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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,146 @@ | ||
| #ifndef AMREX_LU_SOLVER_H_ | ||
| #define AMREX_LU_SOLVER_H_ | ||
| #include <AMReX_Config.H> | ||
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| #include <AMReX_Arena.H> | ||
| #include <AMReX_Array.H> | ||
| #include <cmath> | ||
| #include <limits> | ||
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| namespace amrex { | ||
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| // https://en.wikipedia.org/wiki/LU_decomposition | ||
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| template <int N, typename T> | ||
| class LUSolver | ||
| { | ||
| public: | ||
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| LUSolver () = default; | ||
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| LUSolver (Array2D<T, 0, N-1, 0, N-1, Order::C> const& a_mat); | ||
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| void define (Array2D<T, 0, N-1, 0, N-1, Order::C> const& a_mat); | ||
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| AMREX_GPU_HOST_DEVICE AMREX_FORCE_INLINE | ||
| void operator() (T* AMREX_RESTRICT x, T const* AMREX_RESTRICT b) const | ||
| { | ||
| for (int i = 0; i < N; ++i) { | ||
| x[i] = b[m_piv(i)]; | ||
| for (int k = 0; k < i; ++k) { | ||
| x[i] -= m_mat(i,k) * x[k]; | ||
| } | ||
| } | ||
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| for (int i = N-1; i >= 0; --i) { | ||
| for (int k = i+1; k < N; ++k) { | ||
| x[i] -= m_mat(i,k) * x[k]; | ||
| } | ||
| x[i] *= m_mat(i,i); | ||
| } | ||
| } | ||
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| [[nodiscard]] AMREX_GPU_HOST_DEVICE | ||
| Array2D<T,0,N-1,0,N-1,Order::C> invert () const | ||
| { | ||
| Array2D<T,0,N-1,0,N-1,Order::C> IA; | ||
| for (int j = 0; j < N; ++j) { | ||
| for (int i = 0; i < N; ++i) { | ||
| IA(i,j) = (m_piv(i) == j) ? T(1.0) : T(0.0); | ||
| for (int k = 0; k < i; ++k) { | ||
| IA(i,j) -= m_mat(i,k) * IA(k,j); | ||
| } | ||
| } | ||
| for (int i = N-1; i >= 0; --i) { | ||
| for (int k = i+1; k < N; ++k) { | ||
| IA(i,j) -= m_mat(i,k) * IA(k,j); | ||
| } | ||
| IA(i,j) *= m_mat(i,i); | ||
| } | ||
| } | ||
| return IA; | ||
| } | ||
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| [[nodiscard]] AMREX_GPU_HOST_DEVICE | ||
| T determinant () const | ||
| { | ||
| T det = m_mat(0,0); | ||
| for (int i = 1; i < N; ++i) { | ||
| det *= m_mat(i,i); | ||
| } | ||
| det = T(1.0) / det; | ||
| return (m_npivs % 2 == 0) ? det : -det; | ||
| } | ||
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| private: | ||
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| void define_innard (); | ||
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| Array2D<T, 0, N-1, 0, N-1, Order::C> m_mat; | ||
| Array1D<int, 0, N-1> m_piv; | ||
| int m_npivs = 0; | ||
| }; | ||
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| template <int N, typename T> | ||
| LUSolver<N,T>::LUSolver (Array2D<T, 0, N-1, 0, N-1, Order::C> const& a_mat) | ||
| : m_mat(a_mat) | ||
| { | ||
| define_innard(); | ||
| } | ||
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| template <int N, typename T> | ||
| void LUSolver<N,T>::define (Array2D<T, 0, N-1, 0, N-1, Order::C> const& a_mat) | ||
| { | ||
| m_mat = a_mat; | ||
| define_innard(); | ||
| } | ||
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| template <int N, typename T> | ||
| void LUSolver<N,T>::define_innard () | ||
| { | ||
| static_assert(N > 1); | ||
| static_assert(std::is_floating_point_v<T>); | ||
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| for (int i = 0; i < N; ++i) { m_piv(i) = i; } | ||
| m_npivs = 0; | ||
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| for (int i = 0; i < N; ++i) { | ||
| T maxA = 0; | ||
| int imax = i; | ||
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| for (int k = i; k < N; ++k) { | ||
| auto const absA = std::abs(m_mat(k,i)); | ||
| if (absA > maxA) { | ||
| maxA = absA; | ||
| imax = k; | ||
| } | ||
| } | ||
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| if (maxA < std::numeric_limits<T>::min()) { | ||
| amrex::Abort("LUSolver: matrix is degenerate"); | ||
| } | ||
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| if (imax != i) { | ||
| std::swap(m_piv(i), m_piv(imax)); | ||
| for (int j = 0; j < N; ++j) { | ||
| std::swap(m_mat(i,j), m_mat(imax,j)); | ||
| } | ||
| ++m_npivs; | ||
| } | ||
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| for (int j = i+1; j < N; ++j) { | ||
| m_mat(j,i) /= m_mat(i,i); | ||
| for (int k = i+1; k < N; ++k) { | ||
| m_mat(j,k) -= m_mat(j,i) * m_mat(i,k); | ||
| } | ||
| } | ||
| } | ||
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| for (int i = 0; i < N; ++i) { | ||
| m_mat(i,i) = T(1) / m_mat(i,i); | ||
| } | ||
| } | ||
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| } | ||
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| #endif |
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