CDM: numerical_Hessian – R documentation

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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, θ_i) where θ_i denotes the ith 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

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)

CDM

Cognitive Diagnosis Modeling

v7.5-15

GPL (>= 2)

Authors

Alexander Robitzsch [aut, cre], Thomas Kiefer [aut], Ann Cathrice George [aut], Ali Uenlue [aut]

Initial release

2020-03-10 14:19:21