Integration in numpy array with positive area only

Question

I want to be able to compute following integral using numpys trapz function

numpy.trapz([-1, 1]) # returns 0

But I don't want to allow negative areas. Is there an efficient way to do this or do I have to look for the minimum point and transform the array by hand?

Does numpy.trapz(numpy.abs([-1, 1])) make sense?

Answer 1

If you want to discard negative contributions to the integrated area we can simply grab the np.trapz source code and rewrite it:

def abstrapz(y, x=None, dx=1.0):
    y = np.asanyarray(y)
    if x is None:
        d = dx
    else:
        x = np.asanyarray(x)
        d = np.diff(x)
    ret = (d * (y[1:] +y[:-1]) / 2.0)
    return ret[ret>0].sum()  #The important line

A quick test:

np.trapz([-1,0,1])
0.0

abstrapz([-1,0,1])
0.5

If you just want to avoid areas where y is less then zero simply mask 'y' values less then zero to zero:

arr = np.array([-2,-1,0.5,1,2,1,0,5,3,0])
np.trapz(arr)
10.5

arr[arr<0] = 0
np.trapz(arr)
12.5

This isn't the best way to do it, but it is a good approximation. If this is what you mean I can update this.

I had to change your example slightly as trapz([-1,1]) will always return 0 by definition. We do remove some functionality this way, if you need to do this on multidimensional arrays it is easy to add it back in.