// license:GPL-2.0+ // copyright-holders:Couriersud /* * nld_ms_direct.h * * * Sherman-Morrison Solver * * Computes the updated inverse of A given that the change in A is * * A <- A + (u x v) u,v vectors * * In this specific implementation, u is a unit vector specifying the row which * changed. Thus v contains the changed column. * * Than z = A^-1 u , w = transpose(A^-1) v , lambda = v z * * A^-1 <- 1.0 / (1.0 + lambda) * (z x w) * * The approach is iterative and applied for each row changed. * * The performance for a typical circuit like kidniki compared to Gaussian * elimination is poor: * * a) The code needs to be run for each row change. * b) The inverse of A typically is fully occupied. * * It may have advantages for circuits with a high number of elements and only * few dynamic/active components. * */ #ifndef NLD_MS_SM_H_ #define NLD_MS_SM_H_ #include "nld_matrix_solver.h" #include "nld_solver.h" #include "plib/vector_ops.h" #include namespace netlist { namespace devices { template class matrix_solver_sm_t: public matrix_solver_t { friend class matrix_solver_t; public: using float_ext_type = FT; using float_type = FT; // FIXME: dirty hack to make this compile static constexpr const std::size_t storage_N = 100; matrix_solver_sm_t(netlist_state_t &anetlist, const pstring &name, const solver_parameters_t *params, const std::size_t size); void vsetup(analog_net_t::list_t &nets) override; void reset() override { matrix_solver_t::reset(); } protected: unsigned vsolve_non_dynamic(const bool newton_raphson) override; unsigned solve_non_dynamic(const bool newton_raphson); constexpr std::size_t size() const { return m_dim; } void LE_invert(); template void LE_compute_x(T * x); template float_ext_type &A(const T1 &r, const T2 &c) { return m_A[r][c]; } template float_ext_type &W(const T1 &r, const T2 &c) { return m_W[r][c]; } template float_ext_type &Ainv(const T1 &r, const T2 &c) { return m_Ainv[r][c]; } template float_ext_type &RHS(const T1 &r) { return m_RHS[r]; } template float_ext_type &lA(const T1 &r, const T2 &c) { return m_lA[r][c]; } template float_ext_type &lAinv(const T1 &r, const T2 &c) { return m_lAinv[r][c]; } private: static constexpr std::size_t m_pitch = ((( storage_N) + 7) / 8) * 8; float_ext_type m_A[storage_N][m_pitch]; float_ext_type m_Ainv[storage_N][m_pitch]; float_ext_type m_W[storage_N][m_pitch]; float_ext_type m_RHS[storage_N]; // right hand side - contains currents float_ext_type m_lA[storage_N][m_pitch]; float_ext_type m_lAinv[storage_N][m_pitch]; //float_ext_type m_RHSx[storage_N]; const std::size_t m_dim; std::size_t m_cnt; }; // ---------------------------------------------------------------------------------------- // matrix_solver_direct // ---------------------------------------------------------------------------------------- template void matrix_solver_sm_t::vsetup(analog_net_t::list_t &nets) { matrix_solver_t::setup_base(nets); /* FIXME: Shouldn't be necessary */ for (std::size_t k = 0; k < size(); k++) state().save(*this, RHS(k), this->name(), plib::pfmt("RHS.{1}")(k)); } template void matrix_solver_sm_t::LE_invert() { const std::size_t kN = size(); for (std::size_t i = 0; i < kN; i++) { for (std::size_t j = 0; j < kN; j++) { W(i,j) = lA(i,j) = A(i,j); Ainv(i,j) = 0.0; } Ainv(i,i) = 1.0; } /* down */ for (std::size_t i = 0; i < kN; i++) { /* FIXME: Singular matrix? */ const float_type f = 1.0 / W(i,i); const auto * const p = m_terms[i]->m_nzrd.data(); const std::size_t e = m_terms[i]->m_nzrd.size(); /* Eliminate column i from row j */ const auto * const pb = m_terms[i]->m_nzbd.data(); const std::size_t eb = m_terms[i]->m_nzbd.size(); for (std::size_t jb = 0; jb < eb; jb++) { const unsigned j = pb[jb]; const float_type f1 = - W(j,i) * f; if (f1 != 0.0) { for (std::size_t k = 0; k < e; k++) W(j,p[k]) += W(i,p[k]) * f1; for (std::size_t k = 0; k <= i; k ++) Ainv(j,k) += Ainv(i,k) * f1; } } } /* up */ for (std::size_t i = kN; i-- > 0; ) { /* FIXME: Singular matrix? */ const float_type f = 1.0 / W(i,i); for (std::size_t j = i; j-- > 0; ) { const float_type f1 = - W(j,i) * f; if (f1 != 0.0) { for (std::size_t k = i; k < kN; k++) W(j,k) += W(i,k) * f1; for (std::size_t k = 0; k < kN; k++) Ainv(j,k) += Ainv(i,k) * f1; } } for (std::size_t k = 0; k < kN; k++) { Ainv(i,k) *= f; lAinv(i,k) = Ainv(i,k); } } } template template void matrix_solver_sm_t::LE_compute_x( T * x) { const std::size_t kN = size(); for (std::size_t i=0; i unsigned matrix_solver_sm_t::solve_non_dynamic(const bool newton_raphson) { static constexpr const bool incremental = true; const std::size_t iN = size(); float_type new_V[storage_N]; // = { 0.0 }; if ((m_cnt % 50) == 0) { /* complete calculation */ this->LE_invert(); } else { if (!incremental) { for (std::size_t row = 0; row < iN; row ++) for (std::size_t k = 0; k < iN; k++) Ainv(row,k) = lAinv(row, k); } for (std::size_t row = 0; row < iN; row ++) { float_type v[m_pitch] = {0}; std::size_t cols[m_pitch]; std::size_t colcount = 0; auto &nz = m_terms[row]->m_nz; for (unsigned & col : nz) { v[col] = A(row,col) - lA(row,col); if (incremental) lA(row,col) = A(row,col); if (v[col] != 0.0) cols[colcount++] = col; } if (colcount > 0) { float_type lamba = 0.0; float_type w[m_pitch] = {0}; float_type z[m_pitch]; /* compute w and lamba */ for (std::size_t i = 0; i < iN; i++) z[i] = Ainv(i, row); /* u is row'th column */ for (std::size_t j = 0; j < colcount; j++) lamba += v[cols[j]] * z[cols[j]]; for (std::size_t j=0; jLE_compute_x(new_V); const float_type err = (newton_raphson ? delta(new_V) : 0.0); store(new_V); return (err > this->m_params.m_accuracy) ? 2 : 1; } template unsigned matrix_solver_sm_t::vsolve_non_dynamic(const bool newton_raphson) { this->build_LE_A(*this); this->build_LE_RHS(*this); this->m_stat_calculations++; return this->solve_non_dynamic(newton_raphson); } template matrix_solver_sm_t::matrix_solver_sm_t(netlist_state_t &anetlist, const pstring &name, const solver_parameters_t *params, const std::size_t size) : matrix_solver_t(anetlist, name, NOSORT, params) , m_dim(size) , m_cnt(0) { } } // namespace devices } // namespace netlist #endif /* NLD_MS_DIRECT_H_ */