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/*
ARPACK++ v1.2 2/20/2000
c++ interface to ARPACK code.
MODULE ceupp.h.
Interface to ARPACK subroutines zneupd and cneupd.
ARPACK Authors
Richard Lehoucq
Danny Sorensen
Chao Yang
Dept. of Computational & Applied Mathematics
Rice University
Houston, Texas
*/
#ifndef CEUPP_H
#define CEUPP_H
#include <cstddef>
#include "arch.h"
#include "arpackf.h"
inline void ceupp(bool rvec, char HowMny, arcomplex<double> d[],
arcomplex<double> Z[], ARint ldz, arcomplex<double> sigma,
arcomplex<double> workev[], char bmat, ARint n, char* which,
ARint nev, double tol, arcomplex<double> resid[], ARint ncv,
arcomplex<double> V[], ARint ldv, ARint iparam[],
ARint ipntr[], arcomplex<double> workd[],
arcomplex<double> workl[], ARint lworkl, double rwork[],
ARint& info)
/*
c++ version of ARPACK routine zneupd.
This subroutine returns the converged approximations to eigenvalues
of A*z = lambda*B*z and (optionally):
(1) the corresponding approximate eigenvectors,
(2) an orthonormal basis for the associated approximate
invariant subspace,
There is negligible additional cost to obtain eigenvectors. An
orthonormal basis is always computed. There is an additional storage cost
of n*nev if both are requested (in this case a separate array Z must be
supplied).
The approximate eigenvalues and eigenvectors of A*z = lambda*B*z
are derived from approximate eigenvalues and eigenvectors of
of the linear operator OP prescribed by the MODE selection in the
call to caupp. caupp must be called before this routine is called.
These approximate eigenvalues and vectors are commonly called Ritz
values and Ritz vectors respectively. They are referred to as such
in the comments that follow. The computed orthonormal basis for the
invariant subspace corresponding to these Ritz values is referred to
as a Schur basis.
See documentation in the header of the subroutine caupp for
definition of OP as well as other terms and the relation of computed
Ritz values and Ritz vectors of OP with respect to the given problem
A*z = lambda*B*z. For a brief description, see definitions of
iparam[7], MODE and which in the documentation of caupp.
Parameters:
rvec (Input) Specifies whether a basis for the invariant subspace
corresponding to the converged Ritz value approximations for
the eigenproblem A*z = lambda*B*z is computed.
rvec = false: Compute Ritz values only.
rvec = true : Compute the Ritz vectors or Schur vectors.
See Remarks below.
HowMny (Input) Specifies the form of the basis for the invariant
subspace corresponding to the converged Ritz values that
is to be computed.
= 'A': Compute nev Ritz vectors;
= 'P': Compute nev Schur vectors;
d (Output) Array of dimension nev+1. D contains the Ritz
approximations to the eigenvalues lambda for A*z = lambda*B*z.
Z (Output) Array of dimension nev*n. If rvec = TRUE. and
HowMny = 'A', then Z contains approximate eigenvectors (Ritz
vectors) corresponding to the NCONV=iparam[5] Ritz values for
eigensystem A*z = lambda*B*z.
If rvec = .FALSE. or HowMny = 'P', then Z is not referenced.
NOTE: If if rvec = .TRUE. and a Schur basis is not required,
the array Z may be set equal to first nev+1 columns of
the Arnoldi basis array V computed by caupp. In this
case the Arnoldi basis will be destroyed and overwritten
with the eigenvector basis.
ldz (Input) Dimension of the vectors contained in Z. This
parameter MUST be set to n.
sigma (Input) If iparam[7] = 3, sigma represents the shift. Not
referenced if iparam[7] = 1 or 2.
workv (Workspace) Array of dimension 2*ncv.
V (Input/Output) Array of dimension n*ncv+1.
Upon Input: V contains the ncv vectors of the Arnoldi basis
for OP as constructed by caupp.
Upon Output: If rvec = TRUE the first NCONV=iparam[5] columns
contain approximate Schur vectors that span the
desired invariant subspace.
NOTE: If the array Z has been set equal to first nev+1 columns
of the array V and rvec = TRUE. and HowMny = 'A', then
the Arnoldi basis held by V has been overwritten by the
desired Ritz vectors. If a separate array Z has been
passed then the first NCONV=iparam[5] columns of V will
contain approximate Schur vectors that span the desired
invariant subspace.
workl (Input / Output) Array of length lworkl+1.
workl[1:ncv*ncv+3*ncv] contains information obtained in
caupp. They are not changed by ceupp.
workl[ncv*ncv+3*ncv+1:3*ncv*ncv+4*ncv] holds the untransformed
Ritz values, the untransformed error estimates of the Ritz
values, the upper triangular matrix for H, and the associated
matrix representation of the invariant subspace for H.
ipntr (Input / Output) Array of length 14. Pointer to mark the
starting locations in the workl array for matrices/vectors
used by caupp and ceupp.
ipntr[9]: pointer to the ncv RITZ values of the original
system.
ipntr[11]: pointer to the ncv corresponding error estimates.
ipntr[12]: pointer to the ncv by ncv upper triangular
Schur matrix for H.
ipntr[13]: pointer to the ncv by ncv matrix of eigenvectors
of the upper Hessenberg matrix H. Only referenced
by ceupp if rvec = TRUE. See Remark 2 below.
info (Output) Error flag.
