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include/Linalg/linalg.h
- Committer:
- alexpirciu
- Date:
- 2019-03-28
- Revision:
- 1:ceee5a608e7c
File content as of revision 1:ceee5a608e7c:
#ifndef LINALG_H #define LINALG_H // #include <mbed.h> #include <stdint.h> #include <array> namespace linalg { template <class T, uint32_t M, uint32_t N> class CMatrix { public: using CThisType = CMatrix<T,M,N>; using CTransposeType = CMatrix<T,N,M>; using CContainerType = std::array<std::array<T,N>,M>; using CDataType =T; template <uint32_t P> using CLeftMultipliableType = CMatrix<T,P,M>; template <uint32_t P> using CRightMultipliableType = CMatrix<T,N,P>; template <uint32_t P> using CLeftMultiplicationResultType = CMatrix<T,P,N>; template <uint32_t P> using CRightMultiplicationResultType = CMatrix<T,M,P>; friend class CMatrix<T,N,M>; CMatrix() : m_data() {} CMatrix(const CThisType& f_matrix) : m_data(f_matrix.m_data) {} CMatrix(const CThisType&& f_matrix) : m_data(f_matrix.m_data) {} CMatrix(const CContainerType& f_data) : m_data(f_data) {} CMatrix(const CContainerType&& f_data) : m_data(f_data) {} CThisType& operator=(const CThisType& f_matrix) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] = f_matrix.m_data[l_row][l_col]; } } return *this; } CThisType& operator=(const CThisType&& f_matrix) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] = f_matrix.m_data[l_row][l_col]; } } return *this; } std::array<T,N>& operator[](uint32_t f_row) { return m_data[f_row]; } CDataType& operator()(uint32_t f_row, uint32_t f_col) { return m_data[f_row][f_col]; } const std::array<T,N>& operator[](uint32_t f_row) const { return m_data[f_row]; } const CDataType& operator()(uint32_t f_row, uint32_t f_col) const { return m_data[f_row][f_col]; } // template<> // CMatrix<T,1,1>::operator CDataType() // { // return m_data[0][0]; // } CThisType& operator+() {return *this;} CThisType operator-() { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = -this->m_data[l_row][l_col]; } } return l_matrix; } CThisType operator+(const CThisType& f_matrix) { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = this->m_data[l_row][l_col] + f_matrix.m_data[l_row][l_col]; } } return l_matrix; } CThisType operator-(const CThisType& f_matrix) { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = this->m_data[l_row][l_col] - f_matrix.m_data[l_row][l_col]; } } return l_matrix; } CThisType& operator+=(const CThisType& f_matrix) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] += f_matrix.m_data[l_row][l_col]; } } return *this; } CThisType& operator-=(const CThisType& f_matrix) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] -= f_matrix.m_data[l_row][l_col]; } } return *this; } CThisType operator+(const CDataType& f_val) { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = this->m_data[l_row][l_col] + f_val; } } return l_matrix; } CThisType operator-(const CDataType& f_val) { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = this->m_data[l_row][l_col] - f_val; } } return l_matrix; } CThisType& operator+=(const CDataType& f_val) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] += f_val; } } return *this; } CThisType& operator-=(const CDataType& f_val) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] -= f_val; } } return *this; } CThisType& operator*=(const CDataType& f_val) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] *= f_val; } } return *this; } CThisType& operator*=(const CThisType& f_val) { CThisType& l_thisRef(*this); l_thisRef = l_thisRef * f_val; return l_thisRef; } CThisType& operator/=(const CDataType& f_val) { for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { this->m_data[l_row][l_col] /= f_val; } } return *this; } CThisType operator*(const CDataType& f_val) { CThisType l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_matrix.m_data[l_row][l_col] = this->m_data[l_row][l_col] * f_val; } } return l_matrix; } template <uint32_t P> CRightMultiplicationResultType<P> operator*(const CRightMultipliableType<P>& f_matrix) { CRightMultiplicationResultType<P> l_matrix; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < P; ++l_col) { l_matrix[l_row][l_col] = 0; for (uint32_t l_idx = 0; l_idx < N; ++l_idx) { l_matrix[l_row][l_col] += this->m_data[l_row][l_idx] * f_matrix[l_idx][l_col]; } } } return l_matrix; } CThisType inv(); CTransposeType transpose() { CTransposeType l_trsp; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_trsp.m_data[l_col][l_row] = this->m_data[l_row][l_col]; } } return l_trsp; } template <uint32_t P> CRightMultiplicationResultType<P> solve(const CRightMultipliableType<P>& f_B) { return CLUDecomposition(*this).solve(); } static CThisType zeros() { CThisType l_res; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_res[l_row][l_col] = 0; } } return l_res; } static CThisType ones() { CThisType l_res; for (uint32_t l_row = 0; l_row < M; ++l_row) { for (uint32_t l_col = 0; l_col < N; ++l_col) { l_res[l_row][l_col] = 1; } } return l_res; } static CThisType eye() { CThisType l_res(CThisType::zeros()); uint32_t l_minDim = std::min(M,N); for (uint32_t l_row = 0; l_row < l_minDim; ++l_row) { l_res[l_row][l_row] = 1; } return l_res; } protected: std::array<std::array<T,N>,M> m_data; }; template<class T, uint32_t N> class CLUDecomposition { public: using CThisType = CLUDecomposition<T,N>; using COriginalType = CMatrix<T,N,N>; using CDataType =T; template <uint32_t P> using CLeftMultipliableType = CMatrix<T,P,N>; template <uint32_t P> using CRightMultipliableType = CMatrix<T,N,P>; template <uint32_t P> using CLeftMultiplicationResultType = CMatrix<T,P,N>; template <uint32_t P> using CRightMultiplicationResultType = CMatrix<T,N,P>; CLUDecomposition(const CThisType& f_decomposition) : m_L(f_decomposition.m_L), m_U(f_decomposition.m_U), m_P(f_decomposition.m_P) {} CLUDecomposition(const CThisType&& f_decomposition) : m_L(f_decomposition.m_L), m_U(f_decomposition.m_U), m_P(f_decomposition.m_P) {} CLUDecomposition(const COriginalType& f_matrix) : m_L(), m_U(), m_P() {decompose(f_matrix);} CLUDecomposition(const COriginalType&& f_matrix) : m_L(), m_U(), m_P() {decompose(f_matrix);} operator COriginalType() { return m_L * m_U; } COriginalType inv() { return triUInv() * triLInv(); } COriginalType triLInv() { COriginalType l_invL(m_L); for (uint32_t l_jdx = 0; l_jdx < N; ++l_jdx) { l_invL[l_jdx][l_jdx] = 1/l_invL[l_jdx][l_jdx]; for (uint32_t l_idx = l_jdx+1; l_idx < N; ++l_idx) { l_invL[l_idx][l_jdx] = 0; for (uint32_t l_kdx = l_jdx; l_kdx < l_idx; ++l_kdx) { l_invL[l_idx][l_jdx] -= m_L[l_idx][l_kdx]*l_invL[l_kdx][l_jdx]; } l_invL[l_idx][l_jdx] /= l_invL[l_idx][l_idx]; } } return l_invL; } COriginalType triUInv() { COriginalType l_invU(m_U); for (int32_t l_jdx = (N-1); l_jdx >= 0; --l_jdx) { l_invU[l_jdx][l_jdx] = 1/l_invU[l_jdx][l_jdx]; for (int32_t l_idx = (l_jdx-1); l_idx >= 0; --l_idx) { l_invU[l_idx][l_jdx] = 0; for (int32_t l_kdx = (l_idx+1); l_kdx < (l_jdx+1); ++l_kdx) { l_invU[l_idx][l_jdx] -= m_U[l_idx][l_kdx]*l_invU[l_kdx][l_jdx]; } l_invU[l_idx][l_jdx] /= l_invU[l_idx][l_idx]; } } return l_invU; } template <uint32_t P> CRightMultiplicationResultType<P> solve(const CRightMultipliableType<P>& f_B) { CRightMultipliableType<P> l_B; for (uint32_t l_idx = 0; l_idx < N; ++l_idx) { for (uint32_t l_jdx = 0; l_jdx < P; ++l_jdx) { l_B[l_idx][l_jdx] = f_B[m_P[l_idx]][l_jdx]; } } return sTriL(sTriU(l_B)); } template <uint32_t P> CRightMultiplicationResultType<P> sTriU(const CRightMultipliableType<P>& f_B) { return triUInv()*f_B; } template <uint32_t P> CRightMultiplicationResultType<P> sTriL(const CRightMultipliableType<P>& f_B) { // return triLInv()*f_B; } // private: void decompose(const CMatrix<T,N,N>& f_matrix) { m_U = f_matrix; for (uint32_t l_kdx = 0; l_kdx < (N-1); ++l_kdx) { m_L[l_kdx][l_kdx] = 1; m_P[l_kdx] = l_kdx; for(uint32_t l_idx = l_kdx+1; l_idx < N; ++l_idx) { m_L[l_idx][l_kdx] = m_U[l_idx][l_kdx]/m_U[l_kdx][l_kdx]; m_U[l_idx][l_kdx] = 0; for(uint32_t l_jdx = l_kdx+1; l_jdx < N; ++l_jdx) { m_U[l_idx][l_jdx] = m_U[l_idx][l_jdx] - m_L[l_idx][l_kdx]*m_U[l_kdx][l_jdx]; } } } m_L[N-1][N-1] = 1; m_P[N-1] = N-1; } CMatrix<T,N,N> m_L; CMatrix<T,N,N> m_U; std::array<uint32_t,N> m_P; }; template <class T, uint32_t N> using CColVector = CMatrix<T,N,1>; template <class T, uint32_t N> using CVector = CColVector<T,N>; template <class T, uint32_t N> using CRowVector = CMatrix<T,1,N>; }; #include "linalg.inl" #endif // LINALG_H