MFImplicitMF

Collaboration diagram for MFImplicitMF:


Modules

 IMFFlat
 IMFSphereOnExpansion
 MFAUTOBV
 MFEdgeIn3SpaceMF
 MFPolygonIn3SpaceMF
 MFAlgebraicMF
 MFCircleMF
 MFFlatMF
 MFNSpaceMF
 MFPlaneMF
 MFSphereMF
 MFTPBVPMF
 MFTorusMF
 MFLOCAIMF

Classes

class  MFImplicitMF
 A manifold, defined by an equation F(u)=0. More...

Functions

char * MFImplicitMFId (MFImplicitMF M, MFErrorHandler e)
 Returns a character string which assigns a type to an ImplicitMF. Do not change or free the string!
int MFIMF_N (MFImplicitMF M, MFErrorHandler e)
 Gets the embedding space dimension of an ImplicitMF.
int MFIMF_K (MFImplicitMF M, MFErrorHandler e)
 Gets the dimension of an ImplicitMF.
MFNSpace MFIMFNSpace (MFImplicitMF M, MFErrorHandler e)
 Gets the space in which the manifold is embedded.
int MFIMFProjectFromCenter (MFImplicitMF M, MFNVector u0, MFNKMatrix Phi0, MFKVector s, MFNVector u, MFErrorHandler e)
 This is the generalizatio of the prediction and correction operations in pseudo-arclength continuation. The prediction is u0+Phi0.s, and the correction is from this point to M orthogonal to Phi0.
int MFIMFProject (MFImplicitMF M, MFNVector u0, MFNKMatrix Phi0, MFNVector u, MFErrorHandler e)
 Projects a point u0 onto an ImplicitMF orthogonal to a tangent space Phi0.
MFNKMatrix MFIMFTangentSpace (MFImplicitMF M, MFNVector u, MFErrorHandler e)
 Computes and returns an orthonormal basis for the tangent space of M at the point u on M.
MFNKMatrix MFIMFTangentSpaceWithGuess (MFImplicitMF M, MFNVector u, MFNKMatrix guess, MFErrorHandler e)
 Computes and returns an orthonormal basis for the tangent space of M at the point u on M.
double MFIMFScale (MFImplicitMF M, MFNVector u, MFNKMatrix Tan, MFErrorHandler e)
 Estimates the radius of a spherical ball in the tangent space of M at u on M.
int MFIMFProjectToSave (MFImplicitMF M, MFNVector u, double *x, MFErrorHandler e)
 Projects a point so that it can be saved to file (used for the centerfile).
int MFIMFProjectToDraw (MFImplicitMF M, MFNVector u, double *x, MFErrorHandler e)
 Projects a point so that it can be drawn (used for the plotfile).
int MFIMFProjectToBB (MFImplicitMF M, MFNVector u, double *x, MFErrorHandler e)
 Projects a point so that it can be placed in the hierarchical bounding boxes that are used to speed up the location of neighboring charts.
void * MFIMFGetData (MFImplicitMF M, MFErrorHandler e)
 Returns a pointer to the internal data used by the manifold. Be very careful using this. You need to know what you're doing.
double MFIMFGetR (MFImplicitMF M, MFErrorHandler e)
 Returns the radius currently associated with a manifold. It provides a guess if no other information about the scale is available.
void MFIMFSetR (MFImplicitMF M, double R, MFErrorHandler e)
 Associates a radius with a manifold. It provides a guess if no other information about the scale is available.
double MFIMFGetRMin (MFImplicitMF M, MFErrorHandler e)
 Returns the current value of the radius that the user has provided as a smallest radius for the manifold.
void MFIMFSetRMin (MFImplicitMF M, double R, MFErrorHandler e)
 Allows the user to set a smallest radius for a manifold. A continuation method may ignore it, but it is there.
MFNVector MFIMFVectorFactory (MFImplicitMF M, MFErrorHandler e)
 This is a factory to create an NVector that is the approriate type for a point on this manifold. All allocation of vectors in multifario is by cloning, so the type of this vector is important. NVectors and ImplicitMF's are both base classes, so the user has no other way (besides the documentation) of knowing the type of NVector to use as an initial point.
MFNKMatrix MFIMFMatrixFactory (MFImplicitMF M, MFErrorHandler e)
 This is a factory to create an NKMatrix that is the approriate type for a point on this manifold. Unless the manifold uses a dense array of doubles the columns of the matrix will be NVectors of the appropriate type.
void MFRefImplicitMF (MFImplicitMF M, MFErrorHandler e)
 Adds a reference to an MFImplicitMF.
void MFFreeImplicitMF (MFImplicitMF this, MFErrorHandler e)
 Frees a reference to the ImplicitMF, and deletes the ImplicitMF if there are no references left.
void MFWriteImplicitMF (FILE *fid, MFImplicitMF M, MFErrorHandler e)
 Writes a ImplicitMF to a file.
MFImplicitMF MFReadImplicitMF (FILE *fid, MFErrorHandler e)
 Reads a ImplicitMF from a file.

