Pandas dataframe: Check if data is monotonically decreasing

You could use one of the is_monotonic functions from algos:

In [10]: months = ['Jan', 'Feb', 'Mar', 'Apr']

In [11]: df.loc[:, months].apply(lambda x: pd.algos.is_monotonic_float64(-x)[0],
                                       axis=1)
Out[11]:
0    False
1     True
2    False
3     True
4    False
dtype: bool

The is_monotonic checks whether an array it's decreasing hence the -x.values.

(This seems substantially faster than Tom's solution, even using the small DataFrame provided.)

months = ['Jan', 'Feb', 'Mar', 'Apr']

Transpose so that we can use the diff method (which doesn't take an axis argument). We fill in the first row (January) with 0. Otherwise it's NaN.

In [77]: df[months].T.diff().fillna(0) <= 0
Out[77]: 
         0     1      2     3      4
Jan   True  True   True  True   True
Feb  False  True   True  True  False
Mar   True  True  False  True   True
Apr  False  True   True  True  False

To check if it's monotonically decreasing, use the .all() method. By default this goes over axis 0, the rows (months).

In [78]: is_decreasing = (df[months].T.diff().fillna(0) <= 0).all()

In [79]: is_decreasing
Out[79]: 
0    False
1     True
2    False
3     True
4    False
dtype: bool

In [80]: df['is_decreasing'] = is_decreasing

In [81]: df
Out[81]: 
    Balance       Jan       Feb       Mar       Apr is_decreasing
0  9.724135  0.389376  0.464451  0.229964  0.691504         False
1  1.114782  0.838406  0.679096  0.185135  0.143883          True
2  7.613946  0.960876  0.220274  0.788265  0.606402         False
3  0.144517  0.800086  0.287874  0.223539  0.206002          True
4  1.332838  0.430812  0.939402  0.045262  0.388466         False

And like you suggested, we can groupby is_decreasing and sum:

In [83]: df.groupby('is_decreasing')['Balance'].sum()
Out[83]: 
is_decreasing
False            18.670919
True              1.259299
Name: Balance, dtype: float64

It's times like these when I love pandas.

Pandas 0.19 added a Series.is_monotonic attribute (as mentioned, the algos module was removed from Pandas public API).

As @Liam notes in his answer, is_monotonic is in fact an alias for is_monotonic_increasing, so for clarity I'd recommended directly using either is_monotonic_increasing or is_monotonic_decreasing.

Anyway, both are non-strict (i.e. is_monotonic_decreasing returns True when the sequence is either decreasing or equal), but you can combine them with is_unqiue if you need strictness.

my_df = pd.DataFrame({'A':[1,2,3],'B':[1,1,1],'C':[3,2,1]})
my_df

Out[32]: 
   A  B  C
0  1  1  3
1  2  1  2
2  3  1  1

my_df.apply(lambda x: x.is_monotonic_increasing)  # row-wise monotonic (default axis is 0)

Out[33]: 
A     True
B     True
C    False
dtype: bool

my_df.apply(lambda x: x.is_monotonic_increasing, axis=1)  # column-wise monotonic

Out[34]: 
0     True
1    False
2    False
dtype: bool