SciPy Optimization syntax

**Robert Kern** · Sep 20 '06, 07:45 PM

Re: SciPy Optimization syntax

tkpmep@hotmail. com wrote:

I'm trying to optimize a function using SciPy's optimize.fmin, but am
clearly getting the syntax wrong, and would be grateful for some
guiidance.

You will want to ask such questions on the scipy mailing lists.

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http://www.scipy.org/Mailing_Lists

First, here's the function
>
def func(Y,x):
"""Y holds samples of a function sampled at t=-3,-2,-1,0,1,2,3.
Y[3]=0 always.
func returns the absolute value of the maximum NEGATIVE
error from a straight line fit with slope x and intercept 0"""
>
Y[0] = Y[0] - 3*x
Y[1] = Y[1] - 2*x
Y[2] = Y[2] - x
Y[3] = 0
Y[4] = Y[4] + x
Y[5] = Y[5] + 2*x
Y[6] = Y[6] + 3*x
>
error = abs(max(min(Y), 0)
>
return 0

If func(Y,x) == 0 for any Y or x, what exactly do you intend to minimize?

Also, do you really want to modify Y every time? fmin() will call this function
multiple times with different values of x (if you call it correctly); your
original data will be destroyed and your result will be meaningless.

Thirdly, it looks like you used the wrong sign for finding the residuals, or I'm
misunderstandin g the docstring. I'll assume that the docstring is correct for
the following.

I'd now like to minimize this using optimize.fmin. I first defined

>>Y = [0, 0, 0, 0, 1, 2, 3]
>>x = 1

>
and then typed

>>optimize.fmin (func, args=(Y,x) )

>
I expected the function to retun x=0 as the optimal value, but instead
got the following error messsage:
Traceback (most recent call last):
File "<pyshell#2 4>", line 1, in -toplevel-
optimize.fmin(f unc,args=(optio nPnL,x))
TypeError: fmin() takes at least 2 non-keyword arguments (1 given)

Yes, fmin() requires two arguments, the function to minimize and an initial
value. The docstring is pretty clear on this:

Type: function
Base Class: <type 'function'>
String Form: <function fmin at 0x2028670>
Namespace: Interactive
File:
/Library/Frameworks/Python.framewor k/Versions/2.4/lib/python2.4/site-packages/scipy-0.5.2.dev2196-py2.4-
macosx-10.4-ppc.egg/scipy/optimize/optimize.py
Definition: optimize.fmin(f unc, x0, args=(), xtol=0.0001, ftol=0.0001,
maxiter=None, maxfun=None, full_output=0, dis
p=1, retall=0, callback=None)
Docstring:
Minimize a function using the downhill simplex algorithm.

Description:

Uses a Nelder-Mead simplex algorithm to find the minimum of function
of one or more variables.

Inputs:

func -- the Python function or method to be minimized.
x0 -- the initial guess.
args -- extra arguments for func.
callback -- an optional user-supplied function to call after each
iteration. It is called as callback(xk), where xk is the
current parameter vector.

Outputs: (xopt, {fopt, iter, funcalls, warnflag})

xopt -- minimizer of function

fopt -- value of function at minimum: fopt = func(xopt)
iter -- number of iterations
funcalls -- number of function calls
warnflag -- Integer warning flag:
1 : 'Maximum number of function evaluations.'
2 : 'Maximum number of iterations.'
allvecs -- a list of solutions at each iteration

Additional Inputs:

xtol -- acceptable relative error in xopt for convergence.
ftol -- acceptable relative error in func(xopt) for convergence.
maxiter -- the maximum number of iterations to perform.
maxfun -- the maximum number of function evaluations.
full_output -- non-zero if fval and warnflag outputs are desired.
disp -- non-zero to print convergence messages.
retall -- non-zero to return list of solutions at each iteration

I then tried

>>optimize.fmin (func, x0 =x, args=(Y,x) )

>
and got a slightly different error message:
Traceback (most recent call last):
File "<pyshell#2 5>", line 1, in -toplevel-
optimize.fmin(f unc,x0=x, args=(optionPnL ,1))
File "C:\Python24\li b\site-packages\scipy\ optimize\optimi ze.py", line
176, in fmin
N = len(x0)
TypeError: len() of unsized object

fmin() minimizes functions which take arrays. They should have a signature like
this:

def func(x):
return stuff

If you need to pass in other arguments, like data, they need to come *after* the
array fmin() is trying to find the optimal value for.

def func(x, Y):
return stuff

xopt = optimize.fmin(f unc, x0=array([0.0, 1.0]), args=(my_data,) )

However, since you are not doing multivariable optimization, you will want to
use one of the univariable optimizers

Scalar function minimizers

fminbound -- Bounded minimization of a scalar function.
brent -- 1-D function minimization using Brent method.
golden -- 1-D function minimization using Golden Section method
bracket -- Bracket a minimum (given two starting points)

For example:

from numpy import array, arange, clip, inf
from scipy import optimize

def func(x, Y):
residuals = Y - x*arange(-3, 4)
error = -clip(residuals, -inf, 0).min()
return error

optionPnL = array([0.0, 0, 0, 0, 1, 2, 3])
x = optimize.brent( func, args=(optionPnL ,))

Of course, there are an infinite number of solutions for this data since there
is a cusp and a weird residual function. Any x in [0, 1] will yield 0 error
since it is always on or below the data.

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco

SciPy Optimization syntax

SciPy Optimization syntax

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