Function Documentation

void MFFreeImplicitMF (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Frees a reference to the ImplicitMF, and deletes the ImplicitMF if there are no references left.

Parameters:
M The ImplicitMF being unreferenced.
e A place to return errors.
See also:
ReferenceCounting MFRefImplicitMF

int MFIMF_K (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Gets the dimension of an ImplicitMF.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The dimension of the manifold (k).

int MFIMF_N (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Gets the embedding space dimension of an ImplicitMF.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The dimension of the embedding space (n).

void * MFIMFGetData (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Returns a pointer to the internal data used by the manifold. Be very careful using this. You need to know what you're doing.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
A pointer to the internal data.

double MFIMFGetR (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Returns the radius currently associated with a manifold. It provides a guess if no other information about the scale is available.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The radius.

double MFIMFGetRMin (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Returns the current value of the radius that the user has provided as a smallest radius for the manifold.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The radius.

MFNKMatrix MFIMFMatrixFactory (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

This is a factory to create an NKMatrix that is the approriate type for a point on this manifold. Unless the manifold uses a dense array of doubles the columns of the matrix will be NVectors of the appropriate type.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
A clean and shiny new NKMatrix of the right type for the tangent space of this manifold.

MFNSpace MFIMFNSpace (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Gets the space in which the manifold is embedded.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The embedding space.

int MFIMFProject (  MFImplicitMF  M,
MFNVector  u0,
MFNKMatrix  Phi0,
MFNVector  u,
MFErrorHandler  e
) 
 

Projects a point u0 onto an ImplicitMF orthogonal to a tangent space Phi0.

Parameters:
M The implicitly defined manifold.
u0 The point to be projected.
Phi0 The tangent space.
u The projected point, which lies on M and Phi0^T(u-u0)-0.
e A place to return errors.
Returns:
TRUE if the projection was sucessful

int MFIMFProjectFromCenter (  MFImplicitMF  M,
MFNVector  u0,
MFNKMatrix  Phi0,
MFKVector  s,
MFNVector  u,
MFErrorHandler  e
) 
 

This is the generalizatio of the prediction and correction operations in pseudo-arclength continuation. The prediction is u0+Phi0.s, and the correction is from this point to M orthogonal to Phi0.

Parameters:
M The implicitly defined manifold.
u0 The point to be projected.
Phi0 The tangent space.
s The point in the tangent space that is to be projected.
u The projected point, which lies on M and Phi0^T(u-u0)-0.
e A place to return errors.
Returns:
TRUE if the projection was sucessful

int MFIMFProjectToBB (  MFImplicitMF  M,
MFNVector  u,
double *  x,
MFErrorHandler  e
) 
 

Projects a point so that it can be placed in the hierarchical bounding boxes that are used to speed up the location of neighboring charts.

The convention is that if x is NULL, the routine returns the dimension of x, so that the user can allocate storage.

Parameters:
M The implicitly defined manifold.
u The point that is to be projected, or (double*)NULL if the dimension is needed.
x The implicitly defined manifold.
e A place to return errors.
Returns:
The dimension of the projected point if x is (double*)NULL.

int MFIMFProjectToDraw (  MFImplicitMF  M,
MFNVector  u,
double *  x,
MFErrorHandler  e
) 
 

Projects a point so that it can be drawn (used for the plotfile).

