SciPy is a collection of mathematical algorithms and convenience functions built on the Numpy extension of Python. It adds significant power to the interactive Python session by providing the user with high-level commands and classes for manipulating and visualizing data. With SciPy an interactive Python session becomes a data-processing and system-prototyping environment rivaling systems such as MATLAB, IDL, Octave, R-Lab, and SciLab.
The additional benefit of basing SciPy on Python is that this also makes a powerful programming language available for use in developing sophisticated programs and specialized applications. Scientific applications using SciPy benefit from the development of additional modules in numerous niches of the software landscape by developers across the world. Everything from parallel programming to web and data-base subroutines and classes have been made available to the Python programmer. All of this power is available in addition to the mathematical libraries in SciPy.
Note the underscore before 'minimize' when importing from scipy.optimize; '_minimize' Also, i tested the functions from this link before doing this section, and found I had less trouble/it worked faster, if I imported 'special' separately. The Rosenbrock function on the linked page was incorrect - you have to configure the colorbar first; I've posted alternate code but think it could be better.
Further examples to come.
See here for an explanation of Hessian Matrix