def reduce_adaptive_greedy(d, reductor, validation_mus,
extension_alg_name, max_extensions, use_estimator,
rho, gamma, theta, pool):
from pymor.algorithms.adaptivegreedy import adaptive_greedy
# run greedy
greedy_data = adaptive_greedy(d, reductor, validation_mus=-validation_mus,
use_estimator=use_estimator, error_norm=d.h1_0_semi_norm,
extension_params={'method': extension_alg_name}, max_extensions=max_extensions,
rho=rho, gamma=gamma, theta=theta, pool=pool)
rd = greedy_data['rd']
# generate summary
real_rb_size = rd.solution_space.dim
# the validation set consists of `validation_mus` random parameters plus the centers of the adaptive sample set cells
validation_mus += 1
summary = '''Adaptive greedy basis generation:
initial size of validation set: {validation_mus}
error estimator used: {use_estimator}
extension method: {extension_alg_name}
prescribed basis size: {max_extensions}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
'''.format(**locals())
return rd, summary
def reduce_adaptive_greedy(d, reductor, validation_mus, extension_alg_name,
max_extensions, use_estimator, rho, gamma, theta,
pool):
from pymor.algorithms.adaptivegreedy import adaptive_greedy
# run greedy
greedy_data = adaptive_greedy(
d,
reductor,
validation_mus=-validation_mus,
use_estimator=use_estimator,
error_norm=d.h1_0_semi_norm,
extension_params={'method': extension_alg_name},
max_extensions=max_extensions,
rho=rho,
gamma=gamma,
theta=theta,
pool=pool)
rd = greedy_data['reduced_discretization']
# generate summary
real_rb_size = rd.solution_space.dim
# the validation set consists of `validation_mus` random parameters plus the centers of the adaptive sample set cells
validation_mus += 1
summary = '''Adaptive greedy basis generation:
initial size of validation set: {validation_mus}
error estimator used: {use_estimator}
extension method: {extension_alg_name}
prescribed basis size: {max_extensions}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
'''.format(**locals())
return rd, summary
def reduce_adaptive_greedy(
d, reductor, validation_mus, extension_alg_name, max_extensions, use_estimator, rho, gamma, theta, pool
):
from pymor.algorithms.basisextension import trivial_basis_extension, gram_schmidt_basis_extension
from pymor.algorithms.adaptivegreedy import adaptive_greedy
# choose basis extension algorithm
if extension_alg_name == "trivial":
extension_algorithm = trivial_basis_extension
elif extension_alg_name == "gram_schmidt":
extension_algorithm = gram_schmidt_basis_extension
elif extension_alg_name == "h1_gram_schmidt":
extension_algorithm = partial(gram_schmidt_basis_extension, product=d.h1_0_semi_product)
else:
assert False
# run greedy
greedy_data = adaptive_greedy(
d,
reductor,
validation_mus=-validation_mus,
use_estimator=use_estimator,
error_norm=d.h1_0_semi_norm,
extension_algorithm=extension_algorithm,
max_extensions=max_extensions,
rho=rho,
gamma=gamma,
theta=theta,
pool=pool,
)
rd, rc = greedy_data["reduced_discretization"], greedy_data["reconstructor"]
# generate summary
real_rb_size = rd.solution_space.dim
validation_mus += 1 # the validation set consists of `validation_mus` random parameters
# plus the centers of the adaptive sample set cells
summary = """Adaptive greedy basis generation:
initial size of validation set: {validation_mus}
error estimator used: {use_estimator}
extension method: {extension_alg_name}
prescribed basis size: {max_extensions}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
""".format(
**locals()
)
return rd, rc, summary
def reduce_adaptive_greedy(d, reductor, validation_mus, extension_alg_name,
max_extensions, use_estimator, rho, gamma, theta,
pool):
from pymor.algorithms.basisextension import trivial_basis_extension, gram_schmidt_basis_extension
from pymor.algorithms.adaptivegreedy import adaptive_greedy
# choose basis extension algorithm
if extension_alg_name == 'trivial':
extension_algorithm = trivial_basis_extension
elif extension_alg_name == 'gram_schmidt':
extension_algorithm = gram_schmidt_basis_extension
elif extension_alg_name == 'h1_gram_schmidt':
extension_algorithm = partial(gram_schmidt_basis_extension,
product=d.h1_0_semi_product)
else:
assert False
# run greedy
greedy_data = adaptive_greedy(d,
reductor,
validation_mus=-validation_mus,
use_estimator=use_estimator,
error_norm=d.h1_0_semi_norm,
extension_algorithm=extension_algorithm,
max_extensions=max_extensions,
rho=rho,
gamma=gamma,
theta=theta,
pool=pool)
rd, rc = greedy_data['reduced_discretization'], greedy_data[
'reconstructor']
# generate summary
real_rb_size = rd.solution_space.dim
validation_mus += 1 # the validation set consists of `validation_mus` random parameters
# plus the centers of the adaptive sample set cells
summary = '''Adaptive greedy basis generation:
initial size of validation set: {validation_mus}
error estimator used: {use_estimator}
extension method: {extension_alg_name}
prescribed basis size: {max_extensions}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
'''.format(**locals())
return rd, rc, summary
def thermalblock_demo(args):
args['--grid'] = int(args['--grid'])
args['RBSIZE'] = int(args['RBSIZE'])
args['--test'] = int(args['--test'])
args['--ipython-engines'] = int(args['--ipython-engines'])
args['--estimator-norm'] = args['--estimator-norm'].lower()
assert args['--estimator-norm'] in {'trivial', 'h1'}
args['--extension-alg'] = args['--extension-alg'].lower()
assert args['--extension-alg'] in {'trivial', 'gram_schmidt', 'h1_gram_schmidt'}
args['--reductor'] = args['--reductor'].lower()
assert args['--reductor'] in {'traditional', 'residual_basis'}
args['--cache-region'] = args['--cache-region'].lower()
args['--validation-mus'] = int(args['--validation-mus'])
args['--rho'] = float(args['--rho'])
args['--gamma'] = float(args['--gamma'])
args['--theta'] = float(args['--theta'])
print('Solving on TriaGrid(({0},{0}))'.format(args['--grid']))
print('Setup Problem ...')
