Mastering Python for Finance - Second Edition

General nonlinear solvers

The scipy.optimize module also contains multidimensional general solvers that we can use to our advantage. The root and fsolve functions are some examples with the following function properties:

• root(fun, x0[, args, method, jac, tol, ...]): This finds a root of a vector function.
• fsolve(func, x0[, args, fprime, ...]): This finds the roots of a function.

The outputs are returned as dictionary objects. Using our example as input to these functions, we will get the following output:

In [ ]:    import scipy.optimize as optimize    y = lambda x: x**3 + 2.*x**2 - 5.    dy = lambda x: 3.*x**2 + 4.*x    print(optimize.fsolve(y, 5., fprime=dy))Out[ ]:        [1.24189656]In [ ]:    print(optimize.root(y, 5.))Out[ ]: fjac: array([[-1.]]) fun: ...