R: Laplacian Operator

laplacian {pracma} | R Documentation

## Laplacian Operator

### Description

Numerically compute the Laplacian of a function.

### Usage

    laplacian(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 Laplacian operator f_{x_1 x_1} + … + f_{x_n x_n} based on the three-point central difference formula, expanded to this special case.

Assumes that the function has continuous partial derivatives.

### Value

Real number.

### References

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

### See Also

`hessian`

### Examples

    f <- function(x) x[1]^2 + 2*x[1]*x[2] + x[2]^2
    laplacian(f, c(1,1))

[Package pracma version 2.0.4 Index]