// license:GPL-2.0+ // copyright-holders:Couriersud /* * nld_ms_direct.h * * * Woodbury Solver * * Computes the updated solution of A given that the change in A is * * A <- A + (U x transpose(V)) U,V matrices * * The approach is describes in "Numerical Recipes in C", Second edition, Page 75ff * * Whilst the book proposes to invert the matrix R=(I+transpose(V)*Z) we define * * w = transpose(V)*y * a = R⁻¹ * w * * and consequently * * R * a = w * * And solve for a using Gaussian elimination. This is a lot faster. * * One fact omitted in the book is the fact that actually the matrix Z which contains * in it's columns the solutions of * * A * zk = uk * * for uk being unit vectors for full rank (max(k) == n) is identical to the * inverse of A. * * The approach performs relatively well for matrices up to n ~ 40 (kidniki using frontiers). * Kidniki without frontiers has n==88. Here, the average number of Newton-Raphson * loops increase to 20. It looks like that the approach for larger matrices * introduces numerical instability. */ #ifndef NLD_MS_W_H_ #define NLD_MS_W_H_ #include #include "solver/nld_solver.h" #include "solver/nld_matrix_solver.h" #include "solver/vector_base.h" namespace netlist { namespace devices { //#define nl_ext_double _float128 // slow, very slow //#define nl_ext_double long double // slightly slower #define nl_ext_double nl_double template class matrix_solver_w_t: public matrix_solver_t { friend class matrix_solver_t; public: matrix_solver_w_t(netlist_t &anetlist, const pstring &name, const solver_parameters_t *params, const int size); virtual ~matrix_solver_w_t(); virtual void vsetup(analog_net_t::list_t &nets) override; virtual void reset() override { matrix_solver_t::reset(); } protected: virtual int vsolve_non_dynamic(const bool newton_raphson) override; int solve_non_dynamic(const bool newton_raphson); inline unsigned N() const { if (m_N == 0) return m_dim; else return m_N; } void LE_invert(); template void LE_compute_x(T * RESTRICT x); template inline nl_ext_double &A(const T1 &r, const T2 &c) { return m_A[r][c]; } template inline nl_ext_double &W(const T1 &r, const T2 &c) { return m_W[r][c]; } /* access to Ainv for fixed columns over row, there store transposed */ template inline nl_ext_double &Ainv(const T1 &r, const T2 &c) { return m_Ainv[c][r]; } template inline nl_ext_double &RHS(const T1 &r) { return m_RHS[r]; } template inline nl_ext_double &lA(const T1 &r, const T2 &c) { return m_lA[r][c]; } nl_double m_last_RHS[storage_N]; // right hand side - contains currents private: static const std::size_t m_pitch = ((( storage_N) + 7) / 8) * 8; nl_ext_double m_A[storage_N][m_pitch]; nl_ext_double m_Ainv[storage_N][m_pitch]; nl_ext_double m_W[storage_N][m_pitch]; nl_ext_double m_RHS[storage_N]; // right hand side - contains currents nl_ext_double m_lA[storage_N][m_pitch]; /* temporary */ nl_double H[storage_N][m_pitch] ; unsigned rows[storage_N]; unsigned cols[storage_N][m_pitch]; unsigned colcount[storage_N]; unsigned m_cnt; //nl_ext_double m_RHSx[storage_N]; const unsigned m_dim; }; // ---------------------------------------------------------------------------------------- // matrix_solver_direct // ---------------------------------------------------------------------------------------- template matrix_solver_w_t::~matrix_solver_w_t() { } template void matrix_solver_w_t::vsetup(analog_net_t::list_t &nets) { if (m_dim < nets.size()) log().fatal("Dimension {1} less than {2}", m_dim, nets.size()); matrix_solver_t::setup_base(nets); netlist().save(*this, m_last_RHS, "m_last_RHS"); for (unsigned k = 0; k < N(); k++) netlist().save(*this, RHS(k), plib::pfmt("RHS.