Matrix.hpp

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/*
   Copyright 2022 Rishi Challa
 
   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at
 
       http://www.apache.org/licenses/LICENSE-2.0
 
   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.
*/
 
#pragma once
 
#include <Kale/Math/Vector/Vector.hpp>
 
#include <array>
#include <algorithm>
#include <ostream>
#include <iomanip>
#include <type_traits>
#include <limits>
 
#ifdef KALE_DEBUG
#include <stdexcept>
#endif
 
#include <nlohmann/json.hpp>
 
namespace Kale {
 
    using JSON = nlohmann::json;
    
    template <size_t w, size_t h, typename T>
    class Matrix {
    public:
 
        std::array<T, w*h> data;
        
        Matrix() {
            data.fill(static_cast<T>(0));
        }
 
        Matrix(const std::array<T, w*h>& arr) : data(arr) {
            // Empty Body
        }
 
        Matrix(std::array<T, w*h>&& arr) : data(std::move(arr)) {
            // Empty Body
        }
 
        inline size_t width() const {
            return w;
        }
 
        inline size_t height() const {
            return h;
        }
 
        inline T& operator[](size_t i) {
            #ifdef KALE_DEBUG
            if (i > w*h) throw std::runtime_error("Invalid matrix index");
            #endif
            return data[i];
        }
 
        inline const T& operator[](size_t i) const {
            #ifdef KALE_DEBUG
            if (i > w*h) throw std::runtime_error("Invalid matrix index");
            #endif
            return data[i];
        }
 
        inline T& operator()(size_t col, size_t row) {
            #ifdef KALE_DEBUG
            if (col > w || row > h) throw std::runtime_error("Invalid matrix column/row");
            #endif
            return data[row * w + col];
        }
 
        inline const T& operator()(size_t col, size_t row) const {
            #ifdef KALE_DEBUG
            if (col > w || row > h) throw std::runtime_error("Invalid matrix column/row");
            #endif
            return data[row * w + col];
        }
 
        inline T& get(size_t i) {
            return data[i];
        }
 
        inline const T& get(size_t i) const {
            return data[i];
        }
 
        inline T& get(size_t col, size_t row) {
            return data[row * w + col];
        }
 
        inline const T& get(size_t col, size_t row) const {
            return data[row * w + col];
        }
 
        Matrix<w, h, T> operator+(const Matrix<w, h, T>& other) const {
            Matrix<w, h, T> mat;
            for (size_t i = 0; i < w*h; i++) mat.data[i] = data[i] + other.data[i];
            return mat;
        }
 
        Matrix<w, h, T> operator+(Matrix<w, h, T>&& other) const {
            for (size_t i = 0; i < w*h; i++) other.data[i] += data[i];
            return Matrix<w, h, T>(std::move(other));
        }
 
        void operator+=(const Matrix<w, h, T>& other) {
            for (size_t i = 0; i < w*h; i++) data[i] += other.data[i];
        }
 
        Matrix<w, h, T> operator-(const Matrix<w, h, T>& other) const {
            Matrix<w, h, T> mat;
            for (size_t i = 0; i < w*h; i++) mat.data[i] = data[i] - other.data[i];
            return mat;
        }
 
        Matrix<w, h, T> operator-(Matrix<w, h, T>&& other) const {
            for (size_t i = 0; i < w*h; i++) other.data[i] = data[i] - other.data[i];
            return Matrix<w, h, T>(std::move(other));
        }
        
        void operator-=(const Matrix<w, h, T>& other) {
            for (size_t i = 0; i < w*h; i++) data[i] -= other.data[i];
        }
 
        Matrix<w, h, T> operator*(T scalar) const {
            Matrix<w, h, T> mat;
            for (size_t i = 0; i < w*h; i++) mat.data[i] = data[i] * scalar;
            return mat;
        }
 
        void operator*=(T scalar) {
            for (size_t i = 0; i < w*h; i++) data[i] *= scalar;
        }
 
        template <size_t w2> Matrix<w2, h, T> operator*(const Matrix<w2, w, T>& other) const {
            Matrix<w2, h, T> mat;
            for (size_t i = 0; i < h; i++)
                for (size_t j = 0; j < w2; j++)
                    for (size_t k = 0; k < w; k++)
                        mat.get(j, i) += get(k, i) * other.get(j, k);
            return mat;
        }
 
