Geometric_certificates.h

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#ifndef GEOMETRIC_CERTIFICATES_H
#define GEOMETRIC_CERTIFICATES_H
 
#include "../../Constants.h"
 
#include <complex>
#include <vector>
 
struct DwShellPoint {
    double re = 0.0;     
    double im = 0.0;     
    double gain2 = 0.0;  
};
 
struct NumericalRangeCertificate {
    std::vector<std::complex<double>> boundary; 
    double min_real = 0.0;       
    double max_phase_deg = 0.0;  
    double zero_margin = 0.0;    
    bool contains_zero = false;
    bool pass_phase = false;     
    bool pass_zero_outside = false;
};
 
struct DwShellCertificate {
    std::vector<DwShellPoint> samples;
    NumericalRangeCertificate nr;
    double max_singular = 0.0;   
    double excess_passivity = 0.0;
    double shortage_passivity = 0.0;
    double xz_min_re = 0.0;      
    double xz_max_gain2 = 0.0;   
    bool pass_small_gain = false;
    bool pass_excess = false;
};
 
double excessPassivity(const Eigen::MatrixXcd& A);
double shortagePassivity(const Eigen::MatrixXcd& A);
 
double spectralNorm(const Eigen::MatrixXcd& A);
 
std::vector<std::complex<double>> numericalRangeBoundary(
    const Eigen::MatrixXcd& A,
    int n_theta = 180);
 
NumericalRangeCertificate certifyNumericalRange(
    const Eigen::MatrixXcd& A,
    double phase_limit_deg = 90.0,
    int n_theta = 180);
 
DwShellCertificate certifyDwShell(
    const Eigen::MatrixXcd& A,
    double phase_limit_deg = 90.0,
    double gain_limit = 1.0,
    double excess_eps = 0.0,
    int n_theta = 180,
    int n_sphere = 24);
 
Eigen::MatrixXcd loopShiftedSector(
    const Eigen::MatrixXcd& A,
    double alpha,
    double beta);
 
bool certifySector(
    const Eigen::MatrixXcd& A,
    double alpha,
    double beta,
    double eps = 0.0);
 
#endif // GEOMETRIC_CERTIFICATES_H