Inzynierka/Lib/site-packages/scipy/optimize/cython_optimize/__init__.py
2023-06-02 12:51:02 +02:00

133 lines
4.7 KiB
Python

"""
Cython optimize zeros API
=========================
The underlying C functions for the following root finders can be accessed
directly using Cython:
- `~scipy.optimize.bisect`
- `~scipy.optimize.ridder`
- `~scipy.optimize.brenth`
- `~scipy.optimize.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 `~scipy.optimize.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 `~scipy.optimize.cython_optimize` requires Cython to write callbacks
that are compiled into C. For more information on compiling Cython, see the
`Cython Documentation <http://docs.cython.org/en/latest/index.html>`_.
These are the basic steps:
1. Create a Cython ``.pyx`` file, for example: ``myexample.pyx``.
2. Import the desired root finder from `~scipy.optimize.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 `~scipy.optimize.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 `~scipy.optimize.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 zeros_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}
"""