= 0 : Normal exit.
= 1 : The Schur form computed by LAPACK routine csheqr
could not be reordered by LAPACK routine ztrsen.
Re-enter subroutine ceupp with iparam[5] = ncv and
increase the size of the array D to have
dimension at least dimension ncv and allocate at least
ncv columns for Z. NOTE: Not necessary if Z and V share
the same space. Please notify the authors if this error
occurs.
= -1 : n must be positive.
= -2 : nev must be positive.
= -3 : ncv must satisfy nev+1 <= ncv <= n.
= -5 : which must be one of 'LM','SM','LR','SR','LI','SI'.
= -6 : bmat must be one of 'I' or 'G'.
= -7 : Length of private work workl array is not sufficient.
= -8 : Error return from LAPACK eigenvalue calculation.
This should never happened.
= -9 : Error return from calculation of eigenvectors.
Informational error from LAPACK routine ztrevc.
= -10: iparam[7] must be 1, 2 or 3.
= -11: iparam[7] = 1 and bmat = 'G' are incompatible.
= -12: HowMny = 'S' not yet implemented.
= -13: HowMny must be one of 'A' or 'P' if rvec = TRUE.
= -14: caupp did not find any eigenvalues to sufficient
accuracy.
NOTE: The following arguments
bmat, n, which, nev, tol, resid, ncv, V, ldv, iparam,
ipntr, workd, workl, lworkl, rwork, info
must be passed directly to ceupp following the last call
to caupp. These arguments MUST NOT BE MODIFIED between
the the last call to caupp and the call to ceupp.
Remarks
1. Currently only HowMny = 'A' and 'P' are implemented.
2. Schur vectors are an orthogonal representation for the basis of
Ritz vectors. Thus, their numerical properties are often superior.
Let X' denote the transpose of X. If rvec = .TRUE. then the
relationship A * V[:,1:iparam[5]] = V[:,1:iparam[5]] * T, and
V[:,1:iparam[5]]' * V[:,1:iparam[5]] = I are approximately satisfied.
Here T is the leading submatrix of order iparam[5] of the real
upper quasi-triangular matrix stored workl[ipntr[12]].
*/
{
ARint irvec;
ARlogical* iselect;
arcomplex<double>* iZ;
irvec = (ARint) rvec;
iselect = new ARlogical[ncv];
iZ = (Z == NULL) ? &V[1] : Z;
F77NAME(zneupd)(&irvec, &HowMny, iselect, d, iZ, &ldz, &sigma,
&workev[1], &bmat, &n, which, &nev, &tol, resid,
&ncv, &V[1], &ldv, &iparam[1], &ipntr[1],
&workd[1], &workl[1], &lworkl, &rwork[1], &info);
delete[] iselect;
} // ceupp (arcomplex<double>).
inline void ceupp(bool rvec, char HowMny, arcomplex<float> d[],
arcomplex<float> Z[], ARint ldz, arcomplex<float> sigma,
arcomplex<float> workev[], char bmat, ARint n, char* which,
ARint nev, float tol, arcomplex<float> resid[], ARint ncv,
arcomplex<float> V[], ARint ldv, ARint iparam[],
ARint ipntr[], arcomplex<float> workd[],
arcomplex<float> workl[], ARint lworkl, float rwork[],
ARint& info)
/*
c++ version of ARPACK routine cneupd. The only difference between
cneupd and zneupd is that in the former function all vectors have
single precision elements and in the latter all vectors have double
precision elements.
*/
{
ARint irvec;
ARlogical* iselect;
arcomplex<float>* iZ;
irvec = (ARint) rvec;
iselect = new ARlogical[ncv];
iZ = (Z == NULL) ? &V[1] : Z;
F77NAME(cneupd)(&irvec, &HowMny, iselect, d, iZ, &ldz, &sigma,
&workev[1], &bmat, &n, which, &nev, &tol, resid,
&ncv, &V[1], &ldv, &iparam[1], &ipntr[1],
&workd[1], &workl[1], &lworkl, &rwork[1], &info);
delete[] iselect;
} // ceupp (arcomplex<float>).
#endif // CEUPP_H
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