naginterfaces.library.sparseig.complex_option¶
- naginterfaces.library.sparseig.complex_option(optstr, comm, io_manager=None)[source]¶
complex_option
is an option setting function in a suite of functions consisting ofcomplex_init()
,complex_iter()
,complex_proc()
,complex_option
andcomplex_monit()
; it supplies individual options tocomplex_iter()
andcomplex_proc()
.complex_option
is also an option setting function in a suite of functions consisting ofcomplex_option
,complex_band_init()
andcomplex_band_solve()
; it supplies individual options tocomplex_band_solve()
.The initialization function for the appropriate suite,
complex_init()
orcomplex_band_init()
, must have been called prior to callingcomplex_option
.Note: this function uses optional algorithmic parameters, see also:
complex_iter()
,complex_proc()
,complex_band_solve()
,complex_init()
,complex_band_init()
.For full information please refer to the NAG Library document for f12ar
https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/f12/f12arf.html
- Parameters
- optstrstr
A single valid option string (as described in Notes and Other Parameters).
- commdict, communication object, modified in place
Communication structure.
This argument must have been initialized by a prior call to
complex_init()
orcomplex_band_init()
.- io_managerFileObjManager, optional
Manager for I/O in this routine.
- Other Parameters
- ‘Advisory’int
Default
The destination for advisory messages.
- ‘Defaults’valueless
This special keyword may be used to reset all options to their default values.
- ‘Exact Shifts’valueless
Default
During the Arnoldi iterative process, shifts are applied as part of the implicit restarting scheme. The shift strategy used by default and selected by the option ‘Exact Shifts’ is strongly recommended over the alternative ‘Supplied Shifts’ and will always be used by
complex_band_solve()
.If ‘Exact Shifts’ are used then these are computed internally by the algorithm in the implicit restarting scheme. This strategy is generally effective and cheaper to apply in terms of number of operations than using explicit shifts.
If ‘Supplied Shifts’ are used then, during the Arnoldi iterative process, you must supply shifts through array arguments of
complex_iter()
whencomplex_iter()
returns with ; the complex shifts are returned in (or in when the option is set). This option should only be used if you are an experienced user since this requires some algorithmic knowledge and because more operations are usually required than for the implicit shift scheme. Details on the use of explicit shifts and further references on shift strategies are available in Lehoucq et al. (1998).- ‘Supplied Shifts’valueless
During the Arnoldi iterative process, shifts are applied as part of the implicit restarting scheme. The shift strategy used by default and selected by the option ‘Exact Shifts’ is strongly recommended over the alternative ‘Supplied Shifts’ and will always be used by
complex_band_solve()
.If ‘Exact Shifts’ are used then these are computed internally by the algorithm in the implicit restarting scheme. This strategy is generally effective and cheaper to apply in terms of number of operations than using explicit shifts.
If ‘Supplied Shifts’ are used then, during the Arnoldi iterative process, you must supply shifts through array arguments of
complex_iter()
whencomplex_iter()
returns with ; the complex shifts are returned in (or in when the option is set). This option should only be used if you are an experienced user since this requires some algorithmic knowledge and because more operations are usually required than for the implicit shift scheme. Details on the use of explicit shifts and further references on shift strategies are available in Lehoucq et al. (1998).- ‘Iteration Limit’int
Default
The limit on the number of Arnoldi iterations that can be performed before
complex_iter()
orcomplex_band_solve()
exits. If not all requested eigenvalues have converged to within ‘Tolerance’ and the number of Arnoldi iterations has reached this limit thencomplex_iter()
orcomplex_band_solve()
exits with an error;complex_band_solve()
returns the number of converged eigenvalues, the converged eigenvalues and, if requested, the corresponding eigenvectors, whilecomplex_proc()
can be called subsequent tocomplex_iter()
to do the same.- ‘Largest Magnitude’valueless
Default
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Largest Imaginary’valueless
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Largest Real’valueless
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Smallest Imaginary’valueless
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Smallest Magnitude’valueless
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Smallest Real’valueless
The Arnoldi iterative method converges on a number of eigenvalues with given properties. The default is for
complex_iter()
orcomplex_band_solve()
to compute the eigenvalues of largest magnitude using ‘Largest Magnitude’. Alternatively, eigenvalues may be chosen which have ‘Largest Real’ part, ‘Largest Imaginary’ part, ‘Smallest Magnitude’, ‘Smallest Real’ part or ‘Smallest Imaginary’ part.Note that these options select the eigenvalue properties for eigenvalues of (and for ‘Generalized’ problems), the linear operator determined by the computational mode and problem type.
