Fixing phase unwrapping errors in Numpy

Question

I have a series of unwrapped phases, with some unwrapping errors that consist of a jump of +/- a multiple of Pi:

import numpy
a = numpy.array([0.5, 1.3, 2.4, 10.3, 10.8, 10.2, 7.6, 3.2, 2.9])

In this example there is a first jump of 2 cycles between 2.4 and 10.3, and a jump of -1 cycle between 7.6 and 3.2. I want to remove the jumps. The catch is that when you remove a jump, you need to increase or decrease the rest of the series accordingly, not just the value where the jump occurs.

Is there a cleaner way (no/less loops, faster) of doing this:

jumpsexist = 1
while jumpsexist:
    # Look for absolute differences greater than Pi
    jump = numpy.abs((numpy.roll(a,-1) -a)) > numpy.pi
    if jump[:-1].any():
        # Find the index of the first jump
        jumpind = numpy.argmax(jump) + 1
        # Calculate the number of cycles in that jump
        cycles = ((a[jumpind] - a[jumpind- 1]) / numpy.pi).astype("Int8")
        # Remove the cycles
        a[jumpind:] -= cycles * numpy.pi
    else:
        break

Answer 1

NumPy offers the function numpy.unwrap() for phase unwrapping. With the default parameter values, it will correct an array of phases modulo 2π such that all jumps are less than or equal to π:

>>> a = numpy.array([0.5, 1.3, 2.4, 10.3, 10.8, 10.2, 7.6, 3.2, 2.9])
>>> numpy.unwrap(a)
array([ 0.5       ,  1.3       ,  2.4       ,  4.01681469,  4.51681469,
        3.91681469,  1.31681469,  3.2       ,  2.9       ])