cythonized example of scipy.optimized.newton to solve solar-cell for 100,000 different cases

newton_example.pyx

from __future__ import division, print_function, absolute_import
from math import exp, sin

from scipy.optimize.cython_optimize cimport zeros

NUM_OF_IRRAD = 10
IL = [sin(il) + 6.0 for il in range(NUM_OF_IRRAD)]


# governing equations
cdef double f_solarcell(double i, tuple args):
    v, il, io, rs, rsh, vt = args
    vd = v + i * rs
    return il - io * (exp(vd / vt) - 1.0) - vd / rsh - i


cdef double fprime(double i, tuple args):
    v, il, io, rs, rsh, vt = args
    return -io * exp((v + i * rs) / vt) * rs / vt - rs / rsh - 1


#solver
cdef double solarcell_newton(tuple args):
    """test newton with array"""
    return zeros.newton(f_solarcell, 6.0, fprime, args)


# cython
def bench_cython_newton(v=5.25, il=IL, args=(1e-09, 0.004, 10, 0.27456)):
    return map(solarcell_newton,
               ((v, il_,) + args for il_ in il))

zeros.pxd

ctypedef double (*callback_type)(double, tuple);

cdef double newton(callback_type func, double x0, callback_type fprime, tuple args)

zeros.pyx

from __future__ import division, print_function, absolute_import

import warnings

TOL = 1.48e-8
MAXITER = 50


cdef double newton(callback_type func, double p0, callback_type fprime, tuple args):
    # Newton-Rapheson method
    for iter in range(MAXITER):
        fder = fprime(p0, args)
        if fder == 0:
            msg = "derivative was zero."
            warnings.warn(msg, RuntimeWarning)
            return p0
        fval = func(p0, args)
        # Newton step
        p = p0 - fval / fder
        if abs(p - p0) < TOL:  # np_abs(p - p0).max() < tol:
            return p
        p0 = p
    msg = "Failed to converge after %d iterations, value is %s" % (MAXITER, p)
    raise RuntimeError(msg)

Cool!