Sigmoid Train
Evaluate a train of sigmoid functions at t.
sigmoid_train(t, ranges, rc)
t |
Vector (or coerced to a vector) of time values at which the sigmoids are calculated. |
ranges |
Matrix or array with 2 columns containing the time values
within |
rc |
Time constant. Either a scalar or a matrix or array with 2 columns
containing the rising and falling time constants of each sigmoid. If a
matrix or array is passed in |
The number and duration of each sigmoid is determined from ranges. Each row
of ranges represents a real interval, e.g. if sigmoid i starts
at t = 0.1 and ends at t = 0.5, then ranges[i, ] = c(0.1,
0.5). The input rc is an array that defines the rising and falling
time constants of each sigmoid. Its size must equal the size of ranges.
The individual sigmoids are returned in s. The combined sigmoid train
is returned in the vector y of length equal to t, and such that
y = max(s).
A list consisting two variables; y the combined sigmoid train
(length identical to t), and s, the individual sigmoids
(number of rows equal to number of rows in ranges and rc.
Juan Pablo Carbajal, carbajal@ifi.uzh.ch.
Conversion to R by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
t <- seq(0, 2, length.out = 500)
ranges <- rbind(c(0.1, 0.4), c(0.6, 0.8), c(1, 2))
rc <- rbind(c(1e-2, 1e-3), c(1e-3, 2e-2), c(2e-2, 1e-2))
st <- sigmoid_train (t, ranges, rc)
plot(t, st$y[1,], type="n", xlab = "Time(s)", ylab = "S(t)",
main = "Vectorized use of sigmoid train")
for (i in 1:3) rect(ranges[i, 1], 0, ranges[i, 2], 1,
border = NA, col="pink")
for (i in 1:3) lines(t, st$y[i,])
# The colored regions show the limits defined in range.
t <- seq(0, 2, length.out = 500)
ranges <- rbind(c(0.1, 0.4), c(0.6, 0.8), c(1, 2))
rc <- rbind(c(1e-2, 1e-3), c(1e-3, 2e-2), c(2e-2, 1e-2))
amp <- c(4, 2, 3)
st <- sigmoid_train (t, ranges, rc)
y <- amp %*% st$y
plot(t, y[1,], type="l", xlab = 'time', ylab = 'signal',
main = 'Varying amplitude sigmoid train', col="blue")
lines(t, st$s, col = "orange")
legend("topright", legend = c("Sigmoid train", "Components"),
lty = 1, col = c("blue", "orange"))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.