cumulative argmax of a numpy array

Question

Consider the array a

np.random.seed([3,1415])
a = np.random.randint(0, 10, (10, 2))
a

array([[0, 2],
       [7, 3],
       [8, 7],
       [0, 6],
       [8, 6],
       [0, 2],
       [0, 4],
       [9, 7],
       [3, 2],
       [4, 3]])

What is a vectorized way to get the cumulative argmax?

array([[0, 0],  <-- both start off as max position
       [1, 1],  <-- 7 > 0 so 1st col = 1, 3 > 2 2nd col = 1
       [2, 2],  <-- 8 > 7 1st col = 2, 7 > 3 2nd col = 2
       [2, 2],  <-- 0 < 8 1st col stays the same, 6 < 7 2nd col stays the same
       [2, 2],  
       [2, 2],
       [2, 2],
       [7, 2],  <-- 9 is new max of 2nd col, argmax is now 7
       [7, 2],
       [7, 2]])

---

Here is a non-vectorized way to do it.

Notice that as the window expands, argmax applies to the growing window.

pd.DataFrame(a).expanding().apply(np.argmax).astype(int).values

array([[0, 0],
       [1, 1],
       [2, 2],
       [2, 2],
       [2, 2],
       [2, 2],
       [2, 2],
       [7, 2],
       [7, 2],
       [7, 2]])

Answer 1

Here's a vectorized pure NumPy solution that performs pretty snappily:

def cumargmax(a):
    m = np.maximum.accumulate(a)
    x = np.repeat(np.arange(a.shape[0])[:, None], a.shape[1], axis=1)
    x[1:] *= m[:-1] < m[1:]
    np.maximum.accumulate(x, axis=0, out=x)
    return x

Then we have:

>>> cumargmax(a)
array([[0, 0],
       [1, 1],
       [2, 2],
       [2, 2],
       [2, 2],
       [2, 2],
       [2, 2],
       [7, 2],
       [7, 2],
       [7, 2]])

Some quick testing on arrays with thousands to millions of values suggests that this is anywhere between 10-50 times faster than looping at the Python level (either implicitly or explicitly).

Answer 2

I cant think of a way to vectorize this over both columns easily; but if the number of columns is small relative to the number of rows, that shouldn't be an issue and a for loop should suffice for that axis:

import numpy as np
import numpy_indexed as npi
a = np.random.randint(0, 10, (10))
max = np.maximum.accumulate(a)
idx = npi.indices(a, max)
print(idx)

Answer 3

I would like to make a function that computes cumulative argmax for 1d array and then apply it to all columns. This is the code:

import numpy as np

np.random.seed([3,1415])
a = np.random.randint(0, 10, (10, 2))

def cumargmax(v):
    uargmax = np.frompyfunc(lambda i, j: j if v[j] > v[i] else i, 2, 1)
    return uargmax.accumulate(np.arange(0, len(v)), 0, dtype=np.object).astype(v.dtype)

np.apply_along_axis(cumargmax, 0, a)

The reason for converting to np.object and then converting back is a workaround for Numpy 1.9, as mentioned in generalized cumulative functions in NumPy/SciPy?