{1}")(k)); } template void matrix_solver_w_t::LE_invert() { const unsigned kN = N(); for (unsigned i = 0; i < kN; i++) { for (unsigned 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 (unsigned i = 0; i < kN; i++) { /* FIXME: Singular matrix? */ const nl_double f = 1.0 / W(i,i); const auto * 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 auto * 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 auto j = pb[jb]; const nl_double f1 = - W(j,i) * f; if (f1 != 0.0) { for (unsigned k = 0; k < e; k++) W(j,p[k]) += W(i,p[k]) * f1; for (unsigned k = 0; k <= i; k ++) Ainv(j,k) += Ainv(i,k) * f1; } } } /* up */ for (int i = kN - 1; i >= 0; i--) { /* FIXME: Singular matrix? */ const nl_double f = 1.0 / W(i,i); for (int j = i - 1; j>=0; j--) { const nl_double f1 = - W(j,i) * f; if (f1 != 0.0) { for (unsigned k = i; k < kN; k++) W(j,k) += W(i,k) * f1; for (unsigned k = 0; k < kN; k++) Ainv(j,k) += Ainv(i,k) * f1; } } for (unsigned k = 0; k < kN; k++) { Ainv(i,k) *= f; } } } template template void matrix_solver_w_t::LE_compute_x( T * RESTRICT x) { const unsigned kN = N(); for (unsigned i=0; i int matrix_solver_w_t::solve_non_dynamic(ATTR_UNUSED const bool newton_raphson) { const auto iN = N(); nl_double new_V[storage_N]; // = { 0.0 }; if ((m_cnt % 100) == 0) { /* complete calculation */ this->LE_invert(); this->LE_compute_x(new_V); } else { /* Solve Ay = b for y */ this->LE_compute_x(new_V); /* determine changed rows */ unsigned rowcount=0; #define VT(r,c) (A(r,c) - lA(r,c)) for (unsigned row = 0; row < iN; row ++) { unsigned cc=0; auto &nz = m_terms[row]->m_nz; for (auto & col : nz) { if (A(row,col) != lA(row,col)) cols[rowcount][cc++] = col; } if (cc > 0) { colcount[rowcount] = cc; rows[rowcount++] = row; } } if (rowcount > 0) { /* construct w = transform(V) * y * dim: rowcount x iN * */ nl_double w[storage_N]; for (unsigned i = 0; i < rowcount; i++) { const unsigned r = rows[i]; double tmp = 0.0; for (unsigned k = 0; k < iN; k++) tmp += VT(r,k) * new_V[k]; w[i] = tmp; } for (unsigned i = 0; i < rowcount; i++) for (unsigned k=0; k< rowcount; k++) H[i][k] = 0.0; for (unsigned i = 0; i < rowcount; i++) H[i][i] = 1.0; /* Construct H = (I + VT*Z) */ for (unsigned i = 0; i < rowcount; i++) for (unsigned k=0; k< colcount[i]; k++) { const unsigned col = cols[i][k]; nl_double f = VT(rows[i],col); if (f!=0.0) for (unsigned j= 0; j < rowcount; j++) H[i][j] += f * Ainv(col,rows[j]); } /* Gaussian elimination of H */ for (unsigned i = 0; i < rowcount; i++) { if (H[i][i] == 0.0) printf("%s H singular\n", this->name().cstr()); const nl_double f = 1.0 / H[i][i]; for (unsigned j = i+1; j < rowcount; j++) { const nl_double f1 = - f * H[j][i]; if (f1!=0.0) { nl_double *pj = &H[j][i+1]; const nl_double *pi = &H[i][i+1]; for (unsigned k = 0; k < rowcount-i-1; k++) pj[k] += f1 * pi[k]; //H[j][k] += f1 * H[i][k]; w[j] += f1 * w[i]; } } } /* Back substitution */ //inv(H) w = t w = H t nl_double t[storage_N]; // FIXME: convert to member for (int j = rowcount - 1; j >= 0; j--) { nl_double tmp = 0; const nl_double *pj = &H[j][j+1]; const nl_double *tj = &t[j+1]; for (unsigned k = 0; k < rowcount-j-1; k++) tmp += pj[k] * tj[k]; //tmp += H[j][k] * t[k]; t[j] = (w[j] - tmp) / H[j][j]; } /* x = y - Zt */ for (unsigned i=0; i 1e-6) printf("%s failed on row %d: %f RHS: %f\n", this->name().cstr(), i, std::abs(tmp-RHS(i)), RHS(i)); } 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 inline int matrix_solver_w_t::vsolve_non_dynamic(const bool newton_raphson) { build_LE_A(); build_LE_RHS(); for (unsigned i=0, iN=N(); i < iN; i++) m_last_RHS[i] = RHS(i); this->m_stat_calculations++; return this->solve_non_dynamic(newton_raphson); } template matrix_solver_w_t::matrix_solver_w_t(netlist_t &anetlist, const pstring &name, const solver_parameters_t *params, const int size) : matrix_solver_t(anetlist, name, NOSORT, params) ,m_cnt(0) , m_dim(size) { for (unsigned k = 0; k < N(); k++) { m_last_RHS[k] = 0.0; } } } //namespace devices } // namespace netlist #endif /* NLD_MS_DIRECT_H_ */