# laplacian

From calculus v0.1.0
by Emanuele Guidotti

##### Numerical and Symbolic Laplacian

Computes the laplacian of functions, expressions and characters.

##### Usage

```
laplacian(f, var, accuracy = 2, stepsize = NULL,
coordinates = "cartesian")
```f %laplacian% var

##### Arguments

- f
function, expression or character array.

- var
character vector, giving the variable names with respect to which derivatives will be computed. If a named vector is provided, derivatives will be computed at that point.

- accuracy
accuracy degree for numerical derivatives.

- stepsize
finite differences stepsize for numerical derivatives. Auto-optimized by default.

- coordinates
coordinate system to use. One of:

`cartesian`

,`polar`

,`spherical`

,`cylindrical`

,`parabolic`

,`parabolic-cylindrical`

or a character vector of scale factors for each varibale.

##### Value

laplacian array.

##### Functions

`laplacian`

: arbitrary coordinate system`%laplacian%`

: cartesian coordinates

##### Examples

```
# NOT RUN {
# laplacian of a scalar field
f <- 'x^2+y^2+z^2'
laplacian(f, var = c('x','y','z'))
f %laplacian% c('x','y','z')
# laplacian of scalar fields
f <- c('x^2','y^3','z^4')
laplacian(f, var = c('x','y','z'))
f %laplacian% c('x','y','z')
# numerical laplacian of scalar fields
f <- c(function(x,y,z) x^2, function(x,y,z) y^3, function(x,y,z) z^4)
laplacian(f, var = c('x'=1,'y'=1,'z'=1))
f %laplacian% c('x'=1,'y'=1,'z'=1)
# laplacian of array of scalar fields
f1 <- c('x^2','y^3','z^4')
f2 <- c('x','y','z')
a <- matrix(c(f1,f2), nrow = 2, byrow = TRUE)
laplacian(a, var = c('x','y','z'))
a %laplacian% c('x','y','z')
# laplacian in polar coordinates
f <- c('sqrt(r)/10','sqrt(r)')
laplacian(f, var = c('r','phi'), coordinates = 'polar')
# }
```

*Documentation reproduced from package calculus, version 0.1.0, License: GPL-3*

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