def nr_step(self): """ Single step using Newton-Raphson method. Returns ------- float maximum absolute mismatch """ system = self.system # evaluate discrete, differential, algebraic, and Jacobians system.dae.clear_fg() system.l_update_var(self.models, niter=self.niter, err=self.mis[-1]) system.s_update_var(self.models) system.f_update(self.models) system.g_update(self.models) system.l_update_eq(self.models) system.fg_to_dae() if self.config.method == 'NR': system.j_update(models=self.models) elif self.config.method == 'dishonest': if self.niter < self.config.n_factorize: system.j_update(self.models) # prepare and solve linear equations self.inc = -matrix([matrix(system.dae.f), matrix(system.dae.g)]) self.A = sparse([[system.dae.fx, system.dae.gx], [system.dae.fy, system.dae.gy]]) if not self.config.linsolve: self.inc = self.solver.solve(self.A, self.inc) else: self.inc = self.solver.linsolve(self.A, self.inc) system.dae.x += np.ravel(np.array(self.inc[:system.dae.n])) system.dae.y += np.ravel(np.array(self.inc[system.dae.n:])) # find out variables associated with maximum mismatches fmax = 0 if system.dae.n > 0: fmax_idx = np.argmax(np.abs(system.dae.f)) fmax = system.dae.f[fmax_idx] logger.debug("Max. diff mismatch %.10g on %s", fmax, system.dae.x_name[fmax_idx]) gmax_idx = np.argmax(np.abs(system.dae.g)) gmax = system.dae.g[gmax_idx] logger.debug("Max. algeb mismatch %.10g on %s", gmax, system.dae.y_name[gmax_idx]) mis = max(abs(fmax), abs(gmax)) if self.niter == 0: self.mis[0] = mis else: self.mis.append(mis) system.vars_to_models() return mis
def nr_step(self): """ Single stepping for Newton Raphson method Returns ------- """ system = self.system # evaluate discrete, differential, algebraic, and jacobians system.e_clear() system.l_update_var() system.f_update() system.g_update() system.l_check_eq() system.l_set_eq() system.fg_to_dae() system.j_update() # prepare and solve linear equations self.inc = -matrix([matrix(system.dae.f), matrix(system.dae.g)]) self.A = sparse([[system.dae.fx, system.dae.gx], [system.dae.fy, system.dae.gy]]) self.inc = self.solver.solve(self.A, self.inc) system.dae.x += np.ravel(np.array(self.inc[:system.dae.n])) system.dae.y += np.ravel(np.array(self.inc[system.dae.n:])) mis = np.max(np.abs(system.dae.fg)) self.mis.append(mis) system.vars_to_models() return mis
def calc_jac(tds, gxs, gys): """ Build full Jacobian matrix ``Ac`` for Trapezoid method. """ dae = tds.system.dae return sparse([[tds.Teye - tds.h * 0.5 * dae.fx, gxs], [-tds.h * 0.5 * dae.fy, gys]], 'd')
def _calc_state_matrix(self, fx, fy, gx, gy, Tf, dense=True): """ Kernel function for calculating state matrix. """ gyx = matrix(gx) self.solver.linsolve(gy, gyx) Tfnz = Tf + np.ones_like(Tf) * np.equal(Tf, 0.0) iTf = spdiag((1 / Tfnz).tolist()) if dense: return iTf * (fx - fy * gyx) else: return sparse(iTf * (fx - fy * gyx))
def nr_step(self): """ Single step using Newton-Raphson method. Returns ------- float maximum absolute mismatch """ system = self.system # evaluate discrete, differential, algebraic, and Jacobians system.dae.clear_fg() system.l_update_var(self.models, niter=self.niter, err=self.mis[-1]) system.s_update_var(self.models) system.f_update(self.models) system.g_update(self.models) system.l_update_eq(self.models) system.fg_to_dae() if self.config.method == 'NR': system.j_update(models=self.models) elif self.config.method == 'dishonest': if self.niter < self.config.n_factorize: system.j_update(self.models) # prepare and solve linear equations self.inc = -matrix([matrix(system.dae.f), matrix(system.dae.g)]) self.A = sparse([[system.dae.fx, system.dae.gx], [system.dae.fy, system.dae.gy]]) if not self.config.linsolve: self.inc = self.solver.solve(self.A, self.inc) else: self.inc = self.solver.linsolve(self.A, self.inc) system.dae.x += np.ravel(np.array(self.inc[:system.dae.n])) system.dae.y += np.ravel(np.array(self.inc[system.dae.n:])) mis = np.max(np.abs(system.dae.fg)) if self.niter == 0: self.mis[0] = mis else: self.mis.append(mis) system.vars_to_models() return mis
def _reduce(self, fx, fy, gx, gy, Tf, dense=True): """ Reduce algebraic equations (or states associated with zero time constants). Returns ------- spmatrix The reduced state matrix """ gyx = matrix(gx) self.solver.linsolve(gy, gyx) Tfnz = Tf + np.ones_like(Tf) * np.equal(Tf, 0.0) iTf = spdiag((1 / Tfnz).tolist()) if dense: return iTf * (fx - fy * gyx) else: return sparse(iTf * (fx - fy * gyx))
def reorder_As(self): """ reorder As by moving rows and cols associated with zero time constants to the end. Returns `fx`, `fy`, `gx`, `gy`, `Tf`. """ system = self.system rows = np.arange(system.dae.n, dtype=int) cols = np.arange(system.dae.n, dtype=int) vals = np.ones(system.dae.n, dtype=float) swaps = [] bidx = self.non_zeros for ii in range(system.dae.n - self.non_zeros): if ii in self.singular_idx: while (bidx in self.singular_idx): bidx += 1 cols[ii] = bidx rows[bidx] = ii swaps.append((ii, bidx)) # swap the variable names for fr, bk in swaps: bk_name = self.x_name[bk] self.x_name[fr] = bk_name self.x_name = self.x_name[:self.non_zeros] # compute the permutation matrix for `As` containing non-states perm = spmatrix(matrix(vals), matrix(rows), matrix(cols)) As_perm = perm * sparse(self.As) * perm self.As_perm = As_perm nfx = As_perm[:self.non_zeros, :self.non_zeros] nfy = As_perm[:self.non_zeros, self.non_zeros:] ngx = As_perm[self.non_zeros:, :self.non_zeros] ngy = As_perm[self.non_zeros:, self.non_zeros:] nTf = np.delete(system.dae.Tf, self.singular_idx) return nfx, nfy, ngx, ngy, nTf
def _implicit_step(self): """ Integrate for a single given step. This function has an internal Newton-Raphson loop for algebraized semi-explicit DAE. The function returns the convergence status when done but does NOT progress simulation time. Returns ------- bool Convergence status in ``self.converged``. """ system = self.system dae = self.system.dae self.mis = [] self.niter = 0 self.converged = False self.x0 = np.array(dae.x) self.y0 = np.array(dae.y) self.f0 = np.array(dae.f) while True: system.e_clear(models=self.pflow_tds_models) system.l_update_var(models=self.pflow_tds_models) system.f_update(models=self.pflow_tds_models) system.g_update(models=self.pflow_tds_models) system.l_check_eq(models=self.pflow_tds_models) system.l_set_eq(models=self.pflow_tds_models) system.fg_to_dae() # lazy jacobian update if dae.t == 0 or self.niter > 3 or (dae.t - self._last_switch_t < 0.2): system.j_update(models=self.pflow_tds_models) self.solver.factorize = True # solve trapezoidal rule integration In = spdiag([1] * dae.n) self.Ac = sparse([[In - self.h * 0.5 * dae.fx, dae.gx], [-self.h * 0.5 * dae.fy, dae.gy]], 'd') # reset q as well q = dae.x - self.x0 - self.h * 0.5 * (dae.f + self.f0) for item in system.antiwindups: if len(item.x_set) > 0: for key, val in item.x_set: