python - Select rows in pandas MultiIndex DataFrame

Question

What are the most common pandas ways to select/filter rows of a dataframe whose index is a MultiIndex?

• Slicing based on a single value/label
• Slicing based on multiple labels from one or more levels
• Filtering on boolean conditions and expressions
• Which methods are applicable in what circumstances

Assumptions for simplicity:

1. input dataframe does not have duplicate index keys
2. input dataframe below only has two levels. (Most solutions shown here generalize to N levels)

---

Example input:

mux = pd.MultiIndex.from_arrays([
    list('aaaabbbbbccddddd'),
    list('tuvwtuvwtuvwtuvw')
], names=['one', 'two'])

df = pd.DataFrame({'col': np.arange(len(mux))}, mux)

         col
one two     
a   t      0
    u      1
    v      2
    w      3
b   t      4
    u      5
    v      6
    w      7
    t      8
c   u      9
    v     10
d   w     11
    t     12
    u     13
    v     14
    w     15

Question 1: Selecting a Single Item

How do I select rows having "a" in level "one"?

         col
one two     
a   t      0
    u      1
    v      2
    w      3

Additionally, how would I be able to drop level "one" in the output?

     col
two     
t      0
u      1
v      2
w      3

Question 1b
How do I slice all rows with value "t" on level "two"?

         col
one two     
a   t      0
b   t      4
    t      8
d   t     12

Question 2: Selecting Multiple Values in a Level

How can I select rows corresponding to items "b" and "d" in level "one"?

         col
one two     
b   t      4
    u      5
    v      6
    w      7
    t      8
d   w     11
    t     12
    u     13
    v     14
    w     15

Question 2b
How would I get all values corresponding to "t" and "w" in level "two"?

         col
one two     
a   t      0
    w      3
b   t      4
    w      7
    t      8
d   w     11
    t     12
    w     15

Question 3: Slicing a Single Cross Section (x, y)

How do I retrieve a cross section, i.e., a single row having a specific values for the index from df? Specifically, how do I retrieve the cross section of ('c', 'u'), given by

         col
one two     
c   u      9

Question 4: Slicing Multiple Cross Sections [(a, b), (c, d), ...]

How do I select the two rows corresponding to ('c', 'u'), and ('a', 'w')?

         col
one two     
c   u      9
a   w      3

Question 5: One Item Sliced per Level

How can I retrieve all rows corresponding to "a" in level "one" or "t" in level "two"?

         col
one two     
a   t      0
    u      1
    v      2
    w      3
b   t      4
    t      8
d   t     12

Question 6: Arbitrary Slicing

How can I slice specific cross sections? For "a" and "b", I would like to select all rows with sub-levels "u" and "v", and for "d", I would like to select rows with sub-level "w".

         col
one two     
a   u      1
    v      2
b   u      5
    v      6
d   w     11
    w     15

Question 7 will use a unique setup consisting of a numeric level:

np.random.seed(0)
mux2 = pd.MultiIndex.from_arrays([
    list('aaaabbbbbccddddd'),
    np.random.choice(10, size=16)
], names=['one', 'two'])

df2 = pd.DataFrame({'col': np.arange(len(mux2))}, mux2)

         col
one two     
a   5      0
    0      1
    3      2
    3      3
b   7      4
    9      5
    3      6
    5      7
    2      8
c   4      9
    7     10
d   6     11
    8     12
    8     13
    1     14
    6     15

Question 7: Filtering by numeric inequality on individual levels of the multiindex

How do I get all rows where values in level "two" are greater than 5?

         col
one two     
b   7      4
    9      5
c   7     10
d   6     11
    8     12
    8     13
    6     15

---

Note: This post will not go through how to create MultiIndexes, how to perform assignment operations on them, or any performance related discussions (these are separate topics for another time).

Answer 1

MultiIndex / Advanced Indexing

Note
This post will be structured in the following manner:

1. The questions put forth in the OP will be addressed, one by one
2. For each question, one or more methods applicable to solving this problem and getting the expected result will be demonstrated.

Notes (much like this one) will be included for readers interested in learning about additional functionality, implementation details, and other info cursory to the topic at hand. These notes have been compiled through scouring the docs and uncovering various obscure features, and from my own (admittedly limited) experience.

All code samples have created and tested on pandas v0.23.4, python3.7. If something is not clear, or factually incorrect, or if you did not find a solution applicable to your use case, please feel free to suggest an edit, request clarification in the comments, or open a new question, ....as applicable.

Here is an introduction to some common idioms (henceforth referred to as the Four Idioms) we will be frequently re-visiting

1. DataFrame.loc - A general solution for selection by label (+ pd.IndexSlice for more complex applications involving slices)

2. DataFrame.xs - Extract a particular cross section from a Series/DataFrame.

3. DataFrame.query - Specify slicing and/or filtering operations dynamically (i.e., as an expression that is evaluated dynamically. Is more applicable to some scenarios than others. Also see this section of the docs for querying on MultiIndexes.

4. Boolean indexing with a mask generated using MultiIndex.get_level_values (often in conjunction with Index.isin, especially when filtering with multiple values). This is also quite useful in some circumstances.

It will be beneficial to look at the various slicing and filtering problems in terms of the Four Idioms to gain a better understanding what can be applied to a given situation. It is very important to understand that not all of the idioms will work equally well (if at all) in every circumstance. If an idiom has not been listed as a potential solution to a problem below, that means that idiom cannot be applied to that problem effectively.

