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+//
+// Copyright 2015 The ANGLE Project Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+//
+// Matrix:
+// Utility class implementing various matrix operations.
+// Supports matrices with minimum 2 and maximum 4 number of rows/columns.
+//
+// TODO: Check if we can merge Matrix.h in sample_util with this and replace it with this implementation.
+// TODO: Rename this file to Matrix.h once we remove Matrix.h in sample_util.
+
+#ifndef COMMON_MATRIX_UTILS_H_
+#define COMMON_MATRIX_UTILS_H_
+
+#include <vector>
+
+#include "common/debug.h"
+#include "common/mathutil.h"
+
+namespace angle
+{
+
+template<typename T>
+class Matrix
+{
+ public:
+ Matrix(const std::vector<T> &elements, const unsigned int &numRows, const unsigned int &numCols)
+ : mElements(elements),
+ mRows(numRows),
+ mCols(numCols)
+ {
+ ASSERT(rows() >= 1 && rows() <= 4);
+ ASSERT(columns() >= 1 && columns() <= 4);
+ }
+
+ Matrix(const std::vector<T> &elements, const unsigned int &size)
+ : mElements(elements),
+ mRows(size),
+ mCols(size)
+ {
+ ASSERT(rows() >= 1 && rows() <= 4);
+ ASSERT(columns() >= 1 && columns() <= 4);
+ }
+
+ Matrix(const T *elements, const unsigned int &size)
+ : mRows(size),
+ mCols(size)
+ {
+ ASSERT(rows() >= 1 && rows() <= 4);
+ ASSERT(columns() >= 1 && columns() <= 4);
+ for (size_t i = 0; i < size * size; i++)
+ mElements.push_back(elements[i]);
+ }
+
+ const T &operator()(const unsigned int &rowIndex, const unsigned int &columnIndex) const
+ {
+ return mElements[rowIndex * columns() + columnIndex];
+ }
+
+ T &operator()(const unsigned int &rowIndex, const unsigned int &columnIndex)
+ {
+ return mElements[rowIndex * columns() + columnIndex];
+ }
+
+ const T &at(const unsigned int &rowIndex, const unsigned int &columnIndex) const
+ {
+ return operator()(rowIndex, columnIndex);
+ }
+
+ Matrix<T> operator*(const Matrix<T> &m)
+ {
+ ASSERT(columns() == m.rows());
+
+ unsigned int resultRows = rows();
+ unsigned int resultCols = m.columns();
+ Matrix<T> result(std::vector<T>(resultRows * resultCols), resultRows, resultCols);
+ for (unsigned int i = 0; i < resultRows; i++)
+ {
+ for (unsigned int j = 0; j < resultCols; j++)
+ {
+ T tmp = 0.0f;
+ for (unsigned int k = 0; k < columns(); k++)
+ tmp += at(i, k) * m(k, j);
+ result(i, j) = tmp;
+ }
+ }
+
+ return result;
+ }
+
+ unsigned int size() const
+ {
+ ASSERT(rows() == columns());
+ return rows();
+ }
+
+ unsigned int rows() const { return mRows; }
+
+ unsigned int columns() const { return mCols; }
+
+ std::vector<T> elements() const { return mElements; }
