# NAG CL Interfacef12fec (real_​symm_​monit)

Note: this function uses optional parameters to define choices in the problem specification. If you wish to use default settings for all of the optional parameters, then the option setting function f12fdc need not be called. If, however, you wish to reset some or all of the settings please refer to Section 11 in f12fdc for a detailed description of the specification of the optional parameters.

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## 1Purpose

f12fec can be used to return additional monitoring information during computation. It is in a suite of functions which includes f12fac, f12fbc, f12fcc and f12fdc.

## 2Specification

 #include
 void f12fec (Integer *niter, Integer *nconv, double ritz[], double rzest[], const Integer icomm[], const double comm[])
The function may be called by the names: f12fec, nag_sparseig_real_symm_monit or nag_real_symm_sparse_eigensystem_monit.

## 3Description

The suite of functions is 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 sparse, real and symmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and symmetric problems.
On an intermediate exit from f12fbc with ${\mathbf{irevcm}}=4$, f12fec may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by f12fec is:
• the number of the current Arnoldi iteration;
• the number of converged eigenvalues at this point;
• the real and imaginary parts of the converged eigenvalues;
• the error bounds on the converged eigenvalues.
f12fec does not have an equivalent function from the ARPACK package which prints various levels of detail of monitoring information through an output channel controlled via an argument value (see Lehoucq et al. (1998) for details of ARPACK routines). f12fec should not be called at any time other than immediately following an ${\mathbf{irevcm}}=4$ return from f12fbc.
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

## 5Arguments

1: $\mathbf{niter}$Integer * Output
On exit: the number of the current Arnoldi iteration.
2: $\mathbf{nconv}$Integer * Output
On exit: the number of converged eigenvalues so far.
3: $\mathbf{ritz}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array ritz must be at least ${\mathbf{ncv}}$ (see f12fac).
On exit: the first nconv locations of the array ritz contain the real converged approximate eigenvalues.
4: $\mathbf{rzest}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array rzest must be at least ${\mathbf{ncv}}$ (see f12fac).
On exit: the first nconv locations of the array rzest contain the Ritz estimates (error bounds) on the real nconv converged approximate eigenvalues.
5: $\mathbf{icomm}\left[\mathit{dim}\right]$const Integer Communication Array
Note: the dimension, dim, of the array icomm must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{licomm}}\right)$, where licomm is passed to the setup function  (see f12fac).
On entry: the array icomm output by the preceding call to f12fbc.
6: $\mathbf{comm}\left[\mathit{dim}\right]$const double Communication Array
Note: the dimension, dim, of the array comm must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left(1,{\mathbf{lcomm}}\right)$, where lcomm is passed to the setup function  (see f12fac).
On entry: the array comm output by the preceding call to f12fbc.

None.

## 7Accuracy

A Ritz value, $\lambda$, is deemed to have converged if its Ritz estimate $\le {\mathbf{Tolerance}}×|\lambda |$. The default ${\mathbf{Tolerance}}$ used is the machine precision given by X02AJC.

## 8Parallelism and Performance

f12fec is not threaded in any implementation.

None.

## 10Example

This example solves $Kx=\lambda {K}_{G}x$ using the ${\mathbf{Buckling}}$ option (see f12fdc, where $K$ and ${K}_{G}$ are obtained by the finite element method applied to the one-dimensional discrete Laplacian operator $\frac{{\partial }^{2}u}{\partial {x}^{2}}$ on $\left[0,1\right]$, with zero Dirichlet boundary conditions using piecewise linear elements. The shift, $\sigma$, is a real number, and the operator used in the Buckling iterative process is $\mathrm{op}=\text{inv}\left(K-\sigma {K}_{G}\right)×K$ and $B=K$.

### 10.1Program Text

Program Text (f12fece.c)

### 10.2Program Data

Program Data (f12fece.d)

### 10.3Program Results

Program Results (f12fece.r)