def action_ZeroOperator(self, op):
dim_range, dim_source = self.dim_range, self.dim_source
range_space = op.range if dim_range is None else NumpyVectorSpace(
dim_range)
source_space = op.source if dim_source is None else NumpyVectorSpace(
dim_source)
return ZeroOperator(range_space, source_space, name=op.name)
def apply(self, U, mu=None):
assert self.parameters.assert_compatible(mu)
if len(self.interpolation_dofs) == 0:
return self.range.zeros(len(U))
if hasattr(self, 'restricted_operator'):
U_dofs = NumpyVectorSpace.make_array(U.dofs(self.source_dofs))
AU = self.restricted_operator.apply(U_dofs, mu=mu)
else:
AU = NumpyVectorSpace.make_array(
self.operator.apply(U, mu=mu).dofs(self.interpolation_dofs))
try:
if self.triangular:
interpolation_coefficients = solve_triangular(
self.interpolation_matrix,
AU.to_numpy().T,
lower=True,
unit_diagonal=True).T
else:
interpolation_coefficients = solve(self.interpolation_matrix,
AU.to_numpy().T).T
except ValueError: # this exception occurs when AU contains NaNs ...
interpolation_coefficients = np.empty(
(len(AU), len(self.collateral_basis))) + np.nan
return self.collateral_basis.lincomb(interpolation_coefficients)
def action_EmpiricalInterpolatedOperator(self,
op,
range_basis,
source_basis,
product=None):
if len(op.interpolation_dofs) == 0:
return self.apply(ZeroOperator(op.source, op.range, op.name),
range_basis, source_basis, product)
elif not hasattr(op, 'restricted_operator') or source_basis is None:
raise RuleNotMatchingError(
'Has no restricted operator or source_basis is None')
else:
if range_basis is not None:
if product is None:
projected_collateral_basis = NumpyVectorSpace.make_array(
op.collateral_basis.dot(range_basis), op.range.id)
else:
projected_collateral_basis = NumpyVectorSpace.make_array(
product.apply2(op.collateral_basis, range_basis),
op.range.id)
else:
projected_collateral_basis = op.collateral_basis
return ProjectedEmpiciralInterpolatedOperator(
op.restricted_operator, op.interpolation_matrix,
NumpyVectorSpace.make_array(
source_basis.components(op.source_dofs)),
projected_collateral_basis, op.triangular, op.source.id, None,
op.name)
def visualize(self, U, codim=2, **kwargs):
"""Visualize scalar data associated to the grid as a patch plot.
Parameters
----------
U
|NumPy array| of the data to visualize. If `U.dim == 2 and len(U) > 1`, the
data is visualized as a time series of plots. Alternatively, a tuple of
|Numpy arrays| can be provided, in which case a subplot is created for
each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in `U` is attached to (either 0 or 2).
kwargs
See :func:`~pymor.gui.qt.visualize_patch`
"""
from pymor.gui.qt import visualize_patch
from pymor.vectorarrays.interfaces import VectorArrayInterface
from pymor.vectorarrays.numpy import NumpyVectorSpace, NumpyVectorArray
if isinstance(U, (np.ndarray, VectorArrayInterface)):
U = (U, )
assert all(
isinstance(u, (np.ndarray, VectorArrayInterface)) for u in U)
U = tuple(
NumpyVectorSpace.make_array(u) if isinstance(u, np.ndarray) else
u if isinstance(u, NumpyVectorArray
) else NumpyVectorSpace.make_array(u.to_numpy())
for u in U)
bounding_box = kwargs.pop('bounding_box', self.domain)
visualize_patch(self,
U,
codim=codim,
bounding_box=bounding_box,
**kwargs)
class NumpyGenericOperator(Operator):
"""Wraps an arbitrary Python function between |NumPy arrays| as an |Operator|.
Parameters
----------
mapping
The function to wrap. If `parameters` is `None`, the function is of
the form `mapping(U)` and is expected to be vectorized. In particular::
mapping(U).shape == U.shape[:-1] + (dim_range,).
If `parameters` is not `None`, the function has to have the signature
`mapping(U, mu)`.
adjoint_mapping
The adjoint function to wrap. If `parameters` is `None`, the function is of
the form `adjoint_mapping(U)` and is expected to be vectorized. In particular::
adjoint_mapping(U).shape == U.shape[:-1] + (dim_source,).
If `parameters` is not `None`, the function has to have the signature
`adjoint_mapping(U, mu)`.
dim_source
Dimension of the operator's source.
dim_range
Dimension of the operator's range.
linear
Set to `True` if the provided `mapping` and `adjoint_mapping` are linear.
parameters
The |Parameters| the depends on.
solver_options
The |solver_options| for the operator.
name
Name of the operator.