problem = ThermalBlockProblem(num_blocks=(2, 2))
functionals = [ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2,)}),
ExpressionParameterFunctional('diffusion[1]**2', {'diffusion': (2,)}),
ExpressionParameterFunctional('diffusion[0]', {'diffusion': (2,)}),
ExpressionParameterFunctional('diffusion[1]', {'diffusion': (2,)})]
problem = EllipticProblem(domain=problem.domain,
diffusion_functions=problem.diffusion_functions,
diffusion_functionals=functionals,
rhs=problem.rhs,
parameter_space=CubicParameterSpace({'diffusion': (2,)}, 0.1, 1.))
print('Discretize ...')
discretization, _ = discretize_elliptic_cg(problem, diameter=1. / args['--grid'])
if args['--list-vector-array']:
from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array
discretization = convert_to_numpy_list_vector_array(discretization)
if args['--cache-region'] != 'none':
discretization.enable_caching(args['--cache-region'])
print('The parameter type is {}'.format(discretization.parameter_type))
if args['--plot-solutions']:
print('Showing some solutions')
Us = ()
legend = ()
for mu in discretization.parameter_space.sample_randomly(2):
print('Solving for diffusion = \n{} ... '.format(mu['diffusion']))
sys.stdout.flush()
Us = Us + (discretization.solve(mu),)
legend = legend + (str(mu['diffusion']),)
discretization.visualize(Us, legend=legend, title='Detailed Solutions for different parameters', block=True)
print('RB generation ...')
product = discretization.h1_0_semi_product if args['--estimator-norm'] == 'h1' else None
coercivity_estimator=ExpressionParameterFunctional('min([diffusion[0], diffusion[1]**2])', discretization.parameter_type)
reductors = {'residual_basis': partial(reduce_coercive, product=product,
coercivity_estimator=coercivity_estimator),
'traditional': partial(reduce_coercive_simple, product=product,
coercivity_estimator=coercivity_estimator)}
reductor = reductors[args['--reductor']]
extension_algorithms = {'trivial': trivial_basis_extension,
'gram_schmidt': gram_schmidt_basis_extension,
'h1_gram_schmidt': partial(gram_schmidt_basis_extension, product=discretization.h1_0_semi_product)}
extension_algorithm = extension_algorithms[args['--extension-alg']]
pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'], ipython_profile=args['--ipython-profile'])
greedy_data = adaptive_greedy(discretization, reductor,
validation_mus=args['--validation-mus'], rho=args['--rho'], gamma=args['--gamma'],
theta=args['--theta'],
use_estimator=not args['--without-estimator'], error_norm=discretization.h1_0_semi_norm,
extension_algorithm=extension_algorithm, max_extensions=args['RBSIZE'],
visualize=args['--visualize-refinement'])
rb_discretization, reconstructor = greedy_data['reduced_discretization'], greedy_data['reconstructor']
if args['--pickle']:
print('\nWriting reduced discretization to file {} ...'.format(args['--pickle'] + '_reduced'))
with open(args['--pickle'] + '_reduced', 'wb') as f:
dump(rb_discretization, f)
print('Writing detailed discretization and reconstructor to file {} ...'.format(args['--pickle'] + '_detailed'))
with open(args['--pickle'] + '_detailed', 'wb') as f:
dump((discretization, reconstructor), f)
print('\nSearching for maximum error on random snapshots ...')
results = reduction_error_analysis(rb_discretization,
discretization=discretization,
reconstructor=reconstructor,
estimator=True,
error_norms=(discretization.h1_0_semi_norm,),
condition=True,
test_mus=args['--test'],
basis_sizes=25 if args['--plot-error-sequence'] else 1,
plot=True,
pool=pool)
real_rb_size = rb_discretization.solution_space.dim
print('''
*** RESULTS ***
Problem:
number of blocks: 2x2
h: sqrt(2)/{args[--grid]}
Greedy basis generation:
estimator disabled: {args[--without-estimator]}
estimator norm: {args[--estimator-norm]}
extension method: {args[--extension-alg]}
prescribed basis size: {args[RBSIZE]}
actual basis size: {real_rb_size}
elapsed time: {greedy_data[time]}
'''.format(**locals()))
print(results['summary'])
sys.stdout.flush()
if args['--plot-error-sequence']:
from matplotlib import pyplot as plt
plt.show(results['figure'])
if args['--plot-err']:
mumax = results['max_error_mus'][0, -1]
U = discretization.solve(mumax)
URB = reconstructor.reconstruct(rb_discretization.solve(mumax))
discretization.visualize((U, URB, U - URB), legend=('Detailed Solution', 'Reduced Solution', 'Error'),
title='Maximum Error Solution', separate_colorbars=True, block=True)
