JACOBFCN Function
Computes the Jacobian of a user-supplied function.
Usage
j = jacobfcn (f, x, d)
Input Parameters
f—Name of a user-supplied, m-valued function of n variables with an input of: (p,n) array z of p points in the independent variables, and an output of: (p,m) array b where b(i,*) = f(z(i,*)).
x—A (q,n) array of q points in the independent variable space.
d—An n-element vector specifying the step sizes to use for the central difference approximation of the Jacobian.
Returned Value
j—An (m,n,q) array where j(*,*,i) is df/dx at x(i,*).
Keywords
None.
Discussion
The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. It represents the best linear approximation to a differentiable function near a given point.
For example, the Jacobian of a function y = f(x) of n equations in n variables
(x1, ..., xn) would be:
(x1, ..., xn) would be:
Example
See wave/lib/user/examples/jacobfcnex.pro for an example of the JACOBFCN function.
See Also
