""" 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
[docs]class ScipyGMRES(LinearSolver):
""" Scipy's GMRES Solver. This is a serial solver, so
it should never be used in an MPI setting.
"""
def __init__(self):
super(ScipyGMRES, self).__init__()
opt = self.options
opt.add_option('atol', 1e-12,
desc='Absolute convergence tolerance.')
opt.add_option('maxiter', 100,
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('precondition', False,
desc='Set to True to turn on preconditioning.')
# 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
[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 = {}
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.options['precondition'] == True:
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'],
callback=self.monitor)
self.system = None
if info > 0:
msg = "ERROR in solve in '{}': gmres failed to converge " \
"after {} iterations"
print(msg.format(system.name, options['maxiter']))
msg = 'FAILED to converge after hitting max iterations'
#logger.error(msg, system.name, info)
elif info < 0:
msg = "ERROR in solve in '{}': gmres failed"
print(msg.format(system.name))
msg = 'FAILED to converge'
#logger.error(msg, system.name)
else:
msg = 'Converged'
if self.options['iprint'] > 0:
self.print_norm('GMRES', 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.apply_linear(mode, ls_inputs=self.system._ls_inputs, vois=(voi,))
#print("arg", arg)
#print("result", rhs_vec.vec)
return rhs_vec.vec
[docs] def precon(self, arg):
""" GMRES Callback: applies a preconditioner by calling
solve_nonlinear 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 = {}
dumat[voi] = system.dumat[voi]
drmat = {}
drmat[voi] = system.drmat[voi]
system.solve_linear(dumat, drmat, (voi, ), mode=mode, precon=True)
#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('GMRES', self.system.pathname, self.iter_count,
f_norm, self._norm0, indent=1, solver='LN')
self.iter_count += 1
