[SciPy-user] newbie python & optimization

[Daniel Davidson]

Im taking a course in fixed income asset pricing and professor *strongly* suggests matlab with optimization, financial toolbox, statistics toolbox and spline toolbox (~$360 ouch). Have following questions:

* What is probability that Python with scipy will do the trick?

* Have been reading python and playing. The NumPy pdf docs I read specify a certain behavior for ufuncs, which I see until I import optimize. What causes this and can I use optimize without this happening?:

>>> from Numeric import *
>>> a = array(([1,2,3]))
>>> a*a
array([1, 4, 9])
>>> import scipy.optimize
>>> a*a
array([0, 0, 0])

I can get around this by putting Numeric in everywhere Numeric.multiply(a,a), but I would prefer not.

* I successfully use fmin to minimize a particular form function
(Nelson Siegel) to curve fit a yield to some data points. I try 3 cases and the first two smaller cases succeed (approach 0) and the last does not really. Yet my partner was able to do the 3rd one in excel solver. When I take his spreadsheat and change the 'guess' (there are four parameters) and try to solve again it also fails - so maybe this is not the algorithm to use (maybe local minima)?

* When using optimizations routines you pass it a function to evaluate. The algorithm picks numbers to put in. What is a good strategy for handling errors due to the choice (e.g. OverflowError,....)?

Any ideas or suggestions welcome.

Cordially,
Dan

PS Here is the funcion and I welcome any criticisms.

def ZHat(args, P, C):
    """
    args: optimization parameterized arguments (e.g. theta's and lambda)
    P: Price Matrix
    C: Cashflow Matrix
    """
    j=arange(1,size(P)+1)
    partialPeriod = Numeric.divide(j,args[3])
    expPartialPeriod = Numeric.exp(Numeric.multiply(-1.0, partialPeriod))
    r = args[0] + Numeric.multiply((args[1]+args[2]),(Numeric.divide((1.0-expPartialPeriod),partialPeriod))) \
        - Numeric.multiply(args[2],expPartialPeriod)
    return 100.0*(Numeric.power(Numeric.divide(1.0,Numeric.add(1.0,r)),j))

def PHat(args,P,C):
    zhat = ZHat(args,P,C)
    return matrixmultiply(C,zhat)

globalPrevObj = 1e+100
def funcFormHelper(args, P, C):
    """
    The functional form to be curve fitted.

    args: optimization parameterized arguments (e.g. theta's and lambda)
    P: Price Matrix
    C: Cashflow Matrix
    """
    try:
        p_hat = PHat(args,P,C)
        difference = P-p_hat
        difference_sq = Numeric.power(difference,2)
        obj = add.reduce(difference_sq)
    except Exception:
        print "Unexpected Error:", sys.exc_info()[0]
        obj = YieldExtractor.globalPrevObj + 1

    YieldExtractor.globalPrevObj = obj
    return obj

def createFuncForm(P, C):
    """
    Helper function used just to pass P, C cleanly to functional form
    """
    return lambda args: funcFormHelper(args, P, C)

Invoked like:

            self.optimVars = fmin(createFuncForm(self.P,self.C), \
                                  [0.1,1.0,0,1.1], \
                                  maxfun=100000, maxiter=100000, \
                                  xtol=1e-10, ftol=1e-10, disp=1)




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