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]