL < N - 1, DSTEBZ and |
|
********** DSTEIN are called |
|
* |
|
* UPLO (input) CHARACTER*1 |
|
* = 'U': Upper triangle of A is stored; |
|
* = 'L': Lower triangle of A is stored. |
|
* |
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* N (input) INTEGER |
|
* The order of the matrix A. N >= 0. |
|
* |
|
* A (input/output) DOUBLE PRECISION array, dimension (LDA, N) |
|
* On entry, the symmetric matrix A. If UPLO = 'U', the |
|
* leading N-by-N upper triangular part of A contains the |
|
* upper triangular part of the matrix A. If UPLO = 'L', |
|
* the leading N-by-N lower triangular part of A contains |
|
* the lower triangular part of the matrix A. |
|
* On exit, the lower triangle (if UPLO='L') or the upper |
|
* triangle (if UPLO='U') of A, including the diagonal, is |
|
* destroyed. |
|
* |
|
* LDA (input) INTEGER |
|
* The leading dimension of the array A. LDA >= max(1,N). |
|
* |
|
* VL (input) DOUBLE PRECISION |
|
* VU (input) DOUBLE PRECISION |
|
* If RANGE='V', the lower and upper bounds of the interval to |
|
* be searched for eigenvalues. VL < VU. |
|
* Not referenced if RANGE = 'A' or 'I'. |
|
* |
|
* IL (input) INTEGER |
|
* IU (input) INTEGER |
|
* If RANGE='I', the indices (in ascending order) of the |
|
* smallest and largest eigenvalues to be returned. |
|
* 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. |
|
* Not referenced if RANGE = 'A' or 'V'. |
|
* |
|
* ABSTOL (input) DOUBLE PRECISION |
|
* The absolute error tolerance for the eigenvalues. |
|
* An approximate eigenvalue is accepted as converged |
|
* when it is determined to lie in an interval [a,b] |
|
* of width less than or equal to |
|
* |
|
* ABSTOL + EPS * max( |a|,|b| ) , |
|
* |
|
* where EPS is the machine precision. If ABSTOL is less than |
|
* or equal to zero, then EPS*|T| will be used in its place, |
|
* where |T| is the 1-norm of the tridiagonal matrix obtained |
|
* by reducing A to tridiagonal form. |
|
* |
|
* See "Computing Small Singular Values of Bidiagonal Matrices |
|
* with Guaranteed High Relative Accuracy," by Demmel and |
|
* Kahan, LAPACK Working Note #3. |
|
* |
|
* If high relative accuracy is important, set ABSTOL to |
|
* DLAMCH( 'Safe minimum' ). Doing so will guarantee that |
|
* eigenvalues are computed to high relative accuracy when |
|
* possible in future releases. The current code does not |
|
* make any guarantees about high relative accuracy, but |
|
* future releases will. See J. Barlow and J. Demmel, |
|
* "Computing Accurate Eigensystems of Scaled Diagonally |
|
* Dominant Matrices", LAPACK Working Note #7, for a discussion |
|
* of which matrices define their eigenvalues to high relative |
|
* accuracy. |
|
* |
|
* M (output) INTEGER |
|
* The total number of eigenvalues found. 0 <= M <= N. |
|
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. |
|
* |
|
* W (output) DOUBLE PRECISION array, dimension (N) |
|
* The first M elements contain the selected eigenvalues in |
|
* ascending order. |
|
* |
|
* Z (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M)) |
|
* If JOBZ = 'V', then if INFO = 0, the first M columns of Z |
|
* contain the orthonormal eigenvectors of the matrix A |
|
* corresponding to the selected eigenvalues, with the i-th |
|
* column of Z holding the eigenvector associated with W(i). |
|
* If JOBZ = 'N', then Z is not referenced. |
|
* Note: the user must ensure that at least max(1,M) columns are |
|
* supplied in the array Z; if RANGE = 'V', the exact value of M |
|
* is not known in advance and an upper bound must be used. |
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* Supplying N columns is always safe. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1, and if |
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* JOBZ = 'V', LDZ >= max(1,N). |
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* |
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* ISUPPZ (output) INTEGER array, dimension ( 2*max(1,M) ) |
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* The support of the eigenvectors in Z, i.e., the indices |
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* indicating the nonzero elements in Z. The i-th eigenvector |
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* is nonzero only in elements ISUPPZ( 2*i-1 ) through |
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* ISUPPZ( 2*i ). |
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********** Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1 |
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* |
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* WORK (workspace/output) DOUBLE PRECISION 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. LWORK >= max(1,26*N). |
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* For optimal efficiency, LWORK >= (NB+6)*N, |
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* where NB is the max of the blocksize for DSYTRD and DORMTR |
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* returned by ILAENV. |
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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 LWORK. |
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* |
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* LIWORK (input) INTEGER |
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* The dimension of the array IWORK. LIWORK >= max(1,10*N). |
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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: Internal error |
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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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* Inderjit Dhillon, IBM Almaden, USA |
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* Osni Marques, LBNL/NERSC, USA |
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* Ken Stanley, Computer Science Division, University of |
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* California at Berkeley, USA |
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* Jason Riedy, Computer Science Division, University of |
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* California at Berkeley, USA |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
Line 339
|
Line 454
|
W( 1 ) = A( 1, 1 ) |
W( 1 ) = A( 1, 1 ) |
END IF |
END IF |
END IF |
END IF |
IF( WANTZ ) |
IF( WANTZ ) THEN |
$ Z( 1, 1 ) = ONE |
Z( 1, 1 ) = ONE |
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ISUPPZ( 1 ) = 1 |
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ISUPPZ( 2 ) = 1 |
|
END IF |
RETURN |
RETURN |
END IF |
END IF |
* |
* |
Line 357
|
Line 475
|
* |
* |
ISCALE = 0 |
ISCALE = 0 |
ABSTLL = ABSTOL |
ABSTLL = ABSTOL |
VLL = VL |
IF (VALEIG) THEN |
VUU = VU |
VLL = VL |
|
VUU = VU |
|
END IF |
ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) |
ANRM = DLANSY( 'M', UPLO, N, A, LDA, WORK ) |
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN |
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN |
ISCALE = 1 |
ISCALE = 1 |
Line 419
|
Line 539
|
* returns INFO > 0. |
* returns INFO > 0. |
INDIFL = INDISP + N |
INDIFL = INDISP + N |
* INDIWO is the offset of the remaining integer workspace. |
* INDIWO is the offset of the remaining integer workspace. |
INDIWO = INDISP + N |
INDIWO = INDIFL + N |
|
|
* |
* |
* Call DSYTRD to reduce symmetric matrix to tridiagonal form. |
* Call DSYTRD to reduce symmetric matrix to tridiagonal form. |