+
+ Matrix<T> compMult(const Matrix<T> &mat1) const
+ {
+ Matrix result(std::vector<T>(mElements.size()), size());
+ for (unsigned int i = 0; i < columns(); i++)
+ for (unsigned int j = 0; j < rows(); j++)
+ result(i, j) = at(i, j) * mat1(i, j);
+
+ return result;
+ }
+
+ Matrix<T> outerProduct(const Matrix<T> &mat1) const
+ {
+ unsigned int cols = mat1.columns();
+ Matrix result(std::vector<T>(rows() * cols), rows(), cols);
+ for (unsigned int i = 0; i < rows(); i++)
+ for (unsigned int j = 0; j < cols; j++)
+ result(i, j) = at(i, 0) * mat1(0, j);
+
+ return result;
+ }
+
+ Matrix<T> transpose() const
+ {
+ Matrix result(std::vector<T>(mElements.size()), columns(), rows());
+ for (unsigned int i = 0; i < columns(); i++)
+ for (unsigned int j = 0; j < rows(); j++)
+ result(i, j) = at(j, i);
+
+ return result;
+ }
+
+ T determinant() const
+ {
+ ASSERT(rows() == columns());
+
+ switch (size())
+ {
+ case 2:
+ return at(0, 0) * at(1, 1) - at(0, 1) * at(1, 0);
+
+ case 3:
+ return at(0, 0) * at(1, 1) * at(2, 2) +
+ at(0, 1) * at(1, 2) * at(2, 0) +
+ at(0, 2) * at(1, 0) * at(2, 1) -
+ at(0, 2) * at(1, 1) * at(2, 0) -
+ at(0, 1) * at(1, 0) * at(2, 2) -
+ at(0, 0) * at(1, 2) * at(2, 1);
+
+ case 4:
+ {
+ const float minorMatrices[4][3 * 3] =
+ {
+ {
+ at(1, 1), at(2, 1), at(3, 1),
+ at(1, 2), at(2, 2), at(3, 2),
+ at(1, 3), at(2, 3), at(3, 3),
+ },
+ {
+ at(1, 0), at(2, 0), at(3, 0),
+ at(1, 2), at(2, 2), at(3, 2),
+ at(1, 3), at(2, 3), at(3, 3),
+ },
+ {
+ at(1, 0), at(2, 0), at(3, 0),
+ at(1, 1), at(2, 1), at(3, 1),
+ at(1, 3), at(2, 3), at(3, 3),
+ },
+ {
+ at(1, 0), at(2, 0), at(3, 0),
+ at(1, 1), at(2, 1), at(3, 1),
+ at(1, 2), at(2, 2), at(3, 2),
+ }
+ };
+ return at(0, 0) * Matrix<T>(minorMatrices[0], 3).determinant() -
+ at(0, 1) * Matrix<T>(minorMatrices[1], 3).determinant() +
+ at(0, 2) * Matrix<T>(minorMatrices[2], 3).determinant() -
+ at(0, 3) * Matrix<T>(minorMatrices[3], 3).determinant();
+ }
+
+ default:
+ UNREACHABLE();
+ break;
+ }
+
+ return T();
+ }
+
+ Matrix<T> inverse() const
+ {
+ ASSERT(rows() == columns());
+
+ Matrix<T> cof(std::vector<T>(mElements.size()), rows(), columns());
+ switch (size())
+ {
+ case 2:
+ cof(0, 0) = at(1, 1);
+ cof(0, 1) = -at(1, 0);
+ cof(1, 0) = -at(0, 1);
+ cof(1, 1) = at(0, 0);
+ break;
+
+ case 3:
+ cof(0, 0) = at(1, 1) * at(2, 2) -
+ at(2, 1) * at(1, 2);
+ cof(0, 1) = -(at(1, 0) * at(2, 2) -
+ at(2, 0) * at(1, 2));
+ cof(0, 2) = at(1, 0) * at(2, 1) -
+ at(2, 0) * at(1, 1);
+ cof(1, 0) = -(at(0, 1) * at(2, 2) -
+ at(2, 1) * at(0, 2));
+ cof(1, 1) = at(0, 0) * at(2, 2) -
