symmetrize_pwc

Graph.symmetrize_pwc(pwc, *, name=None)

Create the symmetrization of a piecewise-constant function.

Parameters:

pwc (Pwc) – The piecewise-constant function \(v(t)\) to symmetrize.
name (str or None, optional) – The name of the node.

Returns:

The piecewise-constant function \(w(t)\) defined by \(w(t)=v(t)\) for \(0\leq t\leq \tau\) and \(w(t)=v(2\tau-t)\) for \(\tau\leq t\leq 2\tau\), where \(\tau\) is the duration of \(v(t)\).

Return type:

Pwc

See also

pwc_signal: Create Pwc signals from (possibly complex) values.
time_reverse_pwc: Reverse Pwcs in time.

Notes

For more information on Pwc nodes see the Working with time-dependent functions in Boulder Opal topic.

Examples

Create a symmetric piecewise-constant function.

>>> x = graph.pwc(durations=np.array([0.1, 0.3]), values=np.array([1, 2]))
>>> graph.symmetrize_pwc(x, name="symmetrize")
<Pwc: name="symmetrize", operation_name="symmetrize_pwc", value_shape=(), batch_shape=()>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["symmetrize"])
>>> result.output["symmetrize"]
[
    {"value": 1.0, "duration": 0.1},
    {"value": 2.0, "duration": 0.3},
    {"value": 2.0, "duration": 0.3},
    {"value": 1.0, "duration": 0.1},
]

See more examples in the How to optimize controls with time symmetrization user guide.