        Matrix<h, w, T> transpose() const {
            Matrix<h, w, T> mat;
            for (size_t c = 0; c < w; c++)
                for (size_t r = 0; r < h; r++)
                    mat.get(r, c) = get(c, r);
            return mat;
        }
 
        // >------------------- Elementary Row Operations -------------------<
 
        void swapRows(size_t row1, size_t row2) {
            #ifdef KALE_DEBUG
            if (row1 > h || row2 > h) throw std::runtime_error("Invalid matrix row");
            #endif
            std::swap_ranges(data.begin() + row1 * w, data.begin() + row1 * w + w, data.begin() + row2 * w);
        }
 
        void scaleRow(size_t row, T scalar) {
            #ifdef KALE_DEBUG
            if (row > h) throw std::runtime_error("Invalid matrix row");
            #endif
            for (size_t x = 0; x < w; x++) {
                get(x, row) *= scalar;
            }
        }
 
        void addScaledRow(size_t row1, size_t row2, T scalar) {
            #ifdef KALE_DEBUG
            if (row1 > h || row2 > h) throw std::runtime_error("Invalid matrix row");
            #endif
            for (size_t x = 0; x < w; x++) {
                get(x, row1) += scalar * get(x, row2);
            }
        }
 
        // >------------------- Template Specializations -------------------<
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 2 && H == 2, Vector2<T>>::type
        operator*(const Vector2<T>& vec) const {
            return Vector2<T>(data[0] * vec.x + data[1] * vec.y, data[2] * vec.x + data[2] * vec.y);
        }
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 2 && H == 2, Vector2<T>>::type
        operator*(Vector2<T>&& vec) const {
            vec.x = data[0] * vec.x + data[1] * vec.y;
            vec.y = data[2] * vec.x + data[2] * vec.y;
            return Vector2<T>(std::move(vec));
        }
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 3 && H == 3, Vector3<T>>::type
        operator*(const Vector3<T>& vec) const {
            return Vector3<T>(
                data[0] * vec.x + data[1] * vec.y + data[2] * vec.z,
                data[3] * vec.x + data[4] * vec.y + data[5] * vec.z,
                data[6] * vec.x + data[7] * vec.y + data[8] * vec.z
            );
        }
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 3 && H == 3, Vector3<T>>::type
        operator*(Vector3<T>&& vec) const {
            vec.x = data[0] * vec.x + data[1] * vec.y + data[2] * vec.z;
            vec.y = data[3] * vec.x + data[4] * vec.y + data[5] * vec.z;
            vec.z = data[6] * vec.x + data[7] * vec.y + data[8] * vec.z;
            return Vector3<T>(std::move(vec));
        }
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 4 && H == 4, Vector4<T>>::type
        operator*(const Vector4<T>& vec) const {
            return Vector4<T>(
                data[0] * vec.x + data[1] * vec.y + data[2] * vec.z + data[3] * vec.w,
                data[4] * vec.x + data[5] * vec.y + data[6] * vec.z + data[7] * vec.w,
                data[8] * vec.x + data[9] * vec.y + data[10] * vec.z + data[11] * vec.w,
                data[12] * vec.x + data[13] * vec.y + data[14] * vec.z + data[15] * vec.w
            );
        }
 
        template <size_t W = w, size_t H = h> typename std::enable_if<W == 4 && H == 4, Vector4<T>>::type
        operator*(Vector4<T>&& vec) const {
            vec.x = data[0] * vec.x + data[1] * vec.y + data[2] * vec.z + data[3] * vec.w;
            vec.y = data[4] * vec.x + data[5] * vec.y + data[6] * vec.z + data[7] * vec.w;
            vec.z = data[8] * vec.x + data[9] * vec.y + data[10] * vec.z + data[11] * vec.w;
            vec.w = data[12] * vec.x + data[13] * vec.y + data[14] * vec.z + data[15] * vec.w;
            return Vector4<T>(std::move(vec));
        }
 
