def __init__(self, args):
self.args = args
self.first = True
self.problem = thermal_block_problem(num_blocks=(args['XBLOCKS'], args['YBLOCKS']),
parameter_range=(PARAM_MIN, PARAM_MAX))
self.m, pack = discretize_stationary_cg(self.problem, diameter=1. / args['--grid'])
self.grid = pack['grid']
def elliptic_gmsh_demo(args):
args['ANGLE'] = float(args['ANGLE'])
args['NUM_POINTS'] = int(args['NUM_POINTS'])
args['CLSCALE'] = float(args['CLSCALE'])
problem = StationaryProblem(
domain=CircularSectorDomain(args['ANGLE'],
radius=1,
num_points=args['NUM_POINTS']),
diffusion=ConstantFunction(1, dim_domain=2),
rhs=ConstantFunction(np.array(0.), dim_domain=2, name='rhs'),
dirichlet_data=ExpressionFunction('sin(polar(x)[1] * pi/angle)',
2, (), {}, {'angle': args['ANGLE']},
name='dirichlet'))
print('Discretize ...')
m, data = discretize_stationary_cg(analytical_problem=problem,
diameter=args['CLSCALE'])
grid = data['grid']
print(grid)
print()
print('Solve ...')
U = m.solve()
solution = ExpressionFunction(
'(lambda r, phi: r**(pi/angle) * sin(phi * pi/angle))(*polar(x))', 2,
(), {}, {'angle': args['ANGLE']})
U_ref = U.space.make_array(solution(grid.centers(2)))
m.visualize((U, U_ref, U - U_ref),
legend=('Solution', 'Analytical solution (circular boundary)',
'Error'),
separate_colorbars=True)
def __init__(self, args):
self.args = args
self.first = True
self.problem = thermal_block_problem(num_blocks=(args['XBLOCKS'], args['YBLOCKS']),
parameter_range=(PARAM_MIN, PARAM_MAX))
self.discretization, pack = discretize_stationary_cg(self.problem, diameter=1. / args['--grid'])
self.grid = pack['grid']
def elliptic_gmsh_demo(args):
args['ANGLE'] = float(args['ANGLE'])
args['NUM_POINTS'] = int(args['NUM_POINTS'])
args['CLSCALE'] = float(args['CLSCALE'])
problem = StationaryProblem(
domain=CircularSectorDomain(args['ANGLE'], radius=1, num_points=args['NUM_POINTS']),
diffusion=ConstantFunction(1, dim_domain=2),
rhs=ConstantFunction(np.array(0.), dim_domain=2, name='rhs'),
dirichlet_data=ExpressionFunction('sin(polar(x)[1] * pi/angle)', 2, (),
{}, {'angle': args['ANGLE']}, name='dirichlet')
)
print('Discretize ...')
m, data = discretize_stationary_cg(analytical_problem=problem, diameter=args['CLSCALE'])
grid = data['grid']
print(grid)
print()
print('Solve ...')
