The `linearDecay()` 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.
linearDecay(decay = 0.001, pdist = 0.15, 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 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 `linearDecay()` constructor creates a simple linear decay model. It describes how a signal decreases proportionally with distance.
The decay function is defined as: $$y = signal \times \left(1 - (1 - decay) \times \frac{x}{pdist}\right)$$
where \(signal\) represents the initial intensity, \(decay\) defines the relative signal level at \(pdist\), and \(x\) is a vector of normalized distances. The signal decreases uniformly from its initial value to \(pdist\), which is a reference distance that anchors the model such that:
\(y = signal\) when \(x = 0\)
\(y = signal \times decay\) when \(x = pdist\)
This makes the linear form consistent with the exponential and Weibull decay functions, both of which also reach \(signal \times decay\) at the reference distance.
expDecay, weibullDecay
# Return a decay function
decay_fun <- linearDecay(decay = 0.5, pdist = 0.25)
# Plot decay model parameters
# linearDecay(decay = 0.5, pdist = 0.25, plot = TRUE)
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