def _run_preconditioners(linear_operator, rhs, x0, preconditioners):
tol = 1.0e-10
maxiter = 5000
relresvecs = {}
for prec in preconditioners:
print 'Solving the system with', prec['name'], '...'
start_time = time.clock()
sol, info, relresvec = nm.cg_wrap(linear_operator, rhs,
x0=x0,
tol=tol,
maxiter=maxiter,
M=prec['precondictioner']
)
end_time = time.clock()
relresvecs[prec['name']] = relresvec
if info == 0:
print 'success!',
else:
print 'no convergence.',
print ' (', end_time - start_time, 's,', len(relresvec)-1, ' iters).'
return relresvecs
def _run_preconditioners(linear_operator, rhs, x0, preconditioners):
tol = 1.0e-10
maxiter = 5000
relresvecs = {}
for prec in preconditioners:
print("Solving the system with", prec["name"], "...")
start_time = time.clock()
sol, info, relresvec = nm.cg_wrap(
linear_operator,
rhs,
x0=x0,
tol=tol,
maxiter=maxiter,
M=prec["precondictioner"],
)
end_time = time.clock()
relresvecs[prec["name"]] = relresvec
if info == 0:
print("success!", end=" ")
else:
print("no convergence.", end=" ")
print(" (", end_time - start_time, "s,", len(relresvec) - 1, " iters).")
return relresvecs
def _run_preconditioners(linear_operator, rhs, x0, preconditioners):
tol = 1.0e-10
maxiter = 5000
relresvecs = {}
for prec in preconditioners:
print("Solving the system with", prec["name"], "...")
start_time = time.clock()
sol, info, relresvec = nm.cg_wrap(
linear_operator,
rhs,
x0=x0,
tol=tol,
maxiter=maxiter,
M=prec["precondictioner"],
)
end_time = time.clock()
relresvecs[prec["name"]] = relresvec
if info == 0:
print("success!", end=" ")
else:
print("no convergence.", end=" ")
print(" (", end_time - start_time, "s,",
len(relresvec) - 1, " iters).")
return relresvecs
def _main():
'''
Main function.
'''
# parse input arguments
opts, args = _parse_input_arguments()
state_files = sorted( glob.glob( str(opts.foldername) + '/solution*.vtu' ) )
print state_files[0]
tol = 1.0e-8
maxiter = 5000
# Create the model evaluator.
# Get mu and mesh for the first grid. This way, the mesh doesn't need to
# be reset in each step; this assumes of course that the mesh doesn't
# change throughout the computation.
print "Reading the state \"" + state_files[0] + "\"..."
try:
mesh, psi, field_data = vtkio.read_mesh( state_files[0] )
except AttributeError:
print "Could not read from file ", state_files[0], "."
raise
print " done."
ginla_modelval = ginla_model_evaluator( field_data["mu"] )
ginla_modelval.set_mesh( mesh )
# create precondictioner object
precs = preconditioners( ginla_modelval )
precs.set_mesh( mesh )
# --------------------------------------------------------------------------
# loop over the meshes and compute
num_iterations = []
for state_file in state_files:
# ----------------------------------------------------------------------
# read and set the mesh
print
print "Reading the state \"" + state_file + "\"..."
try:
mesh, psi, field_data = vtkio.read_mesh( state_file )
except AttributeError:
print "Could not read from file ", state_file, "."
raise
print " done."
mu = field_data["mu"]
ginla_modelval.set_parameter( mu )
ginla_modelval.set_current_psi( psi )
precs.set_parameter( mu )
# ----------------------------------------------------------------------
# recreate all the objects necessary to perform the precondictioner run
num_unknowns = len( mesh.nodes )
# create preconditioner
prec_keolu = LinearOperator( (num_unknowns, num_unknowns),
matvec = precs.keo_lu,
dtype = complex
)
# create the linear operator
ginla_jacobian = LinearOperator( (num_unknowns, num_unknowns),
matvec = ginla_modelval.compute_jacobian,
dtype = complex
)
# create right hand side and initial guess
rhs = np.zeros( num_unknowns )
# initial guess for all operations
psi0 = np.random.rand( num_unknowns ) \
+ 1j * np.random.rand( num_unknowns )
# ----------------------------------------------------------------------
# build the kinetic energy operator
print "Building the KEO..."
start_time = time.clock()
ginla_modelval._assemble_kinetic_energy_operator()
end_time = time.clock()
print "done. (", end_time - start_time, "s)."
