api/html/codac2__peibos_8h_source.html

#pragma once


#include "codac2_Parallelepiped.h"

#include "codac2_AnalyticFunction.h"

#include "codac2_OctaSym.h"

#include "codac2_inversion.h"

#include "codac2_OctaSym_operator.h"

#include "codac2_IntvFullPivLU.h"


namespace codac2

{

  double split (const IntervalVector& X, double eps, vector<IntervalVector>& boxes);


  double error(const IntervalVector& Y, const Vector& z, const IntervalMatrix& Jf, const Matrix& A, const IntervalVector& X);


  Matrix inflate_flat_parallelepiped (const Matrix& A, const Vector& e_vec, double rho);


  Parallelepiped parallelepiped_inclusion(const IntervalVector& Y, const IntervalMatrix& Jf, const Matrix& Jf_tild, const AnalyticFunction<VectorType>& psi_0, const OctaSym& sigma, const IntervalVector& X);


  vector<Parallelepiped> PEIBOS(const AnalyticFunction<VectorType>& f, const AnalyticFunction<VectorType>& psi_0, const vector<OctaSym>& Sigma, double epsilon, bool verbose = false);


  vector<Parallelepiped> PEIBOS(const AnalyticFunction<VectorType>& f, const AnalyticFunction<VectorType>& psi_0, const vector<OctaSym>& Sigma, double epsilon, const Vector& offset, bool verbose = false);

}

codac2::Parallelepiped
Class representing a parallelepiped .
Definition codac2_Parallelepiped.h:30

codac2_AnalyticFunction.h

codac2_IntvFullPivLU.h

codac2_OctaSym.h

codac2_OctaSym_operator.h

codac2_Parallelepiped.h

codac2_inversion.h

codac2
Definition codac2_OctaSym.h:21

codac2::Vector
Eigen::Matrix< double,-1, 1 > Vector
Alias for a dynamically-sized column vector of doubles.
Definition codac2_Vector.h:24

codac2::inflate_flat_parallelepiped
Matrix inflate_flat_parallelepiped(const Matrix &A, const Vector &e_vec, double rho)
Inflate the flat parallelepiped  by .

codac2::IntervalVector
Eigen::Matrix< Interval,-1, 1 > IntervalVector
Alias for a dynamic-size column vector of intervals.
Definition codac2_IntervalVector.h:25

codac2::PEIBOS
vector< Parallelepiped > PEIBOS(const AnalyticFunction< VectorType > &f, const AnalyticFunction< VectorType > &psi_0, const vector< OctaSym > &Sigma, double epsilon, bool verbose=false)
Compute a set of parallelepipeds enclosing  for each symmetry  in the set of symmetries ....

codac2::error
double error(const IntervalVector &Y, const Vector &z, const IntervalMatrix &Jf, const Matrix &A, const IntervalVector &X)
Compute the error term for the parallelepiped inclusion. The error is later used to inflate the flat ...

codac2::Matrix
Eigen::Matrix< double,-1,-1 > Matrix
Alias for a dynamic-size matrix of doubles.
Definition codac2_Matrix.h:26

codac2::parallelepiped_inclusion
Parallelepiped parallelepiped_inclusion(const IntervalVector &Y, const IntervalMatrix &Jf, const Matrix &Jf_tild, const AnalyticFunction< VectorType > &psi_0, const OctaSym &sigma, const IntervalVector &X)
Used in PEIBOS. Compute a parallelepiped enclosing of  where .

codac2::IntervalMatrix
Eigen::Matrix< Interval,-1,-1 > IntervalMatrix
Alias for a dynamic-size matrix of intervals.
Definition codac2_IntervalMatrix.h:25

codac2::split
double split(const IntervalVector &X, double eps, vector< IntervalVector > &boxes)
Recursively split a box until the maximum diameter of each box is less than eps. Note that the result...