add a constraint function generator with support for symbolic math

[mmckerns]

add support for symbolic math (i.e. sympy)

add a constraint function generator. should have the ability to turn symbolic math into a constraints function

[mmckerns]

from Chris Farrow:

The best way I found to make callables is with the lambdify function. It seems that this is the only way to process equations that require numpy arrays as input. Sympy is quite fast, it beat diffpy.srfit.equation in several of my tests.

There is one major problem that I have with sympy, and that is you can't compose symbolic and numeric routines. For example, the Debye equation requires some numerical integration. This could be implemented by sympy.Integral, but it seems more natural (and common) to write a numeric routine. Furthermore, legacy code will be numeric, not symbolic. So, once I have a numeric routine, how do I use sympy to compose this with another routine? As far as I can tell this cannot be done easily. Perhaps some string magic and lambda functions would do the trick, but then we're not really using sympy.

Some follow-up: It looks like  openopt.FuncDesigner might be able to satisfy my use case.

[mmckerns]

expanded slightly to cover ticket #122

[mmckerns]

in building a constraints function, one should be able to also import required functions to evaluate the constraints...

implementation options/decisions:

• allow import statement in symbolic constraints string ?
• allow passing of relevant imported objects ?
• allow function generator to pull any imported function from globals() and locals() ?

[mmckerns]

also look at diffpy.srfit's "equation" and "fitbase" at  http://danse.us/trac/diffraction/browser/diffraction/diffpy.srfit/trunk/diffpy/srfit

[mmckerns]

improved and added basic "symbolic to constrains" capabilities in the "decorate" branch in r611. Does not require sympy; however, with a little more work, sympy can be used to speed up the existing generated constraints solvers.

[mmckerns]

sympy seems pretty limited when it comes to solving with a 'math' function like "x1 = cos(x2)"... and also when there's an inequality, although solving for inequalities in sympy seems to be improving as of late. Punting on sympy for a while seems to be a good plan.

Sympy also seems to not care about backward compatibility too much... so the functions that use sympy should be checked against a few versions of sympy.

Then maybe check out srfit's "equation" and "fitbase"... (see above entry)

[mmckerns]

as of r620, the symbolic solver works pretty well for equalities, but not inequalities, using sympy.

splitting off a simplified symbolic inequality solver to ticket #198, closing the current ticket