+ at(2, 0) * at(0, 2);
+ cof(1, 2) = -(at(0, 0) * at(2, 1) -
+ at(2, 0) * at(0, 1));
+ cof(2, 0) = at(0, 1) * at(1, 2) -
+ at(1, 1) * at(0, 2);
+ cof(2, 1) = -(at(0, 0) * at(1, 2) -
+ at(1, 0) * at(0, 2));
+ cof(2, 2) = at(0, 0) * at(1, 1) -
+ at(1, 0) * at(0, 1);
+ break;
+
+ case 4:
+ cof(0, 0) = at(1, 1) * at(2, 2) * at(3, 3) +
+ at(2, 1) * at(3, 2) * at(1, 3) +
+ at(3, 1) * at(1, 2) * at(2, 3) -
+ at(1, 1) * at(3, 2) * at(2, 3) -
+ at(2, 1) * at(1, 2) * at(3, 3) -
+ at(3, 1) * at(2, 2) * at(1, 3);
+ cof(0, 1) = -(at(1, 0) * at(2, 2) * at(3, 3) +
+ at(2, 0) * at(3, 2) * at(1, 3) +
+ at(3, 0) * at(1, 2) * at(2, 3) -
+ at(1, 0) * at(3, 2) * at(2, 3) -
+ at(2, 0) * at(1, 2) * at(3, 3) -
+ at(3, 0) * at(2, 2) * at(1, 3));
+ cof(0, 2) = at(1, 0) * at(2, 1) * at(3, 3) +
+ at(2, 0) * at(3, 1) * at(1, 3) +
+ at(3, 0) * at(1, 1) * at(2, 3) -
+ at(1, 0) * at(3, 1) * at(2, 3) -
+ at(2, 0) * at(1, 1) * at(3, 3) -
+ at(3, 0) * at(2, 1) * at(1, 3);
+ cof(0, 3) = -(at(1, 0) * at(2, 1) * at(3, 2) +
+ at(2, 0) * at(3, 1) * at(1, 2) +
+ at(3, 0) * at(1, 1) * at(2, 2) -
+ at(1, 0) * at(3, 1) * at(2, 2) -
+ at(2, 0) * at(1, 1) * at(3, 2) -
+ at(3, 0) * at(2, 1) * at(1, 2));
+ cof(1, 0) = -(at(0, 1) * at(2, 2) * at(3, 3) +
+ at(2, 1) * at(3, 2) * at(0, 3) +
+ at(3, 1) * at(0, 2) * at(2, 3) -
+ at(0, 1) * at(3, 2) * at(2, 3) -
+ at(2, 1) * at(0, 2) * at(3, 3) -
+ at(3, 1) * at(2, 2) * at(0, 3));
+ cof(1, 1) = at(0, 0) * at(2, 2) * at(3, 3) +
+ at(2, 0) * at(3, 2) * at(0, 3) +
+ at(3, 0) * at(0, 2) * at(2, 3) -
+ at(0, 0) * at(3, 2) * at(2, 3) -
+ at(2, 0) * at(0, 2) * at(3, 3) -
+ at(3, 0) * at(2, 2) * at(0, 3);
+ cof(1, 2) = -(at(0, 0) * at(2, 1) * at(3, 3) +
+ at(2, 0) * at(3, 1) * at(0, 3) +
+ at(3, 0) * at(0, 1) * at(2, 3) -
+ at(0, 0) * at(3, 1) * at(2, 3) -
+ at(2, 0) * at(0, 1) * at(3, 3) -
+ at(3, 0) * at(2, 1) * at(0, 3));
+ cof(1, 3) = at(0, 0) * at(2, 1) * at(3, 2) +
+ at(2, 0) * at(3, 1) * at(0, 2) +
+ at(3, 0) * at(0, 1) * at(2, 2) -
+ at(0, 0) * at(3, 1) * at(2, 2) -
+ at(2, 0) * at(0, 1) * at(3, 2) -
+ at(3, 0) * at(2, 1) * at(0, 2);
+ cof(2, 0) = at(0, 1) * at(1, 2) * at(3, 3) +
+ at(1, 1) * at(3, 2) * at(0, 3) +
+ at(3, 1) * at(0, 2) * at(1, 3) -
+ at(0, 1) * at(3, 2) * at(1, 3) -
+ at(1, 1) * at(0, 2) * at(3, 3) -
+ at(3, 1) * at(1, 2) * at(0, 3);
+ cof(2, 1) = -(at(0, 0) * at(1, 2) * at(3, 3) +
+ at(1, 0) * at(3, 2) * at(0, 3) +
+ at(3, 0) * at(0, 2) * at(1, 3) -
+ at(0, 0) * at(3, 2) * at(1, 3) -
+ at(1, 0) * at(0, 2) * at(3, 3) -
+ at(3, 0) * at(1, 2) * at(0, 3));
+ cof(2, 2) = at(0, 0) * at(1, 1) * at(3, 3) +
+ at(1, 0) * at(3, 1) * at(0, 3) +