U = m.solve()
solution = ExpressionFunction('(lambda r, phi: r**(pi/angle) * sin(phi * pi/angle))(*polar(x))', 2, (),
{}, {'angle': args['ANGLE']})
U_ref = U.space.make_array(solution(grid.centers(2)))
m.visualize((U, U_ref, U-U_ref),
legend=('Solution', 'Analytical solution (circular boundary)', 'Error'),
separate_colorbars=True)
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = StationaryProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, diffusion=diffusion)
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
discretization, data = discretize_stationary_cg(analytical_problem=problem, grid=grid, boundary_info=bi)
U = discretization.solve()
try:
visualize_patch(data['grid'], U=U, backend=backend)
except PySideMissing as ie:
pytest.xfail("PySide missing")
finally:
stop_gui_processes()
def test_visualize_patch(backend_gridtype):
backend, gridtype = backend_gridtype
domain = LineDomain() if gridtype is OnedGrid else RectDomain()
dim = 1 if gridtype is OnedGrid else 2
rhs = GenericFunction(lambda X: np.ones(X.shape[:-1]) * 10, dim) # NOQA
dirichlet = GenericFunction(lambda X: np.zeros(X.shape[:-1]), dim) # NOQA
diffusion = GenericFunction(lambda X: np.ones(X.shape[:-1]), dim) # NOQA
problem = StationaryProblem(domain=domain, rhs=rhs, dirichlet_data=dirichlet, diffusion=diffusion)
grid, bi = discretize_domain_default(problem.domain, grid_type=gridtype)
d, data = discretize_stationary_cg(analytical_problem=problem, grid=grid, boundary_info=bi)
U = d.solve()
try:
visualize_patch(data['grid'], U=U, backend=backend)
except QtMissing as ie:
pytest.xfail("Qt missing")
finally:
stop_gui_processes()
def thermalblock_factory(xblocks, yblocks, diameter, seed):
from pymor.analyticalproblems.thermalblock import thermal_block_problem
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.functions.basic import GenericFunction
from pymor.operators.cg import InterpolationOperator
p = thermal_block_problem((xblocks, yblocks))
d, d_data = discretize_stationary_cg(p, diameter)
f = GenericFunction(lambda X, mu: X[..., 0]**mu['exp'] + X[..., 1],
dim_domain=2, parameter_type={'exp': ()})
iop = InterpolationOperator(d_data['grid'], f)
U = d.operator.source.empty()
V = d.operator.range.empty()
np.random.seed(seed)
for exp in np.random.random(5):
U.append(iop.as_vector(exp))
for exp in np.random.random(6):
V.append(iop.as_vector(exp))
return d.operator, d.parameter_space.sample_randomly(1, seed=seed)[0], U, V, d.h1_product, d.l2_product
def thermalblock_factory(xblocks, yblocks, diameter, seed):
from pymor.analyticalproblems.thermalblock import thermal_block_problem
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.functions.basic import GenericFunction
from pymor.operators.cg import InterpolationOperator
p = thermal_block_problem((xblocks, yblocks))
m, m_data = discretize_stationary_cg(p, diameter)
f = GenericFunction(lambda X, mu: X[..., 0]**mu['exp'] + X[..., 1],
dim_domain=2, parameter_type={'exp': ()})
iop = InterpolationOperator(m_data['grid'], f)
U = m.operator.source.empty()
V = m.operator.range.empty()
np.random.seed(seed)
for exp in np.random.random(5):
U.append(iop.as_vector(exp))
for exp in np.random.random(6):
V.append(iop.as_vector(exp))
return m.operator, m.parameter_space.sample_randomly(1, seed=seed)[0], U, V, m.h1_product, m.l2_product
def discretize_pymor(xblocks, yblocks, grid_num_intervals, use_list_vector_array):
from pymor.analyticalproblems.thermalblock import thermal_block_problem
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array
print('Discretize ...')
# setup analytical problem
problem = thermal_block_problem(num_blocks=(xblocks, yblocks))
# discretize using continuous finite elements
fom, _ = discretize_stationary_cg(problem, diameter=1. / grid_num_intervals)
if use_list_vector_array:
fom = convert_to_numpy_list_vector_array(fom)
summary = f'''pyMOR model:
number of blocks: {xblocks}x{yblocks}
grid intervals: {grid_num_intervals}
ListVectorArray: {use_list_vector_array}
'''
return fom, summary
def discretize_pymor(xblocks, yblocks, grid_num_intervals, use_list_vector_array):
from pymor.analyticalproblems.thermalblock import thermal_block_problem
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array
print('Discretize ...')
