trapezoidal_integration {workloopR}

Approximate the definite integral via the trapezoidal rule

Description

Mostly meant for internal use in our analysis functions, but made available for other use cases. Accordingly, it does not strictly rely on objects of class muscle_stim.

Usage

trapezoidal_integration(x, f)

Arguments

x

a variable, e.g. vector of positions

f

integrand, e.g. vector of forces

Details

In the functions analyze_workloop(), read_analyze_wl() , and read_analyze_wl_dir(), work is calculated as the difference between the integral of the upper curve and the integral of the lower curve of a work loop.

Value

A numerical value indicating the value of the integral.

Author(s)

Vikram B. Baliga

References

Atkinson, Kendall E. (1989), An Introduction to Numerical Analysis (2nd ed.), New York: John Wiley & Sons

See Also

analyze_workloop, read_analyze_wl, read_analyze_wl_dir

Examples

# create a circle centered at (x = 10, y = 20) with radius 2
t <- seq(0, 2 * pi, length = 1000)
coords <- t(rbind(10 + sin(t) * 2, 20 + cos(t) * 2))


# use the function to get the area
trapezoidal_integration(coords[, 1], coords[, 2])

# does it match (pi * r^2)?
3.14159265358 * (2^2) # very close