Question

This is gonna be a fairly simple question to which I wonder if there is a quick and clean workaround in Python.

Let say I have a nd-array defined as such:

In [10]: C = np.random.rand(2,3,3)

In [11]: C
Out[11]: 
array([[[ 0.43588471,  0.06600133,  0.81145749],
        [ 0.20270693,  0.85879686,  0.75778422],
        [ 0.68253449,  0.98287412,  0.63804605]],

       [[ 0.61591433,  0.36453861,  0.23798795],
        [ 0.26761896,  0.00657165,  0.04083067],
        [ 0.11177481,  0.55245769,  0.97274592]]])

Then I calculate the difference between a value and the previous value in the array for the 3rd dimension as follow:

In [12]: C[:, :, 1:] = C[:, :, 1:] - C[:, :, 0:C.shape[2]-1]

In [13]: C
Out[13]: 
array([[[ 0.43588471, -0.36988337,  0.74545616],
        [ 0.20270693,  0.65608994, -0.10101264],
        [ 0.68253449,  0.30033963, -0.34482807]],

       [[ 0.61591433, -0.25137572, -0.12655065],
        [ 0.26761896, -0.26104731,  0.03425902],
        [ 0.11177481,  0.44068288,  0.42028823]]])

Is it possible to come back to the original values using a similar technique or do I have to use a for loop and temporary variables?

For example, this doesn’t do the trick:

In [15]: C[:, :, 1:] = C[:, :, 0:C.shape[2]-1] + C[:, :, 1:]

In [16]: C
Out[16]: 
array([[[ 0.43588471,  0.06600133,  0.37557278],
        [ 0.20270693,  0.85879686,  0.5550773 ],
        [ 0.68253449,  0.98287412, -0.04448843]],

       [[ 0.61591433,  0.36453861, -0.37792638],
        [ 0.26761896,  0.00657165, -0.22678829],
        [ 0.11177481,  0.55245769,  0.86097111]]])

Answer 1

First, to compute the difference, instead of

C[:, :, 1:] - C[:, :, 0:C.shape[2]-1]

you could use numpy.diff:

np.diff(C, axis = -1)

---

In [27]: C = np.random.rand(2,3,3)

In [28]: D = C[:, :, 1:] - C[:, :, 0:C.shape[2]-1]

In [29]: E = np.diff(C, axis = -1)

In [30]: np.allclose(D, E)
Out[30]: True

---

Next, if you know you want to retrieve the original C, perhaps it is better not to overwrite the values in the first place. Just save the differences in a separate array:

E = np.diff(C, axis = -1)

After all, there is no quicker way to perform a calculation than to not compute at all :).

But if you really do want to overwrite the values, then, to retrieve the original values, use np.cumsum:

In [20]: C = np.random.rand(2,3,3)

In [21]: D = C.copy()

In [22]: C[:, :, 1:] = np.diff(C, axis = -1)

In [23]: C = np.cumsum(C, axis = -1)

In [24]: np.allclose(C,D)
Out[24]: True