Calculating cumulative minimum with numpy arrays

Question

I'd like to calculate the "cumulative minimum" array--basically, the minimum value of an array up to each index such as:

import numpy as np
nums = np.array([5.,3.,4.,2.,1.,1.,2.,0.])
cumulative_min = np.zeros(nums.size, dtype=float)
for i,num in enumerate(nums):
    cumulative_min[i] = np.min(nums[0:i+1])

This works (it returns the correct array([ 5., 3., 3., 2., 1., 1., 1., 0.]) ), but I'd like to avoid the for loop if I can. I thought it might be faster to construct a 2-d array and use the np.amin() function, but I needed a loop for that as well.

user2357112 · Accepted Answer · 2020-10-31 00:50:16Z

47

For any 2-argument NumPy universal function, its accumulate method is the cumulative version of that function. Thus, numpy.minimum.accumulate is what you're looking for:

>>> numpy.minimum.accumulate([5,4,6,10,3])
array([5, 4, 4, 4, 3])

edited Oct 31, 2020 at 0:50

answered May 13, 2014 at 3:56

user2357112

286k32 gold badges490 silver badges571 bronze badges

Sign up to request clarification or add additional context in comments.

1 Comment

SnzFor16Min Over a year ago

Cool design! NumPy's documentation gives a full list of ufuncs, including maximum, fmin, and fmax.

koffein · Accepted Answer · 2014-05-13 04:03:49Z

1

Create a matrix which lower triangle (np.tril) is filled with values of your array nums and your upper triangle (np.triu, with second parameter 1, so the diagonal stays free) is filled with the maximum of the array. (EDIT: instead of the maximum, the first element of the array is the better way. -> comments)

nums = np.array([5.,3.,4.,2.,1.,1.,2.,0.])
oneSquare = np.ones((nums.size, nums.size))

A = nums * np.tril(oneSquare)
B = np.triu(oneSquare, 1) * nums[0]
A, B

Out:

(array([[ 5.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 5.,  3.,  0.,  0.,  0.,  0.,  0.,  0.],
       [ 5.,  3.,  4.,  0.,  0.,  0.,  0.,  0.],
       [ 5.,  3.,  4.,  2.,  0.,  0.,  0.,  0.],
       [ 5.,  3.,  4.,  2.,  1.,  0.,  0.,  0.],
       [ 5.,  3.,  4.,  2.,  1.,  1.,  0.,  0.],
       [ 5.,  3.,  4.,  2.,  1.,  1.,  2.,  0.],
       [ 5.,  3.,  4.,  2.,  1.,  1.,  2.,  0.]]),
 array([[ 0.,  5.,  5.,  5.,  5.,  5.,  5.,  5.],
       [ 0.,  0.,  5.,  5.,  5.,  5.,  5.,  5.],
       [ 0.,  0.,  0.,  5.,  5.,  5.,  5.,  5.],
       [ 0.,  0.,  0.,  0.,  5.,  5.,  5.,  5.],
       [ 0.,  0.,  0.,  0.,  0.,  5.,  5.,  5.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  5.,  5.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  5.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]]))

Now take the minimum of each row:

(A+B).min(axis=1)

Out:

array([ 5.,  3.,  3.,  2.,  1.,  1.,  1.,  0.])

edited May 13, 2014 at 4:03

answered May 13, 2014 at 3:39

koffein

1,92214 silver badges21 bronze badges

5 Comments

Blckknght Over a year ago

You could also use infinity for the values in the upper triangle, rather than nums.max().

koffein Over a year ago

@Blckknght Tried it, did not work at first glance, so I took the maximum... I tried again and infinity would change the 0-part of B to NaN

I.P. Freeley Over a year ago

nice. Didn't know about the triangle functions, very useful.

Blckknght Over a year ago

Ah, you're right. I didn't think of 0*inf being an issue, but it is. You could use nums[0], since that's always a potential minimum value already. And really, using max wasn't too bad (it only adds an O(N)` term onto an already O(N^2) algorithm.

koffein Over a year ago

@Blckknght nums[0] is a good idea... I am going to change that.. Thanks!

Collectives™ on Stack Overflow

Calculating cumulative minimum with numpy arrays

2 Answers 2

1 Comment

5 Comments

Your Answer

Linked

Hot Network Questions

Collectives™ on Stack Overflow

2 Answers 2

1 Comment

5 Comments

Your Answer

Sign up or log in

Post as a guest

Linked

Related