Using Cython

We show how to use Cython to accelerate the computation of a cost function and how to avoid some pitfalls.

If you do not care specifically about Cython and just want to make your code faster, prefer Numba (see the corresponding Numba tutorial for more details), or try to run iminuit in the PyPy interpreter. Numba is more powerful and easier to use, and you don’t have to learn the awkward Cython dialect. Cython is a good choice when you have to call into C code from Python, but it is not a good choice to call into C++ code, for this pybind11 is the ideal choice. Cython does not fully support the C++ language, it was designed for C.

With that disclaimer out of the way, let’s see how to use iminuit with a Cython-compiled function.

[1]:
# setup of the notebook
%load_ext Cython
from iminuit import Minuit, describe
import numpy as np
import traceback
---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
Input In [1], in <cell line: 2>()
      1 # setup of the notebook
----> 2 get_ipython().run_line_magic('load_ext', 'Cython')
      3 from iminuit import Minuit, describe
      4 import numpy as np

File /usr/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
   2303     kwargs['local_ns'] = self.get_local_scope(stack_depth)
   2304 with self.builtin_trap:
-> 2305     result = fn(*args, **kwargs)
   2306 return result

File /usr/lib/python3.10/site-packages/IPython/core/magics/extension.py:33, in ExtensionMagics.load_ext(self, module_str)
     31 if not module_str:
     32     raise UsageError('Missing module name.')
---> 33 res = self.shell.extension_manager.load_extension(module_str)
     35 if res == 'already loaded':
     36     print("The %s extension is already loaded. To reload it, use:" % module_str)

File /usr/lib/python3.10/site-packages/IPython/core/extensions.py:76, in ExtensionManager.load_extension(self, module_str)
     69 """Load an IPython extension by its module name.
     70
     71 Returns the string "already loaded" if the extension is already loaded,
     72 "no load function" if the module doesn't have a load_ipython_extension
     73 function, or None if it succeeded.
     74 """
     75 try:
---> 76     return self._load_extension(module_str)
     77 except ModuleNotFoundError:
     78     if module_str in BUILTINS_EXTS:

File /usr/lib/python3.10/site-packages/IPython/core/extensions.py:92, in ExtensionManager._load_extension(self, module_str)
     90 if module_str not in sys.modules:
     91     with prepended_to_syspath(self.ipython_extension_dir):
---> 92         mod = import_module(module_str)
     93         if mod.__file__.startswith(self.ipython_extension_dir):
     94             print(("Loading extensions from {dir} is deprecated. "
     95                    "We recommend managing extensions like any "
     96                    "other Python packages, in site-packages.").format(
     97                   dir=compress_user(self.ipython_extension_dir)))

File /usr/lib/python3.10/importlib/__init__.py:126, in import_module(name, package)
    124             break
    125         level += 1
--> 126 return _bootstrap._gcd_import(name[level:], package, level)

File <frozen importlib._bootstrap>:1050, in _gcd_import(name, package, level)

File <frozen importlib._bootstrap>:1027, in _find_and_load(name, import_)

File <frozen importlib._bootstrap>:1004, in _find_and_load_unlocked(name, import_)

ModuleNotFoundError: No module named 'Cython'

The following cell is Cython code and will be compiled to machine code behind the scenes.

[2]:
%%cython

def cython_func(double x, double y, double z):
    return (x - 1.) ** 2 + (y - 2.) ** 2 + (z - 3.) ** 2 + 1.
UsageError: Cell magic `%%cython` not found.

Unfortunately, if we try to pass starting values to Minuit via keywords, we get a failure.

[3]:
try:
    m = Minuit(cython_func, x=1, y=2, z=3)
except:
    traceback.print_exc()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
      1 try:
----> 2     m = Minuit(cython_func, x=1, y=2, z=3)
      3 except:

NameError: name 'Minuit' is not defined

During handling of the above exception, another exception occurred:

NameError                                 Traceback (most recent call last)
Input In [3], in <cell line: 1>()
      2     m = Minuit(cython_func, x=1, y=2, z=3)
      3 except:
----> 4     traceback.print_exc()

NameError: name 'traceback' is not defined

What happened? Minuit uses the describe tool which uses introspection to read the function signature, but this failed here. Without that, Minuit does not know how many parameters this function accepts and their names.

Python built-in functions (like min) normally do not have a function signature. Functions from cython and swig also do not have one.

There are a few ways to fix this.

  • One can pass parameter names explicitly to Minuit, then it works.

  • One can use positional arguments.

  • One can tell Cython to embed a signature.

[4]:
m = Minuit(cython_func, name=("x", "y", "z"), x=0, y=0, z=0)
m.errordef = Minuit.LEAST_SQUARES
m.migrad()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 m = Minuit(cython_func, name=("x", "y", "z"), x=0, y=0, z=0)
      2 m.errordef = Minuit.LEAST_SQUARES
      3 m.migrad()

NameError: name 'Minuit' is not defined

Alternatively, one can use positional arguments without specifying parameter names.

[5]:
m = Minuit(cython_func, 0, 0, 0)
m.errordef = Minuit.LEAST_SQUARES
m.migrad()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [5], in <cell line: 1>()
----> 1 m = Minuit(cython_func, 0, 0, 0)
      2 m.errordef = Minuit.LEAST_SQUARES
      3 m.migrad()

NameError: name 'Minuit' is not defined

A nicer solution is to ask Cython to add the missing function signature. This can be achieved with the embedsignature(true) decorator.

[6]:
%%cython
cimport cython

@cython.embedsignature(True)  # generate a signature that iminuit can extract
def cython_f(double x, double y, double z):
    return (x - 1.) ** 2 + (y - 2.) ** 2 + (z - 3.) ** 2 + 1.
UsageError: Cell magic `%%cython` not found.

Now it works.

[7]:
m = Minuit(cython_f, x=0, y=0, z=0)
m.errordef = Minuit.LEAST_SQUARES
m.migrad()
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Input In [7], in <cell line: 1>()
----> 1 m = Minuit(cython_f, x=0, y=0, z=0)
      2 m.errordef = Minuit.LEAST_SQUARES
      3 m.migrad()

NameError: name 'Minuit' is not defined