Hessian utilities

Fast multiplication of Hessian and vector where computation of the full Hessian is not needed. Or determine the diagonal of the Hessian when non-diagonal entries are not needed or are nearly zero.

hessvec(f, x, v, csd = FALSE, ...)

  hessdiag(f, x, ...)

Arguments

f

function whose hessian is to be computed.

x

point in R^n.

v

vector of length n.

csd

logocal, shall complex-step be applied.

...

more arguments to be passed to the function.

Details

hessvec computes the product of a Hessian of a function times a vector without deriving the full Hessian by approximating the gradient (see the reference). If the function allows for the complex-step method, the gradient can be calculated much more accurate (see grad_csd).

hessdiag computes only the diagonal of the Hessian by applying the central difference formula of second order to approximate the partial derivatives.

Value

hessvec returns the product H(f,x) * v as a vector.

hessdiag returns the diagonal of the Hessian of f.

References

B.A. Pearlmutter, Fast Exact Multiplication by the Hessian, Neural Computation (1994), Vol. 6, Issue 1, pp. 147-160.

See also

hessian

Examples