#include "ov.h"
#include "defun-dld.h"
#include "error.h"
#include "gripes.h"
#include "quit.h"
#include "variables.h"
#include "ov-re-sparse.h"
#include "ov-cx-sparse.h"
#include "oct-map.h"
#include "pager.h"
#include "unwind-prot.h"
#include "eigs-base.cc"

Include dependency graph for eigs.cc:

Functions
	DEFUN_DLD (eigs, args, nargout,"-- texinfo --\n\ @deftypefn {Loadable Function} {@var{d} =} eigs (@var{A})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{k})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{k}, @var{sigma}, @var{opts})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{B})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{B}, @var{k})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{A}, @var{B}, @var{k}, @var{sigma}, @var{opts})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{B})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{k})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{k}, @var{sigma}, @var{opts})\n\ @deftypefnx {Loadable Function} {@var{d} =} eigs (@var{af}, @var{n}, @var{B}, @var{k}, @var{sigma}, @var{opts})\n\ @deftypefnx {Loadable Function} {[@var{V}, @var{d}] =} eigs (@var{A}, @dots{})\n\ @deftypefnx {Loadable Function} {[@var{V}, @var{d}] =} eigs (@var{af}, @var{n}, @dots{})\n\ @deftypefnx {Loadable Function} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{A}, @dots{})\n\ @deftypefnx {Loadable Function} {[@var{V}, @var{d}, @var{flag}] =} eigs (@var{af}, @var{n}, @dots{})\n\ Calculate a limited number of eigenvalues and eigenvectors of @var{A},\n\ based on a selection criteria. The number of eigenvalues and eigenvectors to\n\ calculate is given by @var{k} and defaults to 6.\n\ \n\ By default, @code{eigs} solve the equation\n\ @tex\n\ $A \\nu = \\lambda \\nu$,\n\ @end tex\n\ @ifinfo\n\ @code{A * v = lambda * v},\n\ @end ifinfo\n\ where\n\ @tex\n\ $\\lambda$ is a scalar representing one of the eigenvalues, and $\\nu$\n\ @end tex\n\ @ifinfo\n\ @code{lambda} is a scalar representing one of the eigenvalues, and @code{v}\n\ @end ifinfo\n\ is the corresponding eigenvector. If given the positive definite matrix\n\ @var{B} then @code{eigs} solves the general eigenvalue equation\n\ @tex\n\ $A \\nu = \\lambda B \\nu$.\n\ @end tex\n\ @ifinfo\n\ @code{A * v = lambda * B * v}.\n\ @end ifinfo\n\ \n\ The argument @var{sigma} determines which eigenvalues are returned.\n\ @var{sigma} can be either a scalar or a string. When @var{sigma} is a\n\ scalar, the @var{k} eigenvalues closest to @var{sigma} are returned. If\n\ @var{sigma} is a string, it must have one of the following values.\n\ \n\ @table @asis\n\ @item 'lm'\n\ Largest Magnitude (default).\n\ \n\ @item 'sm'\n\ Smallest Magnitude.\n\ \n\ @item 'la'\n\ Largest Algebraic (valid only for real symmetric problems).\n\ \n\ @item 'sa'\n\ Smallest Algebraic (valid only for real symmetric problems).\n\ \n\ @item 'be'\n\ Both Ends, with one more from the high-end if @var{k} is odd (valid only for\n\ real symmetric problems).\n\ \n\ @item 'lr'\n\ Largest Real part (valid only for complex or unsymmetric problems).\n\ \n\ @item 'sr'\n\ Smallest Real part (valid only for complex or unsymmetric problems).\n\ \n\ @item 'li'\n\ Largest Imaginary part (valid only for complex or unsymmetric problems).\n\ \n\ @item 'si'\n\ Smallest Imaginary part (valid only for complex or unsymmetric problems).\n\ @end table\n\ \n\ If @var{opts} is given, it is a structure defining possible options that\n\ @code{eigs} should use. The fields of the @var{opts} structure are:\n\ \n\ @table @code\n\ @item issym\n\ If @var{af} is given, then flags whether the function @var{af} defines a\n\ symmetric problem. It is ignored if @var{A} is given. The default is false.