metagenomeSeq (version 1.14.0)

trapz: Trapezoidal Integration

Description

Compute the area of a function with values 'y' at the points 'x'. Function comes from the pracma package.

Usage

trapz(x, y)

Arguments

x

x-coordinates of points on the x-axis

y

y-coordinates of function values

Value

Approximated integral of the function from 'min(x)' to 'max(x)'. Or a matrix of the same size as 'y'.

Examples

# Calculate the area under the sine curve from 0 to pi:
 n <- 101
 x <- seq(0, pi, len = n)
 y <- sin(x)
 trapz(x, y)          #=> 1.999835504

# Use a correction term at the boundary: -h^2/12*(f'(b)-f'(a))
 h  <- x[2] - x[1]
 ca <- (y[2]-y[1]) / h
 cb <- (y[n]-y[n-1]) / h
 trapz(x, y) - h^2/12 * (cb - ca)  #=> 1.999999969