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1
pandas: a Foundational Python Library for Data
Analysis and Statistics
Wes McKinney
F
Abstract—In this paper we will discuss pandas, a Python library of rich
data structures and tools for working with structured data sets common to
statistics, finance, social sciences, and many other fields. The library provides
integrated, intuitive routines for performing common data manipulations and
analysis on such data sets. It aims to be the foundational layer for the future of
statistical computing in Python. It serves as a strong complement to the existing
scientific Python stack while implementing and improving upon the kinds of data
manipulation tools found in other statistical programming languages such as
R. In addition to detailing its design and features of pandas, we will discuss
future avenues of work and growth opportunities for statistics and data analysis
applications in the Python language.
Introduction
Python is being used increasingly in scientific applications
traditionally dominated by [R], [MATLAB], [Stata], [SAS],
other commercial or open-source research environments. The
maturity and stability of the fundamental numerical li-
braries ([NumPy], [SciPy], and others), quality of documenta-
tion, and availability of “kitchen-sink” distributions ([EPD],
[Pythonxy]) have gone a long way toward making Python
accessible and convenient for a broad audience. Additionally
[matplotlib] integrated with [IPython] provides an interactive
research and development environment with data visualization
suitable for most users. However, adoption of Python for
applied statistical modeling has been relatively slow compared
with other areas of computational science.
One major issue for would-be statistical Python program-
mers in the past has been the lack of libraries implementing
standard models and a cohesive framework for specifying
models. However, in recent years there have been significant
new developments in econometrics ([StaM]), Bayesian statis-
tics ([PyMC]), and machine learning ([SciL]), among others
fields. However, it is still difficult for many statisticians to
choose Python over R given the domain-specific nature of the
R language and breadth of well-vetted open-source libraries
available to R users ([CRAN]). In spite of this obstacle, we
believe that the Python language and the libraries and tools
currently available can be leveraged to make Python a superior
environment for data analysis and statistical computing.
Another issue preventing many from using Python in the
past for data analysis applications has been the lack of rich data
structures with integrated handling of metadata. By metadata
we mean labeling information about data points. For example,
Corresponding author can be contacted at: wesmckinn@gmail.com.
c
○2011 Wes McKinney
a table or spreadsheet of data will likely have labels for the
columns and possibly also the rows. Alternately, some columns
in a table might be used for grouping and aggregating data into
a pivot or contingency table. In the case of a time series data
set, the row labels could be time stamps. It is often necessary
to have the labeling information available to allow many kinds
of data manipulations, such as merging data sets or performing
an aggregation or “group by” operation, to be expressed in an
intuitive and concise way. Domain-specific database languages
like SQL and statistical languages like R and SAS have a
wealth of such tools. Until relatively recently, Python had few
tools providing the same level of richness and expressiveness
for working with labeled data sets.
The pandas library, under development since 2008, is
intended to close the gap in the richness of available data
analysis tools between Python, a general purpose systems
and scientific computing language, and the numerous domain-
specific statistical computing platforms and database lan-
guages. We not only aim to provide equivalent functionality
but also implement many features, such as automatic data
alignment and hierarchical indexing, which are not readily
available in such a tightly integrated way in any other libraries
or computing environments to our knowledge. While initially
developed for financial data analysis applications, we hope that
pandas will enable scientific Python to be a more attractive
and practical statistical computing environment for academic
and industry practitioners alike. The library’s name derives
from panel data, a common term for multidimensional data
sets encountered in statistics and econometrics.
While we offer a vignette of some of the main features of
interest in pandas, this paper is by no means comprehensive.
For more, we refer the interested reader to the online docu-
mentation at http://pandas.sf.net ([pandas]).
