Cython Optimize Zeros API

The underlying C functions for the following root finders can be accessed directly using Cython:

• bisect

• ridder

• brenth

• brentq

The Cython API for the zeros functions is similar except there is no disp argument. Import the zeros functions using cimport from scipy.optimize.cython_optimize.

from scipy.optimize.cython_optimize cimport bisect, ridder, brentq, brenth

Callback Signature

The zeros functions in cython_optimize expect a callback that takes a double for the scalar independent variable as the 1st argument and a user defined struct with any extra parameters as the 2nd argument.

double (*callback_type)(double, void*)

Examples

Usage of cython_optimize requires Cython to write callbacks that are compiled into C. For more information on compiling Cython see the Cython Documentation.

These are the basic steps:

1. Create a Cython .pyx file, for example: myexample.pyx.

2. Import the desired root finder from cython_optimize.

3. Write the callback function, and call the selected zeros function passing the callback, any extra arguments, and the other solver parameters.

   from scipy.optimize.cython_optimize cimport brentq
   
   # import math from Cython
   from libc cimport math
   
   myargs = {'C0': 1.0, 'C1': 0.7}  # a dictionary of extra arguments
   XLO, XHI = 0.5, 1.0  # lower and upper search boundaries
   XTOL, RTOL, MITR = 1e-3, 1e-3, 10  # other solver parameters
   
   # user defined struct for extra parameters
   ctypedef struct test_params:
       double C0
       double C1
   
   
   # user defined callback
   cdef double f(double x, void *args):
       cdef test_params *myargs = <test_params *> args
       return myargs.C0 - math.exp(-(x - myargs.C1))
   
   
   # Cython wrapper function
   cdef double brentq_wrapper_example(dict args, double xa, double xb,
                                      double xtol, double rtol, int mitr):
       # Cython automatically casts dictionary to struct
       cdef test_params myargs = args  
       return brentq(
           f, xa, xb, <test_params *> &myargs, xtol, rtol, mitr, NULL)
   
   
   # Python function
   def brentq_example(args=myargs, xa=XLO, xb=XHI, xtol=XTOL, rtol=RTOL,
                      mitr=MITR):
       '''Calls Cython wrapper from Python.'''
       return brentq_wrapper_example(args, xa, xb, xtol, rtol, mitr)
   

4. If you want to call your function from Python, create a Cython wrapper, and a Python function that calls the wrapper, or use cpdef. Then in Python you can import and run the example.

   from myexample import brentq_example
   
   x = brentq_example()
   # 0.6999942848231314
   

5. Create a Cython .pxd file if you need to export any Cython functions.

Full Output

The functions in cython_optimize can also copy the full output from the solver to a C struct that is passed as its last argument. If you don’t want the full output just pass NULL. The full output struct must be type zeros_full_output, which is defined in scipy.optimize.cython_optimize with the following fields:

• int funcalls: number of function calls

• int iterations: number of iterations

• int error_num: error number

• double root: root of function

The root is copied by cython_optimize to the full output struct. An error number of -1 means a sign error, -2 means a convergence error, and 0 means the solver converged. Continuing from the previous example:

from scipy.optimize.cython_optimize cimport zeros_full_output


# cython brentq solver with full output
cdef brent_full_output brentq_full_output_wrapper_example(
        dict args, double xa, double xb, double xtol, double rtol,
        int mitr):
    cdef test_params myargs = args
    cdef zeros_full_output my_full_output
    # use my_full_output instead of NULL
    brentq(f, xa, xb, &myargs, xtol, rtol, mitr, &my_full_output)
    return my_full_output


# Python function
def brent_full_output_example(args=myargs, xa=XLO, xb=XHI, xtol=XTOL,
                              rtol=RTOL, mitr=MITR):
    '''Returns full output'''
    return brentq_full_output_wrapper_example(args, xa, xb, xtol, rtol,
                                              mitr)

result = brent_full_output_example()
# {'error_num': 0,
#  'funcalls': 6,
#  'iterations': 5,
#  'root': 0.6999942848231314}