- vs -= operators with numpy

Question

I'm having some strange behavior in my python code related to - and -=. I'm writing a QR decomposition using numpy, and have the following line of code in a double loop:

v = v - r[i,j] * q[:,i]

where q and r are both numpy.array, and v is a slice of another numpy.array taken as v = x[:,j].

The above code doesn't work as expected in all cases. However, if I make the following change:

v -= r[i,j] * q[:,i]

Then everything works flawlessly.

I was under the impression that those two lines should be identical. To test whether -= and _ = _ - were working differently, I created the following snippet

import numpy

x = numpy.array(range(0,6))
y = numpy.array(range(0,6))

u = x[3:5]
v = y[3:5]

print u,v

u = u - [1,1]
v -= [1,1]

print u,v

which again works as expected, producing [2 3] [2 3] at both print statements.

So I'm entirely confused why those two lines perform differently. The only possible thing I can think of is that I am dealing with extremely small numbers sometimes (on the order of 10^-8 or smaller) and there is some precision issue that -= is better at? The first line performs increasingly worse as the elements of x get smaller.

I apologize if there's any other posts about this similar issue, I can't search for - and -= and I don't know if there's any correct terms for these besides assignment/operators.

Thanks for any help!

Answer 1

When v is a slice, then v -= X and v = v - X produce very different results. Consider

>>> x = np.arange(6)
>>> v = x[1:4]
>>> v -= 1
>>> v
array([0, 1, 2])
>>> x
array([0, 0, 1, 2, 4, 5])

where v -= 1 updates the slice, and therefore the array that it views, in-place, vs.

>>> x = np.arange(6)
>>> v = x[1:4]
>>> v = v - 1
>>> v
array([0, 1, 2])
>>> x
array([0, 1, 2, 3, 4, 5])

where v = v - 1 resets the variable v while leaving x untouched. To obtain the former result without -=, you'd have to do

v[:] = v - 1