Python numpy addition error

Question

I'm getting a very odd error using a basic shortcut method in python. It seems, unless I'm being very stupid, I get different values for A = A + B, and A += B. Here is my code:

def variance(phi,sigma,numberOfIterations):
    variance = sigma
    for k in range(1,numberOfIterations):
        phik = np.linalg.matrix_power(phi,k)
        variance = variance + phik*sigma*phik.T
    return variance

This basically just calculates the covariance of a vector autoregression. So for:

phi    = np.matrix('0.7 0.2 -0.1; 0.001 0.8 0.1; 0.001 0.002 0.9')
sigma  = np.matrix('0.07 0.01 0.001; 0.01 0.05 0.004; 0.001 0.004 0.01')

I get:

variance(phi,sigma,10) = 
[[ 0.1825225   0.07054728  0.00430524]
 [ 0.07054728  0.14837229  0.02659357]
 [ 0.00430524  0.02659357  0.04657858]]

This is correct I believe (agrees with Matlab). Now if I change the line above to

variance += phik*sigma*(phik.T)

I get:

variance(phi,sigma,10) =
[[ 0.34537165  0.20258329  0.04365378]
 [ 0.20258329  0.33471052  0.1529369 ]
 [ 0.04365378  0.1529369   0.19684553]]

Whats going on?

Many thanks

Dan

Answer 1

The culprit is:

variance = sigma

If you change that to:

variance = sigma.copy()

You'll see the correct result.

This is because += actually performs a (more efficient) in-place addition… And since both variance and sigma reference the same array, both will be updated. For example:

>>> sigma = np.array([1])
>>> variance = sigma
>>> variance += 3
>>> sigma
array([4])