hessian {pracma}

Hessian Matrix

Description

Numerically compute the Hessian matrix.

Usage

hessian(f, x0, h = .Machine$double.eps^(1/4), ...)

Arguments

f

univariate function of several variables.

x0

point in R^n.

h

step size.

...

variables to be passed to f.

Details

Computes the hessian matrix based on the three-point central difference formula, expanded to two variables.

Assumes that the function has continuous partial derivatives.

Value

An n-by-n matrix with \frac{\partial^2 f}{\partial x_i \partial x_j} as (i, j) entry.

References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

See Also

hessdiag, hessvec, laplacian

Examples

f <- function(x) cos(x[1] + x[2])
x0 <- c(0, 0)
hessian(f, x0)

f <- function(u) {
    x <- u[1]; y <- u[2]; z <- u[3]
    return(x^3 + y^2 + z^2 +12*x*y + 2*z)
}
x0 <- c(1,1,1)
hessian(f, x0)