"""
def __init__(self, mapping, adjoint_mapping=None, dim_source=1, dim_range=1, linear=False, parameters={},
source_id=None, range_id=None, solver_options=None, name=None):
self.__auto_init(locals())
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.parameters_own = parameters
def apply(self, U, mu=None):
assert U in self.source
assert self.parameters.assert_compatible(mu)
if self.parametric:
return self.range.make_array(self.mapping(U.to_numpy(), mu=mu))
else:
return self.range.make_array(self.mapping(U.to_numpy()))
def apply_adjoint(self, V, mu=None):
if self.adjoint_mapping is None:
raise ValueError('NumpyGenericOperator: adjoint mapping was not defined.')
assert V in self.range
assert self.parameters.assert_compatible(mu)
V = V.to_numpy()
if self.parametric:
return self.source.make_array(self.adjoint_mapping(V, mu=mu))
else:
return self.source.make_array(self.adjoint_mapping(V))
def action_ProjectedEmpiciralInterpolatedOperator(self,
op,
dim_range=None,
dim_source=None):
if not isinstance(op.projected_collateral_basis.space,
NumpyVectorSpace):
raise NotImplementedError
restricted_operator = op.restricted_operator
old_pcb = op.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(
old_pcb.data[:, :dim_range], old_pcb.space.id)
old_sbd = op.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(
old_sbd.data[:dim_source])
return ProjectedEmpiciralInterpolatedOperator(
restricted_operator,
op.interpolation_matrix,
source_basis_dofs,
projected_collateral_basis,
op.triangular,
op.source.id,
solver_options=op.solver_options,
name=op.name)
def __init__(self,
operator,
range_basis,
source_basis,
product=None,
solver_options=None,
name=None):
assert isinstance(operator, OperatorInterface)
assert source_basis is None or source_basis in operator.source
assert range_basis is None or range_basis in operator.range
assert product is None \
or (isinstance(product, OperatorInterface)
and range_basis is not None
and operator.range == product.source
and product.range == product.source)
self.build_parameter_type(inherits=(operator, ))
self.source = NumpyVectorSpace(
len(source_basis)) if source_basis is not None else operator.source
self.range = NumpyVectorSpace(
len(range_basis)) if range_basis is not None else operator.range
self.solver_options = solver_options
self.name = name
self.operator = operator
self.source_basis = source_basis.copy(
) if source_basis is not None else None
self.range_basis = range_basis.copy(
) if range_basis is not None else None
self.linear = operator.linear
self.product = product
def test_to_matrix_ZeroOperator():
n = 3
m = 4
Z = np.zeros((n, m))
Zop = ZeroOperator(NumpyVectorSpace(n), NumpyVectorSpace(m))
assert_type_and_allclose(Z, Zop, 'sparse')
def projected_to_subbasis(self, dim_range=None, dim_source=None, dim_collateral=None, name=None):
assert dim_source is None or dim_source <= self.source.dim
assert dim_range is None or dim_range <= self.range.dim
assert dim_collateral is None or dim_collateral <= self.restricted_operator.range.dim
if not isinstance(self.projected_collateral_basis.space, NumpyVectorSpace):
raise NotImplementedError
name = name or '{}_projected_to_subbasis'.format(self.name)
interpolation_matrix = self.interpolation_matrix[:dim_collateral, :dim_collateral]
if dim_collateral is not None:
restricted_operator, source_dofs = self.restricted_operator.restricted(np.arange(dim_collateral))
else:
restricted_operator = self.restricted_operator
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.data[:dim_collateral, :dim_range],
old_pcb.space.id)
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.data[:dim_source]) if dim_collateral is None \
else NumpyVectorSpace.make_array(old_sbd.data[:dim_source, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, interpolation_matrix,
source_basis_dofs, projected_collateral_basis, self.triangular,
self.source.id, solver_options=self.solver_options, name=name)
def visualize(self, U, codim=2, **kwargs):
"""Visualize scalar data associated to the grid as a patch plot.
Parameters
----------
U
|NumPy array| of the data to visualize. If `U.dim == 2 and len(U) > 1`, the
data is visualized as a time series of plots. Alternatively, a tuple of
|Numpy arrays| can be provided, in which case a subplot is created for
each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in `U` is attached to (either 0 or 2).