# ----------------------------------------------------------------------
# Run the preconditioners and gather the relative residuals.
print "Solving the system with KEO/LU precondictioning..."
start_time = time.clock()
sol, info, relresvec = nm.cg_wrap( ginla_jacobian,
rhs,
x0 = psi0,
tol = tol,
maxiter = maxiter,
M = prec_keolu,
inner_product = 'real'
)
end_time = time.clock()
if info == 0:
print "success!",
else:
print "no convergence.",
print " (", end_time - start_time, "s,", len(relresvec)-1 ," iters)."
#pp.semilogy( relresvec )
#pp.show()
# ----------------------------------------------------------------------
# append the number of iterations to the data
num_iterations.append( len( relresvec ) - 1 )
# ----------------------------------------------------------------------
print ( num_iterations )
# plot the number of iterations
pp.plot( num_iterations, 'o' )
# add title and so forth
pp.title( 'CG convergence for $J$' )
pp.xlabel( 'Continuation step $k$' )
pp.ylabel( "Number of CG iterations till $<10^{-10}$" )
matplotlib2tikz.save( "pcg-iterations.tikz",
figurewidth = "\\figurewidth",
figureheight = "\\figureheight"
)
# pp.show()
return
def _main():
"""
Main function.
"""
# parse input arguments
opts, args = _parse_input_arguments()
state_files = sorted(glob.glob(str(opts.foldername) + "/solution*.vtu"))
print(state_files[0])
tol = 1.0e-8
maxiter = 5000
# Create the model evaluator.
# Get mu and mesh for the first grid. This way, the mesh doesn't need to
# be reset in each step; this assumes of course that the mesh doesn't
# change throughout the computation.
print('Reading the state "' + state_files[0] + '"...')
try:
mesh, psi, field_data = vtkio.read_mesh(state_files[0])
except AttributeError:
print("Could not read from file ", state_files[0], ".")
raise
print(" done.")
ginla_modelval = ginla_model_evaluator(field_data["mu"])
ginla_modelval.set_mesh(mesh)
# create precondictioner object
precs = preconditioners(ginla_modelval)
precs.set_mesh(mesh)
# loop over the meshes and compute
num_iterations = []
for state_file in state_files:
# read and set the mesh
print()
print('Reading the state "' + state_file + '"...')
try:
mesh, psi, field_data = vtkio.read_mesh(state_file)
except AttributeError:
print("Could not read from file ", state_file, ".")
raise
print(" done.")
mu = field_data["mu"]
ginla_modelval.set_parameter(mu)
ginla_modelval.set_current_psi(psi)
precs.set_parameter(mu)
# recreate all the objects necessary to perform the precondictioner run
num_unknowns = len(mesh.nodes)
# create preconditioner
prec_keolu = LinearOperator((num_unknowns, num_unknowns),
matvec=precs.keo_lu,
dtype=complex)
# create the linear operator
ginla_jacobian = LinearOperator(
(num_unknowns, num_unknowns),
matvec=ginla_modelval.compute_jacobian,
dtype=complex,
)
# create right hand side and initial guess
rhs = np.zeros(num_unknowns)
# initial guess for all operations
psi0 = np.random.rand(num_unknowns) + 1j * np.random.rand(num_unknowns)
# build the kinetic energy operator
print("Building the KEO...")
start_time = time.clock()
ginla_modelval._assemble_kinetic_energy_operator()
end_time = time.clock()
print("done. (", end_time - start_time, "s).")
# Run the preconditioners and gather the relative residuals.
print("Solving the system with KEO/LU precondictioning...")
start_time = time.clock()
sol, info, relresvec = nm.cg_wrap(
ginla_jacobian,
rhs,
x0=psi0,
tol=tol,
maxiter=maxiter,
M=prec_keolu,
inner_product="real",
)
end_time = time.clock()
if info == 0:
print("success!", end=" ")
else:
print("no convergence.", end=" ")
print(" (", end_time - start_time, "s,",
len(relresvec) - 1, " iters).")
# pp.semilogy( relresvec )
# pp.show()
# append the number of iterations to the data
num_iterations.append(len(relresvec) - 1)
print(num_iterations)
# plot the number of iterations
pp.plot(num_iterations, "o")
# add title and so forth
pp.title("CG convergence for $J$")
pp.xlabel("Continuation step $k$")
pp.ylabel("Number of CG iterations till $<10^{-10}$")
matplotlib2tikz.save(
"pcg-iterations.tikz",
figurewidth="\\figurewidth",
figureheight="\\figureheight",
)
# pp.show()
return
