Permutation of values on numpy array/matrix

Question

I'm looking for a code that speed up a creation of permutation matrix. i.e., I want to create a matrix of n columns, where each column value iterates over m values, creating a n^m combinations on each row. On the example below, there are 2 methods to create the matrix, in this case n=7 and m=5 that creates a matrix similar to:

1 1 1 1 1 1 1
1 1 1 1 1 1 2
1 1 1 1 1 1 3
1 1 1 1 1 1 4
1 1 1 1 1 1 5
1 1 1 1 1 2 1
...
5 5 5 5 5 5 5

The order of the rows doesn't matter, only that all combinations are created. I have written the following 2 methods to create the arrays, but the metod1 is very slow (although very verbose and clear to understand) and method2 is faster using numpy functions. But I still need to find a faster methodology to create the matrix.

import numpy as np

############################################
def permArray_meth1():

    allArray = np.zeros((1,7))

    for a1  in range(1,6):
        for a2  in range(1,6):
            for a3  in range(1,6):
                for a4  in range(1,6):
                    for a5  in range(1,6):
                        for a6  in range(1,6):
                            for a7  in range(1,6):

                                allArray = np.append(allArray, np.array([a1,a2,a3,a4,a5,a6,a7]).reshape(1,7), axis=0)

    allArray = np.delete(allArray, 0, 0)
    return allArray

############################################
def permArray_meth2():

    ##### Create permutation matrix #####
    a = np.arange(np.power(5,7)).reshape(5,5,5,5,5,5,5)
    allArray = [(a1,a2,a3,a4,a5,a6,a7) for a1,a2,a3,a4,a5,a6,a7 in np.ndindex(a.shape)]

    ##### Convert list to array #####
    allArray = np.asarray(allArray)+1
    return allArray


############################################
if __name__ == "__main__":

    allArray = permArray_meth1()    #  (50sec)
    print 'allArray1', np.shape(allArray)

    allArray = permArray_meth2()    #  (1sec)
    print 'allArray2', np.shape(allArray)

I know that the speed is dependent also on the used CPU hardware, but I'm looking for a relatively faster code thatn the shown above.

Is there any other method/code?

May I ask what you want to do with the matrix? Are you applying functions on the whole matrix or just line by line? — plonser
– plonser, Commented Jan 19, 2015 at 12:25

ali_m · Accepted Answer · 2015-07-28 16:43:04Z

2

You could do this by creating an (n, m, m, ..., m) array of indices for column 1, column 2, ..., column n using np.indices(), then reshaping the output into an (n ** m, n) array:

import numpy as np

def permgrid(m, n):
    inds = np.indices((m,) * n)
    return inds.reshape(n, -1).T

For example:

print(permgrid(2, 3))

# [[0 0 0]
#  [0 0 1]
#  [0 1 0]
#  [0 1 1]
#  [1 0 0]
#  [1 0 1]
#  [1 1 0]
#  [1 1 1]]

edited Jul 28, 2015 at 16:43

answered Jan 19, 2015 at 13:45

ali_m

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