Useful functions between 0 and 1

zero-to-one-fun

rm(list=ls())
graphics.off()

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# The Exponential decay function 
# http://en.wikipedia.org/wiki/Exponential_function

# a sequence of x-values from 0 to 1000
x <- seq(0, 100, length=100)

y.1 <- exp(- 0.01 * x)
y.2 <- exp(- 0.1 * x)
y.3 <- exp(- 1 * x)
y.4 <- exp(- 10 * x)

par(mfrow = c(1,2))

matplot(x, cbind(y.1, y.2, y.3, y.4), type = "l", ylab = "exp(x)",
        bty = "L")
legend("topright", y = NULL, legend = paste(c(0.01, 0.1, 1, 10)),
       lty = 1, lwd = 1, col = 1:4, bty = "n", title = "Decay Rate" )

matplot(x, 1 - cbind(y.1, y.2, y.3, y.4), type = "l", ylab = "1 - exp(x)",
        bty = "L")
legend("bottomright", y = NULL, legend = paste(c(0.01, 0.1, 1, 10)),
       lty = 1, lwd = 1, col = 1:4, bty = "n", title = "Decay Rate" )


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# The gaussian function
# http://en.wikipedia.org/wiki/Gaussian_function

# a sequence
z <- seq(-3, 3, length = 500)

a <- 1
b <- 0
c <- 0.25 # this makes the denominator = 1

w <- a * exp(-((z - b)^2 / c)) 

par(mfrow = c(1,2))

plot(z, w, type = "l", bty = "L", main = "Gaussian")

plot(z, 1 - w, type = "l", bty = "L", main = "1 - Gaussian")

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