NumericalRangeCertificate Struct Reference

Numerical-range / small-phase summary for one matrix. More...

#include <Geometric_certificates.h>

Collaboration diagram for NumericalRangeCertificate:

Public Attributes
std::vector< std::complex< double > >	boundary
	Support-function samples of ∂W(A)
double	min_real = 0.0
	min Re W(A) = λ_min(Her A)
double	max_phase_deg = 0.0
	max |arg z| over ∂W (180 if 0 ∈ W)
double	zero_margin = 0.0
	>0 ⇒ 0 ∉ W; ≤0 ⇒ 0 ∈ W (approx.)
bool	contains_zero = false
bool	pass_phase = false
	max_phase ≤ limit (and preferably 0 ∉ W)
bool	pass_zero_outside = false

Detailed Description

Numerical-range / small-phase summary for one matrix.

Member Data Documentation

boundary

std::vector<std::complex<double> > NumericalRangeCertificate::boundary

Support-function samples of ∂W(A)

Referenced by certifyNumericalRange(), plot_certificate_dw_slice(), and plot_certificate_numerical_range().

contains_zero

bool NumericalRangeCertificate::contains_zero = false

Referenced by certifyNumericalRange(), and plot_certificate_dw_slice().

max_phase_deg

double NumericalRangeCertificate::max_phase_deg = 0.0

max |arg z| over ∂W (180 if 0 ∈ W)

Referenced by certifyNumericalRange(), plot_certificate_dw_shell(), plot_certificate_dw_slice(), and plot_certificate_numerical_range().

min_real

double NumericalRangeCertificate::min_real = 0.0

min Re W(A) = λ_min(Her A)

Referenced by certifyDwShell(), certifyNumericalRange(), and plot_certificate_dw_slice().

pass_phase

bool NumericalRangeCertificate::pass_phase = false

max_phase ≤ limit (and preferably 0 ∉ W)

Referenced by certifyNumericalRange(), plot_certificate_dw_shell(), and plot_certificate_numerical_range().

pass_zero_outside

bool NumericalRangeCertificate::pass_zero_outside = false

Referenced by certifyNumericalRange().

zero_margin

double NumericalRangeCertificate::zero_margin = 0.0

>0 ⇒ 0 ∉ W; ≤0 ⇒ 0 ∈ W (approx.)

Referenced by certifyNumericalRange(), plot_certificate_dw_slice(), and plot_certificate_numerical_range().

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The documentation for this struct was generated from the following file:

• harmony/src/Solver/Certificate/Geometric_certificates.h