CDM (version 7.4-19)

numerical_Hessian: Numerical Computation of the Hessian Matrix

Description

Computes numerically the Hessian matrix of a given function for all coordinates (numerical_Hessian), for a selected direction (numerical_Hessian_partial) or the gradient of a multivariate function (numerical_gradient).

Usage

numerical_Hessian(par, FUN, h=1e-05, gradient=FALSE,
       hessian=TRUE, diag_only=FALSE, ...)
numerical_Hessian_partial(par, FUN, h=1e-05, coordinate=1, ... )
numerical_gradient(par, FUN, h=1E-5, ...)

Arguments

par

Parameter vector

FUN

Specified function with argument vector x

h

Numerical differentiation parameter. Can be also a vector. The increment in the numerical approximation of the derivative is defined as \(h_i \max ( 1, \theta_i)\) where \(\theta_i\) denotes the \(i\)th parameter.

gradient

Logical indicating whether the gradient should be calculated.

hessian

Logical indicating whether the Hessian matrix should be calculated.

diag_only

Logical indicating whether only the diagonal of the hessian should be computed.

…

Further arguments to be passed to FUN.

coordinate

Coordinate index for partial derivative

Value

Gradient vector or Hessian matrix or a list of both elements

See Also

See the numDeriv package and the mirt::numerical_deriv function from the mirt package.

Examples

# NOT RUN {
#############################################################################
# EXAMPLE 1: Toy example for Hessian matrix
#############################################################################

# define function
f <- function(x){
     3*x[1]^3 - 4*x[2]^2 - 5*x[1]*x[2] + 10 * x[1] * x[3]^2 + 6*x[2]*sqrt(x[3])
}
# define point for evaluating partial derivatives
par <- c(3,8,4)

#--- compute gradient
CDM::numerical_Hessian( par=par, FUN=f, gradient=TRUE, hessian=FALSE)
# }
# NOT RUN {
mirt::numerical_deriv(par=par, f=f, gradient=TRUE)

#--- compute Hessian matrix
CDM::numerical_Hessian( par=par, FUN=f )
mirt::numerical_deriv(par=par, f=f, gradient=FALSE)
numerical_Hessian( par=par, FUN=f, h=1E-4 )

#--- compute gradient and Hessian matrix
CDM::numerical_Hessian( par=par, FUN=f, gradient=TRUE, hessian=TRUE)
# }