kwargs
See :func:`~pymor.gui.qt.visualize_patch`
"""
from pymor.gui.qt import visualize_patch
from pymor.vectorarrays.interfaces import VectorArrayInterface
from pymor.vectorarrays.numpy import NumpyVectorSpace, NumpyVectorArray
if isinstance(U, (np.ndarray, VectorArrayInterface)):
U = (U,)
assert all(isinstance(u, (np.ndarray, VectorArrayInterface)) for u in U)
U = tuple(NumpyVectorSpace.make_array(u) if isinstance(u, np.ndarray) else
u if isinstance(u, NumpyVectorArray) else
NumpyVectorSpace.make_array(u.data)
for u in U)
bounding_box = kwargs.pop('bounding_box', self.domain)
visualize_patch(self, U, codim=codim, bounding_box=bounding_box, **kwargs)
def with_cb_dim(self, dim):
assert dim <= self.restricted_operator.range.dim
interpolation_matrix = self.interpolation_matrix[:dim, :dim]
restricted_operator, source_dofs = self.restricted_operator.restricted(
np.arange(dim))
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(
old_pcb.to_numpy()[:dim, :], old_pcb.space.id)
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(
old_sbd.to_numpy()[:, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(
restricted_operator,
interpolation_matrix,
source_basis_dofs,
projected_collateral_basis,
self.triangular,
self.source.id,
solver_options=self.solver_options,
name=self.name)
def projected(self, range_basis, source_basis, product=None, name=None):
assert source_basis is None or source_basis in self.source
assert range_basis is None or range_basis in self.range
assert product is None or product.source == product.range == self.range
if len(self.interpolation_dofs) == 0:
return ZeroOperator(self.source, self.range, self.name).projected(range_basis, source_basis, product, name)
elif not hasattr(self, 'restricted_operator') or source_basis is None:
return super().projected(range_basis, source_basis, product, name)
else:
name = name or self.name + '_projected'
if range_basis is not None:
if product is None:
projected_collateral_basis = NumpyVectorSpace.make_array(self.collateral_basis.dot(range_basis),
self.range.id)
else:
projected_collateral_basis = NumpyVectorSpace.make_array(product.apply2(self.collateral_basis,
range_basis),
self.range.id)
else:
projected_collateral_basis = self.collateral_basis
return ProjectedEmpiciralInterpolatedOperator(self.restricted_operator, self.interpolation_matrix,
NumpyVectorSpace.make_array(source_basis.components(self.source_dofs)),
projected_collateral_basis, self.triangular,
self.source.id, None, name)
def action_ConstantOperator(self, op):
dim_range, dim_source = self.dim_range, self.dim_srouce
source = op.source if dim_source is None else NumpyVectorSpace(
dim_source, op.source.id)
value = op._value if dim_range is None else NumpyVectorSpace(
op._value.data[:, :dim_range], op.range.id)
return ConstantOperator(value, source, name=op.name)
def action_ConstantOperator(self, op):
dim_range, dim_source = self.dim_range, self.dim_source
source = op.source if dim_source is None else NumpyVectorSpace(
dim_source)
value = op.value if dim_range is None else NumpyVectorSpace(
op.value.to_numpy()[:, :dim_range])
return ConstantOperator(value, source, name=op.name)
def __init__(self,
matrix,
source_id=None,
range_id=None,
solver_options=None,
name=None):
super().__init__(matrix,
source_id=source_id,
range_id=range_id,
solver_options=solver_options,
name=name)
functional = self.range_id is None
vector = self.source_id is None
if functional and vector:
raise NotImplementedError
if vector:
self.source = NumpyVectorSpace(1, source_id)
else:
self.source = NumpyListVectorSpace(matrix.shape[1], source_id)
if functional:
self.range = NumpyVectorSpace(1, range_id)
else:
self.range = NumpyListVectorSpace(matrix.shape[0], range_id)
self.functional = functional
self.vector = vector
def test_project_array():
np.random.seed(123)
U = NumpyVectorSpace.from_numpy(np.random.random((2, 10)))
basis = NumpyVectorSpace.from_numpy(np.random.random((3, 10)))
U_p = project_array(U, basis, orthonormal=False)
onb = gram_schmidt(basis)
U_p2 = project_array(U, onb, orthonormal=True)
assert np.all(relative_error(U_p, U_p2) < 1e-10)
def __init__(self, claw):
self.claw = claw
self.num_eqn = claw.solution.state.q.shape[0]
self.mx = claw.solution.state.q.shape[1]
self.my = claw.solution.state.q.shape[2]
self.mz = claw.solution.state.q.shape[3]
self.solution_space = NumpyVectorSpace(claw.solution.state.q.size)
self.claw.start_frame = self.claw.solution.start_frame
def test_project_array():
np.random.seed(123)
U = NumpyVectorSpace.from_numpy(np.random.random((2, 10)))
basis = NumpyVectorSpace.from_numpy(np.random.random((3, 10)))
U_p = project_array(U, basis, orthonormal=False)
onb = gram_schmidt(basis)
U_p2 = project_array(U, onb, orthonormal=True)
assert np.all(relative_error(U_p, U_p2) < 1e-10)
def numpy_vector_array_factory(length, dim, seed):
np.random.seed(seed)
