Matrix

Matrix operations (relating to the class cotila::matrix) More...

Functions
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	cotila::conj (const matrix< T, M, N > &m)
	computes the elementwise complex conjugate More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< detail::remove_complex_t< T >, M, N >	cotila::real (const matrix< T, M, N > &m)
	computes the elementwise real More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< detail::remove_complex_t< T >, M, N >	cotila::imag (const matrix< T, M, N > &m)
	computes the elementwise imag More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, N, M >	cotila::transpose (const matrix< T, M, N > &m)
	computes the transpose More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, N, M >	cotila::hermitian (const matrix< T, M, N > &m)
	computes the Hermitian transpose More...
template<typename T , std::size_t M, std::size_t N, std::size_t P>
constexpr matrix< T, M, P >	cotila::matmul (const matrix< T, M, N > &a, const matrix< T, N, P > &b)
	computes the matrix product More...
template<typename T , std::size_t M, std::size_t N, std::size_t P, std::size_t Q>
constexpr matrix< T, M *P, N *Q >	cotila::kron (const matrix< T, M, N > &a, const matrix< T, P, Q > &b)
	Computes the kronecker tensor product. More...
template<typename T , std::size_t M, std::size_t N>
constexpr T	cotila::macs (const matrix< T, M, N > &m)
	Computes the maximum absolute column sum norm. More...
template<typename T , std::size_t M, std::size_t N>
constexpr T	cotila::mars (const matrix< T, M, N > &m)
	Computes the maximum absolute row sum norm. More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	cotila::rref (const matrix< T, M, N > &m)
	Compute the reduced row echelon form. More...
template<typename T , std::size_t M, std::size_t N>
constexpr matrix< T, M, N >	cotila::rref (const matrix< T, M, N > &m, T tolerance)
	Compute the reduced row echelon form. More...
template<typename T , std::size_t M, std::size_t N>
constexpr std::size_t	cotila::rank (const matrix< T, M, N > &m)
	Compute the rank. More...
template<typename T , std::size_t M>
constexpr T	cotila::det (const matrix< T, M, M > &m)
	Compute the determinant. More...
template<typename T , std::size_t M>
constexpr matrix< T, M, M >	cotila::inverse (const matrix< T, M, M > &m)
	computes the matrix inverse More...
template<typename T , std::size_t M>
constexpr T	cotila::trace (const matrix< T, M, M > &m)
	computes the trace More...
template<typename T , std::size_t N, std::size_t M>
constexpr bool	cotila::operator== (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	checks equality of two matrices More...
template<typename T , std::size_t N, std::size_t M>
constexpr bool	cotila::operator!= (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	checks inequality of two matrices More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator+ (const matrix< T, N, M > &m, T a)
	computes the sum of a matrix and a scalar More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator+ (T a, const matrix< T, N, M > &m)
	computes the sum of a matrix and a scalar More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator+ (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the matrix sum More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator* (const matrix< T, N, M > &m, T a)
	computes the product of a matrix and a scalar More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator* (T a, const matrix< T, N, M > &m)
	computes the product of a matrix and a scalar More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator* (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the Hadamard product More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator/ (T a, const matrix< T, N, M > &m)
	computes the quotient between a matrix and a scalar More...
template<typename T , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::operator/ (const matrix< T, N, M > &a, const matrix< T, N, M > &b)
	computes the elementwise matrix quotient More...
template<typename F , typename T , typename... Matrices, typename U = std::invoke_result_t<F, T, typename Matrices::value_type...>, std::size_t N = detail::all_same_value<std::size_t, Matrices::column_size...>::value, std::size_t M = detail::all_same_value<std::size_t, Matrices::row_size...>::value>
constexpr matrix< U, N, M >	cotila::elementwise (F f, const matrix< T, N, M > &m, const Matrices &... matrices)
	applies a function elementwise between many matrices More...
template<typename T , typename U , std::size_t N, std::size_t M>
constexpr matrix< T, N, M >	cotila::cast (const matrix< U, N, M > &m)
	casts a vector to another type More...
template<std::size_t N, std::size_t M, typename F >
decltype(auto) constexpr	cotila::generate (F &&f)
	generates a matrix as a function of its indices More...
template<std::size_t N, std::size_t M, typename T >
constexpr matrix< T, N, M >	cotila::fill (T value)
	generates a matrix containing a single value More...
template<std::size_t Row, std::size_t Col, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M *Row, N *Col >	cotila::repmat (const matrix< T, M, N > &m)
	repeats a matrix More...
template<std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M, N >	cotila::swaprow (matrix< T, M, N > m, std::size_t a, std::size_t b)
	swaps rows of a matrix More...
template<std::size_t M, std::size_t N, typename T >
constexpr matrix< T, M, N >	cotila::swapcol (matrix< T, M, N > m, std::size_t a, std::size_t b)
	swaps columns of a matrix More...
template<std::size_t M, std::size_t N, std::size_t P, typename T >
constexpr matrix< T, M, N+P >	cotila::horzcat (const matrix< T, M, N > &a, const matrix< T, M, P > &b)
	horizontally concatenates two matrices More...
template<std::size_t M, std::size_t N, std::size_t P, typename T >
constexpr matrix< T, M+N, P >	cotila::vertcat (const matrix< T, M, P > &a, const matrix< T, N, P > &b)
	vertically concatenates two matrices More...
template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, P, Q >	cotila::submat (const matrix< T, M, N > &m, std::size_t a, std::size_t b)
	extracts the submatrix of a matrix More...
template<std::size_t P, std::size_t Q, std::size_t M, std::size_t N, typename T >
constexpr matrix< T, P, Q >	cotila::reshape (const matrix< T, M, N > &m)
	reshapes a matrix More...
template<typename T , std::size_t N>
constexpr matrix< T, N, 1 >	cotila::as_column (const vector< T, N > &v)
	converts a vector into a column vector More...
template<typename T , std::size_t N>
constexpr matrix< T, 1, N >	cotila::as_row (const vector< T, N > &v)
	converts a vector into a row vector More...

Variables
template<typename T , std::size_t N>
constexpr matrix< T, N, N >	cotila::identity = generate<N, N>([](std::size_t i, std::size_t j) { return T(i == j ? 1 : 0); })
	the matrix identity More...

cotila::matrix deduction guides
template<typename T , std::size_t M, std::size_t N>
	cotila::matrix (const T(&)[M][N]) -> matrix< T, M, N >
	deduction guide for aggregate initialization More...
template<typename T , std::size_t M, std::size_t N>
	cotila::matrix (const T(&)[M][N][2]) -> matrix< std::complex< T >, M, N >
	deduction guide for complex-valued aggregate initialization More...
template<typename T , std::size_t M, std::size_t N>
	matrix (const T(&)[M][N]) -> matrix< T, M, N >
	deduction guide for aggregate initialization More...
template<typename T , std::size_t M, std::size_t N>
	matrix (const T(&)[M][N][2]) -> matrix< std::complex< T >, M, N >
	deduction guide for complex-valued aggregate initialization More...

Detailed Description