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# nested for loop

 P: n/a Hi, I want to iterate over all 2x2 matrices with elements in range 0..25 (crypto-stuff). To produce them, first I wrote a fourfold nested for loop: M=26 for a in range(M): for b in range (M): for c in range (M): for d in range (M): matr = [[a,b],[c,d]] (dosomething) Then I had a look in comp.lang.python and found: for (a,b,c,d) in [(x,y,z,t) for x in range(M) for y in range(M) for z in range(M) for t in range(M)] : matr = [[a,b],[c,d]] Is there a shorter (and probably, with respect to exec time, faster) way to write such a 4for loop? (I want to scan 3x3, 4x4 matrices too (;-) -- Wolfgang Jul 18 '05 #1
8 Replies

 P: n/a wj****@web.de (Wolfgang Buechel) writes: for (a,b,c,d) in [(x,y,z,t) for x in range(M) for y in range(M) for z in range(M) for t in range(M)] : matr = [[a,b],[c,d]] Try assigning range(M) to a variable instead of creating four copies of it. For larger ranges, experiment using xrange instead. Jul 18 '05 #2

 P: n/a Wolfgang Buechel wrote: I want to iterate over all 2x2 matrices with elements in range 0..25 (crypto-stuff). To produce them, first I wrote a fourfold nested for loop: M=26 for a in range(M): for b in range (M): for c in range (M): for d in range (M): matr = [[a,b],[c,d]] (dosomething) Then I had a look in comp.lang.python and found: for (a,b,c,d) in [(x,y,z,t) for x in range(M) for y in range(M) for z in range(M) for t in range(M)] : matr = [[a,b],[c,d]] Is there a shorter (and probably, with respect to exec time, faster) way to write such a 4for loop? Hmm... why would you want something shorter, as it would probably be less readable? Also, how fast do you need it to run, or how many times faster than the above would you like it to run? (The second one is a facetious question... the first is more serious. In effect: what's wrong with what you have?) -Peter Jul 18 '05 #3

 P: n/a "Wolfgang Buechel" wrote in message news:46**************************@posting.google.c om... Hi, I want to iterate over all 2x2 matrices with elements in range 0..25 (crypto-stuff). To produce them, first I wrote a fourfold nested for loop: M=26 for a in range(M): for b in range (M): for c in range (M): for d in range (M): matr = [[a,b],[c,d]] (dosomething) This is completely clear and space efficient. Then I had a look in comp.lang.python and found: Oh dear... for (a,b,c,d) in [(x,y,z,t) for x in range(M) for y in range(M) for z in range(M) for t in range(M)] : matr = [[a,b],[c,d]] This is less clear. It took me about 10 seconds (versus 1) to see as equivalent. It produces a list with M**4 elements that you don't actually need and soon throw away. Is there a shorter (and probably, with respect to exec time, faster) way to write such a 4for loop? Write a C extension, maybe with Pyrex. However, an hour of your time is worth lots of hours of PC time. But for a million runs, it might be worth it. Terry J. Reedy Jul 18 '05 #4

 P: n/a "Wolfgang Buechel" wrote in message news:46**************************@posting.google.c om... Hi, I want to iterate over all 2x2 matrices with elements in range 0..25 (crypto-stuff). [snip] Is there a shorter (and probably, with respect to exec time, faster) way to write such a 4for loop? (I want to scan 3x3, 4x4 matrices too (;-) -- Wolfgang Hi. The following code isn't necessarily shorter or faster (or more readable), but it's a bit more general: # slightly modified code from http://twistedmatrix.com/wiki/python/PostYourCode def sequences(n, things): "generates sequences of n items from a set of things" if n == 0: yield [] else: for x in things: for y in sequences(n-1, things): yield [x] + y def nXn_matrices(n, elements): "generates nXn matrices from elements" for s in sequences(n*n, elements): yield [s[i*n:(i+1)*n] for i in xrange(n)] # we'll try it over a small range ... M = 3 for m in nXn_matrices(2, range(M)): print m Output: [[0, 0], [0, 0]] [[0, 0], [0, 1]] [[0, 0], [0, 2]] [[0, 0], [1, 0]] [[0, 0], [1, 1]] [[0, 0], [1, 2]] [[0, 0], [2, 0]] .... .... [[2, 2], [2, 0]] [[2, 2], [2, 1]] [[2, 2], [2, 2]] # now 3X3 ... this takes a _l_o_n_g_ time ... M = 3 for m in nXn_matrices(3,range(M)): print m Output: [[0, 0, 0], [0, 0, 0], [0, 0, 0]] [[0, 0, 0], [0, 0, 0], [0, 0, 1]] [[0, 0, 0], [0, 0, 0], [0, 0, 2]] [[0, 0, 0], [0, 0, 0], [0, 1, 0]] [[0, 0, 0], [0, 0, 0], [0, 1, 1]] [[0, 0, 0], [0, 0, 0], [0, 1, 2]] .... .... [[2, 2, 2], [2, 2, 2], [2, 1, 0]] [[2, 2, 2], [2, 2, 2], [2, 1, 1]] [[2, 2, 2], [2, 2, 2], [2, 1, 2]] [[2, 2, 2], [2, 2, 2], [2, 2, 0]] [[2, 2, 2], [2, 2, 2], [2, 2, 1]] [[2, 2, 2], [2, 2, 2], [2, 2, 2]] I'm believe there are several opportunities for optimization both in the code and in the algorithm (for instance, it may be possible to take advantage of repetition in the sub-matrices), but I won't be trying that now. Good luck with what you're doing, Sean Jul 18 '05 #5

