IMFExpansion
[IMF]

Collaboration diagram for IMFExpansion:


Classes

class  IMFExpansion
 A chart, which represents a neighborhood on a manifold. More...

Functions

IMFExpansion IMFCreateExpansion (int n, int k, MFErrorHandler e)
 Creates a Taylor series expansion to third order for a mapping from IR^k to IR^n. This is the default constructor, and returns an expansion of the function which is always zero.
void IMFEvaluateExpansion (IMFExpansion E, MFKVector s, MFNVector u, MFErrorHandler e)
 Evaluates an expansion.
void IMFEvaluateExpansionDirectionalDerivative (IMFExpansion E, MFKVector s, MFKVector ds, MFNVector du, MFErrorHandler e)
 Evaluates an expansion.
void IMFEvaluateExpansionSecondDirectionalDerivative (IMFExpansion E, MFKVector s, MFKVector ds0, MFKVector ds1, MFNVector ddu, MFErrorHandler e)
 Evaluates an expansion.
void IMFEvaluateExpansionDerivative (IMFExpansion E, MFKVector s, int d, MFNVector du, MFErrorHandler e)
 Evaluates the derivative of an expansion along a coordinate direction.
void IMFEvaluateExpansionSecondDerivative (IMFExpansion E, MFKVector s, int d0, int d1, MFNVector ddu, MFErrorHandler e)
 Evaluates the second derivative of an expansion along coordinate directions.
void IMFEvaluateExpansionThirdDerivative (IMFExpansion E, MFKVector s, int d0, int d1, int d2, MFNVector dddu, MFErrorHandler e)
 Evaluates the third derivative of an expansion along coordinate directions.
int IMFExpansionN (IMFExpansion E, MFErrorHandler e)
 Returns the dimension of the range of an expansion.
int IMFExpansionK (IMFExpansion E, MFErrorHandler e)
 Returns the dimension of the domain of an expansion.
int IMFExpansionOrder (IMFExpansion E, MFErrorHandler e)
 Returns the order of an expansion (the degree of the highest non-zero term in the Taylor series).
void IMFPrintExpansion (FILE *fid, IMFExpansion E, MFErrorHandler e)
 Prints a \"pretty\" version of the expansion.
IMFExpansion IMFCloneExpansion (IMFExpansion E, MFErrorHandler e)
 Creates a deep copy of an expansion.
IMFExpansion IMFRectify (IMFExpansion E, MFErrorHandler e)
 Changes the metric of the expansion to the identity.
IMFExpansion IMFInflateExpansionWithFlow (IMFExpansion E, IMFFlow f, MFKVector p, MFErrorHandler e)
 Creates the product of an expansion with a trjectory of a flow.
double IMFExpansionR (IMFExpansion E, double epsilon, MFErrorHandler e)
 Estimates a ball such that within the ball the second order terms are bounded in absolute value by epsilon.
MFNKMatrix IMFExpansionTS (IMFExpansion E, MFErrorHandler e)
 Returns a new MFNKMatrix with an orthonormal basis for the tangent space at the origin of the expansion.
void IMFWriteExpansion (FILE *fid, IMFExpansion E, MFErrorHandler e)
 Writes an expansion to a file.
IMFExpansion IMFReadExpansion (FILE *fid, MFErrorHandler e)
 Reads an expansion from a file.
void IMFFreeExpansion (IMFExpansion E, MFErrorHandler e)
 Frees a reference to an expansion, and deletes the expansion if there are no references left.
void IMFRefExpansion (IMFExpansion E, MFErrorHandler e)
 Adds a reference to a expansion.

Function Documentation

IMFExpansion IMFCloneExpansion (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Creates a deep copy of an expansion.

Parameters:
E The expansion.
e A place to return errors.
Returns:
A clone.

IMFExpansion IMFCreateExpansion (  int  n,
int  k,
MFErrorHandler  e
) 
 

Creates a Taylor series expansion to third order for a mapping from IR^k to IR^n. This is the default constructor, and returns an expansion of the function which is always zero.

Parameters:
n The dimension of the range of the expansion.
k The dimension of the domain of the expansion.
e A place to return errors.
Returns:
A third order expansion of the zero valued funciton.

void IMFEvaluateExpansion (  IMFExpansion  E,
MFKVector  s,
MFNVector  u,
MFErrorHandler  e
) 
 

Evaluates an expansion.

Parameters:
E An expansion.
s A point in the domain of the expansion.
u Provided by the user, a place to put the result.
e A place to return errors.

void IMFEvaluateExpansionDerivative (  IMFExpansion  E,
MFKVector  s,
int  d,
MFNVector  du,
MFErrorHandler  e
) 
 

Evaluates the derivative of an expansion along a coordinate direction.

