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]])
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).
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)
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?