fatiando / fatiando / 2088 / 3
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coverage: 69.83% (+6.6%) from 63.186%
PYTHON=2.7 COVERAGE=true BUILD_DOCS=false

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Replace polyprism Cython code with pure numpy (#368)

Replacing the Cython `gravmag.polyprism` forward modeling code 
with simpler pure Python + numpy versions (following #364). 
Using some optimizations and simplifications, the resulting code is just as fast or 
even faster than the Cython version.
The main optimization is combining logarithms, e.g. 
`log(a/b) - log(c/d)`  with `log((a*d)/(b*c))`.

Using the following IPython script to benchmark against `master`:

    from __future__ import division, print_function
    import sys
    import numpy as np
    from fatiando import gridder, utils
    from fatiando.mesher import PolygonalPrism
    # Get processor information
    tmp = !cat /proc/cpuinfo | grep "model name"
    processor = tmp[0].split(':')[1].strip()
    print(processor)
    # Make a model for testing
    vertices = np.transpose(gridder.circular_scatter([-300, 300, -300, 300], 50))
    props = {'density': 1000, 'magnetization': utils.ang2vec(2, 25, -10)}
    model = [PolygonalPrism(vertices, 0, 200, props),
             PolygonalPrism(vertices, 200, 300, props)]
    inc, dec = -30, 50
    x, y, z = gridder.regular((-500, 500, -500, 500), (70, 70), z=-1)
    print('Model size: {}'.format(len(vertices)))
    print('Grid size: {}'.format(x.size))
    # Time the forward modeling of gravity, gradients and mag
    from fatiando.gravmag import polyprism
    print('Times:')
    if len(sys.argv) == 1:
        fields = 'gz gxx gxy gxz gyy gyz gzz tf bz bx by'.split()
    else:
        fields = sys.argv[1:]
    for field in fields:
        print('  {}: '.format(field), end='')
        if field == 'tf':
            args = (x, y, z, model, inc, dec)
        else:
            args = (x, y, z, model)
        %timeit getattr(polyprism, field)(*args)

These are the times for the `master` branch on my laptop:

    Intel(R) Core(TM) i5-4200U CPU @ 1.60GHz
    Model size: 50
    Grid size: 4900
    Times:
      ... (continued)

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Source Files on job 2088.3 (PYTHON=2.7 COVERAGE=true BUILD_DOCS=false)