NAG Library Function Document

nag_real_sparse_eigensystem_sol (f12acc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     nconv – Integer *Output

On exit: the number of converged eigenvalues as found by nag_real_sparse_eigensystem_iter (f12abc).

2:     dr[$\mathit{dim}$] – doubleOutput

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

On exit: the first nconv locations of the array dr contain the real parts of the converged approximate eigenvalues.

3:     di[$\mathit{dim}$] – doubleOutput

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

On exit: the first nconv locations of the array di contain the imaginary parts of the converged approximate eigenvalues.

4:     z[$\mathbf{n}\times \left(\mathbf{nev}+1\right)$] – doubleOutput

On exit: if the default option $\mathbf{Vectors}=\mathrm{RITZ}$ (see nag_real_sparse_eigensystem_option (f12adc)) has been selected then z contains the final set of eigenvectors corresponding to the eigenvalues held in dr and di. The complex eigenvector associated with the eigenvalue with positive imaginary part is stored in two consecutive array segments. The first segment holds the real part of the eigenvector and the second holds the imaginary part. The eigenvector associated with the eigenvalue with negative imaginary part is simply the complex conjugate of the eigenvector associated with the positive imaginary part.

For example, the first eigenvector has real parts stored in locations $\mathbf{z}\left[\mathit{i}-1\right]$, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and imaginary parts stored in $\mathbf{z}\left[\mathit{i}-1\right]$, for $\mathit{i}=\mathbf{n}+1,2\mathbf{n}$.

5:     sigmar – doubleInput

On entry: if one of the $\mathbf{Shifted\; Inverse\; Real}$ modes have been selected then sigmar contains the real part of the shift used; otherwise sigmar is not referenced.

6:     sigmai – doubleInput

On entry: if one of the $\mathbf{Shifted\; Inverse\; Real}$ modes have been selected then sigmai contains the imaginary part of the shift used; otherwise sigmai is not referenced.

7:     resid[$\mathit{dim}$] – const doubleInput

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

On entry: must not be modified following a call to nag_real_sparse_eigensystem_iter (f12abc) since it contains data required by nag_real_sparse_eigensystem_sol (f12acc).

8:     v[$\mathit{dim}$] – doubleInput/Output

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

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

On entry: the ncv sections of v, of length $n$, contain the Arnoldi basis vectors for $\mathrm{OP}$ as constructed by nag_real_sparse_eigensystem_iter (f12abc).

On exit: if the option $\mathbf{Vectors}=\mathrm{SCHUR}$ has been set, or the option $\mathbf{Vectors}=\mathrm{RITZ}$ has been set and a separate array z has been passed (i.e., z does not equal v), then the first nconv sections of v, of length $n$, will contain approximate Schur vectors that span the desired invariant subspace.

9:     comm[$\mathit{dim}$] – 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 from the prior call to nag_real_sparse_eigensystem_iter (f12abc).

On exit: contains data on the current state of the solution.

10:   icomm[$\mathit{dim}$] – 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 from the prior call to nag_real_sparse_eigensystem_iter (f12abc).

On exit: contains data on the current state of the solution.

11:   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.

NE_BAD_PARAM

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

NE_INITIALIZATION

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

NE_INTERNAL_EIGVEC_FAIL

In calculating eigenvectors, an internal call returned with an error. 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.

NE_INVALID_OPTION

On entry, $\mathbf{Vectors}=\mathrm{SELECT}$, but this is not yet implemented.

NE_RITZ_COUNT

Got a different count of the number of converged Ritz values than the value passed to it through the argument icomm: number counted $=〈\mathit{\text{value}}〉$, number expected $=〈\mathit{\text{value}}〉$.

NE_SCHUR_EIG_FAIL

During calculation of a real Schur form, there was a failure to compute $〈\mathit{\text{value}}〉$ eigenvalues in a total of $〈\mathit{\text{value}}〉$ iterations.

NE_SCHUR_REORDER

The computed Schur form could not be reordered by an internal call. This function returned with $\mathbf{fail}\mathbf{.}\mathbf{code}=〈\mathit{\text{value}}〉$. Please contact NAG.

NE_ZERO_EIGS_FOUND

The number of eigenvalues found to sufficient accuracy, as communicated through the argument icomm, is zero. See the function document for further details.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (f12acce.c)

9.2  Program Data

Program Data (f12acce.d)

9.3  Program Results

Program Results (f12acce.r)