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
