numkit-doxy/properties_8hpp_source.html

// toolboxes/linalg/include/nk/linalg/properties.hpp

//

// Scalar properties of a matrix: determinant, trace, rank, condition

// number estimates. Plus the inverse `inv` (returned-matrix form;

// the operator-side `mldivide` (`\`) lives in toolboxes/builtin and uses

// the same underlying `la_solve` kernel).

//

// Migrated from toolboxes/builtin/src/language/arrays/{matrix,linalg_extras}.cpp.


#pragma once


#include <memory_resource>

#include <nk/value/value.hpp>


namespace nk::linalg {


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


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


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


Value rank_of(const Value &A, double tol = -1.0, std::pmr::memory_resource *mr = nullptr);


Value cond_2norm(const Value &A, std::pmr::memory_resource *mr = nullptr);


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


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


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


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


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


} // namespace nk::linalg

nk::Value
Core MATLAB-compatible multidimensional array and scalar value type.
Definition value.hpp:61

nk::linalg::rank_of
Value rank_of(const Value &A, double tol=-1.0, std::pmr::memory_resource *mr=nullptr)
Numerical rank (r = rank(A, tol)).

nk::linalg::condeig
Value condeig(const Value &A, std::pmr::memory_resource *mr=nullptr)
Eigenvalue condition numbers (c = condeig(A)).

nk::linalg::trace
Value trace(const Value &A, std::pmr::memory_resource *mr=nullptr)
Trace = sum of diagonal (t = trace(A)).

nk::linalg::condest
Value condest(const Value &A, std::pmr::memory_resource *mr=nullptr)
1-norm condition number estimate (c = condest(A)).

nk::linalg::det
Value det(const Value &A, std::pmr::memory_resource *mr=nullptr)
Determinant via LU with partial pivoting (d = det(A)).

nk::linalg::inv
Value inv(const Value &A, std::pmr::memory_resource *mr=nullptr)
Matrix inverse via LU (B = inv(A)).

nk::linalg::cond_pnorm
Value cond_pnorm(const Value &A, int p_kind, std::pmr::memory_resource *mr=nullptr)
General p-norm condition number (c = cond(A, p)).

nk::linalg::rcond
Value rcond(const Value &A, std::pmr::memory_resource *mr=nullptr)
Reciprocal 1-norm condition estimate (c = rcond(A)).

nk::linalg::cond_2norm
Value cond_2norm(const Value &A, std::pmr::memory_resource *mr=nullptr)
2-norm condition number (c = cond(A)).

nk::linalg::normest
Value normest(const Value &A, std::pmr::memory_resource *mr=nullptr)
2-norm estimate (n = normest(A)).