numerical_Hessian function

Numerical Computation of the Hessian Matrix

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).

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

Returns

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

#############################################################################
# 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)
## End(Not run)