pymor.vectorarrays.block

Module Contents

Classes

BlockVectorArray	VectorArray where each vector is a direct sum of sub-vectors.
BlockVectorSpace	VectorSpace of BlockVectorArrays.
BlockVectorArrayView	VectorArray where each vector is a direct sum of sub-vectors.

class pymor.vectorarrays.block.BlockVectorArray(blocks, space)

Bases: pymor.vectorarrays.interface.VectorArray

VectorArray where each vector is a direct sum of sub-vectors.

Given a list of equal length VectorArrays blocks, this VectorArray represents the direct sums of the vectors contained in the arrays. The associated VectorSpace is BlockVectorSpace.

BlockVectorArray can be used in conjunction with BlockOperator.

to_numpy(self, ensure_copy=False)

Return (len(self), self.dim) NumPy Array with the data stored in the array.

Parameters

ensure_copy

If False, modifying the returned NumPy array might alter the original VectorArray. If True always a copy of the array data is made.

property real(self)

Real part.

property imag(self)

Imaginary part.

conj(self)

Complex conjugation.

block(self, ind)

Return a copy of a single block or a sequence of blocks.

property num_blocks(self)

__len__(self)

The number of vectors in the array.

__getitem__(self, ind)

Return a VectorArray view onto a subset of the vectors in the array.

__delitem__(self, ind)

Remove vectors from the array.

append(self, other, remove_from_other=False)

Append vectors to the array.

Parameters

other

A VectorArray containing the vectors to be appended.

remove_from_other

If True, the appended vectors are removed from other. For list-like implementations this can be used to prevent unnecessary copies of the involved vectors.

copy(self, deep=False)

Returns a copy of the array.

All VectorArray implementations in pyMOR have copy-on-write semantics: if not specified otherwise by setting deep to True, the returned copy will hold a handle to the same array data as the original array, and a deep copy of the data will only be performed when one of the arrays is modified.

Note that for NumpyVectorArray, a deep copy is always performed when only some vectors in the array are copied.

Parameters

deep

Ensure that an actual copy of the array data is made (see above).

Returns

A copy of the VectorArray.

scal(self, alpha)

BLAS SCAL operation (in-place scalar multiplication).

This method calculates

self = alpha*self

If alpha is a scalar, each vector is multiplied by this scalar. Otherwise, alpha has to be a one-dimensional NumPy array of the same length as self containing the factors for each vector.

Parameters

alpha

The scalar coefficient or one-dimensional NumPy array of coefficients with which the vectors in self are multiplied.

axpy(self, alpha, x)

BLAS AXPY operation.

This method forms the sum

self = alpha*x + self

If the length of x is 1, the same x vector is used for all vectors in self. Otherwise, the lengths of self and x have to agree. If alpha is a scalar, each x vector is multiplied with the same factor alpha. Otherwise, alpha has to be a one-dimensional NumPy array of the same length as self containing the coefficients for each x vector.

Parameters

alpha

The scalar coefficient or one-dimensional NumPy array of coefficients with which the vectors in x are multiplied.

x

A VectorArray containing the x-summands.

inner(self, other, product=None)

Returns the inner products between VectorArray elements.

If product is None, the Euclidean inner product between the dofs of self and other are returned, i.e.

U.inner(V)

is equivalent to:

U.dofs(np.arange(U.dim)) @ V.dofs(np.arange(V.dim)).T

(Note, that dofs is only intended to be called for a small number of DOF indices.)

If a product Operator is specified, this Operator is used to compute the inner products using apply2, i.e. U.inner(V, product) is equivalent to:

product.apply2(U, V)

which in turn is, by default, implemented as:

U.inner(product.apply(V))

In the case of complex numbers, this is antilinear in the first argument, i.e. in ‘self’. Complex conjugation is done in the first argument because most numerical software in the community handles it this way: Numpy, DUNE, FEniCS, Eigen, Matlab and BLAS do complex conjugation in the first argument, only PetSc and deal.ii do complex conjugation in the second argument.

Parameters

other

A VectorArray containing the second factors.

product

If not None an Operator representing the inner product bilinear form.

Returns

A NumPy array result such that

result[i, j] = ( self[i], other[j] ).

pairwise_inner(self, other, product=None)

Returns the pairwise inner products between VectorArray elements.

