d1TCGTO_s Class Reference

The d1GTO_s class provides an interface for the graph transform algorithm. This class should be used in the stable case for a one-dimensional manifold, like an invariant closed curve. This class is intended for the case that the ambient space has at least one truncated coordinate. More...

Public Members

Static Public Members

Detailed Description

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 one 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 "d1baseMan" (representing the initial data) must be created, and a "d1graphMan" object (representing the current manifold of the iteration) must be created.

Member Function Documentation

d1TCGTO_s::d1TCGTO_s(map *fPtr,d1graphMan *gManPtr,Matrix<int> *bndryEltPtr,REAL bndryTol,int numTruncDims)

The explicit constructor for the class d1TCGTO_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 "d1graphMan" which represents a 1 dimensional manifold graphed over the initial manifold (a "d1baseMan"). This "d1graphMan" should be zeroed before being sent to the constructor.; bndryEltPtr - a pointer to a "Matrix" of ints. The "Matrix" has size (numElts x numTruncDims). Each entry is -1, 0, or 1. An entry of 0 in place (i,j) means that element i is not near the boundary in the jth truncated coordinate. Similarly, -1 means the element is near the left boundary (0), and 1 means the element is near the right boundary (2pi).; bndryTol - a "REAL" value indicating the distance to the boundary within which an element is considered a boundary element.; numTruncDims - a positive integer specifying the number of truncated dimensions.

Returns:: a d1TCGTO_s object.

int d1TCGTO_s::iterate(int whichAlg, int fullOutput, int gtMaxit, int newtMaxit, int nprepMesh, VEC gtAcc, REAL nprepMaxdis, REAL newtAcc, REAL projectNeigh, d1graphMan *wgManPtr, char fname[5])

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

Parameters:: whichAlg - an integer, either 1 or 2, specifying which graph transform algorithm to use. Currently, this must be set to 2.; fullOutput - an integer with value 0 or 1 specifying the degree of output. (0 = no graphical output. 1 = graphical output of each step.); gtMaxit - a positive integer specifying the maximum number of iterations to perform before giving up.; newtMaxit - a positive integer specifying the maximum number of iterations of the 1-dimensional Newton/bisection algorithm to perform before giving up. A reasonable value is 100.; nprepMesh - a positive integer specifying the mesh to use in finding sign changes of a real-valued function defined on the invariant curve.; gtAcc - a "VEC" with size 2. Currently, only gtAcc[0] is used. This value specifies the convergence criterion for the graph transform algorithm.; nprepMaxdis - a "REAL" value. A distance from the initial manifold which the final manifold of the graph transform iteration lies within.; newtAcc - a "REAL" value specifying the convergence criterion for the 1-dimensional Newton/bisection method.; 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 "d1graphMan". This "d1graphMan" is used as either the current or the next manifold of the graph transform iteration (the other "d1graphMan" is in the private data of this class).; fname - a character array with length 5 specifying the name for the output file (a .vect file).

Returns:: an integer giving the number of graph transform iterates completed.