NAG C Library Function Document

nag_real_sparse_eigensystem_iter (f12abc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{irevcm}$ – Integer *Input/Output

On initial entry: $\mathbf{irevcm}=0$, otherwise an error condition will be raised.

On intermediate re-entry: must be unchanged from its previous exit value. Changing irevcm to any other value between calls will result in an error.

On intermediate exit: has the following meanings.

$\mathbf{irevcm}=-1$

The calling program must compute the matrix-vector product $y=\mathrm{OP}x$, where $x$ is stored in x and the result $y$ is placed in y. If $B$ is not symmetric semidefinite then the precomputed values in mx should not be used (see the explanation under $\mathbf{irevcm}=2$).

$\mathbf{irevcm}=1$

The calling program must compute the matrix-vector product $y=\mathrm{OP}x$. This is similar to the case $\mathbf{irevcm}=-1$ except that the result of the matrix-vector product $Bx$ (as required in some computational modes) has already been computed and is available in mx.

$\mathbf{irevcm}=2$

The calling program must compute the matrix-vector product $y=Bx$, where $x$ is stored as described in the case $\mathbf{irevcm}=-1$ and $y$ is placed in y. This computation is requested when solving the $\mathbf{Generalized}$ problem using either $\mathbf{Shifted\; Inverse\; Imaginary}$ or $\mathbf{Shifted\; Inverse\; Real}$; in these cases $B$ is used as an inner-product space and requires that $B$ be symmetric semidefinite. If neither $A$ nor $B$ is symmetric semidefinite then the problem should be reformulated in a $\mathbf{Standard}$ form.

$\mathbf{irevcm}=3$

Compute the nshift real and imaginary parts of the shifts where the real parts are to be placed in the first nshift locations of the array y and the imaginary parts are to be placed in the first nshift locations of the array mx. Only complex conjugate pairs of shifts may be applied and the pairs must be placed in consecutive locations. This value of irevcm will only arise if the optional parameter $\mathbf{Supplied\; Shifts}$ is set in a prior call to nag_real_sparse_eigensystem_option (f12adc) which is intended for experienced users only; the default and recommended option is to use exact shifts (see Lehoucq et al. (1998) for details).

$\mathbf{irevcm}=4$

Monitoring step: a call to nag_real_sparse_eigensystem_monit (f12aec) can now be made to return the number of Arnoldi iterations, the number of converged Ritz values, their real and imaginary parts, and the corresponding Ritz estimates.

On final exit: $\mathbf{irevcm}=5$: nag_real_sparse_eigensystem_iter (f12abc) has completed its tasks. The value of fail determines whether the iteration has been successfully completed, or whether errors have been detected. On successful completion nag_real_sparse_eigensystem_sol (f12acc) must be called to return the requested eigenvalues and eigenvectors (and/or Schur vectors).

Constraint: on initial entry, $\mathbf{irevcm}=0$; on re-entry irevcm must remain unchanged.

Note: any values you return to nag_real_sparse_eigensystem_iter (f12abc) as part of the reverse communication procedure should not include floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_real_sparse_eigensystem_iter (f12abc). If your code inadvertently does return any NaNs or infinities, nag_real_sparse_eigensystem_iter (f12abc) is likely to produce unexpected results.

2:    $\mathbf{resid}\left[\mathit{dim}\right]$ – doubleInput/Output

Note: the dimension, dim, of the array resid must be at least $\mathbf{n}$ (see nag_real_sparse_eigensystem_init (f12aac)).

On initial entry: need not be set unless the option $\mathbf{Initial\; Residual}$ has been set in a prior call to nag_real_sparse_eigensystem_option (f12adc) in which case resid should contain an initial residual vector, possibly from a previous run.

On intermediate re-entry: must be unchanged from its previous exit. Changing resid to any other value between calls may result in an error exit.

On intermediate exit: contains the current residual vector.

On final exit: contains the final residual vector.

3:    $\mathbf{v}\left[\mathbf{n}\times \mathbf{ncv}\right]$ – doubleInput/Output

The $\mathit{i}$th element of the $\mathit{j}$th basis vector is stored in location $\mathbf{v}\left[\mathbf{n}\times \left(\mathit{i}-1\right)+\mathit{j}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and $\mathit{j}=1,2,\dots ,\mathbf{ncv}$.

On initial entry: need not be set.

On intermediate re-entry: must be unchanged from its previous exit.

