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d1graphMan Class Reference

This class represents a 1-dimensional attracting manifold, represented as a graph over an initial manifold (a "d1baseMan"). More...

List of all members.

Public Members

• d1graphMan (char wtype[9], d1baseMan *wbManPtr, d1smallGrid *wgridPtr, VEC (*wodePtr)(VEC), int useVF=0)

  The explicit constructor for the class d1graphMan.

• d1graphMan (const d1graphMan &)
• d1graphMan (char wtype[9], int wn, int wm, int wnumElts, VEC (*wodePtr)(VEC), int useVF=0)

  The semi-explicit constructor for the class d1graphMan. This constructor allocates the right memory without filling in all the data.

• ~d1graphMan ()
• void input (const d1smallGrid &)
• void resize (int)
• VEC interpolate (int, REAL, REAL &)
• MAT interpDeriv (int, REAL, REAL &)
• MAT polyDeriv (int, REAL, REAL &)
• VEC interpTanData (int, REAL, REAL &)
• void setBaseManPtr (d1baseMan *)
• int setPolynomials ()
• void setGridPtr (d1smallGrid *)
• void setTangentData ()
• int refineGrid (REAL)
• int getAmbDim ()
• int getNodesPerElt ()
• int getNumElts ()
• char* getPolyType ()
• const int getNumElts () const
• const int getNodesPerElt () const
• const char* getPolyType () const
• d1baseMan* getBaseManPtr ()
• const d1baseMan* getBaseManPtr () const
• d1graphP* polynomialPtr (int)
• d1smallGrid* GridPtr ()
• const d1smallGrid* GridPtr () const
• d1baseGridPt& gridPt (int, int)
• VEC compare (d1graphMan *)
• VEC project (const VEC, const int, int &, REAL &)
• REAL testInvariance (map *, int)
• REAL testPolynomials ()
• void write2dPlotFile (char filename[], int mesh=1)
• void write2dGeomFile (char filename[], int mesh=1, int withTanData=0)
• void write2dGeomFileWTD (char filename[], int mesh=1)
• void write2dGeomFileWOTD (char filename[], int mesh=1)
• void write3dGeomFile (char filename[], int mesh=1)
• void write3dGeomFileWTD (char filename[], int mesh=1, REAL scale=1.0)
• void write3dGeomFileElts (Vector<int> eltNum, int nElts, char filename[], REAL scale=1.0)

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Detailed Description

This class represents a 1-dimensional attracting manifold, represented as a graph over an initial manifold (a "d1baseMan").

This class approximates a manifold locally with Lagrange polynomials (of arbitrary order), defined over intervals. The polynomials are graphed in the local coordinate systems of the initial manifold (a "d1baseMan". More precisely, for each element, the manifold represented by the d1graphMan is approximated by the graph of a polynomial (considered as a function from the tangent space at the basepoint to the normal space at the basepoint).

Examples:

d1StableODE.C.

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Member Function Documentation

d1graphMan::d1graphMan(char wtype[9],d1baseMan *wbManPtr,d1smallGrid *wgridPtr,VEC (*wodePtr)(VEC),int useVF)

The explicit constructor for the class d1graphMan.

Parameters:

type - a character array with size 9. This argument determines the type of polynomial used to approximate the manifold, for example Lagrange or Hermite. Only Lagrange is currently supported.

bManBtr - a pointer to a "d1baseMan ", which represents the initial manifold over which this manifold is graphed.

gridPtr - a pointer to a "d1smallGrid". This data is a set of points in the ambient space giving, for each grid point y of *bManPtr, a point near the normal fiber of *bManPtr at y. These points determine the discrete manifold represented by the "d1graphMan".

odePtr - a pointer to a function with one "VEC" argument, returning a "VEC". The function represents the vector field determining the dynamical system.

useVF - an integer, either 0 or 1, specifying whether to use a vector field to determine the tangent data for the d1graphMan.

Returns:

a d1graphMan object

d1graphMan::d1graphMan(char wtype[9],int wn,int wm,int wnumElts,VEC (*wodePtr)(VEC),int useVF)

The semi-explicit constructor for the class d1graphMan. This constructor allocates the right memory without filling in all the data.

Parameters:

type - a character array with size 9. This argument determines the type of polynomial used to approximate the manifold, for example Lagrange or Hermite. Only Lagrange is currently supported.

n - a positive integer specifying the ambient dimension.

m - a positive integer specifying the number of nodes per element. This determines the order of approximation.

numElts - a positive integer specifying the number of elements used to approximate the manifold.

odePtr - a pointer to a function with one "VEC" argument, returning a "VEC". The function represents the vector field determining the dynamical system.

useVF - an integer, either 0 or 1, specifying whether to use a vector field to determine the tangent data for the d1graphMan.

Returns:

a d1graphMan object

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

• d1graphMan.h
• d1graphMan.C

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