[SciPy-user] non-linear multi-variate optimization

[Sebastian Walter]

The gradient g is only defined for functions f: R^N --> R and is
simply an array with shape (N,)

what you sketched in your post is the Jacobian J of a function f: R^N --> R^M
Typically, the Jacobian J is defined to have the shape (M,N), but
there are exceptions.

hope that helps a little
Sebastian



On Wed, Jul 15, 2009 at 2:00 AM, Chris Colbert<sccolbert at gmail.com> wrote:
> The routines for non-linear optimization in scipy.optimize take an
> argument for a function that computes the gradient.
>
> What should be the format of return value of this function? I am
> assuming that its the gradient of the functions with repect to the
> independent variables in row vector format.
>
> for example say we have:
>
> f(x,y,z; a1, a2, a3) where a1, a2, and a3 are the independent variables.
>
> Should the gradient of N x,y,z points then be of the form:
>
> df/da  =   [[df(X0)/da1, df(X0)/da2, df(X0)/da3],
>               [df(X1)/da1, df(X1)/da2, df(X1)/da3],
>               ....
>               [df(Xn)/da1, df(Xn)/da2, df(Xn)/da3]]
>
> where Xn is the set of (xn, yn, zn) ?
>
> cheers!
>
> Chris
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