On intermediate exit: contains the current set of Arnoldi basis vectors.

On final exit: contains the final set of Arnoldi basis vectors.

4:    $\mathbf{x}$ – double **Input/Output

On initial entry: need not be set, it is used as a convenient mechanism for accessing elements of comm.

On intermediate re-entry: is not normally changed.

On intermediate exit: contains the vector $x$ when irevcm returns the value $-1$, $+1$ or $2$.

On final exit: does not contain useful data.

5:    $\mathbf{y}$ – double **Input/Output

On initial entry: need not be set, it is used as a convenient mechanism for accessing elements of comm.

On intermediate re-entry: must contain the result of $y=\mathrm{OP}x$ when irevcm returns the value $-1$ or $+1$. It must contain the real parts of the computed shifts when irevcm returns the value $3$.

On intermediate exit: does not contain useful data.

On final exit: does not contain useful data.

6:    $\mathbf{mx}$ – double **Input/Output

On initial entry: need not be set, it is used as a convenient mechanism for accessing elements of comm.

On intermediate re-entry: must contain the result of $y=Bx$ when irevcm returns the value $2$. It must contain the imaginary parts of the computed shifts when irevcm returns the value $3$.

On intermediate exit: contains the vector $Bx$ when irevcm returns the value $+1$.

On final exit: does not contain any useful data.

7:    $\mathbf{nshift}$ – Integer *Output

On intermediate exit: if the option $\mathbf{Supplied\; Shifts}$ is set and irevcm returns a value of $3$, nshift returns the number of complex shifts required.

8:    $\mathbf{comm}\left[\mathit{dim}\right]$ – doubleCommunication Array

Note: the dimension, dim, of the array comm must be at least $\max \left(1,\mathbf{lcomm}\right)$ (see nag_real_sparse_eigensystem_init (f12aac)).

On initial entry: must remain unchanged following a call to the setup function nag_real_sparse_eigensystem_init (f12aac).

On exit: contains data defining the current state of the iterative process.

9:    $\mathbf{icomm}\left[\mathit{dim}\right]$ – IntegerCommunication Array

Note: the dimension, dim, of the array icomm must be at least $\max \left(1,\mathbf{licomm}\right)$ (see nag_real_sparse_eigensystem_init (f12aac)).

On initial entry: must remain unchanged following a call to the setup function nag_real_sparse_eigensystem_init (f12aac).

On exit: contains data defining the current state of the iterative process.

10:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

Error details reported in $\mathbf{fail}$ are only valid on final exit. On intermediate exit, returned values of $\mathbf{fail}$ should be ignored.

6

Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INITIALIZATION

Either the initialization function has not been called prior to the first call of this function or a communication array has become corrupted.

NE_INT

The maximum number of iterations $\le 0$, the option $\mathbf{Iteration\; Limit}$ has been set to $〈\mathit{\text{value}}〉$.

NE_INTERNAL_EIGVAL_FAIL

Error in internal call to compute eigenvalues and corresponding error bounds of the current upper Hessenberg matrix. Please contact NAG.

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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_MAX_ITER

The maximum number of iterations has been reached. The maximum number of $\text{iterations}=〈\mathit{\text{value}}〉$. The number of converged eigenvalues $=〈\mathit{\text{value}}〉$. The post-processing function nag_real_sparse_eigensystem_sol (f12acc) may be called to recover the converged eigenvalues at this point. Alternatively, the maximum number of iterations may be increased by a call to the option setting function nag_real_sparse_eigensystem_option (f12adc) and the reverse communication loop restarted. A large number of iterations may indicate a poor choice for the values of nev and ncv; it is advisable to experiment with these values to reduce the number of iterations (see nag_real_sparse_eigensystem_init (f12aac)).

NE_NO_ARNOLDI_FAC

Could not build an Arnoldi factorization. The size of the current Arnoldi factorization $=〈\mathit{\text{value}}〉$.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_NO_SHIFTS_APPLIED

No shifts could be applied during a cycle of the implicitly restarted Arnoldi iteration.

NE_OPT_INCOMPAT

The options $\mathbf{Generalized}$ and $\mathbf{Regular}$ are incompatible.

NE_ZERO_INIT_RESID

The option $\mathbf{Initial\; Residual}$ was selected but the starting vector held in resid is zero.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (f12abce.c)

10.2

Program Data

Program Data (f12abce.d)

10.3

Program Results

Program Results (f12abce.r)