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/* mmmatrix.hpp
* Part of Mathematical library built (ab)using Modern C++ 17 abstractions.
*
* This library is not intended to be _performant_, it does not contain
* hand written SMID / SSE / AVX optimizations. It is instead an example
* of highly inefficient (but abstract!) code, where matrices can contain any
* data type.
*
* Naoki Pross <naopross@thearcway.org>
* 2018 ~ 2019
*/
#pragma once
#include <iostream>
#include <cstring>
namespace mm {
template<typename T, std::size_t Rows, std::size_t Cols>
class basic_matrix;
template<typename T, std::size_t Rows, std::size_t Cols>
class matrix;
template<typename T, std::size_t N>
class square_matrix;
// template<typename T, std::size_t N>
// class diag_matrix;
template<typename T, std::size_t Rows>
class row_vec;
template<typename T, std::size_t Cols>
class col_vec;
}
template<typename T, std::size_t Rows, std::size_t Cols>
class mm::basic_matrix {
public:
using type = T;
static constexpr std::size_t rows = Rows;
static constexpr std::size_t cols = Cols;
basic_matrix(const basic_matrix<T, Rows, Cols>& other);
basic_matrix(basic_matrix<T, Rows, Cols>&& other);
template<std::size_t ORows, std::size_t OCols>
basic_matrix(const basic_matrix<T, ORows, OCols>& other);
basic_matrix(const T (& values)[Rows][Cols]);
basic_matrix(T (&& values)[Rows][Cols]);
// access data
T& at(std::size_t row, std::size_t col);
auto&& operator[](std::size_t index);
void swap_rows(std::size_t x, std::size_t y);
void swap_cols(std::size_t x, std::size_t y);
// mathematical operations
basic_matrix<T, Cols, Rows> transposed();
inline basic_matrix<T, Cols, Rows> trd() { return transposed(); }
// bool is_invertible();
// bool invert();
// basic_matrix<T, Rows, Cols> inverse();
/// downcast to square matrix
inline constexpr bool is_square() { return (Rows == Cols); }
inline constexpr square_matrix<T, Rows> to_square() {
static_assert(is_square());
return static_cast<square_matrix<T, Rows>>(*this);
}
/// downcast to row_vector
inline constexpr bool is_row_vec() { return (Cols == 1); }
inline constexpr row_vec<T, Rows> to_row_vec() {
static_assert(is_row_vec());
return static_cast<row_vec<T, Rows>>(*this);
}
/// downcast to col_vector
inline constexpr bool is_col_vec() { return (Rows == 1); }
inline constexpr col_vec<T, Cols> to_col_vec() {
static_assert(is_col_vec());
return static_cast<col_vec<T, Cols>>(*this);
}
private:
T data[Rows][Cols] = {};
};
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols>::basic_matrix(const mm::basic_matrix<T, Rows, Cols>& other) {
for (int row = 0; row < Rows; row++)
for (int col = 0; col < Cols; col++)
data[row][col] = other.data[row][col];
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols>::basic_matrix(mm::basic_matrix<T, Rows, Cols>&& other) {
data = other.data;
}
template<typename T, std::size_t Rows, std::size_t Cols>
template<std::size_t ORows, std::size_t OCols>
mm::basic_matrix<T, Rows, Cols>::basic_matrix(const mm::basic_matrix<T, ORows, OCols>& other) {
static_assert((ORows <= Rows),
"cannot copy a taller matrix into a smaller one"
);
static_assert((OCols <= Cols),
"cannot copy a larger matrix into a smaller one"
);
for (int row = 0; row < Rows; row++)
for (int col = 0; col < Cols; col++)
data[row][col] = other.data[row][col];
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols>::basic_matrix(const T (& values)[Rows][Cols]) {
std::memcpy(&data, &values, sizeof(data));
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols>::basic_matrix(T (&& values)[Rows][Cols]) {
data = values;
}
/* member functions */
template<typename T, std::size_t Rows, std::size_t Cols>
T& mm::basic_matrix<T, Rows, Cols>::at(std::size_t row, std::size_t col) {
