Question

Problem Hey folks. I’m looking for some advice on python performance. Some background on my problem:

Given:

1. A (x,y) mesh of nodes each with a value (0...255) starting at 0
2. A list of N input coordinates each at a specified location within the range (0...x, 0...y)
3. A value Z that defines the "neighborhood" in count of nodes

Increment the value of the node at the input coordinate and the node’s neighbors. Neighbors beyond the mesh edge are ignored. (No wrapping)

BASE CASE: A mesh of size 1024x1024 nodes, with 400 input coordinates and a range Z of 75 nodes.

Processing should be O(x*y*Z*N). I expect x, y and Z to remain roughly around the values in the base case, but the number of input coordinates N could increase up to 100,000. My goal is to minimize processing time.

Current results Between my start and the comments below, we’ve got several implementations.

Running speed on my 2.26 GHz Intel Core 2 Duo with Python 2.6.1:

  f1: 2.819s
  f2: 1.567s
  f3: 1.593s
   f: 1.579s
 f3b: 1.526s
  f4: 0.978s

f1 is the initial naive implementation: three nested for loops.
f2 is replaces the inner for loop with a list comprehension.
f3 is based on Andrei’s suggestion in the comments and replaces the outer for with map()
f is Chris’s suggestion in the answers below
f3b is kriss’s take on f3
f4 is Alex’s contribution.

Code is included below for your perusal.

Question How can I further reduce the processing time? I’d prefer sub-1.0s for the test parameters.

Please, keep the recommendations to native Python. I know I can move to a third-party package such as numpy, but I’m trying to avoid any third party packages. Also, I’ve generated random input coordinates, and simplified the definition of the node value updates to keep our discussion simple. The specifics have to change slightly and are outside the scope of my question.

thanks much!

---

**`f1` is the initial naive implementation: three nested `for` loops.**

def f1(x,y,n,z):
    rows = [[0]*x for i in xrange(y)]

    for i in range(n):
        inputX, inputY = (int(x*random.random()), int(y*random.random()))
        topleft = (inputX - z, inputY - z)
        for i in xrange(max(0, topleft[0]), min(topleft[0]+(z*2), x)):
            for j in xrange(max(0, topleft[1]), min(topleft[1]+(z*2), y)):
                if rows[i][j] <= 255: rows[i][j] += 1

f2 is replaces the inner for loop with a list comprehension.

def f2(x,y,n,z):
    rows = [[0]*x for i in xrange(y)]

    for i in range(n):
        inputX, inputY = (int(x*random.random()), int(y*random.random()))
        topleft = (inputX - z, inputY - z)
        for i in xrange(max(0, topleft[0]), min(topleft[0]+(z*2), x)):
            l = max(0, topleft[1])
            r = min(topleft[1]+(z*2), y)
            rows[i][l:r] = [j+(j<255) for j in rows[i][l:r]]

UPDATE: f3 is based on Andrei‘s suggestion in the comments and replaces the outer for with map(). My first hack at this requires several out-of-local-scope lookups, specifically recommended against by Guido: local variable lookups are much faster than global or built-in variable lookups I hardcoded all but the reference to the main data structure itself to minimize that overhead.

rows = [[0]*x for i in xrange(y)]

def f3(x,y,n,z):
    inputs = [(int(x*random.random()), int(y*random.random())) for i in range(n)]
    rows = map(g, inputs)

def g(input):
    inputX, inputY = input
    topleft = (inputX - 75, inputY - 75)
    for i in xrange(max(0, topleft[0]), min(topleft[0]+(75*2), 1024)):
        l = max(0, topleft[1])
        r = min(topleft[1]+(75*2), 1024)
        rows[i][l:r] = [j+(j<255) for j in rows[i][l:r]]

UPDATE3: ChristopeD also pointed out a couple improvements.

def f(x,y,n,z):
    rows = [[0] * y for i in xrange(x)]
    rn = random.random
    for i in xrange(n):
        topleft = (int(x*rn()) - z, int(y*rn()) - z)
        l = max(0, topleft[1])
        r = min(topleft[1]+(z*2), y)
        for u in xrange(max(0, topleft[0]), min(topleft[0]+(z*2), x)):
            rows[u][l:r] = [j+(j<255) for j in rows[u][l:r]]

UPDATE4: kriss added a few improvements to f3, replacing min/max with the new ternary operator syntax.

def f3b(x,y,n,z):
    rn = random.random    
    rows = [g1(x, y, z) for x, y in [(int(x*rn()), int(y*rn())) for i in xrange(n)]]

def g1(x, y, z):
    l = y - z if y - z > 0 else 0
    r = y + z if y + z < 1024 else 1024
    for i in xrange(x - z if x - z > 0 else 0, x + z if x + z < 1024 else 1024 ):
        rows[i][l:r] = [j+(j<255) for j in rows[i][l:r]]