 P: n/a "Sean Ross" wrote in message news:VD********************@news20.bellglobal.com. .. [snip] # slightly modified code from http://twistedmatrix.com/wiki/python/PostYourCode def sequences(n, things): "generates sequences of n items from a set of things" if n == 0: yield [] else: for x in things: for y in sequences(n-1, things): yield [x] + y def nXn_matrices(n, elements): "generates nXn matrices from elements" for s in sequences(n*n, elements): yield [s[i*n:(i+1)*n] for i in xrange(n)] [snip] [i] believe there are several opportunities for optimization both in the code and in the algorithm (for instance, it may be possible to take advantage of repetition in the sub-matrices), but I won't be trying that now. Looks like I'll be trying it now after all: def nXn_matrices2(n, elements): for m in sequences(n, list(sequences(n, elements))): yield m This is slightly faster than the first version, but it has more overhead since it builds a list of the submatrices. That could be problem. It can probably be avoided, but I haven't figured out how to do it just yet. We'll see what happens. Sean Jul 18 '05 #6

 P: n/a wj****@web.de (Wolfgang Buechel) wrote: I want to iterate over all 2x2 matrices with elements in range 0..25(crypto-stuff).To produce them, first I wrote a fourfold nested for loop:M=26 for a in range(M): for b in range (M): for c in range (M): for d in range (M): matr = [[a,b],[c,d]] (dosomething) [snip] Is there a shorter (and probably, with respect to exec time, faster)way to write such a 4for loop?(I want to scan 3x3, 4x4 matrices too (;-) This question is very much related to the one in a thread below here (titled "Inverse of int(s, base)?"). In fact with a small adaptation that code can produce this kind of matrices: from itertools import islice def tobase(i,base,digits): R = [] for j in xrange(digits): i,k = divmod(i,base) R.append(k) R.reverse() return R def as_matrix(R,rows,cols): it = iter(R) return[list(islice(it,cols)) for i in xrange(rows)] def test(): for i in range(10): R = tobase(i,25,6) print as_matrix(R,3,2) if __name__=='__main__': test() Anton Jul 18 '05 #7

 P: n/a wj****@web.de (Wolfgang Buechel) wrote in message news:<46**************************@posting.google. com>... Hi, I want to iterate over all 2x2 matrices with elements in range 0..25 (crypto-stuff). Try generators (new in Python 2.3.3). There is an example you can/must adapt: Look at your Python installation: (PythonPath)/Lib/test/test_generators.py def conjoin() and in the whatsnew-documentation: http://www.python.org/doc/2.3.3/what...enerators.html --W. Jul 18 '05 #8

 P: n/a Dan Bishop wrote: What you can do to make your code faster (if you don't change matr once it's created) is to precompute the 676 possible matrix rows. ELEMENT_RANGE = range(26) MATRIX_ROWS = [[x, y] for x in ELEMENT_RANGE for y in ELEMENT_RANGE] for row1 in MATRIX_ROWS: for row2 in MATRIX_ROWS: matr = [row1, row2] That takes only 532 ms -- almost 3 times faster than the original. Nice. Another speed gain (from 435 to 246ms on my machine) is in for you if you use tuples instead of lists. And if you allow for somewhat less elegant code that builds on your recipe, from itertools import izip, repeat ELEMENT_RANGE = range(26) MATRIX_ROWS = [(x, y) for x in ELEMENT_RANGE for y in ELEMENT_RANGE] for row in MATRIX_ROWS: for matr in izip(repeat(row), MATRIX_ROWS): pass you can bring that down to 138ms. For the record: the straightforward solution (the original with tuples and range() factored out) r = range(26) for a in r: for b in r: for c in r: for d in r: matr = ((a,b),(c,d)) takes 478ms. The "improved" variant is evil performance-wise (1598ms): r = range(26) for (a,b,c,d) in [(x,y,z,t) for x in r for y in r for z in r for t in r] : matr = ((a,b),(c,d)) It might be interesting how much this can be improved with 2.4's generator expressions. Peter Jul 18 '05 #9

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