NNS Numerical Differentiation

Determines numerical derivative of a given univariate function using projected secant lines on the y-axis. These projected points infer finite steps h, in the finite step method.

Usage

NNS.diff(
  f,
  point,
  h = abs(point) * 0.1 + 0.01,
  tol = 1e-10,
  max.iter = NULL,
  digits = 12,
  print.trace = FALSE,
  plot = FALSE
)

Arguments

f: an expression or call or a formula with no lhs.
point: numeric; Point to be evaluated for derivative of a given function f.
h: numeric [0, ...]; Initial step for secant projection. Defaults to (h = abs(point) * 0.1 + 0.01).
tol: numeric; Sets the tolerance for the stopping condition of the inferred h. Defaults to (tol = 1e-10).
max.iter: integer; NULL (default) Maximum number of bisection iterations. NULL sets the limit to 100L. For noisy functions the bisection may stall before tol is reached; max.iter provides a hard upper bound.
digits: numeric; Sets the number of digits specification of the output. Defaults to (digits = 12).
print.trace: logical; FALSE (default) Displays each iteration, lower y-intercept, upper y-intercept and inferred h.
plot: logical; plots range, secant lines and y-intercept convergence.

Value

Returns a matrix of values, intercepts, derivatives, inferred step sizes for multiple methods of estimation.

References

Viole, F. and Nawrocki, D. (2013) "Nonlinear Nonparametric Statistics: Using Partial Moments" (ISBN: 1490523995)

Author

Fred Viole, OVVO Financial Systems

Examples

if (FALSE) { # \dontrun{
f <- function(x) sin(x) / x
NNS.diff(f, 4.1)

## Noisy function with explicit iteration cap
f_noisy <- function(x) sin(x) + rnorm(1, 0, 0.001)
NNS.diff(f_noisy, 1.0, max.iter = 100)
} # }