---

Question 1

How do I select rows having "a" in level "one"?

         col
one two     
a   t      0
    u      1
    v      2
    w      3

You can use loc, as a general purpose solution applicable to most situations:

df.loc[['a']]

At this point, if you get

TypeError: Expected tuple, got str

That means you're using an older version of pandas. Consider upgrading! Otherwise, use df.loc[('a', slice(None)), :].

Alternatively, you can use xs here, since we are extracting a single cross section. Note the levels and axis arguments (reasonable defaults can be assumed here).

df.xs('a', level=0, axis=0, drop_level=False)
# df.xs('a', drop_level=False)

Here, the drop_level=False argument is needed to prevent xs from dropping level "one" in the result (the level we sliced on).

Yet another option here is using query:

df.query("one == 'a'")

If the index did not have a name, you would need to change your query string to be "ilevel_0 == 'a'".

Finally, using get_level_values:

df[df.index.get_level_values('one') == 'a']
# If your levels are unnamed, or if you need to select by position (not label),
# df[df.index.get_level_values(0) == 'a']

Additionally, how would I be able to drop level "one" in the output?

     col
two     
t      0
u      1
v      2
w      3

This can be easily done using either

df.loc['a'] # Notice the single string argument instead the list.

Or,

df.xs('a', level=0, axis=0, drop_level=True)
# df.xs('a')

Notice that we can omit the drop_level argument (it is assumed to be True by default).

Note
You may notice that a filtered DataFrame may still have all the levels, even if they do not show when printing the DataFrame out. For example,

v = df.loc[['a']]
print(v)
         col
one two     
a   t      0
    u      1
    v      2
    w      3

print(v.index)
MultiIndex(levels=[['a', 'b', 'c', 'd'], ['t', 'u', 'v', 'w']],
           labels=[[0, 0, 0, 0], [0, 1, 2, 3]],
           names=['one', 'two'])

You can get rid of these levels using MultiIndex.remove_unused_levels:

v.index = v.index.remove_unused_levels()

print(v.index)
MultiIndex(levels=[['a'], ['t', 'u', 'v', 'w']],
           labels=[[0, 0, 0, 0], [0, 1, 2, 3]],
           names=['one', 'two'])

---

Question 1b

How do I slice all rows with value "t" on level "two"?

         col
one two     
a   t      0
b   t      4
    t      8
d   t     12

Intuitively, you would want something involving slice():

df.loc[(slice(None), 't'), :]

It Just Works!? But it is clunky. We can facilitate a more natural slicing syntax using the pd.IndexSlice API here.

idx = pd.IndexSlice
df.loc[idx[:, 't'], :]

This is much, much cleaner.

Note
Why is the trailing slice : across the columns required? This is because, loc can be used to select and slice along both axes (axis=0 or axis=1). Without explicitly making it clear which axis the slicing is to be done on, the operation becomes ambiguous. See the big red box in the documentation on slicing.

If you want to remove any shade of ambiguity, loc accepts an axis parameter:

df.loc(axis=0)[pd.IndexSlice[:, 't']]

Without the axis parameter (i.e., just by doing df.loc[pd.IndexSlice[:, 't']]), slicing is assumed to be on the columns, and a KeyError will be raised in this circumstance.

This is documented in slicers. For the purpose of this post, however, we will explicitly specify all axes.

With xs, it is

df.xs('t', axis=0, level=1, drop_level=False)

With query, it is

df.query("two == 't'")
# Or, if the first level has no name, 
# df.query("ilevel_1 == 't'") 

And finally, with get_level_values, you may do

df[df.index.get_level_values('two') == 't']
# Or, to perform selection by position/integer,
# df[df.index.get_level_values(1) == 't']

All to the same effect.

---

Question 2

How can I select rows corresponding to items "b" and "d" in level "one"?

         col
one two     
b   t      4
    u      5
    v      6
    w      7
    t      8
d   w     11
    t     12
    u     13
    v     14
    w     15

Using loc, this is done in a similar fashion by specifying a list.

df.loc[['b', 'd']]

To solve the above problem of selecting "b" and "d", you can also use query:

items = ['b', 'd']
df.query("one in @items")
# df.query("one == @items", parser='pandas')
# df.query("one in ['b', 'd']")
# df.query("one == ['b', 'd']", parser='pandas')

Note
Yes, the default parser is 'pandas', but it is important to highlight this syntax isn't conventionally python. The Pandas parser generates a slightly different parse tree from the expression. This is done to make some operations more intuitive to specify. For more information, please read my post on Dynamic Expression Evaluation in pandas using pd.eval().

And, with get_level_values + Index.isin:

df[df.index.get_level_values("one").isin(['b', 'd'])]

---

Question 2b

How would I get all values corresponding to "t" and "w" in level "two"?

         col
one two     
a   t      0
    w      3
b   t      4
    w      7
    t      8
d   w     11
    t     12
    w     15

With loc, this is possible only in conjuction with pd.IndexSlice.

df.loc[pd.IndexSlice[:, ['t', 'w']], :] 

The first colon : in pd.IndexSlice[:, ['t', 'w']] means to slice across the first level. As the depth of the level being queried increases, you will need to specify more slices, one per level being sliced across. You will not need to specify more levels beyond the one being sliced, however.

With query, this is

items = ['t', 'w']
df.query("two in @items")
# df.query("two == @items", parser='pandas') 
# df.query("two in ['t', 'w']")
# df.query("two == ['t', 'w']", parser='pandas')

With get_level_values and Index.isin (similar to above):

df[df.index.get_level_values('two').isin(['t', 'w'])]

---

Question 3

How do I retrieve