eig.hpp

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// toolboxes/linalg/include/nk/linalg/eig.hpp
//
// Eigenvalue family — symmetric & general eig, Hessenberg reduction,
// symmetric Schur, characteristic polynomial, Sylvester equation.
// Migrated from toolboxes/builtin/src/language/arrays/matrix.cpp.
 
#pragma once
 
#include <memory_resource>
#include <tuple>
#include <nk/value/value.hpp>
 
namespace nk::linalg {

 

std::tuple<Value, Value>
eig_symmetric(const Value &A, std::pmr::memory_resource *mr = nullptr);

Value eig_values(const Value &A, std::pmr::memory_resource *mr = nullptr);

bool isSymmetricApprox(const Value &A, double tol);

Value poly_of_matrix(const Value &A, std::pmr::memory_resource *mr = nullptr);

Value eig_general_values(const Value &A, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value>
eig_general_VD(const Value &A, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value>
hess(const Value &A, std::pmr::memory_resource *mr = nullptr);

Value hess_H_only(const Value &A, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value>
schur_sym(const Value &A, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value>
schur_general(const Value &A, std::pmr::memory_resource *mr = nullptr);

Value sylvester_sym(const Value &A, const Value &B, const Value &C,
                    std::pmr::memory_resource *mr = nullptr);

Value polyeig_values(Span<const Value> coeffs, std::pmr::memory_resource *mr = nullptr);

std::tuple<Value, Value>
polyeig_VE(Span<const Value> coeffs, std::pmr::memory_resource *mr = nullptr);

Value ordeig(const Value &T, std::pmr::memory_resource *mr = nullptr);
 

} // namespace nk::linalg