R: Hessian Matrix

hessian {pracma} | R Documentation

## 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

`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)

[Package pracma version 2.0.4 Index]