if np.random.randint(2):
return NumpyVectorSpace.from_numpy(np.random.random((length, dim)))
else:
return NumpyVectorSpace.from_numpy(
np.random.random((length, dim)) +
np.random.random((length, dim)) * 1j)
def test_ext(extension_alg):
size = 5
ident = np.identity(size)
current = ident[0]
for i in range(1, size):
c = NumpyVectorSpace.from_data(current)
n, _ = extension_alg(c, NumpyVectorSpace.from_data(ident[i]))
assert np.allclose(n.data, ident[0:i+1])
current = ident[0:i+1]
def test_identity_lincomb():
space = NumpyVectorSpace(10)
identity = IdentityOperator(space)
ones = space.ones()
idid = (identity + identity)
assert almost_equal(ones * 2, idid.apply(ones))
assert almost_equal(ones * 2, idid.apply_adjoint(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse_adjoint(ones))
def test_identity_lincomb():
space = NumpyVectorSpace(10)
identity = IdentityOperator(space)
ones = space.ones()
idid = (identity + identity)
assert almost_equal(ones * 2, idid.apply(ones))
assert almost_equal(ones * 2, idid.apply_adjoint(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse_adjoint(ones))
def action_ConstantOperator(self, op):
range_basis, source_basis = self.range_basis, self.source_basis
if range_basis is not None:
projected_value = NumpyVectorSpace.make_array(range_basis.dot(op.value).T)
else:
projected_value = op.value
if source_basis is None:
return ConstantOperator(projected_value, op.source, name=op.name)
else:
return ConstantOperator(projected_value, NumpyVectorSpace(len(source_basis)), name=op.name)
def action_ZeroOperator(self, op):
range_basis, source_basis = self.range_basis, self.source_basis
if source_basis is not None and range_basis is not None:
from pymor.operators.numpy import NumpyMatrixOperator
return NumpyMatrixOperator(np.zeros((len(range_basis), len(source_basis))),
name=op.name)
else:
new_source = NumpyVectorSpace(len(source_basis)) if source_basis is not None else op.source
new_range = NumpyVectorSpace(len(range_basis)) if range_basis is not None else op.range
return ZeroOperator(new_range, new_source, name=op.name)
def test_project_array_with_product():
np.random.seed(123)
U = NumpyVectorSpace.from_numpy(np.random.random((1, 10)))
basis = NumpyVectorSpace.from_numpy(np.random.random((3, 10)))
product = np.random.random((10, 10))
product = NumpyMatrixOperator(product.T.dot(product))
U_p = project_array(U, basis, product=product, orthonormal=False)
onb = gram_schmidt(basis, product=product)
U_p2 = project_array(U, onb, product=product, orthonormal=True)
assert np.all(relative_error(U_p, U_p2, product) < 1e-10)
def __init__(self, array, transposed=False, name=None):
self._array = array.copy()
if transposed:
self.source = array.space
self.range = NumpyVectorSpace(len(array))
else:
self.source = NumpyVectorSpace(len(array))
self.range = array.space
self.transposed = transposed
self.name = name
def __init__(self, matrix, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
self.source = NumpyVectorSpace(matrix.shape[1])
self.range = NumpyVectorSpace(matrix.shape[0])
self.solver_options = solver_options
self.name = name
self._matrix = matrix
self.sparse = issparse(matrix)
def test_project_array_with_product():
np.random.seed(123)
U = NumpyVectorSpace.from_numpy(np.random.random((1, 10)))
basis = NumpyVectorSpace.from_numpy(np.random.random((3, 10)))
product = np.random.random((10, 10))
product = NumpyMatrixOperator(product.T.dot(product))
U_p = project_array(U, basis, product=product, orthonormal=False)
onb = gram_schmidt(basis, product=product)
U_p2 = project_array(U, onb, product=product, orthonormal=True)
assert np.all(relative_error(U_p, U_p2, product) < 1e-10)
def test_axpy():
x = NumpyVectorSpace.from_data(np.array([1.]))
y = NumpyVectorSpace.from_data(np.array([1.]))
y.axpy(1 + 1j, x)
assert y.data[0, 0] == 2 + 1j
x = NumpyVectorSpace.from_data(np.array([1 + 1j]))
y = NumpyVectorSpace.from_data(np.array([1.]))
y.axpy(-1, x)
assert y.data[0, 0] == -1j
def __init__(self, neural_network, output_functional=None, products=None,
error_estimator=None, visualizer=None, name=None):
super().__init__(products=products, error_estimator=error_estimator, visualizer=visualizer, name=name)
self.__auto_init(locals())
self.solution_space = NumpyVectorSpace(neural_network.output_dimension)
self.linear = output_functional is None or output_functional.linear
if output_functional is not None:
self.output_space = output_functional.range
def __init__(self, array, adjoint=False, space_id=None, name=None):
array = array.copy()
self.__auto_init(locals())
if adjoint:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
def test_axpy():
x = NumpyVectorSpace.from_numpy(np.array([1.]))
y = NumpyVectorSpace.from_numpy(np.array([1.]))
y.axpy(1 + 1j, x)
assert y.to_numpy()[0, 0] == 2 + 1j
x = NumpyVectorSpace.from_numpy(np.array([1 + 1j]))
y = NumpyVectorSpace.from_numpy(np.array([1.]))
