function to be differentiated. The first argument must be
the parameter vector with respect to which it is differentiated.
For numeric gradient, f may return a (numeric) vector, for Hessian it
should return a numeric scalar
grad
function, gradient of f
t0
vector, the parameter values
eps
numeric, the step for numeric differentiation
fixed
logical index vector, fixed parameters.
Derivative is calculated only with respect to the parameters
for which fixed == FALSE, NA is returned for the fixed
parameters. If
missing, all parameters are treated as active.
...
furter arguments for f
Details
numericGradient numerically differentiates a (vector valued)
function with respect to it's (vector valued) argument. If the
functions value is a code{N_val * 1}
vector and the argument is
code{N_par * 1} vector, the resulting
gradient
is a code{NVal * NPar}
matrix.
numericHessian checks whether a gradient function is present.
If yes, it calculates the gradient of the gradient, if not, it
calculates the full
numeric Hessian (numericNHessian).
Value
Matrix. For numericGradient, the number of rows is equal to the
length of the function value vector, and the number of columns is
equal to the length of the parameter vector.
For the numericHessian, both numer of rows and columns is
equal to the length of the parameter vector.
Warning
Be careful when using numerical differentiation in optimization
routines. Although quite precise in simple cases, they may work very
poorly in more complicated conditions.
Author(s)
Ott Toomet
See Also
compareDerivatives, deriv
Examples
# A simple example with Gaussian bell surface
f0 <- function(t0) exp(-t0[1]^2 - t0[2]^2)
numericGradient(f0, c(1,2))
numericHessian(f0, t0=c(1,2))
# An example with the analytic gradient
gradf0 <- function(t0) -2*t0*f0(t0)
numericHessian(f0, gradf0, t0=c(1,2))
# The results should be similar as in the previous case
# The central numeric derivatives are often quite precise
compareDerivatives(f0, gradf0, t0=1:2)
# The difference is around 1e-10