Using NumPy with Cython
NumPy arrays are the work horses of numerical computing with Python, and Cython allows one to work more efficiently with them.
As discussed in week 2, when working with NumPy arrays in Python one should
for-loops and indexing individual elements and instead try to write
operations with NumPy arrays in a vectorized form. The reason is two-fold:
overhead inherent to Python
for-loops and overhead from indexing a NumPy
When taking Cython into the game that is no longer true. When the Python
for structure only loops over integer values (e.g.
for in range(N)),
Cython can convert that into a pure C
for loop. Also, when additional Cython
declarations are made for NumPy arrays, indexing can be as fast as indexing
Compile time defitions for NumPy
In order to create more efficient C-code for NumPy arrays, additional
declarations are needed. To start with, one uses the Cython
statement for getting access to NumPy types:
cimport numpy as cnp
cimport statement imports C data types, C functions and variables, and
extension types. It cannot be used to import any Python objects, and it
doesn’t imply any Python import at run time.
By declaring the type and dimensions of an array before actually creating it, Cython can access the NumPy array more efficiently:
import numpy as np # Normal NumPy import cimport numpy as cnp # Import for NumPY C-API def func(): # declarations can be made only in function scope cdef cnp.ndarray[cnp.int_t, ndim=2] data data = np.empty((N, N), dtype=int) … for i in range(N): for j in range(N): data[i,j] = … # double loop is done in nearly C speed
More indexing enhancements
Python is still performing bounds checking for arrays (i.e. trying to access outside the allocated memory gives an error), and allowing negative indexing. If negative indexing is not needed, and one is certain that there are no out of bounds errors in indexing, performance can be enhanced even more by disabling negative indexing and bounds checking for all indexing operations within the function. This is done by using cython decorators before the function as follows:
import numpy as np # Normal NumPy import cimport numpy as cnp # Import for NumPY C-API cimport cython @cython.boundscheck(False) @cython.wraparound(False) def func(): # declarations can be made only in function scope cdef cnp.ndarray[cnp.int_t, ndim=2] data data = np.empty((N, N), dtype=int) … for i in range(N): for j in range(N): data[i,j] = … # double loop is done in nearly C speed
Efficient NumPy array indexing in Mandelbrot calculation
Our kernel function does not offer further easy optimization, but we can
make the indexing and loops more efficient in the higher level
compute_mandel function. To do this, we provide declarations for the
NumPy arrays, transform the
for -loops to be simple integers, and disable
also the bounds checking and negative indexing:
cimport numpy as cnp import cython ... @cython.boundscheck(False) @cython.wraparound(False) def compute_mandel(double cr, double ci, int N, double bound=1.5, double lim=1000., int cutoff=1000000): cdef cnp.ndarray[cnp.int_t, ndim=2] mandel mandel = np.empty((N, N), dtype=int) cdef cnp.ndarray[cnp.double_t, ndim=1] grid_x grid_x = np.linspace(-bound, bound, N) cdef int i,j cdef double x, y t0 = time() for i in range(N): for j in range(N): x = grid_x[i] y = grid_x[j] mandel[i,j] = kernel(x, y, cr, ci, lim, cutoff) return mandel, time() - t0
After these additions the final timing results are:
- Pure Python: 0.57 s
- Static type declarations in the kernel: 14 ms
- Kernel as C-function: 9.6 ms
- Fast indexing: 2.5 ms
Thus, at the end we were able to increase the speed of the application by a factor of 230! Naturaly, not all application benefit from Cythonization by that much, but at least an order of magnitude improvement in performance is very typical.
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