tanh_ramp_pwc

signals.tanh_ramp_pwc(duration, segment_count, end_value, start_value=None, ramp_duration=None, center_time=None, *, name=None)

Create a Pwc representing a hyperbolic tangent ramp.

Parameters:

duration (float) – The duration of the signal, \(T\).
segment_count (int) – The number of segments in the PWC.
end_value (float or complex or Tensor) – The asymptotic value of the ramp towards \(t \to +\infty\), \(a_+\). It must either be a scalar or contain a single element.
start_value (float or complex or Tensor or None, optional) – The asymptotic value of the ramp towards \(t \to -\infty\), \(a_-\). If passed, it must either be a scalar or contain a single element. Defaults to minus end_value.
ramp_duration (float or Tensor or None, optional) – The characteristic time for the hyperbolic tangent ramp, \(t_\mathrm{ramp}\). If passed, it must either be a scalar or contain a single element. Defaults to \(T/6\).
center_time (float or Tensor or None, optional) – The time at which the ramp has its greatest slope, \(t_0\). If passed, it must either be a scalar or contain a single element. Defaults to \(T/2\).
name (str or None, optional) – The name of the node.

Returns:

The sampled hyperbolic tangent ramp.

Return type:

Pwc

See also

Graph.signals.linear_ramp_pwc: Create a Pwc representing a linear ramp.
boulderopal.signals.tanh_ramp: Create a Signal object representing a hyperbolic tangent ramp.
Graph.signals.tanh_ramp_stf: Corresponding operation with Stf output.
Graph.tanh: Calculate the element-wise hyperbolic tangent of an object.

Notes

The hyperbolic tangent ramp is defined as

\[\mathop{\mathrm{Tanh}}(t) = \frac{a_+ + a_-}{2} + \frac{a_+ - a_-}{2} \tanh\left( \frac{t - t_0}{t_\mathrm{ramp}} \right) ,\]

where the function’s asymptotic values \(a_\pm\) are defined by:

\[a_\pm := \lim_{t\to\pm\infty} \mathop{\mathrm{Tanh}}(t) ,\]

and \(t_0\) is related to \(t_\mathrm{ramp}\) by:

\[\left.\frac{{\rm d}\mathop{\mathrm{Tanh}}(t)}{{\rm d}t}\right|_{t=t_0} = \frac{ (a_+ - a_-)}{2 t_\mathrm{ramp}} .\]

Note that if \(t_0\) is close to the edges of the PWC, for example \(t_0 \lesssim 2 t_\mathrm{ramp}\), then the first and last values of the PWC will differ from the expected asymptotic values.

With the default values of start_value (\(a_-\)), ramp_duration (\(t_\mathrm{ramp}\)), and center_time (\(t_0\)), the ramp expression simplifies to

\[\mathop{\mathrm{Tanh}}(t) = A \tanh\left( \frac{t - T/2}{T/6} \right),\]

where \(A = a_+\) is the end value (the start value is then \(-A\)). This defines a symmetric ramp (around \((T/2, 0)\)) between \(-0.995 A\) (at \(t=0\)) and \(0.995 A\) (at \(t=T\)).

Examples

Define a simple tanh PWC ramp.

>>> graph.signals.tanh_ramp_pwc(
...     duration=5.0, segment_count=50, end_value=1, name="tanh_ramp"
... )
<Pwc: name="tanh_ramp", operation_name="discretize_stf", value_shape=(), batch_shape=()>
>>> result = bo.execute_graph(graph=graph, output_node_names="tanh_ramp")
>>> result["output"]["tanh_ramp"]
{
    'durations': array([0.1, 0.1, ..., 0.1, 0.1]),
    'values': array([-0.99442601, -0.99291942, ..., 0.99291942,  0.99442601]),
    'time_dimension': 0
}

Define a flat-top pulse from two hyperbolic tangent ramps.

>>> ramp = graph.signals.tanh_ramp_pwc(
...     duration=3,
...     segment_count=60,
...     end_value=1,
...     ramp_duration=0.25,
...     center_time=0.5,
... )
>>> flat_top_pulse = 0.5 * (ramp + graph.time_reverse_pwc(ramp))
>>> flat_top_pulse.name="flat_top_pulse"
>>> result = bo.execute_graph(graph=graph, output_node_names="flat_top_pulse")
>>> result["output"]["flat_top_pulse"]
{
    'durations': array([0.05, 0.05, ..., 0.05, 0.05]),
    'values': array([0.02188127, 0.03229546, ..., 0.03229546, 0.02188127]),
    'time_dimension': 0
}

Define a hyperbolic tangent ramp with optimizable parameters.

>>> end_value = graph.optimizable_scalar(
...     lower_bound=0, upper_bound=3e6, name="end_value"
... )
>>> ramp_duration = graph.optimizable_scalar(
...     lower_bound=0.1e-6, upper_bound=0.3e-6, name="ramp_duration"
... )
>>> center_time = graph.optimizable_scalar(
...     lower_bound=0.25e-6, upper_bound=0.75e-6, name="center_time"
... )
>>> graph.signals.tanh_ramp_pwc(
...     duration=1e-6,
...     segment_count=32,
...     end_value=end_value,
...     start_value=0.0,
...     ramp_duration=ramp_duration,
...     center_time=center_time,
...     name="tanh_ramp",
... )
<Pwc: name="tanh_ramp", operation_name="discretize_stf", value_shape=(), batch_shape=()>