CODEWITHSUNDEEP
pythonnumpyscipycorrelation
jhegedus
jhegedus

Reputation: 20653

numpy.correlate vs numpy documentation - is there a contradiction here ? Why is the resulting list reversed ?

I get the following result using numpy's correlate function:

In [153]: np.correlate([1],np.arange(100))
Out[153]:
array([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83,
       82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66,
       65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49,
       48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32,
       31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15,
       14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1,  0])

In [154]:

This result seems to be in contradiction with the 90. page of the numpy book :

enter image description here

Based on the formula above I would have expected an increasing array 0..99, however, the result is a decreasing array 99..0.

Can someone explain what is going on here ?

Why does the implementation contradicts the specification ?

Why does it make sense to reverse the list ?

Upvotes: 2

Views: 281

Answers (1)

tmdavison
tmdavison

Reputation: 69193

Looks like you are expecting the old_behaviour of numpy.correlate. The book you link to is very old (2006), so it looks like numpy.correlate has changed since it was written (it actually changed in numpy v1.4). From the docs for numpy v1.9:

old_behavior : bool

If True, uses the old behavior from Numeric, (correlate(a,v) == correlate(v,a), and the conjugate is not taken for complex arrays). If False, uses the conventional signal processing definition.

In [2]: np.correlate([1],np.arange(100))
Out[2]: 
array([99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83,
   82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66,
   65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49,
   48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32,
   31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15,
   14, 13, 12, 11, 10,  9,  8,  7,  6,  5,  4,  3,  2,  1,  0])

In [3]: np.correlate([1],np.arange(100),old_behavior=True)
Out[3]: 
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
   17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
   34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
   51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
   68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
   85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])

In [4]: np.correlate(np.arange(100),[1])
Out[4]: 
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
   17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33,
   34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50,
   51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67,
   68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84,
   85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99])

EDIT

On further inspection, I think the difference is due to this line in the old definition:

K=len(x)-1 and M=len(y)-1, and we assume K ≥ M (without loss of generality because we can interchange the roles of x and y without effect).

So, I believe for your case, in the old definition, it is making y=[1] and x=np.arange(100), because len(x) must be greater than len(y). The new definition does not do that, instead "input arrays are never swapped", so x=[1] and y=np.arange(100). Thus, the differences.

Upvotes: 6

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