f12 Chapter Contents
f12 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_real_symm_banded_sparse_eigensystem_init (f12ffc)

## 1  Purpose

nag_real_symm_banded_sparse_eigensystem_init (f12ffc) is a setup function for nag_real_symm_banded_sparse_eigensystem_sol (f12fgc) which can be used to find some eigenvalues (and optionally the corresponding eigenvectors) of a standard or generalized eigenvalue problem defined by real, banded, symmetric matrices. The banded matrix must be stored using the LAPACK storage format for real banded nonsymmetric matrices.

## 2  Specification

 #include #include
 void nag_real_symm_banded_sparse_eigensystem_init (Integer n, Integer nev, Integer ncv, Integer icomm[], Integer licomm, double comm[], Integer lcomm, NagError *fail)

## 3  Description

The pair of functions nag_real_symm_banded_sparse_eigensystem_init (f12ffc) and nag_real_symm_banded_sparse_eigensystem_sol (f12fgc) together with the option setting function nag_real_symm_sparse_eigensystem_option (f12fdc) are designed to calculate some of the eigenvalues, $\lambda$, (and optionally the corresponding eigenvectors, $x$) of a standard eigenvalue problem $Ax=\lambda x$, or of a generalized eigenvalue problem $Ax=\lambda Bx$ of order $n$, where $n$ is large and the coefficient matrices $A$ and $B$ are banded real and symmetric.
nag_real_symm_banded_sparse_eigensystem_init (f12ffc) is a setup function which must be called before the option setting function nag_real_symm_sparse_eigensystem_option (f12fdc) and the solver function nag_real_symm_banded_sparse_eigensystem_sol (f12fgc). Internally, nag_real_symm_banded_sparse_eigensystem_sol (f12fgc) makes calls to nag_real_symm_sparse_eigensystem_iter (f12fbc) and nag_real_symm_sparse_eigensystem_sol (f12fcc); the function documents for nag_real_symm_sparse_eigensystem_iter (f12fbc) and nag_real_symm_sparse_eigensystem_sol (f12fcc) should be consulted for details of the algorithm used.
This setup function initializes the communication arrays, sets (to their default values) all options that can be set by you via the option setting function nag_real_symm_sparse_eigensystem_option (f12fdc), and checks that the lengths of the communication arrays as passed by you are of sufficient length. For details of the options available and how to set them, see Section 11.1 in nag_real_symm_sparse_eigensystem_option (f12fdc).

## 4  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, Philidelphia

## 5  Arguments

1:    $\mathbf{n}$IntegerInput
On entry: the order of the matrix $A$ (and the order of the matrix $B$ for the generalized problem) that defines the eigenvalue problem.
Constraint: ${\mathbf{n}}>0$.
2:    $\mathbf{nev}$IntegerInput
On entry: the number of eigenvalues to be computed.
Constraint: $0<{\mathbf{nev}}<{\mathbf{n}}-1$.
3:    $\mathbf{ncv}$IntegerInput
On entry: the number of Lanczos basis vectors to use during the computation.
At present there is no a priori analysis to guide the selection of ncv relative to nev. However, it is recommended that ${\mathbf{ncv}}\ge 2×{\mathbf{nev}}+1$. If many problems of the same type are to be solved, you should experiment with increasing ncv while keeping nev fixed for a given test problem. This will usually decrease the required number of matrix-vector operations but it also increases the work and storage required to maintain the orthogonal basis vectors. The optimal ‘cross-over’ with respect to CPU time is problem dependent and must be determined empirically.
Constraint: ${\mathbf{nev}}<{\mathbf{ncv}}\le {\mathbf{n}}$.
4:    $\mathbf{icomm}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{licomm}}\right)\right]$IntegerCommunication Array
On exit: contains data to be communicated to nag_real_symm_banded_sparse_eigensystem_sol (f12fgc).
5:    $\mathbf{licomm}$IntegerInput
On entry: the dimension of the array icomm.
If ${\mathbf{licomm}}=-1$, a workspace query is assumed and the function only calculates the required dimensions of icomm and comm, which it returns in ${\mathbf{icomm}}\left[0\right]$ and ${\mathbf{comm}}\left[0\right]$ respectively.
Constraint: ${\mathbf{licomm}}\ge 140\text{​ or ​}{\mathbf{licomm}}=-1$.
6:    $\mathbf{comm}\left[\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{lcomm}}\right)\right]$doubleCommunication Array
On exit: contains data to be communicated to nag_real_symm_banded_sparse_eigensystem_sol (f12fgc).
7:    $\mathbf{lcomm}$IntegerInput
On entry: the dimension of the array comm.
If ${\mathbf{lcomm}}=-1$, a workspace query is assumed and the function only calculates the dimensions of icomm and comm required by nag_real_symm_banded_sparse_eigensystem_sol (f12fgc), which it returns in ${\mathbf{icomm}}\left[0\right]$ and ${\mathbf{comm}}\left[0\right]$ respectively.
Constraint: ${\mathbf{lcomm}}\ge 60\text{​ or ​}{\mathbf{lcomm}}=-1$.
8:    $\mathbf{fail}$NagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}>0$.
On entry, ${\mathbf{nev}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{nev}}>0$.
NE_INT_2
The length of the integer array comm is too small ${\mathbf{lcomm}}=〈\mathit{\text{value}}〉$, but must be at least $〈\mathit{\text{value}}〉$.
The length of the integer array icomm is too small ${\mathbf{licomm}}=〈\mathit{\text{value}}〉$, but must be at least $〈\mathit{\text{value}}〉$.
NE_INT_3
On entry, ${\mathbf{ncv}}=〈\mathit{\text{value}}〉$, ${\mathbf{nev}}=〈\mathit{\text{value}}〉$ and ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{ncv}}>{\mathbf{nev}}+1$ and ${\mathbf{ncv}}\le {\mathbf{n}}$.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

Not applicable.

Not applicable.