# NAG CL Interfacef12aec (real_​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 f12adc need not be called. If, however, you wish to reset some or all of the settings please refer to Section 11 in f12adc for a detailed description of the specification of the optional parameters.

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## 1Purpose

f12aec can be used to return additional monitoring information during computation. It is in a suite of functions consisting of f12aac, f12abc, f12acc, f12adc and f12aec.

## 2Specification

 #include
 void f12aec (Integer *niter, Integer *nconv, double ritzr[], double ritzi[], double rzest[], const Integer icomm[], const double comm[])
The function may be called by the names: f12aec, nag_sparseig_real_monit or nag_real_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 nonsymmetric. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real and nonsymmetric problems.
On an intermediate exit from f12abc with ${\mathbf{irevcm}}=4$, f12aec may be called to return monitoring information on the progress of the Arnoldi iterative process. The information returned by f12aec 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.
f12aec 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). f12aec should not be called at any time other than immediately following an ${\mathbf{irevcm}}=4$ return from f12abc.

## 4References

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: $\mathbf{ritzr}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array ritzr must be at least ${\mathbf{ncv}}$ (see f12aac).
On exit: the first nconv locations of the array ritzr contain the real parts of the converged approximate eigenvalues.
4: $\mathbf{ritzi}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array ritzi must be at least ${\mathbf{ncv}}$ (see f12aac).
On exit: the first nconv locations of the array ritzi contain the imaginary parts of the converged approximate eigenvalues.
5: $\mathbf{rzest}\left[\mathit{dim}\right]$double Output
Note: the dimension, dim, of the array rzest must be at least ${\mathbf{ncv}}$ (see f12aac).
On exit: the first nconv locations of the array rzest contain the Ritz estimates (error bounds) on the converged approximate eigenvalues.
6: $\mathbf{icomm}\left[\mathit{dim}\right]$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 f12aac).
On entry: the array icomm output by the preceding call to f12abc.
7: $\mathbf{comm}\left[\mathit{dim}\right]$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 f12aac).
On entry: the array comm output by the preceding call to f12abc.

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

f12aec is not threaded in any implementation.

None.

## 10Example

This example solves $Ax=\lambda Bx$ in shifted-real mode, where $A$ is the tridiagonal matrix with $2$ on the diagonal, $-2$ on the subdiagonal and $3$ on the superdiagonal. The matrix $B$ is the tridiagonal matrix with $4$ on the diagonal and $1$ on the off-diagonals. The shift sigma, $\sigma$, is a complex number, and the operator used in the shifted-real iterative process is $\mathrm{op}=\text{real}\left({\left(A-\sigma B\right)}_{-1}B\right)$.

### 10.1Program Text

Program Text (f12aece.c)

### 10.2Program Data

Program Data (f12aece.d)

### 10.3Program Results

Program Results (f12aece.r)