d1GTO_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. More...

Public Members

Detailed Description

This class has two related functions. One allows the user to iterate the graph transform algorithm to convergence for a fixed value of a specified parameter in the dynamical system. The other function lets the user specify a parameter range over which to continue the invariant manifold. 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

d1GTO_s::d1GTO_s(map *fPtr, d1graphMan *gManPtr)

The explicit constructor for the class d1GTO_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.

Returns:: a d1GTO_s object.

int d1GTO_s::iterate(int fullOutput, int gtMaxit, int newtMaxit, int nprepMesh, VEC gtAcc, REAL nprepMaxdis, REAL newtAcc, REAL projectNeigh, int &check, d1graphMan * &wgManPtr, char fname[5])

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

Parameters:: fullOutput - an integer with value 0 or 1 specifying the degree of 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.; 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, not currently used.; 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.; check - a reference to an integer. Calling this method sets it to either 0 or 1. A returned value of 1 indicates that the grid points of some element of the newly determined d1graphMan do not determine the graph of a polynomial.; gManPtr - a reference to 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, -1 if gtMaxit is exceeded or an iterate failed.

Examples:: d1StableODE.C.

int d1GTO_s::continuation(int contMesh, REAL start, REAL end, int bracketMesh, REAL projectNeigh, REAL maxSlope, VEC gtAcc, d1graphMan *wgManPtr, char fname[5])

This member provides the ability to continue the invariant manifold over a parameter range.

Parameters:: contMesh - an integer specifying the continuation step size as a fraction of the continuation interval.; start - a "REAL" number giving the initial value of the continuation parameter.; end - a "REAL" number giving the value of the continuation parameter to attempt continuation to.; bracketMesh - a positive integer specifying the mesh to use in finding sign changes of a real-valued function defined on the invariant curve.; projectNeigh - a "REAL" value which gives a distance from the initial invariant manifold within which the canonical projection onto the manifold is defined.; maxSlope - a "REAL" value used to determine whether an element should be refined. For each element, in the local coordinate system given by the tangent/normal data of the "d1baseMan", lines are drawn from the base point of the "d1baseMan" through each grid point of the "d1graphMan". If the slope of any of these lines exceeds maxSlope, the element is subdivided.; gtAcc - a "VEC" with size 2. Currently, only gtAcc[0] is used. This value specifies the convergence criterion for the graph transform algorithm.; gManPtr - a reference to 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 which specifies the name of the file which the member outputs data to (a .vect file).

Returns:: an integer specifying the number of continuation steps completed.