y.axpy(-1, x)
assert y.to_numpy()[0, 0] == -1j
def __init__(self, array, adjoint=False, space_id=None, name=None):
self._array = array.copy()
if adjoint:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.adjoint = adjoint
self.space_id = space_id
self.name = name
def __init__(self, array, adjoint=False, space_id=None, name=None):
self._array = array.copy()
if adjoint:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.adjoint = adjoint
self.space_id = space_id
self.name = name
def __init__(self, array, transposed=False, space_id=None, name=None):
self._array = array.copy()
if transposed:
self.source = array.space
self.range = NumpyVectorSpace(len(array), space_id)
else:
self.source = NumpyVectorSpace(len(array), space_id)
self.range = array.space
self.transposed = transposed
self.space_id = space_id
self.name = name
def test_block_identity_lincomb():
space = NumpyVectorSpace(10)
space2 = BlockVectorSpace([space, space])
identity = BlockDiagonalOperator([IdentityOperator(space), IdentityOperator(space)])
identity2 = IdentityOperator(space2)
ones = space.ones()
ones2 = space2.make_array([ones, ones])
idid = identity + identity2
assert almost_equal(ones2 * 2, idid.apply(ones2))
assert almost_equal(ones2 * 2, idid.apply_adjoint(ones2))
assert almost_equal(ones2 * 0.5, idid.apply_inverse(ones2))
assert almost_equal(ones2 * 0.5, idid.apply_inverse_adjoint(ones2))
def __init__(self, matrix, source_id=None, range_id=None, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.solver_options = solver_options
self.name = name
self._matrix = matrix
self.source_id = source_id
self.range_id = range_id
self.sparse = issparse(matrix)
def test_identity_lincomb():
space = NumpyVectorSpace(10)
identity = IdentityOperator(space)
ones = space.ones()
idid = (identity + identity)
idid_ = ExpressionParameterFunctional('2', {}) * identity
assert almost_equal(ones * 2, idid.apply(ones))
assert almost_equal(ones * 2, idid.apply_adjoint(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse(ones))
assert almost_equal(ones * 0.5, idid.apply_inverse_adjoint(ones))
assert almost_equal(ones * 0.5, idid_.apply_inverse(ones))
assert almost_equal(ones * 0.5, idid_.apply_inverse_adjoint(ones))
def test_complex():
np.random.seed(0)
I = np.eye(5)
A = np.random.randn(5, 5)
B = np.random.randn(5, 5)
C = np.random.randn(3, 5)
Iop = NumpyMatrixOperator(I)
Aop = NumpyMatrixOperator(A)
Bop = NumpyMatrixOperator(B)
Cva = NumpyVectorSpace.from_numpy(C)
# lincombs
assert not np.iscomplexobj((Iop * 1 + Bop * 1).assemble().matrix)
assert not np.iscomplexobj((Aop * 1 + Bop * 1).assemble().matrix)
assert np.iscomplexobj((Aop * (1+0j) + Bop * (1+0j)).assemble().matrix)
assert np.iscomplexobj((Aop * 1j + Bop * 1).assemble().matrix)
assert np.iscomplexobj((Bop * 1 + Aop * 1j).assemble().matrix)
# apply_inverse
assert not np.iscomplexobj(Aop.apply_inverse(Cva).to_numpy())
assert np.iscomplexobj((Aop * 1j).apply_inverse(Cva).to_numpy())
assert np.iscomplexobj((Aop * 1 + Bop * 1j).assemble().apply_inverse(Cva).to_numpy())
assert np.iscomplexobj(Aop.apply_inverse(Cva * 1j).to_numpy())
# append
for rsrv in (0, 10):
for o_ind in (slice(None), [0]):
va = NumpyVectorSpace(5).empty(reserve=rsrv)
va.append(Cva)
D = np.random.randn(1, 5) + 1j * np.random.randn(1, 5)
Dva = NumpyVectorSpace.from_numpy(D)
assert not np.iscomplexobj(va.to_numpy())
assert np.iscomplexobj(Dva.to_numpy())
va.append(Dva[o_ind])
assert np.iscomplexobj(va.to_numpy())
# scal
assert not np.iscomplexobj(Cva.to_numpy())
assert np.iscomplexobj((Cva * 1j).to_numpy())
assert np.iscomplexobj((Cva * (1 + 0j)).to_numpy())
# axpy
assert not np.iscomplexobj(Cva.to_numpy())
Cva[0].axpy(1, Dva)
assert np.iscomplexobj(Cva.to_numpy())
Cva = NumpyVectorSpace.from_numpy(C)
assert not np.iscomplexobj(Cva.to_numpy())
Cva[0].axpy(1j, Dva)
assert np.iscomplexobj(Cva.to_numpy())
def __init__(self, mapping, adjoint_mapping=None, dim_source=1, dim_range=1, linear=False, parameter_type=None,
source_id=None, range_id=None, solver_options=None, name=None):
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.solver_options = solver_options
self.name = name
self._mapping = mapping
self._adjoint_mapping = adjoint_mapping
self.linear = linear
if parameter_type is not None:
self.build_parameter_type(parameter_type)
self.source_id = source_id # needed for with_
self.range_id = range_id
def __init__(self, matrix, source_id=None, range_id=None, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
try:
matrix.setflags(write=False) # make numpy arrays read-only
except AttributeError:
pass
self.__auto_init(locals())
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.sparse = issparse(matrix)
