Python - How to check list monotonicity

What would be an efficient and pythonic way to check list monotonicity?
i.e. that it has monotonically increasing or decreasing values?

Examples:

[0, 1, 2, 3, 3, 4]   # This is a monotonically increasing list
[4.3, 4.2, 4.2, -2]  # This is a monotonically decreasing list
[2, 3, 1]            # This is neither

Solution 1:

It's better to avoid ambiguous terms like "increasing" or "decreasing" as it's not clear if equality is acceptable or not. You should always use either for example "non-increasing" (clearly equality is accepted) or "strictly decreasing" (clearly equality is NOT accepted).

def strictly_increasing(L):
    return all(x<y for x, y in zip(L, L[1:]))

def strictly_decreasing(L):
    return all(x>y for x, y in zip(L, L[1:]))

def non_increasing(L):
    return all(x>=y for x, y in zip(L, L[1:]))

def non_decreasing(L):
    return all(x<=y for x, y in zip(L, L[1:]))

def monotonic(L):
    return non_increasing(L) or non_decreasing(L)

Solution 2:

If you have large lists of numbers it might be best to use numpy, and if you are:

import numpy as np

def monotonic(x):
    dx = np.diff(x)
    return np.all(dx <= 0) or np.all(dx >= 0)

should do the trick.

Solution 3:

import itertools
import operator

def monotone_increasing(lst):
    pairs = zip(lst, lst[1:])
    return all(itertools.starmap(operator.le, pairs))

def monotone_decreasing(lst):
    pairs = zip(lst, lst[1:])
    return all(itertools.starmap(operator.ge, pairs))

def monotone(lst):
    return monotone_increasing(lst) or monotone_decreasing(lst)

This approach is O(N) in the length of the list.

Solution 4:

@6502 has the perfect code for lists, I just want to add a general version that works for all sequences:

def pairwise(seq):
    items = iter(seq)
    last = next(items)
    for item in items:
        yield last, item
        last = item

def strictly_increasing(L):
    return all(x<y for x, y in pairwise(L))

def strictly_decreasing(L):
    return all(x>y for x, y in pairwise(L))

def non_increasing(L):
    return all(x>=y for x, y in pairwise(L))

def non_decreasing(L):
    return all(x<=y for x, y in pairwise(L))

Solution 5:

The pandas package makes this convenient.

import pandas as pd

The following commands work with a list of integers or floats.

Monotonically increasing (≥):

pd.Series(mylist).is_monotonic_increasing

Strictly monotonically increasing (>):

myseries = pd.Series(mylist)
myseries.is_unique and myseries.is_monotonic_increasing

Alternative using an undocumented private method:

pd.Index(mylist)._is_strictly_monotonic_increasing

Monotonically decreasing (≤):

pd.Series(mylist).is_monotonic_decreasing

Strictly monotonically decreasing (<):

myseries = pd.Series(mylist)
myseries.is_unique and myseries.is_monotonic_decreasing