[SciPy-User] beginner's question regarding optimize.fmin_l_bfgs_b

Skipper Seabold jsseabold@gmail....
Thu Oct 14 16:21:22 CDT 2010


On Tue, Oct 12, 2010 at 9:10 AM, Tveraa, Torkild <Torkild.Tveraa@nina.no> wrote:
> Dear All,
>
> I have been able to use the optimize.leastsq - module to minimize a given function (see below), but since my data is sparse I have convergence problems and would ideally be able to put bounds on the parameters. If I have understood this correctly this can be done with the optimize.fmin_l_bfgs_b - module, but I am unable to figure out how to do this. Some helps & hints would be most appreciated :-)
>
>        Cheers,
>        Torkild
>
> -------------------------------------------------------
> import numpy
> import pylab
> from scipy import *
> from scipy import optimize
>
> ## This is y-data:
> y_data = (([0.2867, 0.1171, -0.0087, 0.1326, 0.2415, 0.2878, 0.3133, 0.3701, 0.3996, 0.3728, 0.3551, 0.3587, 0.1408, 0.0416, 0.0708, 0.1142, 0, 0, 0]))
>
> ## This is x-data:
> t = (([67, 88, 104, 127, 138, 160, 169, 188, 196, 215, 240, 247, 271, 278, 303, 305, 321, 337, 353]))
>
> ## This is the equation:
> fitfunc = lambda p, x:    p[0] + (p[1] -p[0]) * ((1/(1+exp(-p[2]*(t-p[3])))) + (1/(1+exp(p[4]*(t-p[5])))) -1)
>
> ##
> errfunc = lambda p, x, y: fitfunc(p,x) -y
>
> guess = [0, max(y_data), 0.1, 140, -0.1, 270]
>
> bounds = [(-0.2, 0.1),(0.1,0.97), (0.05,0.8), (120,190), (-0.8, -0.05), (200,300) ]
>
> ## This seems to work ok:
> p2,success = optimize.leastsq(errfunc, guess, args=(t, y_data),full_output=0)
> print 'Estimates from leastsq \n', p2,success
>
>
> ## But this does not:
> best, val, d = optimize.fmin_l_bfgs_b(errfunc, guess, bounds=bounds, args=(t, y_data), iprint=2)

The minimization routines, I believe, in fmin expect a function that
maps from to a scalar.  So you need to tell fmin_l_bfgs that you want
to minimize the sum of squared errors, optimze.leastsq assumes this.
So just define one more function that sums the squared errors and
minimize it

errfuncsumsq = lambda p, x, y: np.sum(errfunc(p,x,y)**2)

Now, run it without bounds to make sure we get the same thing

boundsnone = [(None,None)]*6

Notice that you also have to tell fmin_l_bfgs_b to approximate the
gradient or else it assumes that your objective function also returns
its gradient

best, val, d = optimize.fmin_l_bfgs_b(errfuncsum, guess,
approx_grad=True, bounds=boundsnone, args=(t, y_data), iprint=2)

p2
array([  6.79548883e-02,   3.68922503e-01,   7.55565728e-02,
         1.41378227e+02,   2.91307814e+00,   2.70608242e+02])

best
array([  6.79585333e-02,  -2.33026316e-01,  -7.55409880e-02,
         1.41388265e+02,  -1.36069434e+00,   2.70160779e+02])

Cheers,

Skipper


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