""" OpenMDAO LinearSolver that uses Scipy's GMRES to solve for derivatives."""
from __future__ import print_function
from six import iteritems
import numpy as np
from scipy.sparse.linalg import gmres, LinearOperator
from openmdao.solvers.solver_base import LinearSolver
from collections import OrderedDict
[docs]class ScipyGMRES(LinearSolver):
""" Scipy's GMRES Solver. This is a serial solver, so it should never be
used in an MPI setting. A preconditioner can be specified by placing
another linear solver into `self.preconditioner`.
Options
-------
options['atol'] : float(1e-12)
Absolute convergence tolerance.
options['iprint'] : int(0)
Set to 0 to disable printing, set to 1 to print the residual to stdout each
iteration, set to 2 to print subiteration residuals as well.
options['maxiter'] : int(1000)
Maximum number of iterations.
options['mode'] : str('auto')
Derivative calculation mode, set to 'fwd' for forward mode, 'rev' for reverse
mode, or 'auto' to let OpenMDAO determine the best mode.
options['restart'] : int(20)
Number of iterations between restarts. Larger values increase iteration cost,
but may be necessary for convergence
"""
def __init__(self):
super(ScipyGMRES, self).__init__()
opt = self.options
opt.add_option('atol', 1e-12, lower=0.0,
desc='Absolute convergence tolerance.')
opt.add_option('maxiter', 1000, lower=0,
desc='Maximum number of iterations.')
opt.add_option('mode', 'auto', values=['fwd', 'rev', 'auto'],
desc="Derivative calculation mode, set to 'fwd' for " +
"forward mode, 'rev' for reverse mode, or 'auto' to " +
"let OpenMDAO determine the best mode.")
opt.add_option('restart', 20, lower=0,
desc='Number of iterations between restarts. Larger values ' +
'increase iteration cost, but may be necessary for convergence')
# These are defined whenever we call solve to provide info we need in
# the callback.
self.system = None
self.voi = None
self.mode = None
self._norm0 = 0.0
self.print_name = 'GMRES'
# User can specify another linear solver to use as a preconditioner
self.preconditioner = None
[docs] def setup(self, sub):
""" Initialize sub solvers.
Args
----
sub: `System`
System that owns this solver.
"""
if self.preconditioner:
self.preconditioner.setup(sub)
[docs] def solve(self, rhs_mat, system, mode):
""" Solves the linear system for the problem in self.system. The
full solution vector is returned.
Args
----
rhs_mat : dict of ndarray
Dictionary containing one ndarry per top level quantity of
interest. Each array contains the right-hand side for the linear
solve.
system : `System`
Parent `System` object.
mode : string
Derivative mode, can be 'fwd' or 'rev'.
Returns
-------
dict of ndarray : Solution vectors
"""
options = self.options
self.mode = mode
unknowns_mat = OrderedDict()
for voi, rhs in iteritems(rhs_mat):
# Scipy can only handle one right-hand-side at a time.
self.voi = voi
n_edge = len(rhs)
A = LinearOperator((n_edge, n_edge),
matvec=self.mult,
dtype=float)
# Support a preconditioner
if self.preconditioner:
M = LinearOperator((n_edge, n_edge),
matvec=self._precon,
dtype=float)
else:
M = None
# Call GMRES to solve the linear system
self.system = system
self.iter_count = 0
d_unknowns, info = gmres(A, rhs, M=M,
tol=options['atol'],
maxiter=options['maxiter'],
restart=options['restart'],
callback=self.monitor)
self.system = None
if info > 0:
msg = "Solve in '{}': gmres failed to converge " \
"after {} iterations"
print(msg.format(system.name, options['maxiter']))
#logger.error(msg, system.name, info)
msg = 'FAILED to converge after max iterations'
elif info < 0:
msg = "ERROR in solve in '{}': gmres failed"
print(msg.format(system.name))
#logger.error(msg, system.name)
msg = 'ERROR returned from GMRES'
else:
msg = 'Converged'
if self.options['iprint'] > 0:
self.print_norm(self.print_name, system.pathname, self.iter_count,
0, 0, msg=msg, solver='LN')
unknowns_mat[voi] = d_unknowns
#print(system.name, 'Linear solution vec', d_unknowns)
return unknowns_mat
[docs] def mult(self, arg):
""" GMRES Callback: applies Jacobian matrix. Mode is determined by the
system.
Args
----
arg : ndarray
Incoming vector
Returns
-------
ndarray : Matrix vector product of arg with jacobian
"""
system = self.system
mode = self.mode
voi = self.voi
if mode == 'fwd':
sol_vec, rhs_vec = system.dumat[voi], system.drmat[voi]
else:
sol_vec, rhs_vec = system.drmat[voi], system.dumat[voi]
# Set incoming vector
sol_vec.vec[:] = arg
# Start with a clean slate
rhs_vec.vec[:] = 0.0
system.clear_dparams()
system._sys_apply_linear(mode, self.system._do_apply, vois=(voi,))
#print("arg", arg)
#print("result", rhs_vec.vec)
return rhs_vec.vec
def _precon(self, arg):
""" GMRES Callback: applies a preconditioner by calling
solve_linear on this system's children.
Args
----
arg : ndarray
Incoming vector
Returns
-------
ndarray : Preconditioned vector
"""
system = self.system
mode = self.mode
voi = self.voi
if mode == 'fwd':
sol_vec, rhs_vec = system.dumat[voi], system.drmat[voi]
else:
sol_vec, rhs_vec = system.drmat[voi], system.dumat[voi]
# Set incoming vector
rhs_vec.vec[:] = arg[:]
# Start with a clean slate
system.clear_dparams()
dumat = OrderedDict()
dumat[voi] = system.dumat[voi]
drmat = OrderedDict()
drmat[voi] = system.drmat[voi]
with system._dircontext:
system.solve_linear(dumat, drmat, (voi, ), mode=mode,
solver=self.preconditioner)
#print("arg", arg)
#print("preconditioned arg", precon_rhs)
return sol_vec.vec
[docs] def monitor(self, res):
""" GMRES Callback: Prints the current residual norm.
Args
----
res : ndarray
Current residual.
"""
if self.options['iprint'] > 0:
f_norm = np.linalg.norm(res)
if self.iter_count == 0:
if f_norm != 0.0:
self._norm0 = f_norm
else:
self._norm0 = 1.0
self.print_norm(self.print_name, self.system.pathname, self.iter_count,
f_norm, self._norm0, indent=1, solver='LN')
# The only way to count iterations of gmres is to increment this
# every time monitor is called.
self.iter_count += 1
