Weird results when multiplying large numpy array with itself

Question

I came across weird results when computing large Numpy array.

A=np.matrix('1 2 3;3 4 7;8 9 6') 
A=([[1, 2, 3],
    [3, 4, 7],
    [8, 9, 6]])

A * A completes the dot product as expected:

A*A=([[ 31,  37,  35],
    [ 71,  85,  79],
    [ 83, 106, 123]])

But with a larger matrix 200X200 I get different response:

B=np.random.random_integers(0,10,(n,n))
B=array([[ 2,  0,  6, ...,  7,  3,  7],
   [ 4,  9,  1, ...,  6,  7,  5],
   [ 3,  1,  8, ...,  7,  3,  8],
   ..., 
   [ 8,  4, 10, ...,  5,  4,  4],
   [ 6,  6,  3, ...,  7,  2,  9],
   [ 2, 10, 10, ...,  5,  7,  4]])

Now multiply B with B

B*B
array([[  4,   0,  36, ...,  49,   9,  49],
   [ 16,  81,   1, ...,  36,  49,  25],
   [  9,   1,  64, ...,  49,   9,  64],
   ..., 
   [ 64,  16, 100, ...,  25,  16,  16],
   [ 36,  36,   9, ...,  49,   4,  81],
   [  4, 100, 100, ...,  25,  49,  16]])

I get each element squared and not a matrix * matrix What did I do different?

Is A a numpy array?

Divakar
– Divakar

2015-10-05 08:46:18 +00:00
Commented Oct 5, 2015 at 8:46 — Divakar
– Divakar, Commented Oct 5, 2015 at 8:46
Yes, hopefully the above makes more sense.

icypy
– icypy

2015-10-05 08:51:02 +00:00
Commented Oct 5, 2015 at 8:51 — icypy
– icypy, Commented Oct 5, 2015 at 8:51

Alex Riley · Accepted Answer · 2015-10-05 09:58:24Z

You appear to have created A using the matrix type, while B is of the ndarray type (np.random.random_integers returns an array, not a matrix). The operator * performs matrix multiplication for the former and element-wise multiplication for the latter.

From the documentation of np.matrix:

A matrix is a specialized 2-D array that retains its 2-D nature through operations. It has certain special operators, such as * (matrix multiplication) and ** (matrix power).

As an aside, if you use two different types in the same operation, NumPy will use the operator belonging to the element with the highest priority:

>>> A = np.matrix('1 2 3;3 4 7;8 9 6') 
>>> B = np.array(A) # B is of array type, A is of matrix type
>>> A * B
matrix([[ 31,  37,  35],
        [ 71,  85,  79],
        [ 83, 106, 123]])

>>> B * A
matrix([[ 31,  37,  35],
        [ 71,  85,  79],
        [ 83, 106, 123]])

>>> A.__array_priority__
10.0
>>> B.__array_priority__
0.0

tynn · Accepted Answer · 2015-10-05 08:51:08Z

2

You get this result since B is of type numpy.ndarray not numpy.matrix

>>> type(np.random.random_integers(0,10,(n,n)))
<type 'numpy.ndarray'>

Instead use

B=np.matrix(np.random.random_integers(0,10,(n,n)))

answered Oct 5, 2015 at 8:51

tynn

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