np.put(q, key[np.where(item.zi == 0)], 0) qg = np.hstack((q, dae.g)) inc = self.solver.solve(self.Ac, -matrix(qg)) # check for np.nan first if np.isnan(inc).any(): logger.error(f'NaN found in solution. Convergence not likely') self.niter = self.config.max_iter + 1 self.busted = True break # reset really small values to avoid anti-windup limiter flag jumps inc[np.where(np.abs(inc) < 1e-12)] = 0 # set new values dae.x += np.ravel(np.array(inc[:dae.n])) dae.y += np.ravel(np.array(inc[dae.n: dae.n + dae.m])) system.vars_to_models() # calculate correction mis = np.max(np.abs(inc)) self.mis.append(mis) self.niter += 1 # converged if mis <= self.config.tol: self.converged = True break # non-convergence cases if self.niter > self.config.max_iter: logger.debug(f'Max. iter. {self.config.max_iter} reached for t={dae.t:.6f}, ' f'h={self.h:.6f}, mis={mis:.4g} ' f'({system.dae.xy_name[np.argmax(inc)]})') break if mis > 1000 and (mis > 1e8 * self.mis[0]): logger.error(f'Error increased too quickly. Convergence not likely.') self.busted = True break if not self.converged: dae.x = np.array(self.x0) dae.y = np.array(self.y0) dae.f = np.array(self.f0) system.vars_to_models() return self.converged
def _itm_step(self): """ Integrate with Implicit Trapezoidal Method (ITM) to the current time. This function has an internal Newton-Raphson loop for algebraized semi-explicit DAE. The function returns the convergence status when done but does NOT progress simulation time. Returns ------- bool Convergence status in ``self.converged``. """ system = self.system dae = self.system.dae self.mis = 1 self.niter = 0 self.converged = False self.x0 = np.array(dae.x) self.y0 = np.array(dae.y) self.f0 = np.array(dae.f) while True: self._fg_update(models=system.exist.pflow_tds) # lazy Jacobian update if dae.t == 0 or \ self.config.honest or \ self.custom_event or \ not self.last_converged or \ self.niter > 4 or \ (dae.t - self._last_switch_t < 0.1): system.j_update(models=system.exist.pflow_tds) # set flag in `solver.worker.factorize`, not `solver.factorize`. self.solver.worker.factorize = True # `Tf` should remain constant throughout the simulation, even if the corresponding diff. var. # is pegged by the anti-windup limiters. # solve implicit trapezoidal method (ITM) integration self.Ac = sparse([[self.Teye - self.h * 0.5 * dae.fx, dae.gx], [-self.h * 0.5 * dae.fy, dae.gy]], 'd') # equation `self.qg[:dae.n] = 0` is the implicit form of differential equations using ITM self.qg[:dae.n] = dae.Tf * (dae.x - self.x0) - self.h * 0.5 * (dae.f + self.f0) # reset the corresponding q elements for pegged anti-windup limiter for item in system.antiwindups: for key, _, eqval in item.x_set: np.put(self.qg, key, eqval) self.qg[dae.n:] = dae.g if not self.config.linsolve: inc = self.solver.solve(self.Ac, matrix(self.qg)) else: inc = self.solver.linsolve(self.Ac, matrix(self.qg)) # check for np.nan first if np.isnan(inc).any(): self.err_msg = 'NaN found in solution. Convergence is not likely' self.niter = self.config.max_iter + 1 self.busted = True break # reset small values to reduce chattering inc[np.where(np.abs(inc) < self.tol_zero)] = 0 # set new values dae.x -= inc[:dae.n].ravel() dae.y -= inc[dae.n: dae.n + dae.m].ravel() # store `inc` to self for debugging self.inc = inc system.vars_to_models() # calculate correction mis = np.max(np.abs(inc)) # store initial maximum mismatch if self.niter == 0: self.mis = mis self.niter += 1 # converged if mis <= self.config.tol: self.converged = True break # non-convergence cases if self.niter > self.config.max_iter: tqdm.write(f'* Max. iter. {self.config.max_iter} reached for t={dae.t:.6f}, ' f'h={self.h:.6f}, mis={mis:.4g} ') # debug helpers g_max = np.argmax(abs(dae.g)) inc_max = np.argmax(abs(inc)) self._debug_g(g_max) self._debug_ac(inc_max) break if mis > 1e6 and (mis > 1e6 * self.mis): self.err_msg = 'Error increased too quickly. Convergence not likely.' self.busted = True break if not self.converged: dae.x[:] = np.array(self.x0) dae.y[:] = np.array(self.y0) dae.f[:] = np.array(self.f0) system.vars_to_models() self.last_converged = self.converged return self.converged
def _itm_step(self): """ Integrate with Implicit Trapezoidal Method (ITM) to the current time. This function has an internal Newton-Raphson loop for algebraized semi-explicit DAE. The function returns the convergence status when done but does NOT progress simulation time. Returns ------- bool Convergence status in ``self.converged``. """ system = self.system dae = self.system.dae self.mis = 1 self.niter = 0 self.converged = False self.x0 = np.array(dae.x) self.y0 = np.array(dae.y) self.f0 = np.array(dae.f) while True: self._fg_update(models=system.exist.pflow_tds) # lazy Jacobian update if dae.t == 0 or self.niter > 3 or (dae.t - self._last_switch_t < 0.2): system.j_update(models=system.exist.pflow_tds) self.solver.factorize = True # TODO: set the `Tf` corresponding to the pegged anti-windup limiters to zero. # Although this should not affect anything since corr. mismatches in `self.qg` are reset to zero # solve implicit trapezoidal method (ITM) integration self.Ac = sparse([[self.Teye - self.h * 0.5 * dae.fx, dae.gx], [-self.h * 0.5 * dae.fy, dae.gy]], 'd') # equation `self.qg[:dae.n] = 0` is the implicit form of differential equations using ITM self.qg[:dae.n] = dae.Tf * (dae.x - self.x0) - self.h * 0.5 * (dae.f + self.f0) # reset the corresponding q elements for pegged anti-windup limiter for item in system.antiwindups: for key, val in item.x_set: np.put(self.qg, key, 0) self.qg[dae.n:] = dae.g if not self.config.linsolve: inc = self.solver.solve(self.Ac, -matrix(self.qg)) else: inc = self.solver.linsolve(self.Ac, -matrix(self.qg)) # check for np.nan first if np.isnan(inc).any(): self.err_msg = 'NaN found in solution. Convergence not likely' self.niter = self.config.max_iter + 1 self.busted = True break # reset small values to reduce chattering inc[np.where(np.abs(inc) < self.tol_zero)] = 0 # set new values dae.x += inc[:dae.n].ravel() dae.y += inc[dae.n: dae.n + dae.m].ravel() system.vars_to_models() # calculate correction mis = np.max(np.abs(inc)) if self.niter == 0: self.mis = mis self.niter += 1 # converged if mis <= self.config.tol: self.converged = True break # non-convergence cases if self.niter > self.config.max_iter: logger.debug(f'Max. iter. {self.config.max_iter} reached for t={dae.t:.6f}, ' f'h={self.h:.6f}, mis={mis:.4g} ') # debug helpers g_max = np.argmax(abs(dae.g)) inc_max = np.argmax(abs(inc)) self._debug_g(g_max) self._debug_ac(inc_max) break if mis > 1000 and (mis > 1e8 * self.mis): self.err_msg = 'Error increased too quickly. Convergence not likely.' self.busted = True break if not self.converged: dae.x = np.array(self.x0) dae.y = np.array(self.y0) dae.f = np.array(self.f0) system.vars_to_models() return self.converged