If product is None, the Euclidean inner product between the dofs of self and other are returned, i.e.

U.pairwise_inner(V)

is equivalent to:

np.sum(U.dofs(np.arange(U.dim)) * V.dofs(np.arange(V.dim)), axis=-1)

(Note, that dofs is only intended to be called for a small number of DOF indices.)

If a product Operator is specified, this Operator is used to compute the inner products using pairwise_apply2, i.e. U.inner(V, product) is equivalent to:

product.pairwise_apply2(U, V)

which in turn is, by default, implemented as:

U.pairwise_inner(product.apply(V))

In the case of complex numbers, this is antilinear in the first argument, i.e. in ‘self’. Complex conjugation is done in the first argument because most numerical software in the community handles it this way: Numpy, DUNE, FEniCS, Eigen, Matlab and BLAS do complex conjugation in the first argument, only PetSc and deal.ii do complex conjugation in the second argument.

Parameters

other

A VectorArray containing the second factors.

product

If not None an Operator representing the inner product bilinear form.

Returns

A NumPy array result such that

result[i] = ( self[i], other[i] ).

lincomb(self, coefficients)

Returns linear combinations of the vectors contained in the array.

Parameters

coefficients

A NumPy array of dimension 1 or 2 containing the linear coefficients. coefficients.shape[-1] has to agree with len(self).

Returns

A VectorArray result such that

result[i] = ∑ self[j] * coefficients[i,j]

in case coefficients is of dimension 2, otherwise len(result) == 1 and

result[0] = ∑ self[j] * coefficients[j].

_norm(self)

Implementation of norm for the case that no product is given.

_norm2(self)

Implementation of norm2 for the case that no product is given.

sup_norm(self)

The l-infinity-norms of the vectors contained in the array.

Returns

A NumPy array result such that result[i] contains the norm of self[i].

dofs(self, dof_indices)

Extract DOFs of the vectors contained in the array.

Parameters

dof_indices

List or 1D NumPy array of indices of the DOFs that are to be returned.

Returns

A NumPy array result such that result[i, j] is the dof_indices[j]-th DOF of the i-th vector of the array.

amax(self)

The maximum absolute value of the DOFs contained in the array.

Returns

max_ind

NumPy array containing for each vector a DOF index at which the maximum is attained.

max_val

NumPy array containing for each vector the maximum absolute value of its DOFs.

_blocks_are_valid(self)

_compute_bins(self)

class pymor.vectorarrays.block.BlockVectorSpace(subspaces)

Bases: pymor.vectorarrays.interface.VectorSpace

VectorSpace of BlockVectorArrays.

A BlockVectorSpace is defined by the VectorSpaces of the individual subblocks which constitute a given array. In particular for a given :class`BlockVectorArray` U, we have the identity

(U.blocks[0].space, U.blocks[1].space, ..., U.blocks[-1].space) == U.space.

Parameters

subspaces

The tuple defined above.

__eq__(self, other)

Return self==value.

__hash__(self)

Return hash(self).

property dim(self)

zeros(self, count=1, reserve=0)

Create a VectorArray of null vectors

Parameters

count

The number of vectors.

reserve

Hint for the backend to which length the array will grow.

Returns

A VectorArray containing count vectors with each component zero.

make_array(cls, obj)

Create a VectorArray from raw data.

This method is used in the implementation of Operators and Models to create new VectorArrays from raw data of the underlying solver backends. The ownership of the data is transferred to the newly created array.

The exact signature of this method depends on the wrapped solver backend.

make_block_diagonal_array(self, obj)

from_numpy(self, data, ensure_copy=False)

Create a VectorArray from a NumPy array

Note that this method will not be supported by all vector space implementations.

Parameters

data

NumPy array of shape (len, dim) where len is the number of vectors and dim their dimension.

ensure_copy

If False, modifying the returned VectorArray might alter the original NumPy array. If True always a copy of the array data is made.

Returns

A VectorArray with data as data.

class pymor.vectorarrays.block.BlockVectorArrayView(base, ind)

Bases: BlockVectorArray

VectorArray where each vector is a direct sum of sub-vectors.

Given a list of equal length VectorArrays blocks, this VectorArray represents the direct sums of the vectors contained in the arrays. The associated VectorSpace is BlockVectorSpace.

BlockVectorArray can be used in conjunction with BlockOperator.

is_view = True