crow

Utility library

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Matrix

Crow Library by Ross Smith

#include "crow/matrix.hpp"
namespace Crow;

Matrix class

enum class MatrixLayout {
    row,
    column,
}

Flags indicating the internal layout of a matrix (row major or column major). Column major is the default.

template <ArithmeticType T, int N, MatrixLayout L = MatrixLayout::column>
    class Matrix;

An NxN square matrix type.

using Float2x2 = Matrix<float, 2>;
using Float3x3 = Matrix<float, 3>;
using Float4x4 = Matrix<float, 4>;
using Float2x2c = Matrix<float, 2, MatrixLayout::column>;
using Float3x3c = Matrix<float, 3, MatrixLayout::column>;
using Float4x4c = Matrix<float, 4, MatrixLayout::column>;
using Float2x2r = Matrix<float, 2, MatrixLayout::row>;
using Float3x3r = Matrix<float, 3, MatrixLayout::row>;
using Float4x4r = Matrix<float, 4, MatrixLayout::row>;
using Double2x2 = Matrix<double, 2>;
using Double3x3 = Matrix<double, 3>;
using Double4x4 = Matrix<double, 4>;
using Double2x2c = Matrix<double, 2, MatrixLayout::column>;
using Double3x3c = Matrix<double, 3, MatrixLayout::column>;
using Double4x4c = Matrix<double, 4, MatrixLayout::column>;
using Double2x2r = Matrix<double, 2, MatrixLayout::row>;
using Double3x3r = Matrix<double, 3, MatrixLayout::row>;
using Double4x4r = Matrix<double, 4, MatrixLayout::row>;
using Ldouble2x2 = Matrix<long double, 2>;
using Ldouble3x3 = Matrix<long double, 3>;
using Ldouble4x4 = Matrix<long double, 4>;
using Ldouble2x2c = Matrix<long double, 2, MatrixLayout::column>;
using Ldouble3x3c = Matrix<long double, 3, MatrixLayout::column>;
using Ldouble4x4c = Matrix<long double, 4, MatrixLayout::column>;
using Ldouble2x2r = Matrix<long double, 2, MatrixLayout::row>;
using Ldouble3x3r = Matrix<long double, 3, MatrixLayout::row>;
using Ldouble4x4r = Matrix<long double, 4, MatrixLayout::row>;

Predefined type aliases.

using Matrix::value_type = T;
using Matrix::vector_type = Vector<T, N>;
using Matrix::alt_matrix = Matrix<T, N, ...>;

Member types. The alt_matrix type is a matrix of the same size and element type, but with the opposite layout.

static constexpr int Matrix::dim = N;
static constexpr int Matrix::cells = N * N;
static constexpr MatrixLayout Matrix::layout = L;

Member constants.

constexpr Matrix::Matrix() noexcept;

The default constructor leaves the elements uninitialized.

constexpr explicit Matrix::Matrix(T x) noexcept;

Sets all elements to the same value.

constexpr Matrix::Matrix(T lead, T other) noexcept;

Sets the leading diagonal to one value, and all other elements to another.

constexpr Matrix::Matrix(const alt_matrix& m) noexcept;

Copies a matrix with the opposite layout.

template <typename... Args> constexpr Matrix::Matrix(Args... args) noexcept;

This constructor takes an explicit list of elements, which are copied in the order of the matrix’s internal layout (column by column or row by row); this is defined only for the appropriate number of arguments.

constexpr Matrix::Matrix(const Matrix& m) noexcept;
constexpr Matrix::Matrix(Matrix&& m) noexcept;
constexpr Matrix::~Matrix() noexcept;
constexpr Matrix& Matrix::operator=(const Matrix& m) noexcept;
constexpr Matrix& Matrix::operator=(Matrix&& m) noexcept;

Other life cycle functions.

constexpr T& Matrix::operator()(int r, int c) noexcept;
constexpr const T& Matrix::operator()(int r, int c) const noexcept;

Element access functions. Behaviour is undefined if a row or column index is negative or greater than or equal to N.

constexpr T* Matrix::begin() noexcept;
constexpr const T* Matrix::begin() const noexcept;
constexpr T* Matrix::end() noexcept;
constexpr const T* Matrix::end() const noexcept;

These return pointers to the beginning and past the end of the matrix’s internal data, in the order implied by the layout parameter.

constexpr vector_type Matrix::column(int c) const noexcept;
constexpr vector_type Matrix::row(int r) const noexcept;
constexpr void Matrix::set_column(int c, vector_type v) noexcept;
constexpr void Matrix::set_row(int r, vector_type v) noexcept;

Query or set a complete row or column as a vector. Behaviour is undefined if a row or column index is out of range.

constexpr T Matrix::det() const noexcept;

Returns the determinant of the matrix. (Currently this is only implemented for N<=4).

constexpr bool Matrix::empty() noexcept;

Always false.

size_t Matrix::hash() const noexcept;
struct std::hash<Matrix>;

Hash functions.

constexpr Matrix Matrix::inverse() const noexcept;

Returns the inverse of the matrix. Behaviour is undefined if det()=0. (Currently this is only implemented for N<=4).

constexpr size_t Matrix::size() const noexcept;

Returns N.

constexpr Matrix Matrix::swap_columns(int c1, int c2) const noexcept;
constexpr Matrix Matrix::swap_rows(int r1, int r2) const noexcept;

Swap two rows or columns. Behaviour is undefined if a row or column index is out of range.

std::string Matrix::str(const FormatSpec& spec = {}) const;
std::ostream& operator<<(std::ostream& out, const Matrix& m);

The str() function formats a matrux as a string, broken down by rows, in the form "[[a,b,c],[d,e,f],[g,h,i]]". The format spec is interpreted in the usual way for T. The output operator calls m.str().

constexpr Matrix Matrix::transposed() const noexcept;

Returns the transpose of the matrix.

constexpr Matrix Matrix::operator+() const noexcept;
constexpr Matrix Matrix::operator-() const noexcept;
constexpr Matrix& Matrix::operator+=(const Matrix& m) noexcept;
constexpr Matrix& Matrix::operator-=(const Matrix& m) noexcept;
constexpr Matrix& Matrix::operator*=(const Matrix& m) noexcept;
constexpr Matrix operator+(const Matrix& a, const Matrix& b) noexcept;
constexpr Matrix operator-(const Matrix& a, const Matrix& b) noexcept;
constexpr Matrix operator*(const Matrix& a, const Matrix& b) noexcept;

Matrix arithmetic operators.

constexpr vector_type
    operator*(const Matrix& a, const vector_type& b) noexcept;
constexpr vector_type
    operator*(const vector_type& a, const Matrix& b) noexcept;

Matrix-vector arithmetic operators.

constexpr Matrix& Matrix::operator*=(T x) noexcept;
constexpr Matrix& Matrix::operator/=(T x) noexcept;
constexpr Matrix operator*(const Matrix& a, T b) noexcept;
constexpr Matrix operator*(T a, const Matrix& b) noexcept;
constexpr Matrix operator/(const Matrix& a, T b) noexcept;

Matrix-scalar arithmetic operators.

constexpr bool operator==(const Matrix& a, const Matrix& b) noexcept;
constexpr bool operator!=(const Matrix& a, const Matrix& b) noexcept;

Comparison operators.

constexpr static Matrix identity() noexcept;

Returns the identity matrix (equivalent to Matrix(1,0)).

constexpr static Matrix null() noexcept;

Returns the zero matrix (equivalent to Matrix(0)).