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#pragma once
#include <array>
#include <cstring>
#include <initializer_list>
template <typename T, int N>
struct FixedSizeUpperMatrixT : std::array<std::array<T, N>, N> {
using Row = std::array<T, N>;
using std::array<Row, N>::array;
explicit FixedSizeUpperMatrixT(std::initializer_list<Row> rows)
: std::array<Row, N>{
reinterpret_cast<const std::array<Row, N> &>(*rows.begin())} {}
static FixedSizeUpperMatrixT mul_id() {
FixedSizeUpperMatrixT e;
for (int i = 0; i < N; ++i) {
e[i][i] = T::mul_id();
}
return e;
}
FixedSizeUpperMatrixT &operator+=(const FixedSizeUpperMatrixT &o) {
for (int i = 0; i < N; ++i) {
for (int j = i; j < N; ++j) {
(*this)[i][j] += o[i][j];
}
}
return *this;
}
FixedSizeUpperMatrixT operator+(const FixedSizeUpperMatrixT &o) const {
return FixedSizeUpperMatrixT(*this) += o;
}
FixedSizeUpperMatrixT &operator-=(const FixedSizeUpperMatrixT &o) {
for (int i = 0; i < N; ++i) {
for (int j = i; j < N; ++j) {
(*this)[i][j] -= o[i][j];
}
}
return *this;
}
FixedSizeUpperMatrixT operator-(const FixedSizeUpperMatrixT &o) const {
return FixedSizeUpperMatrixT(*this) -= o;
}
FixedSizeUpperMatrixT operator*(const FixedSizeUpperMatrixT &o) const {
static T buffer[N];
FixedSizeUpperMatrixT result;
for (int j = 0; j < N; ++j) {
for (int i = 0; i < N; ++i) {
buffer[i] = o[i][j];
}
for (int i = 0; i <= j; ++i) {
for (int k = i; k <= j; ++k) {
result[i][j] += (*this)[i][k] * buffer[k];
}
}
}
return result;
}
FixedSizeUpperMatrixT &operator*=(const FixedSizeUpperMatrixT &o) {
return *this = *this * o;
}
};
template <typename T, int N>
auto operator*(const typename FixedSizeUpperMatrixT<T, N>::Row &r,
const FixedSizeUpperMatrixT<T, N> &o) {
typename FixedSizeUpperMatrixT<T, N>::Row result;
for (int k = 0; k < N; k++) {
for (int j = k; j < N; j++) {
result[j] += r[k] * o[k][j];
}
}
return result;
}
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