# setup analytical problem
problem = thermal_block_problem(num_blocks=(xblocks, yblocks))
# discretize using continuous finite elements
d, _ = discretize_stationary_cg(problem, diameter=1. / grid_num_intervals)
if use_list_vector_array:
d = convert_to_numpy_list_vector_array(d)
summary = '''pyMOR discretization:
number of blocks: {xblocks}x{yblocks}
grid intervals: {grid_num_intervals}
ListVectorArray: {use_list_vector_array}
'''.format(**locals())
return d, summary
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
from itertools import product
import pytest
from pkg_resources import resource_filename
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.discretizers.fv import discretize_instationary_fv
from pymor.discretizers.disk import discretize_stationary_from_disk, discretize_instationary_from_disk
from pymortests.fixtures.analyticalproblem import (picklable_thermalblock_problems, non_picklable_thermalblock_problems,
burgers_problems)
picklable_discretizaion_generators = \
[lambda p=p, d=d: discretize_stationary_cg(p, diameter=d)[0]
for p, d in product(picklable_thermalblock_problems, [1./50., 1./100.])] + \
[lambda p=p, d=d: discretize_instationary_fv(p, diameter=d, nt=100)[0]
for p, d in product(burgers_problems, [1./10., 1./15.])] + \
[lambda p=p: discretize_stationary_from_disk(parameter_file=p)
for p in (resource_filename('pymortests', 'testdata/parameter_stationary.ini'),)] + \
[lambda p=p: discretize_instationary_from_disk(parameter_file=p)
for p in (resource_filename('pymortests', 'testdata/parameter_instationary.ini'),)]
non_picklable_discretization_generators = \
[lambda p=p, d=d: discretize_stationary_cg(p, diameter=d)[0]
for p, d in product(non_picklable_thermalblock_problems, [1./20., 1./30.])]
discretization_generators = picklable_discretizaion_generators + non_picklable_discretization_generators
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['--extension-alg'] = args['--extension-alg'].lower()
assert args['--extension-alg'] in {'trivial', 'gram_schmidt'}
args['--product'] = args['--product'].lower()
assert args['--product'] in {'trivial', 'h1'}
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'])
problem = thermal_block_problem(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 = problem.with_(
diffusion=problem.diffusion.with_(coefficients=functionals),
parameter_space=CubicParameterSpace({'diffusion': (2, )}, 0.1, 1.))
print('Discretize ...')
fom, _ = discretize_stationary_cg(problem, diameter=1. / args['--grid'])
if args['--list-vector-array']:
from pymor.playground.discretizers.numpylistvectorarray import convert_to_numpy_list_vector_array
fom = convert_to_numpy_list_vector_array(fom)
if args['--cache-region'] != 'none':
fom.enable_caching(args['--cache-region'])
if args['--plot-solutions']:
print('Showing some solutions')
Us = ()
legend = ()
for mu in fom.parameter_space.sample_randomly(2):
print(f"Solving for diffusion = \n{mu['diffusion']} ... ")
sys.stdout.flush()
Us = Us + (fom.solve(mu), )
legend = legend + (str(mu['diffusion']), )
fom.visualize(Us,
legend=legend,
title='Detailed Solutions for different parameters',
block=True)
print('RB generation ...')
product = fom.h1_0_semi_product if args['--product'] == 'h1' else None
coercivity_estimator = ExpressionParameterFunctional(
'min([diffusion[0], diffusion[1]**2])', fom.parameter_type)
reductors = {
'residual_basis':
CoerciveRBReductor(fom,
product=product,
coercivity_estimator=coercivity_estimator),
'traditional':
SimpleCoerciveRBReductor(fom,
product=product,
coercivity_estimator=coercivity_estimator)
}
reductor = reductors[args['--reductor']]
pool = new_parallel_pool(ipython_num_engines=args['--ipython-engines'],
ipython_profile=args['--ipython-profile'])
greedy_data = rb_adaptive_greedy(
fom,
reductor,
validation_mus=args['--validation-mus'],
rho=args['--rho'],
gamma=args['--gamma'],
theta=args['--theta'],
use_estimator=not args['--without-estimator'],
error_norm=fom.h1_0_semi_norm,
max_extensions=args['RBSIZE'],
visualize=not args['--no-visualize-refinement'])
rom = greedy_data['rom']
if args['--pickle']:
print(
f"\nWriting reduced model to file {args['--pickle']}_reduced ...")
with open(args['--pickle'] + '_reduced', 'wb') as f:
dump(rom, f)
print(
f"Writing detailed model and reductor to file {args['--pickle']}_detailed ..."
