codac2_peibos.h File Reference

#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"

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Namespaces
namespace	codac2

Functions
double	codac2::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 resulting boxes are stored in place in the vector boxes.
double	codac2::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 parallelepiped \(\mathbf{z}+\mathbf{A}\cdot(\left[\mathbf{x}\right]-\bar{\mathbf{x}})\).
Matrix	codac2::inflate_flat_parallelepiped (const Matrix &A, const Vector &e_vec, double rho)
	Inflate the flat parallelepiped \(\mathbf{A}\cdot e_{vec}\) by \(\rho\).
Parallelepiped	codac2::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 \(\mathbf{g}([\mathbf{x}])\) where \(\mathbf{g} = \mathbf{f}\circ \sigma \circ \psi_0\).
vector< Parallelepiped >	codac2::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 \(\mathbf{f}(\sigma(\psi_0([-1,1]^m)))\) for each symmetry \(\sigma\) in the set of symmetries \(\Sigma\). Note that \(\left\{\psi_0,\Sigma\right\}\) form a gnomonic atlas.
vector< Parallelepiped >	codac2::PEIBOS (const AnalyticFunction< VectorType > &f, const AnalyticFunction< VectorType > &psi_0, const vector< OctaSym > &Sigma, double epsilon, const Vector &offset, bool verbose=false)
	Compute a set of parallelepipeds enclosing \(\mathbf{f}(\sigma(\psi_0([-1,1]^m)) + offset) \) for each symmetry \(\sigma\) in the set of symmetries \(\Sigma\). Note that \(\left\{\psi_0,\Sigma\right\}\) form a gnomonic atlas.

Detailed Description

Date

2025

Author

Maël Godard

Copyright

Copyright 2024 Codac Team

License: GNU Lesser General Public License (LGPL)