R: Jacobian Matrix

jacobian {pracma} | R Documentation

## Jacobian Matrix

### Description

Jacobian matrix of a function R^n –> R^m .

### Usage

    jacobian(f, x0, heps = .Machine$double.eps^(1/3), ...)

### Arguments

`f` | `m` functions of `n` variables.
`x0` | Numeric vector of length `n`.
`heps` | This is `h` in the derivative formula.
`...` | parameters to be passed to f.

### Details

Computes the derivative of each funktion f_j by variable x_i separately, taking the discrete step h.

### Value

Numeric `m`-by-`n` matrix `J` where the entry `J[j, i]` is \frac{\partial f_j}{\partial x_i}, i.e. the derivatives of function f_j line up in row i for x_1, …, x_n.

### Note

Obviously, this function is not vectorized.

### References

Quarteroni, A., R. Sacco, and F. Saleri (2007). Numerical Mathematics. Second Edition, Springer-Verlag, Berlin Heidelberg.

### See Also

`gradient`

### Examples

    ##  Example function from Quarteroni & Saleri
    f <- function(x) c(x[1]^2 + x[2]^2 - 1, sin(pi*x[1]/2) + x[2]^3)
    jf <- function(x)
              matrix( c(2*x[1], pi/2 * cos(pi*x[1]/2), 2*x[2], 3*x[2]^2), 2, 2)
    all.equal(jf(c(1,1)), jacobian(f, c(1,1)))
    # TRUE

[Package pracma version 2.0.4 Index]