def __init__(self, mapping, transpose_mapping=None, dim_source=1, dim_range=1, linear=False, parameter_type=None,
source_id=None, range_id=None, solver_options=None, name=None):
self.source = NumpyVectorSpace(dim_source, source_id)
self.range = NumpyVectorSpace(dim_range, range_id)
self.solver_options = solver_options
self.name = name
self._mapping = mapping
self._transpose_mapping = transpose_mapping
self.linear = linear
if parameter_type is not None:
self.build_parameter_type(parameter_type)
self.source_id = source_id # needed for with_
self.range_id = range_id
def test_complex():
np.random.seed(0)
I = np.eye(5)
A = np.random.randn(5, 5)
B = np.random.randn(5, 5)
C = np.random.randn(3, 5)
Iop = NumpyMatrixOperator(I)
Aop = NumpyMatrixOperator(A)
Bop = NumpyMatrixOperator(B)
Cva = NumpyVectorSpace.from_data(C)
# assemble_lincomb
assert not np.iscomplexobj(
Aop.assemble_lincomb((Iop, Bop), (1, 1))._matrix)
assert not np.iscomplexobj(
Aop.assemble_lincomb((Aop, Bop), (1, 1))._matrix)
assert np.iscomplexobj(
Aop.assemble_lincomb((Aop, Bop), (1 + 0j, 1 + 0j))._matrix)
assert np.iscomplexobj(Aop.assemble_lincomb((Aop, Bop), (1j, 1))._matrix)
assert np.iscomplexobj(Aop.assemble_lincomb((Bop, Aop), (1, 1j))._matrix)
# apply_inverse
assert not np.iscomplexobj(Aop.apply_inverse(Cva).data)
assert np.iscomplexobj((Aop * 1j).apply_inverse(Cva).data)
assert np.iscomplexobj(
Aop.assemble_lincomb((Aop, Bop), (1, 1j)).apply_inverse(Cva).data)
assert np.iscomplexobj(Aop.apply_inverse(Cva * 1j).data)
# append
for rsrv in (0, 10):
for o_ind in (slice(None), [0]):
va = NumpyVectorSpace(5).empty(reserve=rsrv)
va.append(Cva)
D = np.random.randn(1, 5) + 1j * np.random.randn(1, 5)
Dva = NumpyVectorSpace.from_data(D)
assert not np.iscomplexobj(va.data)
assert np.iscomplexobj(Dva.data)
va.append(Dva[o_ind])
assert np.iscomplexobj(va.data)
# scal
assert not np.iscomplexobj(Cva.data)
assert np.iscomplexobj((Cva * 1j).data)
assert np.iscomplexobj((Cva * (1 + 0j)).data)
# axpy
assert not np.iscomplexobj(Cva.data)
Cva[0].axpy(1, Dva)
assert np.iscomplexobj(Cva.data)
Cva = NumpyVectorSpace.from_data(C)
assert not np.iscomplexobj(Cva.data)
Cva[0].axpy(1j, Dva)
assert np.iscomplexobj(Cva.data)
def save(self):
if not config.HAVE_PYVTK:
msg = QMessageBox(QMessageBox.Critical, 'Error', 'VTK output disabled. Pleas install pyvtk.')
msg.exec_()
return
filename = QFileDialog.getSaveFileName(self, 'Save as vtk file')[0]
base_name = filename.split('.vtu')[0].split('.vtk')[0].split('.pvd')[0]
if base_name:
if len(self.U) == 1:
write_vtk(self.grid, NumpyVectorSpace.make_array(self.U[0]), base_name, codim=self.codim)
else:
for i, u in enumerate(self.U):
write_vtk(self.grid, NumpyVectorSpace.make_array(u), '{}-{}'.format(base_name, i),
codim=self.codim)
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
if not self.transposed:
restricted_value = NumpyVectorSpace.make_array(self._array.components(dofs))
return VectorArrayOperator(restricted_value, False), np.arange(self.source.dim, dtype=np.int32)
else:
raise NotImplementedError
def with_cb_dim(self, dim):
assert dim <= self.restricted_operator.range.dim
interpolation_matrix = self.interpolation_matrix[:dim, :dim]
restricted_operator, source_dofs = self.restricted_operator.restricted(np.arange(dim))
old_pcb = self.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.to_numpy()[:dim, :])
old_sbd = self.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.to_numpy()[:, source_dofs])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, interpolation_matrix,
source_basis_dofs, projected_collateral_basis, self.triangular,
solver_options=self.solver_options, name=self.name)
class RestrictedDuneSpaceOperator(OperatorBase):
linear = False
def __init__(self, impl, range_dofs):
self._impl = impl
self._range_dofs = range_dofs
self.source = NumpyVectorSpace(impl.dimSource)
self.range = NumpyVectorSpace(len(range_dofs))
self.name = 'DuneBurgersSpaceOperator_restricted'
self._source_vec = dune_module.Vector(impl.dimSource, 0.)
self._range_vec = dune_module.Vector(impl.dimRange, 0.)
self._source_array = np.frombuffer(self._source_vec.buffer())
self._range_array = np.frombuffer(self._range_vec.buffer())
self.build_parameter_type({'exponent': tuple()}, local_global=True)
def apply(self, U, ind=None, mu=None):
assert U in self.source
mu = self.parse_parameter(mu)
exponent = float(mu['exponent'])
U = U.data if ind is None else \
U.data[ind] if hasattr(ind, '__len__') else \
U.data[ind:ind + 1]
R = self.range.zeros(len(U))
R_array = R.data
for i, u in enumerate(U):
self._source_array[:] = u
self._range_array[:] = 0
self._impl.apply(self._source_vec, self._range_vec, exponent, 1.)
