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/*
* Copyright (c) 2020, the SerenityOS developers.
*
* SPDX-License-Identifier: BSD-2-Clause
*/
#pragma once
#include <AK/Types.h>
#include <initializer_list>
namespace Gfx {
template<size_t N, typename T>
class Matrix {
template<size_t U, typename V>
friend class Matrix;
public:
static constexpr size_t Size = N;
constexpr Matrix() = default;
constexpr Matrix(std::initializer_list<T> elements)
{
VERIFY(elements.size() == N * N);
size_t i = 0;
for (auto& element : elements) {
m_elements[i / N][i % N] = element;
++i;
}
}
template<typename... Args>
constexpr Matrix(Args... args)
: Matrix({ (T)args... })
{
}
Matrix(Matrix const& other)
{
__builtin_memcpy(m_elements, other.elements(), sizeof(T) * N * N);
}
Matrix& operator=(Matrix const& other)
{
__builtin_memcpy(m_elements, other.elements(), sizeof(T) * N * N);
return *this;
}
constexpr auto elements() const { return m_elements; }
constexpr auto elements() { return m_elements; }
constexpr Matrix operator*(Matrix const& other) const
{
Matrix product;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j) {
auto& element = product.m_elements[i][j];
if constexpr (N == 4) {
element = m_elements[i][0] * other.m_elements[0][j]
+ m_elements[i][1] * other.m_elements[1][j]
+ m_elements[i][2] * other.m_elements[2][j]
+ m_elements[i][3] * other.m_elements[3][j];
} else if constexpr (N == 3) {
element = m_elements[i][0] * other.m_elements[0][j]
+ m_elements[i][1] * other.m_elements[1][j]
+ m_elements[i][2] * other.m_elements[2][j];
} else if constexpr (N == 2) {
element = m_elements[i][0] * other.m_elements[0][j]
+ m_elements[i][1] * other.m_elements[1][j];
} else if constexpr (N == 1) {
element = m_elements[i][0] * other.m_elements[0][j];
} else {
T value {};
for (size_t k = 0; k < N; ++k)
value += m_elements[i][k] * other.m_elements[k][j];
element = value;
}
}
}
return product;
}
constexpr Matrix operator/(T divisor) const
{
Matrix division;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j)
division.m_elements[i][j] = m_elements[i][j] / divisor;
}
return division;
}
[[nodiscard]] constexpr Matrix adjugate() const
{
if constexpr (N == 1)
return Matrix(1);
Matrix adjugate;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j) {
int sign = (i + j) % 2 == 0 ? 1 : -1;
adjugate.m_elements[j][i] = sign * first_minor(i, j);
}
}
return adjugate;
}
[[nodiscard]] constexpr T determinant() const
{
if constexpr (N == 1) {
return m_elements[0][0];
} else {
T result = {};
int sign = 1;
for (size_t j = 0; j < N; ++j) {
result += sign * m_elements[0][j] * first_minor(0, j);
sign *= -1;
}
return result;
}
}
[[nodiscard]] constexpr T first_minor(size_t skip_row, size_t skip_column) const
{
static_assert(N > 1);
VERIFY(skip_row < N);
VERIFY(skip_column < N);
Matrix<N - 1, T> first_minor;
constexpr auto new_size = N - 1;
size_t k = 0;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j) {
if (i == skip_row || j == skip_column)
continue;
first_minor.elements()[k / new_size][k % new_size] = m_elements[i][j];
++k;
}
}
return first_minor.determinant();
}
[[nodiscard]] constexpr static Matrix identity()
{
Matrix result;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j) {
if (i == j)
result.m_elements[i][j] = 1;
else
result.m_elements[i][j] = 0;
}
}
return result;
}
[[nodiscard]] constexpr Matrix inverse() const
{
return adjugate() / determinant();
}
[[nodiscard]] constexpr Matrix transpose() const
{
Matrix result;
for (size_t i = 0; i < N; ++i) {
for (size_t j = 0; j < N; ++j)
result.m_elements[i][j] = m_elements[j][i];
}
return result;
}
template<size_t U>
[[nodiscard]] constexpr Matrix<U, T> submatrix_from_topleft() const requires(U > 0 && U < N)
{
Matrix<U, T> result;
for (size_t i = 0; i < U; ++i) {
for (size_t j = 0; j < U; ++j)
result.m_elements[i][j] = m_elements[i][j];
}
return result;
}
private:
T m_elements[N][N];
};
}
using Gfx::Matrix;
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