Cython Optimize Zeros API

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

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*)


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,
        '''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,

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