Structured data sets
Structured data sets commonly arrive in tabular format, i.e.
as a two-dimensional list of observations and names for the
fields of each observation. Usually an observation can be
uniquely identified by one or more values or labels. We show
an example data set for a pair of stocks over the course of
several days. The NumPy ndarray with structured dtype can
be used to hold this data:
>>> data
array([(’GOOG’, ’2009-12-28’, 622.87, 1697900.0),
2
(’GOOG’, ’2009-12-29’, 619.40, 1424800.0),
(’GOOG’, ’2009-12-30’, 622.73, 1465600.0),
(’GOOG’, ’2009-12-31’, 619.98, 1219800.0),
(’AAPL’, ’2009-12-28’, 211.61, 23003100.0),
(’AAPL’, ’2009-12-29’, 209.10, 15868400.0),
(’AAPL’, ’2009-12-30’, 211.64, 14696800.0),
(’AAPL’, ’2009-12-31’, 210.73, 12571000.0)],
dtype=[(’item’, ’|S4’), (’date’, ’|S10’),
(’price’, ’<f8’), (’volume’, ’<f8’)])
>>> data[’price’]
array([622.87, 619.4, 622.73, 619.98, 211.61, 209.1,
211.64, 210.73])
Structured (or record) NumPy arrays such as this can be
effective in many applications, but in our experience they do
not provide the same level of flexibility and ease of use as
other statistical environments. One major issue is that they do
not integrate well with the rest of NumPy, which is mainly
intended for working with arrays of homogeneous dtype.
R provides the data.frame class which stores mixed-
type data as a collection of independent columns. The core
R language and its 3rd-party libraries were built with the
data.frame object in mind, so most operations on such
a data set are very natural. A data.frame is also flexible
in size, an important feature when assembling a collection of
data. The following code fragment loads the data stored in the
CSV file data into the variable df and adds a new column
of boolean values:
> df <- read.csv(’data’)
item date price volume
1 GOOG 2009-12-28 622.87 1697900
2 GOOG 2009-12-29 619.40 1424800
3 GOOG 2009-12-30 622.73 1465600
4 GOOG 2009-12-31 619.98 1219800
5 AAPL 2009-12-28 211.61 23003100
6 AAPL 2009-12-29 209.10 15868400
7 AAPL 2009-12-30 211.64 14696800
8 AAPL 2009-12-31 210.73 12571000
> df$ind <- df$item == "GOOG"
> df
item date price volume ind
1 GOOG 2009-12-28 622.87 1697900 TRUE
2 GOOG 2009-12-29 619.40 1424800 TRUE
3 GOOG 2009-12-30 622.73 1465600 TRUE
4 GOOG 2009-12-31 619.98 1219800 TRUE
5 AAPL 2009-12-28 211.61 23003100 FALSE
6 AAPL 2009-12-29 209.10 15868400 FALSE
7 AAPL 2009-12-30 211.64 14696800 FALSE
8 AAPL 2009-12-31 210.73 12571000 FALSE
pandas provides a similarly-named DataFrame class
which implements much of the functionality of its R coun-
terpart, though with some important enhancements which we
will discuss. Here we convert the structured array above into
a pandas DataFrame object and similarly add the same
column:
>>> from pandas import DataFrame
>>> data = DataFrame(data)
>>> data
item date price volume
0 GOOG 2009-12-28 622.9 1.698e+06
1 GOOG 2009-12-29 619.4 1.425e+06
2 GOOG 2009-12-30 622.7 1.466e+06
3 GOOG 2009-12-31 620 1.22e+06
4 AAPL 2009-12-28 211.6 2.3e+07
5 AAPL 2009-12-29 209.1 1.587e+07
6 AAPL 2009-12-30 211.6 1.47e+07
7 AAPL 2009-12-31 210.7 1.257e+07
>>> data[’ind’] = data[’item’] == ’GOOG’
>>> data
item date price volume ind
0 GOOG 2009-12-28 622.9 1.698e+06 True
1 GOOG 2009-12-29 619.4 1.425e+06 True
2 GOOG 2009-12-30 622.7 1.466e+06 True
3 GOOG 2009-12-31 620 1.22e+06 True
4 AAPL 2009-12-28 211.6 2.3e+07 False
5 AAPL 2009-12-29 209.1 1.587e+07 False
6 AAPL 2009-12-30 211.6 1.47e+07 False
7 AAPL 2009-12-31 210.7 1.257e+07 False
This data can be reshaped or “pivoted” on the date and
item columns into a different form for future examples by
means of the DataFrame method pivot:
>>> del data[’ind’] # delete ind column
>>> data.pivot(’date’, ’item’)
price volume
item AAPL GOOG AAPL GOOG
date
2009-12-28 211.6 622.9 2.3e+07 1.698e+06
2009-12-29 209.1 619.4 1.587e+07 1.425e+06
2009-12-30 211.6 622.7 1.47e+07 1.466e+06
2009-12-31 210.7 620 1.257e+07 1.22e+06
The result of the pivot operation has a hierarchical index
for the columns. As we will show in a later section, this is
