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d1LocInvTrans_s Class Reference

This class provides access to the linear graph transform algorithm for the purpose of determining the invariant transversal to an invariant manifold. This class handles the case of a stable 1-dimensional manifold, like an invariant closed curve. More...

List of all members.

Public Members

• d1LocInvTrans_s (int, map *, d1baseMan *, vecBundle *)

  The explicit constructor for the d1LocInvTrans_s class. This is the only accessible constructor for this class.

• ~d1LocInvTrans_s ()
• void oneIt_alg1 (const int, const int, const int, const REAL, VEC &, const REAL)
• int iterate_alg1 (const int, const int, const int, const REAL, const int, const REAL, const REAL, const REAL = 1.0)

  This member provides the ability to iterate the linear graph transform algorithm to convergence. Hence it calculates the invariant transversal to the invariant manifold.

• void write2dGeomFile (char filename[] = "d1InvTrans_sInput_n2", int mesh= 1)
• void write3dGeomFile (char filename[] = "d1InvTrans_sInput_n3", int mesh= 1)

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Detailed Description

This class provides access to the linear graph transform algorithm for the purpose of determining the invariant transversal to an invariant manifold. This class handles the case of a stable 1-dimensional manifold, like an invariant closed curve.

Examples:

d1StableODE.C.

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Member Function Documentation

d1LocInvTrans_s::d1LocInvTrans_s(int haveCCS,map *fPtr,d1baseMan *bManPtr,vecBundle *sBundlePtr)

The explicit constructor for the d1LocInvTrans_s class. This is the only accessible constructor for this class.

Parameters:

haveCCS - an integer, not currently used.

fPtr - a pointer to a "map" giving the dynamical system.

bManPtr - a pointer to a "d1baseMan" giving the invariant manifold whose invariant transversal one wishes to find.

sBundlePtr - a pointer to a "vecBundle" which will contain candidates for the invariant transversal, which in this case is a stable bundle.

Returns:

a d1LocInvTrans_s object.

int d1LocInvTrans_s::iterate_alg1(const int mesh,const int maxSearch,const int MAXIT,const REAL xacc,const int gtMaxIt, const REAL gtAcc,const REAL contractTol,const REAL lipTol)

This member provides the ability to iterate the linear graph transform algorithm to convergence. Hence it calculates the invariant transversal to the invariant manifold.

Parameters:

mesh - an integer constant which specifies the number of intervals to divide the domain of an element into, when finding brackets on the root. Can be 1 in most cases.

maxSearch - an integer constant which specifies the maximum number of elements to search in looking for brackets on the root.

MAXIT - an integer constant specifying the maximum number of iterates to take to satisfy the convergence criterion for the 1d-newton/bisection algorithm, before giving up. newtMaxit = 100 is a reasonable value.

xacc - a "REAL" constant specifying the convergence criterion for the d1-newton/bisection algorithm. xacc = 1.0E-6 is a reasonable value.

gtMaxit - an integer constant specifying the maximum number of iterates of the linear graph transform algorithm to take to satisfy the convergence criterion, before giving up.

gtAcc - a "REAL" constant specifying the convergence criterion for the linear graph transform.

contractTol - a "REAL" constant specifying the maximum value for the contraction at a step, before realizing that the algorithm isn't converging and giving up.

lipTol - a "REAL" constant specifying the maximum value allowed for the estimated lipschitz constant of the contraction map represented by the linear graph transform algorithm.

Returns:

the number of iterates required if successful, and -1 if not successful.

Examples:

d1StableODE.C.

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The documentation for this class was generated from the following files:

• d1LocInvTrans_s.h
• d1LocInvTrans_s.C

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