\n\ \n\ @item isreal\n\ If @var{af} is given, then flags whether the function @var{af} defines a\n\ real problem. It is ignored if @var{A} is given. The default is true.\n\ \n\ @item tol\n\ Defines the required convergence tolerance, calculated as\n\ @code{tol * norm (A)}. The default is @code{eps}.\n\ \n\ @item maxit\n\ The maximum number of iterations. The default is 300.\n\ \n\ @item p\n\ The number of Lanzcos basis vectors to use. More vectors will result in\n\ faster convergence, but a greater use of memory. The optimal value of\n\ @code{p} is problem dependent and should be in the range @var{k} to @var{n}.\n\ The default value is @code{2 * @var{k}}.\n\ \n\ @item v0\n\ The starting vector for the algorithm. An initial vector close to the\n\ final vector will speed up convergence. The default is for @sc{arpack}\n\ to randomly generate a starting vector. If specified, @code{v0} must be\n\ an @var{n}-by-1 vector where @code{@var{n} = rows (@var{A})}\n\ \n\ @item disp\n\ The level of diagnostic printout (0\|1\|2). If @code{disp} is 0 then\n\ diagnostics are disabled. The default value is 0.\n\ \n\ @item cholB\n\ Flag if @code{chol (@var{B})} is passed rather than @var{B}. The default is\n\ false.\n\ \n\ @item permB\n\ The permutation vector of the Cholesky@tie{}factorization of @var{B} if\n\ @code{cholB} is true. That is @code{chol (@var{B}(permB, permB))}. The\n\ default is @code{1:@var{n}}.\n\ \n\ @end table\n\ It is also possible to represent @var{A} by a function denoted @var{af}.\n\ @var{af} must be followed by a scalar argument @var{n} defining the length\n\ of the vector argument accepted by @var{af}. @var{af} can be\n\ a function handle, an inline function, or a string. When @var{af} is a\n\ string it holds the name of the function to use.\n\ \n\ @var{af} is a function of the form @code{y = af (x)}\n\ where the required return value of @var{af} is determined by\n\ the value of @var{sigma}. The four possible forms are\n\ \n\ @table @code\n\ @item A * x\n\ if @var{sigma} is not given or is a string other than 'sm'.\n\ \n\ @item A \\ x\n\ if @var{sigma} is 0 or 'sm'.\n\ \n\ @item (A - sigma * I) \\ x\n\ for the standard eigenvalue problem, where @code{I} is the identity matrix of\n\ the same size as @var{A}.\n\ \n\ @item (A - sigma * B) \\ x\n\ for the general eigenvalue problem.\n\ @end table\n\ \n\ The return arguments of @code{eigs} depend on the number of return arguments\n\ requested. With a single return argument, a vector @var{d} of length @var{k}\n\ is returned containing the @var{k} eigenvalues that have been found. With\n\ two return arguments, @var{V} is a @var{n}-by-@var{k} matrix whose columns\n\ are the @var{k} eigenvectors corresponding to the returned eigenvalues. The\n\ eigenvalues themselves are returned in @var{d} in the form of a\n\ @var{n}-by-@var{k} matrix, where the elements on the diagonal are the\n\ eigenvalues.\n\ \n\ Given a third return argument @var{flag}, @code{eigs} returns the status\n\ of the convergence. If @var{flag} is 0 then all eigenvalues have converged.\n\ Any other value indicates a failure to converge.\n\ \n\ This function is based on the @sc{arpack} package, written by R. Lehoucq,\n\ K. Maschhoff, D. Sorensen, and C. Yang. For more information see\n\ @url{http://www.caam.rice.edu/software/ARPACK/}.\n\ \n\ @seealso{eig, svds}\n\ @end deftypefn")
ComplexColumnVector	eigs_complex_func (const ComplexColumnVector &x, int &eigs_error)
ColumnVector	eigs_func (const ColumnVector &x, int &eigs_error)
Variables
static int	call_depth = 0
static octave_function *	eigs_fcn = 0
static bool	warned_imaginary = false