derivatives {irtProb}R Documentation

First and Second Derivatives

Description

Three points first and second derivatives numerical approximation used with the m4plEstimateMore function.

Usage

 fprime( x, FUN = "FP", h = 0.001, names = paste("x", c(1:length(x)), sep = ""))
 fsecond(x, FUN = "FP", h = 0.001, names = paste("x", c(1:length(x)), sep = ""))
 

Arguments

x numeric; vector of values at which the derivation is to be done.
FUN function; function to derive.
h numeric; neighbouring value.
names character; names given to each results. DEFAULT to the existing names of the vector x.

Details

This function could be used for numerical derivation in general, but is dedicated to be used internally by m4plEstimateMore. For other general purposes D, deriv and deriv3 are preferred.

Value

fprime numeric; vector of first derivatives.
fsecond numeric; matrix of second derivatives.

Author(s)

Gilles Raiche, Universite du Quebec a Montreal (UQAM),

Departement d'education et pedagogie

Raiche.Gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

Press, W. H., Vetterling, W. T., Teukolsky, S. A. and Flannery, B. P. (2002). Numerical recipees in C++. The art of scientific computing, 2nd edition. Cambridge, United Kingdom: Cambridge University press.

Yakowitz, S. and Szidarovszky, F. (1986). An introduction to numerical computations. New York, New Jersey: MacMilla.

See Also

D, deriv and deriv3

Examples

## .....................................
 test  <- function(x) 2*x+5
  test(   x=0)
  fprime( x=0, FUN=test)
  fsecond(x=0, FUN=test)
## .....................................
 test2 <- function(x) 2*(x[1]*x[2])+5
  test2(  x=c(0,0))
  fprime( x=c(0,0), FUN=test2)
  fsecond(x=c(0,0), FUN=test2)
 

[Package irtProb version 1.0 Index]