The convention is that if x is NULL, the routine returns the dimension of x, so that the user can allocate storage.

Parameters:
M The implicitly defined manifold.
u The point that is to be projected, or (double*)NULL if the dimension is needed.
x The implicitly defined manifold.
e A place to return errors.
Returns:
The dimension of the projected point if x is (double*)NULL.

int MFIMFProjectToSave (  MFImplicitMF  M,
MFNVector  u,
double *  x,
MFErrorHandler  e
) 
 

Projects a point so that it can be saved to file (used for the centerfile).

The convention is that if x is NULL, the routine returns the dimension of x, so that the user can allocate storage.

Parameters:
M The implicitly defined manifold.
u The point that is to be projected, or (double*)NULL if the dimension is needed.
x The implicitly defined manifold.
e A place to return errors.
Returns:
The dimension of the projected point if x is (double*)NULL.

double MFIMFScale (  MFImplicitMF  M,
MFNVector  u,
MFNKMatrix  Tan,
MFErrorHandler  e
) 
 

Estimates the radius of a spherical ball in the tangent space of M at u on M.

Parameters:
M The implicitly defined manifold.
u The point at which the tangent space is needed.
Tan The tangent space of M at u.
e A place to return errors.
Returns:
The radius.

void MFIMFSetR (  MFImplicitMF  M,
double  R,
MFErrorHandler  e
) 
 

Associates a radius with a manifold. It provides a guess if no other information about the scale is available.

Parameters:
M The implicitly defined manifold.
R The radius.
e A place to return errors.

void MFIMFSetRMin (  MFImplicitMF  M,
double  R,
MFErrorHandler  e
) 
 

Allows the user to set a smallest radius for a manifold. A continuation method may ignore it, but it is there.

Parameters:
M The implicitly defined manifold.
R The radius.
e A place to return errors.

MFNKMatrix MFIMFTangentSpace (  MFImplicitMF  M,
MFNVector  u,
MFErrorHandler  e
) 
 

Computes and returns an orthonormal basis for the tangent space of M at the point u on M.

Parameters:
M The implicitly defined manifold.
u The point at which the tangent space is needed.
e A place to return errors.
Returns:
An orthonormal basis for the tangent space of M at u on M.

MFNKMatrix MFIMFTangentSpaceWithGuess (  MFImplicitMF  M,
MFNVector  u,
MFNKMatrix  guess,
MFErrorHandler  e
) 
 

Computes and returns an orthonormal basis for the tangent space of M at the point u on M.

Parameters:
M The implicitly defined manifold.
u The point at which the tangent space is needed.
guess An approximate tangent space. The new basis will align roughly with the basis in guess.
e A place to return errors.
Returns:
An orthonormal basis for the tangent space of M at u on M.

MFNVector MFIMFVectorFactory (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

This is a factory to create an NVector that is the approriate type for a point on this manifold. All allocation of vectors in multifario is by cloning, so the type of this vector is important. NVectors and ImplicitMF's are both base classes, so the user has no other way (besides the documentation) of knowing the type of NVector to use as an initial point.

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
A clean and shiny new NVector of the right type for computations of this manifold.

char * MFImplicitMFId (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Returns a character string which assigns a type to an ImplicitMF. Do not change or free the string!

Parameters:
M The implicitly defined manifold.
e A place to return errors.
Returns:
The type of the ImplicitMF.

MFImplicitMF MFReadImplicitMF (  FILE *  fid,
MFErrorHandler  e
) 
 

Reads a ImplicitMF from a file.

Parameters:
fid The file to read from.
e A place to return errors.

void MFRefImplicitMF (  MFImplicitMF  M,
MFErrorHandler  e
) 
 

Adds a reference to an MFImplicitMF.

Parameters:
M The an ImplicitMF being referenced.
e A place to return errors.
See also:
ReferenceCounting MFFreeImplicitMF

void MFWriteImplicitMF (  FILE *  fid,
MFImplicitMF  M,
MFErrorHandler  e
) 
 

Writes a ImplicitMF to a file.

Parameters:
fid The file to write to.
M The ImplicitMF being written.
e A place to return errors.

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