naginterfaces.library.sparseig.real_symm_proc¶
- naginterfaces.library.sparseig.real_symm_proc(sigma, resid, v, comm, io_manager=None)[source]¶
real_symm_proc
is a post-processing function in a suite of functions which includesreal_symm_init()
,real_symm_iter()
,real_symm_option()
andreal_symm_monit()
.real_symm_proc
must be called following a final exit fromreal_symm_iter()
.For full information please refer to the NAG Library document for f12fc
https://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/f12/f12fcf.html
- Parameters
- sigmafloat
If one of the ‘Shifted Inverse’ (see
real_symm_option()
) modes has been selected then contains the real shift used; otherwise is not referenced.- residfloat, array-like, shape
Must not be modified following a call to
real_symm_iter()
since it contains data required byreal_symm_proc
.- vfloat, array-like, shape
The columns of contain the Lanczos basis vectors for as constructed by
real_symm_iter()
.- commdict, communication object, modified in place
Communication structure.
This argument must have been initialized by a prior call to
real_symm_init()
.- io_managerFileObjManager, optional
Manager for I/O in this routine.
- Returns
- nconvint
The number of converged eigenvalues as found by
real_symm_iter()
.- dfloat, ndarray, shape
The first locations of the array contain the converged approximate eigenvalues.
- zfloat, ndarray, shape
If the default option (see
real_symm_option()
) has been selected then contains the final set of eigenvectors corresponding to the eigenvalues held in . The real eigenvector associated with an eigenvalue is stored in the corresponding of .- vfloat, ndarray, shape
If the option has been set, or the option has been set and a separate array has been passed (i.e., does not equal ), then the first columns of will contain approximate Schur vectors that span the desired invariant subspace.
- Raises
- NagValueError
- (errno )
On entry, , but this is not yet implemented.
- (errno )
The number of eigenvalues found to sufficient accuracy, as communicated through the argument [‘icomm’], is zero.
- (errno )
Got a different count of the number of converged Ritz values than the value passed to it through the argument [‘icomm’]: number counted , number expected .
- (errno )
During calculation of a tridiagonal form, there was a failure to compute eigenvalues in a total of iterations.
- (errno )
Either the function was called out of sequence (following an initial call to the setup function and following completion of calls to the reverse communication function) or the communication arrays have become corrupted.
- Notes
The suite of functions is designed to calculate some of the eigenvalues, , (and optionally the corresponding eigenvectors, ) of a standard eigenvalue problem , or of a generalized eigenvalue problem of order , where is large and the coefficient matrices and are sparse, real and symmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and symmetric problems.
Following a call to
real_symm_iter()
,real_symm_proc
returns the converged approximations to eigenvalues and (optionally) the corresponding approximate eigenvectors and/or an orthonormal basis for the associated approximate invariant subspace. The eigenvalues (and eigenvectors) are selected from those of a standard or generalized eigenvalue problem defined by real symmetric matrices. There is negligible additional cost to obtain eigenvectors; an orthonormal basis is always computed, but there is an additional storage cost if both are requested.real_symm_proc
is based on the function dseupd from the ARPACK package, which uses the Implicitly Restarted Lanczos iteration method. The method is described in Lehoucq and Sorensen (1996) and Lehoucq (2001) while its use within the ARPACK software is described in great detail in Lehoucq et al. (1998). An evaluation of software for computing eigenvalues of sparse symmetric matrices is provided in Lehoucq and Scott (1996). This suite of functions offers the same functionality as the ARPACK software for real symmetric problems, but the interface design is quite different in order to make the option setting clearer and to simplify some of the interfaces.real_symm_proc
, is a post-processing function that must be called following a successful final exit fromreal_symm_iter()
.real_symm_proc
uses data returned fromreal_symm_iter()
and options, set either by default or explicitly by callingreal_symm_option()
, to return the converged approximations to selected eigenvalues and (optionally):the corresponding approximate eigenvectors;
an orthonormal basis for the associated approximate invariant subspace;
both.
- References
Lehoucq, R B, 2001, Implicitly restarted Arnoldi methods and subspace iteration, SIAM Journal on Matrix Analysis and Applications (23), 551–562
Lehoucq, R B and Scott, J A, 1996, An evaluation of software for computing eigenvalues of sparse nonsymmetric matrices, Preprint MCS-P547-1195, Argonne National Laboratory
Lehoucq, R B and Sorensen, D C, 1996, Deflation techniques for an implicitly restarted Arnoldi iteration, SIAM Journal on Matrix Analysis and Applications (17), 789–821
Lehoucq, R B, Sorensen, D C and Yang, C, 1998, ARPACK Users’ Guide: Solution of Large-scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods, SIAM, Philadelphia