Parameters:
E An expansion.
s A point in the domain of the expansion.
d A coordinate axis in which to find the partial derivative.
du Provided by the user, a place to put the result.
e A place to return errors.

void IMFEvaluateExpansionDirectionalDerivative (  IMFExpansion  E,
MFKVector  s,
MFKVector  ds,
MFNVector  du,
MFErrorHandler  e
) 
 

Evaluates an expansion.

Parameters:
E An expansion.
s A point in the domain of the expansion.
ds A direction in which to find the partial derivative.
du Provided by the user, a place to put the result.
e A place to return errors.

void IMFEvaluateExpansionSecondDerivative (  IMFExpansion  E,
MFKVector  s,
int  d0,
int  d1,
MFNVector  ddu,
MFErrorHandler  e
) 
 

Evaluates the second derivative of an expansion along coordinate directions.

Parameters:
E An expansion.
s A point in the domain of the expansion.
d0 A coordinate axis in which to find the partial derivative.
d1 A second coordinate axis in which to find the partial derivative.
ddu Provided by the user, a place to put the result.
e A place to return errors.

void IMFEvaluateExpansionSecondDirectionalDerivative (  IMFExpansion  E,
MFKVector  s,
MFKVector  ds0,
MFKVector  ds1,
MFNVector  ddu,
MFErrorHandler  e
) 
 

Evaluates an expansion.

Parameters:
E An expansion.
s A point in the domain of the expansion.
ds0 The first direction.
ds1 The second direction.
ddu Provided by the user, a place to put the result.
e A place to return errors.

void IMFEvaluateExpansionThirdDerivative (  IMFExpansion  E,
MFKVector  s,
int  d0,
int  d1,
int  d2,
MFNVector  dddu,
MFErrorHandler  e
) 
 

Evaluates the third derivative of an expansion along coordinate directions.

Parameters:
E An expansion.
s A point in the domain of the expansion.
d0 A coordinate axis in which to find the partial derivative.
d1 A second coordinate axis in which to find the partial derivative.
d2 A third coordinate axis in which to find the partial derivative.
dddu Provided by the user, a place to put the result.
e A place to return errors.

int IMFExpansionK (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Returns the dimension of the domain of an expansion.

Parameters:
E An expansion.
e A place to return errors.
Returns:
The dimension of the domain of the expansion.

int IMFExpansionN (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Returns the dimension of the range of an expansion.

Parameters:
E An expansion.
e A place to return errors.
Returns:
The dimension of the range of the expansion.

int IMFExpansionOrder (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Returns the order of an expansion (the degree of the highest non-zero term in the Taylor series).

Parameters:
E An expansion.
e A place to return errors.
Returns:
The order of the expansion.

double IMFExpansionR (  IMFExpansion  E,
double  epsilon,
MFErrorHandler  e
) 
 

Estimates a ball such that within the ball the second order terms are bounded in absolute value by epsilon.

Parameters:
E The expansion.
epsilon The required bound.
e A place to return errors.
Returns:
The radius of the ball.

MFNKMatrix IMFExpansionTS (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Returns a new MFNKMatrix with an orthonormal basis for the tangent space at the origin of the expansion.

Parameters:
E The expansion.
e A place to return errors.
Returns:
The basis in an MFNKMatrix.

void IMFFreeExpansion (  IMFExpansion  E,
MFErrorHandler  e
) 
 

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

Parameters:
E The expansion being unreferenced.
e A place to return errors.
See also:
ReferenceCounting MFRefExpansion()

IMFExpansion IMFInflateExpansionWithFlow (  IMFExpansion  E,
IMFFlow  f,
MFKVector  p,
MFErrorHandler  e
) 
 

Creates the product of an expansion with a trjectory of a flow.

Parameters:
E The starting expansion.
f The flow. (At the origin of the expansion should be transverse to the surface defined by the expansion).
p The flow's parameter values for the trajectory.
e A place to return errors.
Returns:
A new expansion.

void IMFPrintExpansion (  FILE *  fid,
IMFExpansion  E,
MFErrorHandler  e
) 
 

Prints a \"pretty\" version of the expansion.

Parameters:
fid The file.
E The expansion.
e A place to return errors.

IMFExpansion IMFReadExpansion (  FILE *  fid,
MFErrorHandler  e
) 
 

Reads an expansion from a file.

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

IMFExpansion IMFRectify (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Changes the metric of the expansion to the identity.

Parameters:
E The expansion.
e A place to return errors.
Returns:
A new expansion which has been rectified (the metric changed to the identity).

void IMFRefExpansion (  IMFExpansion  E,
MFErrorHandler  e
) 
 

Adds a reference to a expansion.

Parameters:
E The expansion being referenced.
e A place to return errors.
See also:
ReferenceCounting MFFreeExpansion()

void IMFWriteExpansion (  FILE *  fid,
IMFExpansion  E,
MFErrorHandler  e
) 
 

Writes an expansion to a file.

Parameters:
fid The file to write to.
E The expansion being queried.
e A place to return errors.

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