R_array[i] = self._range_array[:][self._range_dofs]
return R
def action_ProjectedEmpiciralInterpolatedOperator(self, op):
if not isinstance(op.projected_collateral_basis.space, NumpyVectorSpace):
raise NotImplementedError
restricted_operator = op.restricted_operator
old_pcb = op.projected_collateral_basis
projected_collateral_basis = NumpyVectorSpace.make_array(old_pcb.to_numpy()[:, :self.dim_range],
old_pcb.space.id)
old_sbd = op.source_basis_dofs
source_basis_dofs = NumpyVectorSpace.make_array(old_sbd.to_numpy()[:self.dim_source])
return ProjectedEmpiciralInterpolatedOperator(restricted_operator, op.interpolation_matrix,
source_basis_dofs, projected_collateral_basis, op.triangular,
op.source.id, solver_options=op.solver_options, name=op.name)
def __init__(self, matrix, source_id=None, range_id=None, solver_options=None, name=None):
assert matrix.ndim <= 2
if matrix.ndim == 1:
matrix = np.reshape(matrix, (1, -1))
try:
matrix.setflags(write=False) # make numpy arrays read-only
except AttributeError:
pass
self.source = NumpyVectorSpace(matrix.shape[1], source_id)
self.range = NumpyVectorSpace(matrix.shape[0], range_id)
self.solver_options = solver_options
self.name = name
self.matrix = matrix
self.source_id = source_id
self.range_id = range_id
self.sparse = issparse(matrix)
class ComponentProjection(OperatorBase):
"""|Operator| representing the projection of a |VectorArray| on some of its components.
Parameters
----------
components
List or 1D |NumPy array| of the indices of the vector
:meth:`~pymor.vectorarrays.interfaces.VectorArrayInterface.components` that ar
to be extracted by the operator.
source
Source |VectorSpace| of the operator.
name
Name of the operator.
"""
linear = True
def __init__(self, components, source, name=None):
assert all(0 <= c < source.dim for c in components)
self.components = np.array(components, dtype=np.int32)
self.range = NumpyVectorSpace(len(components))
self.source = source
self.name = name
def apply(self, U, mu=None):
assert U in self.source
return self.range.make_array(U.components(self.components))
def restricted(self, dofs):
assert all(0 <= c < self.range.dim for c in dofs)
source_dofs = self.components[dofs]
return IdentityOperator(NumpyVectorSpace(len(source_dofs))), source_dofs
def projected(self, range_basis, source_basis, product=None, name=None):
assert source_basis is None or source_basis in self.source
assert range_basis is None or range_basis in self.range
assert product is None or product.source == product.range == self.range
if range_basis is not None:
if product:
projected_value = NumpyVectorSpace.make_array(product.apply2(range_basis, self._value).T, self.range.id)
else:
projected_value = NumpyVectorSpace.make_array(range_basis.dot(self._value).T, self.range.id)
else:
projected_value = self._value
if source_basis is None:
return ConstantOperator(projected_value, self.source, name=self.name + '_projected')
else:
return ConstantOperator(projected_value, NumpyVectorSpace(len(source_basis), self.source.id),
name=self.name + '_projected')
def test_to_matrix():
np.random.seed(0)
A = np.random.randn(2, 2)
B = np.random.randn(3, 3)
C = np.random.randn(3, 3)
X = np.bmat([[np.eye(2) + A, np.zeros((2, 3))], [np.zeros((3, 2)), B.dot(C.T)]])
C = sps.csc_matrix(C)
Aop = NumpyMatrixOperator(A)
Bop = NumpyMatrixOperator(B)
Cop = NumpyMatrixOperator(C)
Xop = BlockDiagonalOperator([LincombOperator([IdentityOperator(NumpyVectorSpace(2)), Aop],
[1, 1]), Concatenation(Bop, AdjointOperator(Cop))])
assert np.allclose(X, to_matrix(Xop))
assert np.allclose(X, to_matrix(Xop, format='csr').toarray())
np.random.seed(0)
V = np.random.randn(10, 2)
Vva = NumpyVectorSpace.make_array(V.T)
Vop = VectorArrayOperator(Vva)
assert np.allclose(V, to_matrix(Vop))
Vop = VectorArrayOperator(Vva, transposed=True)
assert np.allclose(V, to_matrix(Vop).T)
def action_EmpiricalInterpolatedOperator(self, op):
range_basis, source_basis, product = self.range_basis, self.source_basis, self.product
if len(op.interpolation_dofs) == 0:
return self.apply(ZeroOperator(op.range, op.source, op.name))
elif not hasattr(op, 'restricted_operator') or source_basis is None:
raise RuleNotMatchingError('Has no restricted operator or source_basis is None')
else:
if range_basis is not None:
projected_collateral_basis = NumpyVectorSpace.make_array(op.collateral_basis.inner(range_basis,
product),
op.range.id)
else:
projected_collateral_basis = op.collateral_basis
return ProjectedEmpiciralInterpolatedOperator(op.restricted_operator, op.interpolation_matrix,
NumpyVectorSpace.make_array(source_basis.dofs(op.source_dofs)),
projected_collateral_basis, op.triangular,
op.source.id, None, op.name)
def reconstruct(self, U):
"""Reconstruct high-dimensional vector from reduced vector `U`."""