- ‘Nolist’valueless
Default
Option ‘List’ enables printing of each option specification as it is supplied. ‘Nolist’ suppresses this printing.
- ‘List’valueless
Option ‘List’ enables printing of each option specification as it is supplied. ‘Nolist’ suppresses this printing.
- ‘Monitoring’int
Default
If , monitoring information is output to unit number (see
unit_from_fileobj()
) during the solution of each problem; this may be the same as the ‘Advisory’ unit number (seeunit_from_fileobj()
). The type of information produced is dependent on the value of ‘Print Level’, see the description of the option ‘Print Level’ for details of the information produced. Please see theFileObjManager
methodunit_from_fileobj()
to associate a file with a given unit number (seeunit_from_fileobj()
).- ‘Pointers’valueless
Default
During the iterative process and reverse communication calls to
complex_iter()
, required data can be communicated to and fromcomplex_iter()
in one of two ways. When is selected (the default) then the array arguments and are used to supply you with required data and used to return computed values back tocomplex_iter()
. For example, when ,complex_iter()
returns the vector in and the matrix-vector product in and expects the result or the linear operation to be returned in .If is selected then the data is passed through sections of the array argument . The section corresponding to when begins at a location given by the first element of ; similarly the section corresponding to begins at a location given by the second element of . This option allows
complex_iter()
to perform fewer copy operations on each intermediate exit and entry, but can also lead to less elegant code in the calling program.This option has no affect on
complex_band_solve()
which sets internally.- ‘Print Level’int
Default
This controls the amount of printing produced by
complex_option
as follows.Output
No output except error messages.
The set of selected options.
Problem and timing statistics on final exit from
complex_iter()
orcomplex_band_solve()
.A single line of summary output at each Arnoldi iteration.
If , then at each iteration, the length and additional steps of the current Arnoldi factorization and the number of converged Ritz values; during re-orthogonalization, the norm of initial/restarted starting vector.
Problem and timing statistics on final exit from
complex_iter()
. If , then at each iteration, the number of shifts being applied, the eigenvalues and estimates of the Hessenberg matrix , the size of the Arnoldi basis, the wanted Ritz values and associated Ritz estimates and the shifts applied; vector norms prior to and following re-orthogonalization.If , then on final iteration, the norm of the residual; when computing the Schur form, the eigenvalues and Ritz estimates both before and after sorting; for each iteration, the norm of residual for compressed factorization and the compressed upper Hessenberg matrix ; during re-orthogonalization, the initial/restarted starting vector; during the Arnoldi iteration loop, a restart is flagged and the number of the residual requiring iterative refinement; while applying shifts, the indices of the shifts being applied.
If , then during the Arnoldi iteration loop, the Arnoldi vector number and norm of the current residual; while applying shifts, key measures of progress and the order of ; while computing eigenvalues of , the last rows of the Schur and eigenvector matrices; when computing implicit shifts, the eigenvalues and Ritz estimates of .
If , then during Arnoldi iteration loop: norms of key components and the active column of , norms of residuals during iterative refinement, the final upper Hessenberg matrix ; while applying shifts: number of shifts, shift values, block indices, updated matrix ; while computing eigenvalues of : the matrix , the computed eigenvalues and Ritz estimates.
