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d2GTO_s Class Reference

The d2GTO_s class is a user interface for the graph transform algorithm. This class should be used in the stable case for a two-dimensional manifold, like an invariant torus. More...

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Detailed Description

The d2GTO_s class is a user interface for the graph transform algorithm. This class should be used in the stable case for a two-dimensional manifold, like an invariant torus.

This class has one main function. It allows the user to iterate the graph transform algorithm to convergence for a fixed value of a specified parameter in the dynamical system. The initial data needed to create an object of this class are a discrete two dimensional manifold, together with discrete normal data. The graph transform algorithm iterates this initial data. Before an object of this class may be created, a "map" (representing the dynamical system) must be created, a "d2LTManifold" (representing the initial data) must be created, and a "d2graphMan" object (representing the current manifold of the iteration) must be created.

Examples:
d2StableODE.C.

Member Function Documentation

d2GTO_s::d2GTO_s(map *wfPtr, d2graphMan *wgManPtr, int wrInitSrchData, int wuseInitEltPtr, char filename[], int wnumPElts, int wnumBPElts, int wMAXITS, REAL wTOLF, REAL wTOLMIN, REAL wTOLX, REAL wSTPMX, int wxLgGrid)

The explicit constructor for the class d2GTO_s. This is the only accessible constructor for this class.

Parameters:
fPtr - a pointer to a "map" representing the dynamical system.
gManPtr - a pointer to a "d2graphMan" which represents a 2 dimensional manifold graphed over the initial manifold (a "d2LTManifold"). This "d2graphMan" should be zeroed before being sent to the constructor.
rInitSrchData - an integer, either 0 or 1, which specifies whether to read initial search data into memory (for use in the first graph transform iterate) from a file named in filename[].
useInitEltPtr - an integer, either 0 or 1, which specifies whether to store in memory the location of a patch of elements where the last graph transform root was found, for each vertex grid point. This must be 1 if rInitSrchData = 1.
filename - [] a character array which gives the name of the file from which to read the initial search data, if rInitSrchData = 1. Also gives the name of the file from which to retrieve search data during the iteration of the graph transform algorithm, if useInitEltPtr = 0 or numPElts < numBPElts.
numPElts - a positive integer specifying the number of columns of search data kept in memory, if useInitEltPtr = 1. More generally specifies the number of elements to search for a graph transform root.
numBPElts - a positive integer greater than or equal to numPElts, specifying the number of columns of search data in the search data file named by filename[].
xLgGrid - a non-negative integer, either equal to 0 or the number of vertex nodes (if the number of grid points is large). This allows special measures to be taken for very large grids.

Description of parameters for the multidimensional Newton's algorithm: (there are default arguments for these)

Parameters:
MAXITS - a positive integer specifying the maximum number of iterations.
TOLF - a "REAL" value, the convergence criterion on function values.
TOLMIN - a "REAL" value, the criterion for deciding whether spurious convergence to a minimum of fmin has occurred.
TOLX - a "REAL" value, the convergence criterion on (delta x) = the change in the guess for the root.
STPMX - a "REAL" value, the scaled maximum length allowed in line searches.

Returns:
a d2GTO_s object.

int d2GTO_s::iterate(int fullOutput, int gtMaxit, REAL gtAcc, REAL projectNeigh, baseVector<VEC *> *wgManPtr, char fname[5], char fname2[])

This member provides the ability to iterate the graph transform algorithm to convergence.

Parameters:
fullOutput - an integer with value -1, 0, or 1 specifying the degree of output. (-1 = no graphical output. 0 = graphical output of final manifold computed upon convergence. 1 = graphical output of each step.)
gtMaxit - a positive integer specifying the maximum number of iterations to perform before giving up.
gtAcc - a "REAL" value specifying the convergence criterion for the graph transform algorithm.
projectNeigh - a "REAL" value which gives a distance from the initial invariant manifold within which the canonical projection onto the manifold is defined.
gManPtr - a pointer to a "baseVector" of pointers to "VEC"s, the data structure that each iterate of the graph transform fills in while determining the graph transform of the current manifold.
fname - a character array with length 5 specifying the file names for the output files (.dat and .vect files).
fname2 - a character array specifying the name of the file to output new search data to.
Returns:
an integer giving the number of graph transform iterates completed, -1 if gtMaxit is exceeded.

Examples:
d2StableODE.C.
The documentation for this class was generated from the following files:
Generated at Sat Oct 16 03:55:28 1999 for Computing Invariant Manifolds Library by doxygen  written by Dimitri van Heesch, © 1997-1998