// license:GPL-2.0+ // copyright-holders:Couriersud /* * nld_ms_direct.h * */ #ifndef NLD_MS_DIRECT_H_ #define NLD_MS_DIRECT_H_ #include #include "solver/nld_solver.h" NETLIB_NAMESPACE_DEVICES_START() //#define nl_ext_double __float128 // slow, very slow //#define nl_ext_double long double // slightly slower #define nl_ext_double double template class matrix_solver_direct_t: public matrix_solver_t { public: matrix_solver_direct_t(const solver_parameters_t *params, const int size); matrix_solver_direct_t(const eSolverType type, const solver_parameters_t *params, const int size); virtual ~matrix_solver_direct_t(); virtual void vsetup(analog_net_t::list_t &nets) override; virtual void reset() override { matrix_solver_t::reset(); } ATTR_HOT inline unsigned N() const { if (m_N == 0) return m_dim; else return m_N; } ATTR_HOT inline int vsolve_non_dynamic(const bool newton_raphson); protected: virtual void add_term(int net_idx, terminal_t *term) override; ATTR_HOT virtual nl_double vsolve() override; ATTR_HOT int solve_non_dynamic(const bool newton_raphson); ATTR_HOT void build_LE_A(); ATTR_HOT void build_LE_RHS(nl_double * RESTRICT rhs); ATTR_HOT void LE_solve(); ATTR_HOT void LE_back_subst(nl_double * RESTRICT x); /* Full LU back substitution, not used currently, in for future use */ ATTR_HOT void LE_back_subst_full(nl_double * RESTRICT x); ATTR_HOT nl_double delta(const nl_double * RESTRICT V); ATTR_HOT void store(const nl_double * RESTRICT V); /* bring the whole system to the current time * Don't schedule a new calculation time. The recalculation has to be * triggered by the caller after the netlist element was changed. */ ATTR_HOT nl_double compute_next_timestep(); template inline nl_ext_double &A(const T1 r, const T2 c) { return m_A[r][c]; } ATTR_ALIGN nl_double m_RHS[_storage_N]; ATTR_ALIGN nl_double m_last_RHS[_storage_N]; // right hand side - contains currents ATTR_ALIGN nl_double m_last_V[_storage_N]; terms_t **m_terms; terms_t *m_rails_temp; private: ATTR_ALIGN nl_ext_double m_A[_storage_N][((_storage_N + 7) / 8) * 8]; const unsigned m_dim; }; // ---------------------------------------------------------------------------------------- // matrix_solver_direct // ---------------------------------------------------------------------------------------- template matrix_solver_direct_t::~matrix_solver_direct_t() { for (unsigned k = 0; k < N(); k++) { pfree(m_terms[k]); } pfree_array(m_terms); pfree_array(m_rails_temp); } template ATTR_HOT nl_double matrix_solver_direct_t::compute_next_timestep() { nl_double new_solver_timestep = m_params.m_max_timestep; if (m_params.m_dynamic) { /* * FIXME: We should extend the logic to use either all nets or * only output nets. */ for (unsigned k = 0, iN=N(); k < iN; k++) { analog_net_t *n = m_nets[k]; const nl_double DD_n = (n->m_cur_Analog - m_last_V[k]); const nl_double hn = current_timestep(); nl_double DD2 = (DD_n / hn - n->m_DD_n_m_1 / n->m_h_n_m_1) / (hn + n->m_h_n_m_1); nl_double new_net_timestep; n->m_h_n_m_1 = hn; n->m_DD_n_m_1 = DD_n; if (nl_math::abs(DD2) > NL_FCONST(1e-30)) // avoid div-by-zero new_net_timestep = nl_math::sqrt(m_params.m_lte / nl_math::abs(NL_FCONST(0.5)*DD2)); else new_net_timestep = m_params.m_max_timestep; if (new_net_timestep < new_solver_timestep) new_solver_timestep = new_net_timestep; } if (new_solver_timestep < m_params.m_min_timestep) new_solver_timestep = m_params.m_min_timestep; } //if (new_solver_timestep > 10.0 * hn) // new_solver_timestep = 10.0 * hn; return new_solver_timestep; } template ATTR_COLD void matrix_solver_direct_t::add_term(int k, terminal_t *term) { if (term->m_otherterm->net().isRailNet()) { m_rails_temp[k].add(term, -1, false); } else { int ot = get_net_idx(&term->m_otherterm->net()); if (ot>=0) { m_terms[k]->add(term, ot, true); } /* Should this be allowed ? */ else // if (ot<0) { m_rails_temp[k].add(term, ot, true); log().fatal("found term with missing othernet {1}\n", term->name()); } } } template ATTR_COLD void matrix_solver_direct_t::vsetup(analog_net_t::list_t &nets) { if (m_dim < nets.size()) log().fatal("Dimension {1} less than {2}", m_dim, nets.size()); for (unsigned k = 0; k < N(); k++) { m_terms[k]->clear(); m_rails_temp[k].clear(); } matrix_solver_t::setup(nets); for (unsigned k = 0; k < N(); k++) { m_terms[k]->m_railstart = m_terms[k]->count(); for (unsigned i = 0; i < m_rails_temp[k].count(); i++) this->m_terms[k]->add(m_rails_temp[k].terms()[i], m_rails_temp[k].net_other()[i], false); m_rails_temp[k].clear(); // no longer needed m_terms[k]->set_pointers(); } #if 1 /* Sort in descending order by number of connected matrix voltages. * The idea is, that for Gauss-Seidel algo the first voltage computed * depends on the greatest number of previous voltages thus taking into * account the maximum amout of information. * * This actually improves performance on popeye slightly. Average * GS computations reduce from 2.509 to 2.370 * * Smallest to largest : 2.613 * Unsorted : 2.509 * Largest to smallest : 2.370 * * Sorting as a general matrix pre-conditioning is mentioned in * literature but I have found no articles about Gauss Seidel. * * For Gaussian Elimination however increasing order is better suited. * FIXME: Even better would be to sort on elements right of the matrix diagonal. * */ int sort_order = (type() == GAUSS_SEIDEL ? 1 : -1); for (unsigned k = 0; k < N() / 2; k++) for (unsigned i = 0; i < N() - 1; i++) { if ((m_terms[i]->m_railstart - m_terms[i+1]->m_railstart) * sort_order < 0) { std::swap(m_terms[i],m_terms[i+1]); m_nets.swap(i, i+1); } } for (unsigned k = 0; k < N(); k++) { int *other = m_terms[k]->net_other(); for (unsigned i = 0; i < m_terms[k]->count(); i++) if (other[i] != -1) other[i] = get_net_idx(&m_terms[k]->terms()[i]->m_otherterm->net()); } #endif /* create a list of non zero elements right of the diagonal * These list anticipate the population of array elements by * Gaussian elimination. */ for (unsigned k = 0; k < N(); k++) { terms_t * t = m_terms[k]; /* pretty brutal */ int *other = t->net_other(); t->m_nz.clear(); if (k==0) t->m_nzrd.clear(); else { t->m_nzrd = m_terms[k-1]->m_nzrd; unsigned j=0; while(j < t->m_nzrd.size()) { if (t->m_nzrd[j] < k + 1) t->m_nzrd.remove_at(j); else j++; } } for (unsigned j = 0; j < N(); j++) { for (unsigned i = 0; i < t->m_railstart; i++) { if (!t->m_nzrd.contains(other[i]) && other[i] >= (int) (k + 1)) t->m_nzrd.add(other[i]); if (!t->m_nz.contains(other[i])) t->m_nz.add(other[i]); } } psort_list(t->m_nzrd); t->m_nz.add(k); // add diagonal psort_list(t->m_nz); } /* create a list of non zero elements below diagonal k * This should reduce cache misses ... */ bool touched[_storage_N][_storage_N] = { { false } }; for (unsigned k = 0; k < N(); k++) { m_terms[k]->m_nzbd.clear(); for (unsigned j = 0; j < m_terms[k]->m_nz.size(); j++) touched[k][m_terms[k]->m_nz[j]] = true; } for (unsigned k = 0; k < N(); k++) { for (unsigned row = k + 1; row < N(); row++) { if (touched[row][k]) { if (!m_terms[k]->m_nzbd.contains(row)) m_terms[k]->m_nzbd.add(row); for (unsigned col = k; col < N(); col++) if (touched[k][col]) touched[row][col] = true; } } } if (0) for (unsigned k = 0; k < N(); k++) { pstring line = pfmt("{1}")(k, "3"); for (unsigned j = 0; j < m_terms[k]->m_nzrd.size(); j++) line += pfmt(" {1}")(m_terms[k]->m_nzrd[j], "3"); log().verbose("{1}", line); } /* * save states */ save(NLNAME(m_RHS)); save(NLNAME(m_last_RHS)); save(NLNAME(m_last_V)); for (unsigned k = 0; k < N(); k++) { pstring num = pfmt("{1}")(k); save(m_terms[k]->go(),"GO" + num, m_terms[k]->count()); save(m_terms[k]->gt(),"GT" + num, m_terms[k]->count()); save(m_terms[k]->Idr(),"IDR" + num , m_terms[k]->count()); } } template ATTR_HOT void matrix_solver_direct_t::build_LE_A() { const unsigned iN = N(); for (unsigned k = 0; k < iN; k++) { for (unsigned i=0; i < iN; i++) A(k,i) = 0.0; const unsigned terms_count = m_terms[k]->count(); const unsigned railstart = m_terms[k]->m_railstart; const nl_double * RESTRICT gt = m_terms[k]->gt(); { nl_double akk = 0.0; for (unsigned i = 0; i < terms_count; i++) akk += gt[i]; A(k,k) = akk; } const nl_double * RESTRICT go = m_terms[k]->go(); const int * RESTRICT net_other = m_terms[k]->net_other(); for (unsigned i = 0; i < railstart; i++) A(k,net_other[i]) -= go[i]; } } template ATTR_HOT void matrix_solver_direct_t::build_LE_RHS(nl_double * RESTRICT rhs) { const unsigned iN = N(); for (unsigned k = 0; k < iN; k++) { nl_double rhsk_a = 0.0; nl_double rhsk_b = 0.0; const int terms_count = m_terms[k]->count(); const nl_double * RESTRICT go = m_terms[k]->go(); const nl_double * RESTRICT Idr = m_terms[k]->Idr(); const nl_double * const * RESTRICT other_cur_analog = m_terms[k]->other_curanalog(); for (int i = 0; i < terms_count; i++) rhsk_a = rhsk_a + Idr[i]; for (int i = m_terms[k]->m_railstart; i < terms_count; i++) //rhsk = rhsk + go[i] * terms[i]->m_otherterm->net().as_analog().Q_Analog(); rhsk_b = rhsk_b + go[i] * *other_cur_analog[i]; rhs[k] = rhsk_a + rhsk_b; } } template ATTR_HOT void matrix_solver_direct_t::LE_solve() { const unsigned kN = N(); for (unsigned i = 0; i < kN; i++) { // FIXME: use a parameter to enable pivoting? m_pivot if (m_params.m_pivot) { /* Find the row with the largest first value */ unsigned maxrow = i; for (unsigned j = i + 1; j < kN; j++) { //if (std::abs(m_A[j][i]) > std::abs(m_A[maxrow][i])) if (A(j,i) * A(j,i) > A(maxrow,i) * A(maxrow,i)) maxrow = j; } if (maxrow != i) { /* Swap the maxrow and ith row */ for (unsigned k = 0; k < kN; k++) { std::swap(A(i,k), A(maxrow,k)); } std::swap(m_RHS[i], m_RHS[maxrow]); } /* FIXME: Singular matrix? */ const nl_double f = 1.0 / A(i,i); /* Eliminate column i from row j */ for (unsigned j = i + 1; j < kN; j++) { const nl_double f1 = - A(j,i) * f; if (f1 != NL_FCONST(0.0)) { for (unsigned k = i+1; k < kN; k++) A(j,k) += A(i,k) * f1; m_RHS[j] += m_RHS[i] * f1; } } } else { /* FIXME: Singular matrix? */ const nl_double f = 1.0 / A(i,i); const unsigned * RESTRICT const p = m_terms[i]->m_nzrd.data(); const unsigned e = m_terms[i]->m_nzrd.size(); /* Eliminate column i from row j */ const unsigned * RESTRICT const pb = m_terms[i]->m_nzbd.data(); const unsigned eb = m_terms[i]->m_nzbd.size(); for (unsigned jb = 0; jb < eb; jb++) { const unsigned j = pb[jb]; const nl_double f1 = - A(j,i) * f; for (unsigned k = 0; k < e; k++) { A(j,p[k]) += A(i,p[k]) * f1; } m_RHS[j] += m_RHS[i] * f1; } } } } template ATTR_HOT void matrix_solver_direct_t::LE_back_subst( nl_double * RESTRICT x) { const unsigned kN = N(); /* back substitution */ if (m_params.m_pivot) { for (int j = kN - 1; j >= 0; j--) { nl_double tmp = 0; for (unsigned k = j+1; k < kN; k++) tmp += A(j,k) * x[k]; x[j] = (m_RHS[j] - tmp) / A(j,j); } } else { for (int j = kN - 1; j >= 0; j--) { nl_double tmp = 0; const unsigned *p = m_terms[j]->m_nzrd.data(); const unsigned e = m_terms[j]->m_nzrd.size(); for (unsigned k = 0; k < e; k++) { const unsigned pk = p[k]; tmp += A(j,pk) * x[pk]; } x[j] = (m_RHS[j] - tmp) / A(j,j); } } } template ATTR_HOT void matrix_solver_direct_t::LE_back_subst_full( nl_double * RESTRICT x) { const unsigned kN = N(); /* back substitution */ // int ip; // ii=-1 //for (int i=0; i < kN; i++) // x[i] = m_RHS[i]; for (int i=0; i < kN; i++) { //ip=indx[i]; USE_PIVOT_SEARCH //sum=b[ip]; //b[ip]=b[i]; double sum=m_RHS[i];//x[i]; for (int j=0; j < i; j++) sum -= A(i,j) * x[j]; x[i]=sum; } for (int i=kN-1; i >= 0; i--) { double sum=x[i]; for (int j = i+1; j < kN; j++) sum -= A(i,j)*x[j]; x[i] = sum / A(i,i); } } template ATTR_HOT nl_double matrix_solver_direct_t::delta( const nl_double * RESTRICT V) { /* FIXME: Ideally we should also include currents (RHS) here. This would * need a revaluation of the right hand side after voltages have been updated * and thus belong into a different calculation. This applies to all solvers. */ const unsigned iN = this->N(); nl_double cerr = 0; for (unsigned i = 0; i < iN; i++) cerr = std::max(cerr, nl_math::abs(V[i] - this->m_nets[i]->m_cur_Analog)); return cerr; } template ATTR_HOT void matrix_solver_direct_t::store( const nl_double * RESTRICT V) { for (unsigned i = 0, iN=N(); i < iN; i++) { this->m_nets[i]->m_cur_Analog = V[i]; } } template ATTR_HOT nl_double matrix_solver_direct_t::vsolve() { this->solve_base(this); return this->compute_next_timestep(); } template ATTR_HOT int matrix_solver_direct_t::solve_non_dynamic(ATTR_UNUSED const bool newton_raphson) { nl_double new_V[_storage_N]; // = { 0.0 }; this->LE_back_subst(new_V); if (newton_raphson) { nl_double err = delta(new_V); store(new_V); return (err > this->m_params.m_accuracy) ? 2 : 1; } else { store(new_V); return 1; } } template ATTR_HOT inline int matrix_solver_direct_t::vsolve_non_dynamic(const bool newton_raphson) { this->build_LE_A(); this->build_LE_RHS(m_last_RHS); for (unsigned i=0, iN=N(); i < iN; i++) m_RHS[i] = m_last_RHS[i]; this->LE_solve(); return this->solve_non_dynamic(newton_raphson); } template matrix_solver_direct_t::matrix_solver_direct_t(const solver_parameters_t *params, const int size) : matrix_solver_t(GAUSSIAN_ELIMINATION, params) , m_dim(size) { m_terms = palloc_array(terms_t *, N()); m_rails_temp = palloc_array(terms_t, N()); for (unsigned k = 0; k < N(); k++) { m_terms[k] = palloc(terms_t); m_last_RHS[k] = 0.0; m_last_V[k] = 0.0; } } template matrix_solver_direct_t::matrix_solver_direct_t(const eSolverType type, const solver_parameters_t *params, const int size) : matrix_solver_t(type, params) , m_dim(size) { m_terms = palloc_array(terms_t *, N()); m_rails_temp = palloc_array(terms_t, N()); for (unsigned k = 0; k < N(); k++) { m_terms[k] = palloc(terms_t); m_last_RHS[k] = 0.0; m_last_V[k] = 0.0; } } NETLIB_NAMESPACE_DEVICES_END() #endif /* NLD_MS_DIRECT_H_ */