pracma (version 1.9.9)

hessian: 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.

Value

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

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.

References

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

See Also

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)