static_assert(row < Rows, "out of row bound");
static_assert(col < Cols, "out of column bound");
return data[row][col];
}
template<typename T, std::size_t Rows, std::size_t Cols>
auto&& mm::basic_matrix<T, Rows, Cols>::operator[](std::size_t index) {
if constexpr (is_row_vec())
return data[0][index];
else if constexpr (is_col_vec())
return data[index][0];
return row_vec<T, Rows>(std::move(data[index]));
}
template<typename T, std::size_t Rows, std::size_t Cols>
void mm::basic_matrix<T, Rows, Cols>::swap_rows(std::size_t x, std::size_t y) {
if (x == y)
return;
for (int col = 0; col < Cols; col++)
std::swap(data[x][col], data[y][col]);
}
template<typename T, std::size_t Rows, std::size_t Cols>
void mm::basic_matrix<T, Rows, Cols>::swap_cols(std::size_t x, std::size_t y) {
if (x == y)
return;
for (int row = 0; row < rows; row++)
std::swap(data[row][x], data[row][y]);
}
template<typename T, std::size_t M, std::size_t N>
mm::basic_matrix<T, N, M> mm::basic_matrix<T, M, N>::transposed() {
mm::basic_matrix<T, N, M> result;
for (int row = 0; row < M; row++)
for (int col = 0; col < N; col++)
result[row][col] = this[col][row];
return result;
}
/* operator overloading */
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols> operator+(
const mm::basic_matrix<T, Rows, Cols>& a,
const mm::basic_matrix<T, Rows, Cols>& b
) {
mm::basic_matrix<T, Rows, Cols> result;
for (int row = 0; row < Rows; row++)
for (int col = 0; col < Cols; col++)
result.at(row, col) = a.at(row, col) + a.at(row, col);
return result;
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols> operator*(
const mm::basic_matrix<T, Rows, Cols>& m,
const T& scalar
) {
mm::basic_matrix<T, Rows, Cols> result;
for (int row = 0; row < Rows; row++)
for (int col = 0; col < Cols; col++)
result.at(row, col) = m.at(row, col) * scalar;
return result;
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols> operator*(
const T& scalar,
const mm::basic_matrix<T, Rows, Cols>& m
) {
return m * scalar;
}
template<typename T, std::size_t M, std::size_t P, std::size_t N>
mm::basic_matrix<T, M, N> operator*(
const mm::basic_matrix<T, M, P>& a,
const mm::basic_matrix<T, P, N>& b
) {
mm::basic_matrix<T, M, N> result;
// TODO: use a more efficient algorithm
for (int row = 0; row < M; row++)
for (int col = 0; col < N; col++)
for (int k = 0; k < P; k++)
result.at(row, col) = a.at(row, k) * b.at(k, col);
return result;
}
template<typename T, std::size_t Rows, std::size_t Cols>
mm::basic_matrix<T, Rows, Cols> operator-(
const mm::basic_matrix<T, Rows, Cols>& a,
const mm::basic_matrix<T, Rows, Cols>& b
) {
return a + static_cast<T>(-1) * b;
}
template<typename T, std::size_t Rows, std::size_t Cols>
std::ostream& operator<<(std::ostream& os, const mm::basic_matrix<T, Rows, Cols>& m) {
for (int row = 0; row < Rows; row++) {
os << "[ ";
for (int col = 0; col < (Cols -1); col++) {
os << m.at(row, col);
}
os << m.at(Rows -1, Cols -1) << " ]\n";
}
return os;
}
/* square matrix specializaiton */
template<typename T, std::size_t N>
class mm::square_matrix : public mm::basic_matrix<T, N, N> {
public:
/// in place transpose
void transpose();
inline void tr() { transpose(); }
/// in place inverse
void invert();
};
template<typename T, std::size_t N>
void mm::square_matrix<T, N>::transpose() {
for (int row = 0; row < N; row++)
for (int col = 0; col < row; col++)
std::swap(this->at(row, col), this->at(col, row));
}
/* row vector specialization */
template<typename T, std::size_t Rows>
class mm::row_vec : public mm::basic_matrix<T, Rows, 1> {
public:
};
/* column vector specialization */
template<typename T, std::size_t Cols>
class mm::col_vec : public mm::basic_matrix<T, 1, Cols> {
public:
};
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