a powerful and flexible way of representing and manipulat-
ing multidimensional data. Currently the pivot method of
DataFrame only supports pivoting on two columns to reshape
the data, but could be augmented to consider more than just
two columns. By using hierarchical indexes, we can guarantee
that the result will always be two-dimensional. Later in the
paper we will demonstrate the pivot_table function which
can produce spreadsheet-style pivot table data summaries as
DataFrame objects with hierarchical rows and columns.
Beyond observational data, one will also frequently en-
counter categorical data, which can be used to partition identi-
fiers into broader groupings. For example, stock tickers might
be categorized by their industry or country of incorporation.
Here we have created a DataFrame object cats storing
country and industry classifications for a group of stocks:
>>> cats
country industry
AAPL US TECH
IBM US TECH
SAP DE TECH
GOOG US TECH
C US FIN
SCGLY FR FIN
BAR UK FIN
DB DE FIN
VW DE AUTO
RNO FR AUTO
F US AUTO
TM JP AUTO
pandas data model
Each axis of a pandas data structure has an Index object
which stores labeling information about each tick along that
axis. The most general Index is simply a 1-dimensional
vector of labels (stored in a NumPy ndarray). It’s convenient
to think about the Index as an implementation of an ordered
set. In the stock data above, the row index contains simply
3
sequential observation numbers, while the column index con-
tains the column names. The labels are not required to be
sorted, though a subclass of Index could be implemented to
require sortedness and provide operations optimized for sorted
data (e.g. time series data).
The Index object is used for many purposes:
•Performing lookups to select subsets of slices of an object
•Providing fast data alignment routines for aligning one
object with another
•Enabling intuitive slicing / selection to form new Index
objects
•Forming unions and intersections of Index objects
Here are some examples of how the index is used internally:
>>> index = Index([’a’, ’b’, ’c’, ’d’, ’e’])
>>> ’c’ in index
True
>>> index.get_loc(’d’)
3
>>> index.slice_locs(’b’, ’d’)
(1, 4)
# for aligning data
>>> index.get_indexer([’c’, ’e’, ’f’])
array([ 2, 4, -1], dtype=int32)
The basic Index uses a Python dict internally to map
labels to their respective locations and implement these fea-
tures, though subclasses could take a more specialized and
potentially higher performance approach.
Multidimensional objects like DataFrame are not proper
subclasses of NumPy’s ndarray nor do they use arrays
with structured dtype. In recent releases of pandas there is a
new internal data structure known as BlockManager which
manipulates a collection of n-dimensional ndarray objects
we refer to as blocks. Since DataFrame needs to be able to
store mixed-type data in the columns, each of these internal
Block objects contains the data for a set of columns all
having the same type. In the example from above, we can
examine the BlockManager, though most users would never
need to do this:
>>> data._data
BlockManager
Items: [item date price volume ind]
Axis1:[01234567]
FloatBlock: [price volume], 2 x 8, dtype float64
ObjectBlock: [item date], 2 x 8, dtype object
BoolBlock: [ind], 1 x 8, dtype bool
The key importance of BlockManager is that many
operations, e.g. anything row-oriented (as opposed to column-
oriented), especially in homogeneous DataFrame objects,
are significantly faster when the data are all stored in a
single ndarray. However, as it is common to insert and
delete columns, it would be wasteful to have a reallocate-
copy step on each column insertion or deletion step. As
a result, the BlockManager effectively provides a lazy
evaluation scheme where-in newly inserted columns are stored
in new Block objects. Later, either explicitly or when certain
methods are called in DataFrame, blocks having the same
type will be consolidated, i.e. combined together, to form a
single homogeneously-typed Block:
>>> data[’newcol’] = 1.