assert isinstance(U.space, NumpyVectorSpace)
UU = np.zeros((len(U), self.dim))
UU[:, :self.dim_subbasis] = U.data
UU = NumpyVectorSpace.make_array(UU, U.space.id)
if self.old_recontructor:
return self.old_recontructor.reconstruct(UU)
else:
return UU
def __init__(self, operator, range_basis, source_basis, product=None, solver_options=None):
assert isinstance(operator, OperatorInterface)
assert source_basis is None or source_basis in operator.source
assert range_basis is None or range_basis in operator.range
assert (product is None
or (isinstance(product, OperatorInterface)
and range_basis is not None
and operator.range == product.source
and product.range == product.source))
self.build_parameter_type(operator)
self.source = NumpyVectorSpace(len(source_basis)) if source_basis is not None else operator.source
self.range = NumpyVectorSpace(len(range_basis)) if range_basis is not None else operator.range
self.solver_options = solver_options
self.name = operator.name
self.operator = operator
self.source_basis = source_basis.copy() if source_basis is not None else None
self.range_basis = range_basis.copy() if range_basis is not None else None
self.linear = operator.linear
self.product = product
def apply(self, U, mu=None):
mu = self.parse_parameter(mu)
if len(self.interpolation_dofs) == 0:
return self.range.zeros(len(U))
if hasattr(self, 'restricted_operator'):
U_dofs = NumpyVectorSpace.make_array(U.dofs(self.source_dofs))
AU = self.restricted_operator.apply(U_dofs, mu=mu)
else:
AU = NumpyVectorSpace.make_array(self.operator.apply(U, mu=mu).dofs(self.interpolation_dofs))
try:
if self.triangular:
interpolation_coefficients = solve_triangular(self.interpolation_matrix, AU.to_numpy().T,
lower=True, unit_diagonal=True).T
else:
interpolation_coefficients = solve(self.interpolation_matrix, AU.to_numpy().T).T
except ValueError: # this exception occurs when AU contains NaNs ...
interpolation_coefficients = np.empty((len(AU), len(self.collateral_basis))) + np.nan
return self.collateral_basis.lincomb(interpolation_coefficients)
def test_to_matrix_VectorArrayOperator():
np.random.seed(0)
V = np.random.randn(10, 2)
Vva = NumpyVectorSpace.make_array(V.T)
Vop = VectorArrayOperator(Vva)
assert_type_and_allclose(V, Vop, 'dense')
Vop = VectorArrayOperator(Vva, adjoint=True)
assert_type_and_allclose(V.T, Vop, 'dense')
def test_vtkio(rect_or_tria_grid):
grid = rect_or_tria_grid
steps = 4
for dim in range(1, 2):
for codim, data in enumerate((NumpyVectorSpace.from_numpy(np.zeros((steps, grid.size(c)))) for c in range(grid.dim+1))):
with SafeTemporaryFileName('wb') as out_name:
if codim == 1:
with pytest.raises(NotImplementedError):
write_vtk(grid, data, out_name, codim=codim)
else:
write_vtk(grid, data, out_name, codim=codim)
def test_blk_diag_apply_inverse():
np.random.seed(0)
A = np.random.randn(2, 2)
B = np.random.randn(3, 3)
C = spla.block_diag(A, B)
Aop = NumpyMatrixOperator(A)
Bop = NumpyMatrixOperator(B)
Cop = BlockDiagonalOperator((Aop, Bop))
v1 = np.random.randn(2)
v2 = np.random.randn(3)
v = np.hstack((v1, v2))
v1va = NumpyVectorSpace.from_data(v1)
v2va = NumpyVectorSpace.from_data(v2)
vva = BlockVectorSpace.make_array((v1va, v2va))
wva = Cop.apply_inverse(vva)
w = np.hstack((wva.block(0).data, wva.block(1).data))
assert np.allclose(spla.solve(C, v), w)
def test_scal():
v = np.array([[1, 2, 3],
[4, 5, 6]], dtype=float)
v = NumpyVectorSpace.from_numpy(v)
v.scal(1j)
k = 0
for i in range(2):
for j in range(3):
k += 1
assert v.to_numpy()[i, j] == k * 1j