fptdApprox (version 2.5)

growth.intervals: Studying the Growth of a Vector

Description

For the vector of values resulting from the evaluation of a function, this function determines the positions of the values between which the vector grows.

Usage

growth.intervals(x, y, zeroSlope = 0.01)

Value

This function returns NULL if the vector y is not growing. Otherwise, the function computes a matrix of indexes with two columns. The first column contains the positions of the values from which the vector y starts growing and the second column those at which the vector y stops growing.

Arguments

x

a vector of values.

y

the vector of the corresponding values of a function for the x vector.

zeroSlope

maximum slope (in degrees) required to consider that a growing function is constant.

Author

Patricia Román-Román, Juan J. Serrano-Pérez and Francisco Torres-Ruiz.

Details

The growth.intervals function ignores the pairs of values between which the vector y starts and stops growing if the slope is less than zeroSlope.

Examples

u <- seq(0, 5, length = 200)
v <- sin(u)
w <- growth.intervals(u, v)
w

plot(u, v, type = "l", las = 1)
abline(v = u[as.vector(w)])

## Continuing the FPTL(.) examples:
Lognormal <- diffproc(c("m*x","sigma^2*x^2","dnorm((log(x)-(log(y)+(m-sigma^2/2)*(t-s)))/(sigma*sqrt(t-s)),0,1)/(sigma*sqrt(t-s)*x)", "plnorm(x,log(y)+(m-sigma^2/2)*(t-s),sigma*sqrt(t-s))")) ; 
b <- "4.5 + 4*t^2 + 7*t*sqrt(t)*sin(6*sqrt(t))" ; y <- FPTL(dp = Lognormal, t0 = 0, T = 18, x0 = 1, S = b, list(m = 0.48, sigma = 0.07))
growth.intervals(y$x, y$y)
growth.intervals(y$x, y$y, zeroSlope = 0.001)