        template <typename R, size_t W = w, size_t H = h>
        typename std::enable_if<W == 2 && H == 2, R>::type det() const {
            
            return static_cast<R>(data[0] * data[3] - data[1] * data[2]);
        }
 
        template <typename R, size_t W = w, size_t H = h>
        typename std::enable_if<W == 3 && H == 3, R>::type det() const {
            return static_cast<R>(
                data[0] * data[4] * data[8] +
                data[1] * data[5] * data[6] +
                data[2] * data[3] * data[7] -
                data[6] * data[4] * data[2] -
                data[7] * data[5] * data[0] -
                data[8] * data[3] * data[1]
            );
        }
 
        template <typename R, size_t W = w, size_t H = h>
        typename std::enable_if<W == H && (W > 3) && std::is_signed<R>::value, R>::type det() const {
            throw std::runtime_error("Matrix Determinants are Unimplemented");
        }
 
        template <size_t W = w, size_t H = h>
        typename std::enable_if<W == 2 && H == 2, Matrix<W, H, T>>::type inverse() {
            return Matrix<W, H, T>({
                data[3], -data[1],
                -data[2], data[0]
            }) * (static_cast<T>(1)/det<T>());
        }
 
        template <size_t W = w, size_t H = h>
        typename std::enable_if<W == 3 && H == 3, Matrix<W, H, T>>::type inverse() {
            auto calc = [&](size_t a, size_t b, size_t c, size_t d) -> T {
                return Matrix<2, 2, T>({data[a], data[b], data[c], data[d]}).template det<T>();
            };
            return Matrix<3, 3, T>({
                calc(4, 5, 7, 8), -calc(1, 2, 7, 8), calc(1, 2, 4, 5),
                -calc(3, 5, 6, 8), calc(0, 2, 6, 8), -calc(0, 2, 3, 5),
                calc(3, 4, 6, 7), -calc(0, 1, 6, 7), calc(0, 1, 3, 4)
            }) * (static_cast<T>(1)/det<T>());
        }
    };
 
    typedef Matrix<2, 2, int> Matrix2i;
    typedef Matrix<2, 2, long> Matrix2l;
    typedef Matrix<2, 2, float> Matrix2f;
    typedef Matrix<2, 2, double> Matrix2d;
 
    typedef Matrix<3, 3, int> Matrix3i;
    typedef Matrix<3, 3, long> Matrix3l;
    typedef Matrix<3, 3, float> Matrix3f;
    typedef Matrix<3, 3, double> Matrix3d;
 
    typedef Matrix<4, 4, int> Matrix4i;
    typedef Matrix<4, 4, long> Matrix4l;
    typedef Matrix<4, 4, float> Matrix4f;
    typedef Matrix<4, 4, double> Matrix4d;
 
    template <size_t w, size_t h> using MatrixI = Matrix<w, h, int>;
    template <size_t w, size_t h> using MatrixL = Matrix<w, h, long>;
    template <size_t w, size_t h> using MatrixF = Matrix<w, h, float>;
    template <size_t w, size_t h> using MatrixD = Matrix<w, h, double>;
 
    template <size_t w, size_t h, typename T>
    std::ostream& operator<<(std::ostream& os, const Kale::Matrix<w, h, T>& mat) {
        os << "Mat(Width: " << w << ", Height: " << h << ") :";
        for (size_t y = 0; y < h; y++) {
            os << "\n";
            for (size_t x = 0; x < w; x++) {
                os << std::setw(5) << std::setfill(' ') << mat(x, y) << " ";
            }
        }
        return os;
    }
 
    template <size_t w, size_t h, typename T>
    void from_json(const JSON& j, Matrix<w, h, T>& p) {
        p = j.get<std::array<T, w*h>>();
    }
 
    template <size_t w, size_t h, typename T>
    void to_json(JSON& j, const Matrix<w, h, T>& p) {
        j = JSON(p.data);
    }
 
}