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Class CH.epfl.lcvm.mccc.CollocationDiscretization 

java.lang.Object
   |
   +----CH.epfl.lcvm.mccc.OneDDiscretization
           |
           +----CH.epfl.lcvm.mccc.CollocationDiscretization
public class CollocationDiscretization
extends OneDDiscretization
A collocation 1D discretization. Based on the paper Numerical Analysis and Control of Bifurcation Problems (II) Bifurcation in Infinite Dimensions by E. Doedel.

Variable Index

o domain_
Domain of this class as a Function.
o legendreRoots_
An array which contains the roots of the legendre polynomials.
o range_
Range of this class as a Function.

Constructor Index

o CollocationDiscretization(ODEFunctionWithBC, OneDMesh, int)
A discretization creation function which takes a mesh and a function creates a Collocation discretization discretization.

Method Index

o call(Matrix)
Returns the value of the discretized function over the given mesh
o generateGuess(Matrix, Matrix)
A convience function for generating a solution to the problem given intial conditions.
o getDomain()
Returns the dimension of the domain of the discretized function
o getRange()
Returns the dimension of the range of the discretized function
o main(String[])
Exercise the class by trying the various functions.

Variables

o legendreRoots_ 
 protected static double legendreRoots_[][]
An array which contains the roots of the legendre polynomials. Used as the values at which to evaluate the polynomial approximation.

See Also:
call
o domain_ 
 protected int domain_
Domain of this class as a Function. Equals ((ncol_*ntst_)+1)*ndim+npar where ndim is the dimension of the input system and npar is the number of parameters in the input system.

See Also:
Function
o range_ 
 protected int range_
Range of this class as a Function. Equals ((ncol_*ntst_))*ndim+nbc where ndim is the dimension of the input system and nbc is the number boundary conditions.

See Also:
Function

Constructors

o CollocationDiscretization 
 public CollocationDiscretization(ODEFunctionWithBC func,
                                  OneDMesh mesh,
                                  int ncol)
A discretization creation function which takes a mesh and a function creates a Collocation discretization discretization. The assumes that the problem is of the form x' = func(x) and that the system is square.

Parameters:
func - The function to discretize
mesh - The 1D mesh over which to discretize it
ncol - The number of collocation points in each interval.

Methods

o call 
 public Matrix call(Matrix input)
Returns the value of the discretized function over the given mesh

Parameters:
value - the point at which to call the function. It assumes that the input has rows in the following order par1,...,parM, x0(mesh[0]), x1(mesh[0]), ...xn(mesh[0]),x0(mesh[1])...
Returns:
the return value of the function.
Overrides:
call in class OneDDiscretization
o getRange 
 public int getRange()
Returns the dimension of the range of the discretized function

Returns:
the dimension of the range of the function.
Overrides:
getRange in class OneDDiscretization
o getDomain 
 public int getDomain()
Returns the dimension of the domain of the discretized function

Returns:
the dimension of the domain of the function.
Overrides:
getDomain in class OneDDiscretization
o generateGuess 
 public Matrix generateGuess(Matrix initialValues,
                             Matrix parameterValues) throws MCCCException
A convience function for generating a solution to the problem given intial conditions.

Parameters:
initialValues - Initial values for the IVP solver
parameterValues - Parameter values for the IVP solver
Returns:
A solution to the problem
Throws: MCCCException
In case the method doesn't converge it throws this exception
o main 
 public static void main(String argv[]) throws MCCCException
Exercise the class by trying the various functions.

Throws: MCCCException
In case something fails in the test harness it throws this exception. 
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