`pymor.algorithms.hapod`¶

Module Contents¶

class pymor.algorithms.hapod.FakeExecutor[source]¶

Methods

submit

static submit(f, *args)[source]¶

Async:

class pymor.algorithms.hapod.LifoExecutor(executor, max_workers=None)[source]¶

Methods

`done_callback`
`run_task`
`submit`

done_callback(future, executor_future)[source]¶

async run_task()[source]¶

submit(f, *args)[source]¶

class pymor.algorithms.hapod.Node(tag=None, parent=None, after=None)[source]¶

Methods

`add_child`
`traverse`

add_child(tag=None, after=None, **kwargs)[source]¶

traverse(return_level=False)[source]¶

pymor.algorithms.hapod.default_pod_method(U, eps, is_root_node, product)[source]¶

pymor.algorithms.hapod.dist_hapod(num_slices, snapshots, eps, omega, arity=None, product=None, executor=None, eval_snapshots_in_executor=False)[source]¶

Distributed Hierarchical Approximate POD.

This computes the distributed HAPOD from [HLR18].

Parameters

num_slices: The number of snapshot vector slices.
snapshots: A mapping snapshots(slice) returning for each slice number the associated snapshot vectors.
eps: Desired l2-mean approximation error.
omega: Tuning parameter (0 < omega < 1) to balance performance with approximation quality.
arity: If not None, the arity of the HAPOD tree. Otherwise, a tree of depth 2 is used (one POD per slice and one additional POD of the resulting data).
product: Inner product Operator w.r.t. which to compute the POD.
executor: If not None, a concurrent.futures.Executor object to use for parallelization.
eval_snapshots_in_executor: If True also parallelize the evaluation of the snapshot map.

Returns

modes: The computed POD modes.
svals: The associated singular values.
snap_count: The total number of input snapshot vectors.

pymor.algorithms.hapod.dist_hapod_tree(num_slices, arity=None)[source]¶

pymor.algorithms.hapod.dist_vectorarray_hapod(num_slices, U, eps, omega, arity=None, product=None, executor=None)[source]¶

Distributed Hierarchical Approximate POD.

This computes the distributed HAPOD from [HLR18] of a given VectorArray.

Parameters

num_slices: The number of snapshot vector slices.
U: The VectorArray of which to compute the HAPOD.
eps: Desired l2-mean approximation error.
omega: Tuning parameter (0 < omega < 1) to balance performance with approximation quality.
arity: If not None, the arity of the HAPOD tree. Otherwise, a tree of depth 2 is used (one POD per slice and one additional POD of the resulting data).
product: Inner product Operator w.r.t. which to compute the POD.
executor: If not None, a concurrent.futures.Executor object to use for parallelization.

Returns

modes: The computed POD modes.
svals: The associated singular values.
snap_count: The total number of input snapshot vectors.

pymor.algorithms.hapod.hapod(tree, snapshots, local_eps, product=None, pod_method=default_pod_method, executor=None, eval_snapshots_in_executor=False)[source]¶

Compute the Hierarchical Approximate POD.

This is an implementation of the HAPOD algorithm from [HLR18].

Parameters

tree: A Tree defining the worker topology.
snapshots: A mapping snapshots(node) returning for each leaf node the associated snapshot vectors.
local_eps: A mapping local_eps(node, snap_count, num_vecs) assigning to each tree node node an l2 truncation error tolerance for the local pod based on the number of input vectors num_vecs and the total number of snapshot vectors below the given node snap_count.
product: Inner product Operator w.r.t. which to compute the POD.
pod_method: A function pod_method(U, eps, root_node, product) for computing the POD of the VectorArray U w.r.t. the given inner product product and the l2 error tolerance eps. root_node is set to True when the POD is computed at the root of the tree.
executor: If not None, a concurrent.futures.Executor object to use for parallelization.
eval_snapshots_in_executor: If True also parallelize the evaluation of the snapshot map.

Returns

modes: The computed POD modes.
svals: The associated singular values.
snap_count: The total number of input snapshot vectors.

pymor.algorithms.hapod.inc_hapod(steps, snapshots, eps, omega, product=None, executor=None)[source]¶

Incremental Hierarchical Approximate POD.

This computes the incremental HAPOD from [HLR18].

Parameters

steps: The number of incremental POD updates. Has to agree with the length of snapshots.
snapshots: An iterable returning for each incremental POD step the associated snapshot vectors.
eps: Desired l2-mean approximation error.
omega: Tuning parameter (0 < omega < 1) to balance performance with approximation quality.
product: Inner product Operator w.r.t. which to compute the POD.
executor: If not None, a concurrent.futures.Executor object to use to compute new snapshot vectors and POD updates in parallel.

Returns

modes: The computed POD modes.
svals: The associated singular values.
snap_count: The total number of input snapshot vectors.

pymor.algorithms.hapod.inc_hapod_tree(steps)[source]¶

pymor.algorithms.hapod.inc_vectorarray_hapod(steps, U, eps, omega, product=None)[source]¶

Incremental Hierarchical Approximate POD.

This computes the incremental HAPOD from [HLR18] for a given VectorArray.

Parameters

steps: The number of incremental POD updates.
U: The VectorArray of which to compute the HAPOD.
eps: Desired l2-mean approximation error.
omega: Tuning parameter (0 < omega < 1) to balance performance with approximation quality.
product: Inner product Operator w.r.t. which to compute the POD.

Returns

modes: The computed POD modes.
svals: The associated singular values.
snap_count: The total number of input snapshot vectors.

pymor.algorithms.hapod.std_local_eps(tree, eps, omega, pod_on_leafs=True)[source]¶

pymor.algorithms.hapod¶

Module Contents¶

`pymor.algorithms.hapod`¶