[SciPy-User] 2. Re: optimize.minimize - help me understand arrays as variables

[KURT PETERS]

> Date: Thu, 15 Jan 2015 11:01:56 +1100
> From: Geordie McBain <gdmcbain at freeshell.org>
> Subject: Re: [SciPy-User] optimize.minimize - help me understand
> 	arrays as variables (Andrew Nelson)
> To: SciPy Users List <scipy-user at scipy.org>
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> 2015-01-13 10:26 GMT+11:00 KURT PETERS <peterskurt at msn.com>:
> >  > Date: Sun, 11 Jan 2015 17:55:32 -0700
> >> From: KURT PETERS <peterskurt at msn.com>
> >> Subject: [SciPy-User] optimize.minimize - help me understand arrays as
> >> variables
> >> To: "scipy-user at scipy.org" <scipy-user at scipy.org>
> >> Message-ID: <BLU172-W37473350444550BD9CF90DD8430 at phx.gbl>
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> >>
> >> I'm trying to use scipy.optimize.minimize.
> >> I've tried multiple "multivariate" methods that don't seem to actually
> >> take multivariate data and derivatives. Can someone tell me how I can make
> >> the multivariate part of the solver actually work?
> >>
> >> Here's an example:
> >> My main function the following (typical length for N is 3):
> >>
> >> input guess is a x0=np.array([1,2,3])
> >> the optimization function returns:
> >> def calc_f3d(...):
> >> f3d = np.ones((np.max([3,N]),1)
> >> .... do some assignments to f3d[row,0] ....
> >> return np.linalg.norm(f3d) # numpy.array that's 3x1
> >>
> >> The jacobian returns a Nx3 matrix:
> >> def jacob3d(...):
> >> df = np.ones((np.max([3,N]),3))
> >> ... do some assignments to df[row,col]
> >> return df # note numpy.array that's 3x3
> 
> Hello.  I think that this might be the problem here: the jac should
> have the same shape as x, i.e. (N,), not (N, 3); the components of the
> jac are the partial derivatives of fun with respect to the
> corresponding components of x.  Think of it as the gradient of the
> objective.
> 
> Here's a simple shape=(2,) example, taken from D. M. Greig's
> Optimisation (1980, London: Longman).  The exact minimum is 0 at [1,
> 1].
> 
> def f(x):                       # Greig (1980, p. 48)
>     return (x[1] - x[0]**2)**2 + (1 - x[0])**2
> 
> def g(x):                       # ibid
>     return np.array([-4*x[0]*(x[1] - x[0]**2) - 2 + 2*x[0],
>                      2 * (x[1] - x[0]**2)])
> 
> x = np.zeros(2)
> print('Without Jacobian: ', minimize(f, x))
> print('\nWith:', minimize(f, x, jac=g))

I'm going to try the root function.  I just saw the words "multivariate scalar function" in the documentation for minimize.  Maybe my assumption was that it could handle multiple functions.  As I read further, there's a distinction to multiple functions in the "Root" function, such as with Krylov.  I'm going to see if that behaves the way I would expect.  Perhaps, I misunderstood the documentation.
   I'm going to try that and let the group know how that worked.
Kurt
 		 	   		  
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