)
with open(args['--pickle'] + '_detailed', 'wb') as f:
dump((fom, reductor), f)
print('\nSearching for maximum error on random snapshots ...')
results = reduction_error_analysis(
rom,
fom=fom,
reductor=reductor,
estimator=True,
error_norms=(fom.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 = rom.solution_space.dim
print('''
*** RESULTS ***
Problem:
number of blocks: 2x2
h: sqrt(2)/{args[--grid]}
Greedy basis generation:
estimator disabled: {args[--without-estimator]}
extension method: {args[--extension-alg]}
product: {args[--product]}
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 = fom.solve(mumax)
URB = reductor.reconstruct(rom.solve(mumax))
fom.visualize(
(U, URB, U - URB),
legend=('Detailed Solution', 'Reduced Solution', 'Error'),
title='Maximum Error Solution',
separate_colorbars=True,
block=True)
# License: BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
from itertools import product
import pytest
from pkg_resources import resource_filename
from pymor.discretizers.cg import discretize_stationary_cg
from pymor.discretizers.fv import discretize_instationary_fv
from pymor.discretizers.disk import discretize_stationary_from_disk, discretize_instationary_from_disk
from pymortests.fixtures.analyticalproblem import (picklable_thermalblock_problems, non_picklable_thermalblock_problems,
burgers_problems)
picklable_discretizaion_generators = \
[lambda p=p, d=d: discretize_stationary_cg(p, diameter=d)[0]
for p, d in product(picklable_thermalblock_problems, [1./50., 1./100.])] + \
[lambda p=p, d=d: discretize_instationary_fv(p, diameter=d, nt=100)[0]
for p, d in product(burgers_problems, [1./10., 1./15.])] + \
[lambda p=p: discretize_stationary_from_disk(parameter_file=p)
for p in (resource_filename('pymortests', 'testdata/parameter_stationary.ini'),)] + \
[lambda p=p: discretize_instationary_from_disk(parameter_file=p)
for p in (resource_filename('pymortests', 'testdata/parameter_instationary.ini'),)]
non_picklable_discretization_generators = \
[lambda p=p, d=d: discretize_stationary_cg(p, diameter=d)[0]
for p, d in product(non_picklable_thermalblock_problems, [1./20., 1./30.])]
discretization_generators = picklable_discretizaion_generators + non_picklable_discretization_generators
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 = thermal_block_problem(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 = StationaryProblem(domain=problem.domain,
diffusion=problem.diffusion.with_(coefficients=functionals),
rhs=problem.rhs,
parameter_space=CubicParameterSpace({'diffusion': (2,)}, 0.1, 1.))
print('Discretize ...')
discretization, _ = discretize_stationary_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)
if __name__ == '__main__':
argvs = sys.argv
parser = OptionParser()
parser.add_option("--dir", dest="dir", default="./")
opt, argc = parser.parse_args(argvs)
print(opt, argc)
rhs = ExpressionFunction('(x[..., 0] - 0.5)**2 * 1000', 2, ())
problem = StationaryProblem(
domain=RectDomain(),
rhs=rhs,
diffusion=LincombFunction(
[ExpressionFunction('1 - x[..., 0]', 2, ()),
ExpressionFunction('x[..., 0]', 2, ())],
[ProjectionParameterFunctional(
'diffusionl', 0), ExpressionParameterFunctional('1', {})]
),
parameter_space=CubicParameterSpace({'diffusionl': 0}, 0.01, 0.1),
name='2DProblem'
)
args = {'N': 100, 'samples': 10}
m, data = discretize_stationary_cg(problem, diameter=1. / args['N'])
U = m.solution_space.empty()
for mu in m.parameter_space.sample_uniformly(args['samples']):
U.append(m.solve(mu))
Us = U * 1.5
plot = m.visualize((U, Us), title='Solution for diffusionl=0.5')