+ at(3, 0) * at(0, 1) * at(1, 3) -
+ at(0, 0) * at(3, 1) * at(1, 3) -
+ at(1, 0) * at(0, 1) * at(3, 3) -
+ at(3, 0) * at(1, 1) * at(0, 3);
+ cof(2, 3) = -(at(0, 0) * at(1, 1) * at(3, 2) +
+ at(1, 0) * at(3, 1) * at(0, 2) +
+ at(3, 0) * at(0, 1) * at(1, 2) -
+ at(0, 0) * at(3, 1) * at(1, 2) -
+ at(1, 0) * at(0, 1) * at(3, 2) -
+ at(3, 0) * at(1, 1) * at(0, 2));
+ cof(3, 0) = -(at(0, 1) * at(1, 2) * at(2, 3) +
+ at(1, 1) * at(2, 2) * at(0, 3) +
+ at(2, 1) * at(0, 2) * at(1, 3) -
+ at(0, 1) * at(2, 2) * at(1, 3) -
+ at(1, 1) * at(0, 2) * at(2, 3) -
+ at(2, 1) * at(1, 2) * at(0, 3));
+ cof(3, 1) = at(0, 0) * at(1, 2) * at(2, 3) +
+ at(1, 0) * at(2, 2) * at(0, 3) +
+ at(2, 0) * at(0, 2) * at(1, 3) -
+ at(0, 0) * at(2, 2) * at(1, 3) -
+ at(1, 0) * at(0, 2) * at(2, 3) -
+ at(2, 0) * at(1, 2) * at(0, 3);
+ cof(3, 2) = -(at(0, 0) * at(1, 1) * at(2, 3) +
+ at(1, 0) * at(2, 1) * at(0, 3) +
+ at(2, 0) * at(0, 1) * at(1, 3) -
+ at(0, 0) * at(2, 1) * at(1, 3) -
+ at(1, 0) * at(0, 1) * at(2, 3) -
+ at(2, 0) * at(1, 1) * at(0, 3));
+ cof(3, 3) = at(0, 0) * at(1, 1) * at(2, 2) +
+ at(1, 0) * at(2, 1) * at(0, 2) +
+ at(2, 0) * at(0, 1) * at(1, 2) -
+ at(0, 0) * at(2, 1) * at(1, 2) -
+ at(1, 0) * at(0, 1) * at(2, 2) -
+ at(2, 0) * at(1, 1) * at(0, 2);
+ break;
+
+ default:
+ UNREACHABLE();
+ break;
+ }
+
+ // The inverse of A is the transpose of the cofactor matrix times the reciprocal of the determinant of A.
+ Matrix<T> adjugateMatrix(cof.transpose());
+ T det = determinant();
+ Matrix<T> result(std::vector<T>(mElements.size()), rows(), columns());
+ for (unsigned int i = 0; i < rows(); i++)
+ for (unsigned int j = 0; j < columns(); j++)
+ result(i, j) = det ? adjugateMatrix(i, j) / det : T();
+
+ return result;
+ }
+
+ void setToIdentity()
+ {
+ ASSERT(rows() == columns());
+
+ const auto one = T(1);
+ const auto zero = T(0);
+
+ for (auto &e : mElements)
+ e = zero;
+
+ for (unsigned int i = 0; i < rows(); ++i)
+ {
+ const auto pos = i * columns() + (i % columns());
+ mElements[pos] = one;
+ }
+ }
+
+ template <unsigned int Size>
+ static void setToIdentity(T(&matrix)[Size])
+ {
+ static_assert(gl::iSquareRoot<Size>() != 0, "Matrix is not square.");
+
+ const auto cols = gl::iSquareRoot<Size>();
+ const auto one = T(1);
+ const auto zero = T(0);
+
+ for (auto &e : matrix)
+ e = zero;
+
+ for (unsigned int i = 0; i < cols; ++i)
+ {
+ const auto pos = i * cols + (i % cols);
+ matrix[pos] = one;
+ }
+ }
+
+ private:
+ std::vector<T> mElements;
+ unsigned int mRows;
+ unsigned int mCols;
+};
+
+} // namespace angle
+
+#endif // COMMON_MATRIX_UTILS_H_
+