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from scipy import * | from scipy import optimize, special |

SciPy's optimization package is scipy.optimize. The most basic non-linear optimization functions are:

- optimize.fmin(func, x0), which finds the minimum of f(x) starting x with x0 (x can be a vector)
- optimize.fsolve(func, x0), which finds a solution to func(x) = 0 starting with x = x0 (x can be a vector)
- optimize.fminbound(func, x1, x2), which finds the minimum of a scalar function func(x) for the range [x1,x2] (x1,x2 must be a scalar and func(x) must return a scalar)

See the scipy.optimze documentation for details.

This is a quick demonstration of generating data from several Bessel functions and finding some local maxima using fminbound. This uses ipython with the -pylab switch.

```
1 from scipy import optimize, special
2 from numpy import *
3 from pylab import *
4
5 x = arange(0,10,0.01)
6
7 for k in arange(0.5,5.5):
8 y = special.jv(k,x)
9 plot(x,y)
10 f = lambda x: -special.jv(k,x)
11 x_max = optimize.fminbound(f,0,6)
12 plot([x_max], [special.jv(k,x_max)],'ro')
13
14 title('Different Bessel functions and their local maxima')
15 show()
```

Optimization Example