The `weibullDecay()` constructor either creates a decay function or
returns a `ggplot` object for visualizing the decay model. It is a utility
function used internally by circularProjection and
polarProjection.
weibullDecay(
decay = 0.001,
pdist = 0.15,
shape = 1.05,
plot = FALSE,
demo.signal = 1
)Returns either a function of the form
function(x, signal) { ... } or, if plot = TRUE, a `ggplot`
object illustrating the decay model.
A decay factor (in [0,1]). This term indicates how much a
signal decreases as a function of distance in pathway space.
For example, at a specific distance defined by the pdist parameter,
the signal intensity will be the initial signal multiplied by decay.
A distance normalization term (in (0, 1]) at which the signal
reaches `signal * decay`. This parameter is used to anchor the decay to
a meaningful distance (see `details`). Also, when pdist = 1, it will
represent the diameter of the inscribed circle within the coordinate space
of a `PathwaySpace` object.
A parameter (>=1) of a Weibull function. When shape=1
the Weibull decay follows an exponential decay. When shape>1
the function is first convex, then concave with an inflection point.
A logical value indicating whether to return a `ggplot` object.
A numeric value in `[-Inf, Inf]`, only passed when
plot = TRUE to visualize the decay curve with a specific signal
intensity. The value is ignored by the function constructor, as the decay
function itself is returned without using an initial signal.
Sysbiolab Team
The `weibullDecay()` constructor creates a decay model based on the Weibull distribution. It describes how a signal decreases as a function of distance, controlled by both a decay rate and a shape parameter.
The decay function is defined as:
$$y = signal \times decay^{\left(\frac{x}{pdist}\right)^{shape}}$$
where \(signal\) represents the initial intensity, \(decay\) controls the rate of attenuation, \(x\) is a vector of normalized distances, and \(shape\) adjusts the curvature of the decay. When \(shape = 1\), the function follows an exponential decay. For \(shape > 1\), the curve transitions from convex to concave, exhibiting an inflection point. The \(pdist\) parameter anchors the model such that:
\(y = signal\) when \(x = 0\)
\(y = signal \times decay\) when \(x = pdist\)
linearDecay, expDecay
# Return a decay function
decay_fun <- weibullDecay(decay = 0.5, pdist = 0.4, shape = 2)
# Plot decay model parameters
# weibullDecay(decay = 0.5, pdist = 0.4, shape = 2, plot = TRUE)
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