# NAG CL Interfacef12jec (feast_​symm_​contour)

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## 1Purpose

f12jec is a setup function in a suite of functions consisting of f12jac, f12jbc, f12jec, f12jjc and f12jrc. It is used to find some of the eigenvalues, and the corresponding eigenvectors, of a standard or generalized eigenvalue problem defined by real symmetric or complex Hermitian matrices. The initialization function f12jac must have been called prior to calling f12jec. In addition calls to f12jbc can be made to supply individual optional parameters to f12jec.
The suite of functions is suitable for the solution of large sparse eigenproblems where only a few eigenvalues from a selected range of the spectrum are required.

## 2Specification

 #include
 void f12jec (void *handle, double emin, double emax, NagError *fail)
The function may be called by the names: f12jec or nag_sparseig_feast_symm_contour.

## 3Description

The suite of functions is designed to calculate some of the eigenvalues, $\lambda$, and the corresponding eigenvectors, $x$, of a standard eigenvalue problem $Ax=\lambda x$, or a generalized eigenvalue problem $Ax=\lambda Bx$, where the coefficient matrices $A$ and $B$ are sparse, real symmetric or complex Hermitian. The suite can also be used to find selected eigenvalues/eigenvectors of smaller scale dense, real symmetric or complex Hermitian problems.
f12jec is used to specify a search interval on the real line, $\left[{E}_{\mathrm{min}},{E}_{\mathrm{max}}\right]$, within which eigenvalues will be sought (note that the eigenvalues of real symmetric and complex Hermitian eigenproblems are themselves real). f12jec uses this interval to define nodes and weights for an elliptical contour to be used by the solvers f12jjc or f12jrc. Since this contour is symmetric when reflected in the real line, the function needs only to define the nodes and weights for the upper half-contour.

## 4References

Polizzi E (2009) Density-Matrix-Based Algorithms for Solving Eigenvalue Problems Phys. Rev. B. 79 115112

## 5Arguments

1: $\mathbf{handle}$void * Input
On entry: the handle to the internal data structure used by the NAG FEAST suite. It needs to be initialized by f12jac. It must not be changed between calls to the NAG FEAST suite.
2: $\mathbf{emin}$double Input
On entry: the lower bound of the eigenvalue search interval.
Constraint: ${E}_{\mathrm{min}}<{E}_{\mathrm{max}}$.
3: $\mathbf{emax}$double Input
On entry: the upper bound of the eigenvalue search interval.
Constraint: ${E}_{\mathrm{min}}<{E}_{\mathrm{max}}$.
4: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_HANDLE
The supplied handle does not define a valid handle to the data structure used by the NAG FEAST suite. It has not been properly initialized or it has been corrupted.
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_OPTION
An invalid number of integration points was specified. For Gauss or Zolotarev integration, the values permitted are $1$$20$, $24$, $32$, $40$, $48$, $56$.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_2
On entry, ${E}_{\mathrm{min}}=⟨\mathit{\text{value}}⟩$ and ${E}_{\mathrm{max}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${E}_{\mathrm{min}}<{E}_{\mathrm{max}}$.

Not applicable.

## 8Parallelism and Performance

f12jec is not threaded in any implementation.