UPDATE5: Alex weighed in with his substantive revision, adding a separate map() operation to cap the values at 255 and removing all non-local-scope lookups. The perf differences are non-trivial.

def f4(x,y,n,z):
    rows = [[0]*y for i in range(x)]
    rr = random.randrange
    inc = (1).__add__
    sat = (0xff).__and__
    
    for i in range(n):
        inputX, inputY = rr(x), rr(y)
        b = max(0, inputX - z)
        t = min(inputX + z, x)
        l = max(0, inputY - z)
        r = min(inputY + z, y)
        for i in range(b, t):
            rows[i][l:r] = map(inc, rows[i][l:r])
    for i in range(x):
      rows[i] = map(sat, rows[i])

Also, since we all seem to be hacking around with variations, here’s my test harness to compare speeds: (improved by ChristopheD)

def timing(f,x,y,z,n):
    fn = "%s(%d,%d,%d,%d)" % (f.__name__, x, y, z, n)
    ctx = "from __main__ import %s" % f.__name__ 
    results = timeit.Timer(fn, ctx).timeit(10)
    return "%4.4s: %.3f" % (f.__name__, results / 10.0)

if __name__ == "__main__":
    print timing(f, 1024, 1024, 400, 75)
    #add more here.

Answer 1

On my (slow-ish;-) first-day Macbook Air, 1.6GHz Core 2 Duo, system Python 2.5 on MacOSX 10.5, after saving your code in op.py I see the following timings:

$ python -mtimeit -s'import op' 'op.f1()'
10 loops, best of 3: 5.58 sec per loop
$ python -mtimeit -s'import op' 'op.f2()'
10 loops, best of 3: 3.15 sec per loop

So, my machine is slower than yours by a factor of a bit more than 1.9.

The fastest code I have for this task is:

def f3(x=x,y=y,n=n,z=z):
    rows = [[0]*y for i in range(x)]
    rr = random.randrange
    inc = (1).__add__
    sat = (0xff).__and__

    for i in range(n):
        inputX, inputY = rr(x), rr(y)
        b = max(0, inputX - z)
        t = min(inputX + z, x)
        l = max(0, inputY - z)
        r = min(inputY + z, y)
        for i in range(b, t):
            rows[i][l:r] = map(inc, rows[i][l:r])
    for i in range(x):
      rows[i] = map(sat, rows[i])

which times as:

$ python -mtimeit -s'import op' 'op.f3()'
10 loops, best of 3: 3 sec per loop

so, a very modest speedup, projecting to more than 1.5 seconds on your machine – well above the 1.0 you’re aiming for:-(.

With a simple C-coded extensions, exte.c…:

#include "Python.h"

static PyObject*
dopoint(PyObject* self, PyObject* args)
{
    int x, y, z, px, py;
    int b, t, l, r;
    int i, j;
    PyObject* rows;

    if(!PyArg_ParseTuple(args, "iiiiiO",
                         &x, &y, &z, &px, &py, &rows
        ))
        return 0;

    b = px - z;
    if (b < 0) b = 0;
    t = px + z;
    if (t > x) t = x;
    l = py - z;
    if (l < 0) l = 0;
    r = py + z;
    if (r > y) r = y;

    for(i = b; i < t; ++i) {
        PyObject* row = PyList_GetItem(rows, i);
        for(j = l; j < r; ++j) {
            PyObject* pyitem = PyList_GetItem(row, j);
            long item = PyInt_AsLong(pyitem);
            if (item < 255) {
                PyObject* newitem = PyInt_FromLong(item + 1);
                PyList_SetItem(row, j, newitem);
            }
        }
    }

    Py_RETURN_NONE;
}

static PyMethodDef exteMethods[] = {
    {"dopoint", dopoint, METH_VARARGS, "process a point"},
    {0}
};

void
initexte()
{
    Py_InitModule("exte", exteMethods);
}

(note: I haven’t checked it carefully — I think it doesn’t leak memory due to the correct interplay of reference stealing and borrowing, but it should be code inspected very carefully before being put in production;-), we could do

import exte
def f4(x=x,y=y,n=n,z=z):
    rows = [[0]*y for i in range(x)]
    rr = random.randrange

    for i in range(n):
        inputX, inputY = rr(x), rr(y)
        exte.dopoint(x, y, z, inputX, inputY, rows)

and the timing

$ python -mtimeit -s'import op' 'op.f4()'
10 loops, best of 3: 345 msec per loop

shows an acceleration of 8-9 times, which should put you in the ballpark you desire. I’ve seen a comment saying you don’t want any third-party extension, but, well, this tiny extension you could make entirely your own;-). ((Not sure what licensing conditions apply to code on Stack Overflow, but I’ll be glad to re-release this under the Apache 2 license or the like, if you need that;-)).