calc_gradient {gmvarkit}

Calculate gradient or Hessian matrix

Description

calc_gradient or calc_hessian calculates the gradient or Hessian matrix of the given function at the given point using central difference numerical approximation. get_gradient or get_hessian calculates the gradient or Hessian matrix of the log-likelihood function at the parameter estimates of a class 'gsmvar' object. get_soc returns eigenvalues of the Hessian matrix, and get_foc is the same as get_gradient but named conveniently.

Usage

calc_gradient(x, fn, h = 6e-06, varying_h = NULL, ...)

calc_hessian(x, fn, h = 6e-06, varying_h = NULL, ...)

get_gradient(gsmvar, custom_h = NULL)

get_hessian(gsmvar, custom_h = NULL)

get_foc(gsmvar, custom_h = NULL)

get_soc(gsmvar, custom_h = NULL)

Arguments

x

a numeric vector specifying the point where the gradient or Hessian should be calculated.

fn

a function that takes in argument x as the first argument.

h

difference used to approximate the derivatives.

varying_h

a numeric vector with the same length as x specifying the difference h for each dimension separately. If NULL (default), then the difference given as parameter h will be used for all dimensions.

...

other arguments passed to fn

gsmvar

an object of class 'gsmvar', typically created with fitGSMVAR or GSMVAR.

custom_h

same as varying_h except thaqt if NULL (default), then the difference used for differentiating overly large degrees of freedom parameters is adjusted to avoid numerical problems, and the difference 6e-6 is used for the other parameters.

Details

In particular, the functions get_foc and get_soc can be used to check whether the found estimates denote a (local) maximum point, a saddle point, or something else. Note that profile log-likelihood functions can be conveniently plotted with the function profile_logliks.

Value

Gradient functions return numerical approximation of the gradient and Hessian functions return numerical approximation of the Hessian. get_soc returns eigenvalues of the Hessian matrix.

Warning

No argument checks!

See Also

profile_logliks

Examples

  # Simple function
  foo <- function(x) x^2 + x
  calc_gradient(x=1, fn=foo)
  calc_gradient(x=-0.5, fn=foo)

  # More complicated function
  foo <- function(x, a, b) a*x[1]^2 - b*x[2]^2
  calc_gradient(x=c(1, 2), fn=foo, a=0.3, b=0.1)

  
  # GMVAR(1,2), d=2 model:
  params12 <- c(0.55, 0.112, 0.344, 0.055, -0.009, 0.718, 0.319, 0.005,
   0.03, 0.619, 0.173, 0.255, 0.017, -0.136, 0.858, 1.185, -0.012,
   0.136, 0.674)
  mod12 <- GSMVAR(gdpdef, p=1, M=2, params=params12)
  get_gradient(mod12)
  get_hessian(mod12)
  get_soc(mod12)