- ‘Random Residual’valueless
Default
To begin the Arnoldi iterative process,
complex_iter()
orcomplex_band_solve()
requires an initial residual vector. By defaultcomplex_iter()
orcomplex_band_solve()
provides its own random initial residual vector; this option can also be set using option ‘Random Residual’. Alternatively, you can supply an initial residual vector (perhaps from a previous computation) tocomplex_iter()
orcomplex_band_solve()
through the array argument ; this option can be set using option ‘Initial Residual’.- ‘Initial Residual’valueless
To begin the Arnoldi iterative process,
complex_iter()
orcomplex_band_solve()
requires an initial residual vector. By defaultcomplex_iter()
orcomplex_band_solve()
provides its own random initial residual vector; this option can also be set using option ‘Random Residual’. Alternatively, you can supply an initial residual vector (perhaps from a previous computation) tocomplex_iter()
orcomplex_band_solve()
through the array argument ; this option can be set using option ‘Initial Residual’.- ‘Regular’valueless
Default
These options define the computational mode which in turn defines the form of operation to be performed by
complex_band_solve()
or whencomplex_iter()
returns with or and the matrix-vector product whencomplex_iter()
returns with .Given a ‘Standard’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular’
‘Shifted Inverse’
Given a ‘Generalized’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular Inverse’
‘Shifted Inverse’
- ‘Regular Inverse’valueless
These options define the computational mode which in turn defines the form of operation to be performed by
complex_band_solve()
or whencomplex_iter()
returns with or and the matrix-vector product whencomplex_iter()
returns with .Given a ‘Standard’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular’
‘Shifted Inverse’
Given a ‘Generalized’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular Inverse’
‘Shifted Inverse’
- ‘Shifted Inverse’valueless
These options define the computational mode which in turn defines the form of operation to be performed by
complex_band_solve()
or whencomplex_iter()
returns with or and the matrix-vector product whencomplex_iter()
returns with .Given a ‘Standard’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular’
‘Shifted Inverse’
Given a ‘Generalized’ eigenvalue problem in the form then the following modes are available with the appropriate operator .
‘Regular Inverse’
‘Shifted Inverse’
- ‘Standard’valueless
Default
The problem to be solved is either a standard eigenvalue problem, , or a generalized eigenvalue problem, . The option ‘Standard’ should be used when a standard eigenvalue problem is being solved and the option ‘Generalized’ should be used when a generalized eigenvalue problem is being solved.
- ‘Generalized’valueless
The problem to be solved is either a standard eigenvalue problem, , or a generalized eigenvalue problem, . The option ‘Standard’ should be used when a standard eigenvalue problem is being solved and the option ‘Generalized’ should be used when a generalized eigenvalue problem is being solved.
- ‘Tolerance’float
Default
An approximate eigenvalue has deemed to have converged when the corresponding Ritz estimate is within ‘Tolerance’ relative to the magnitude of the eigenvalue.
- ‘Vectors’valueless
Default
The function
complex_proc()
orcomplex_band_solve()
can optionally compute the Schur vectors and/or the eigenvectors corresponding to the converged eigenvalues. To turn off computation of any vectors the option should be set. To compute only the Schur vectors (at very little extra cost), the option should be set and these will be returned in the array argument ofcomplex_proc()
orcomplex_band_solve()
. To compute the eigenvectors (Ritz vectors) corresponding to the eigenvalue estimates, the option should be set and these will be returned in the array argument ofcomplex_proc()
orcomplex_band_solve()
, if is set equal to then the Schur vectors in are overwritten by the eigenvectors computed bycomplex_proc()
orcomplex_band_solve()
.
- Raises
- NagValueError
- (errno )
Ambiguous keyword:
- (errno )
Keyword not recognized:
- (errno )
Second keyword not recognized:
- (errno )
Either the initialization function has not been called prior to the call of this function or a communication array has become corrupted.
- Notes
complex_option
may be used to supply values for options tocomplex_iter()
andcomplex_proc()
, or tocomplex_band_solve()
. It is only necessary to callcomplex_option
for those arguments whose values are to be different from their default values. One call tocomplex_option
sets one argument value.Each option is defined by a single character string consisting of one or more items. The items associated with a given option must be separated by spaces, or equals signs . Alphabetic characters may be upper or lower case. The string
Iteration Limit = 500
is an example of a string used to set an option. For each option the string contains one or more of the following items:
a mandatory keyword;
a phrase that qualifies the keyword;
a number that specifies an int or float value. Such numbers may be up to contiguous characters in Fortran’s I, F, E or D format.
complex_option
does not have an equivalent function from the ARPACK package which passes options by directly setting values to scalar arguments or to specific elements of array arguments.complex_option
is intended to make the passing of options more transparent and follows the same principle as the single option setting functions in submoduleopt
(seeopt.qpconvex2_sparse_option_string
for an example).The setup function
complex_init()
orcomplex_band_init()
must be called prior to the first call tocomplex_option
, and all calls tocomplex_option
must precede the first call tocomplex_iter()
andcomplex_band_solve()
.A complete list of options, their abbreviations, synonyms and default values is given in Other Parameters.
- 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