[SciPy-Dev] Code review for trapz update

[Eric Moore]

> Trapz finds the area under a one-to-one association of y values with x
> values.  If y(x) > 0, then the area bounded by [a, b] between y(x) and
> x=0 should always be positive.


You could write a trapz that does that, however np.trapz finds the integral
from a to b of y using the sampled data you provide.  The "from" in there
is important.  Since we are integrating samples, the a and b are
essentially the first and last points of the x input. Since a is x[0] and b
is x[-1], the x array is defining the path along which to integrate.


> The core property you have referenced
> above is the very property that should be used in order to achieve the
> equivalence with integrating along a negative path.  Maintaining this
> separation preserves the equivalence of
> np.trapz(y,x) == np.trapz(y[::-1], x[::-1]), which I believe is an
> equivalence that should hold true.
>

This equivalence is false.  For instance both of these results are
correct.  Would they still be with your changes?


In [46]: x = np.exp(1j*np.pi*np.linspace(0,1,100))


In [47]: z = 1/x


In [48]: np.trapz(z, x)

Out[48]: (1.3244509217643717e-18+3.1410654163086975j)


In [49]: np.trapz(z[::-1], x[::-1])

Out[49]: (-1.3244509217643594e-18-3.1410654163086971j)


Eric
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