>>> data._data
BlockManager
Items: [item date price volume ind newcol]
Axis1:[01234567]
FloatBlock: [price volume], 2 x 8
ObjectBlock: [item date], 2 x 8
BoolBlock: [ind], 1 x 8
FloatBlock: [newcol], 1 x 8
>>> data.consolidate()._data
BlockManager
Items: [item date price volume ind newcol]
Axis1:[01234567]
BoolBlock: [ind], 1 x 8
FloatBlock: [price volume newcol], 3 x 8
ObjectBlock: [item date], 2 x 8
The separation between the internal BlockManager ob-
ject and the external, user-facing DataFrame gives the pan-
das developers a significant amount of freedom to modify the
internal structure to achieve better performance and memory
usage.
Label-based data access
While standard []-based indexing (using __getitem__
and __setitem__) is reserved for column access in
DataFrame, it is useful to be able to index both axes of
aDataFrame in a matrix-like way using labels. We would
like to be able to get or set data on any axis using one of the
following:
•A list or array of labels or integers
•A slice, either with integers (e.g. 1:5) or labels (e.g.
lab1:lab2)
•A boolean vector
•A single label
To avoid excessively overloading the []-related methods,
leading to ambiguous indexing semantics in some cases, we
have implemented a special label-indexing attribute ix on all
of the pandas data structures. Thus, we can pass a tuple of
any of the above indexing objects to get or set values.
>>> df
ABCD
2000-01-03 -0.2047 1.007 -0.5397 -0.7135
2000-01-04 0.4789 -1.296 0.477 -0.8312
2000-01-05 -0.5194 0.275 3.249 -2.37
2000-01-06 -0.5557 0.2289 -1.021 -1.861
2000-01-07 1.966 1.353 -0.5771 -0.8608
>>> df.ix[:2, [’D’, ’C’, ’A’]]
DCA
2000-01-03 -0.7135 -0.5397 -0.2047
2000-01-04 -0.8312 0.477 0.4789
>>> df.ix[-2:, ’B’:]
BCD
2000-01-06 0.2289 -1.021 -1.861
2000-01-07 1.353 -0.5771 -0.8608
Setting values also works as expected.
>>> date1, date2 = df.index[[1, 3]]
>>> df.ix[date1:date2, [’A’, ’C’]] = 0
>>> df
A B C D
2000-01-03 -0.6856 0.1362 0.3996 1.585
2000-01-04 0 0.8863 0 1.907
2000-01-05 0 -1.351 0 0.104
2000-01-06 0 -0.8863 0 0.1741
2000-01-07 -0.05927 -1.013 0.9923 -0.4395
4
Data alignment
Operations between related, but differently-sized data sets can
pose a problem as the user must first ensure that the data points
are properly aligned. As an example, consider time series over
different date ranges or economic data series over varying sets
of entities:
>>> s1 >>> s2
AAPL 0.044 AAPL 0.025
IBM 0.050 BAR 0.158
SAP 0.101 C 0.028
GOOG 0.113 DB 0.087
C 0.138 F 0.004
SCGLY 0.037 GOOG 0.154
BAR 0.200 IBM 0.034
DB 0.281
VW 0.040
One might choose to explicitly align (or reindex) one of
these 1D Series objects with the other before adding them,
using the reindex method:
>>> s1.reindex(s2.index)
AAPL 0.0440877763224
BAR 0.199741007422
C 0.137747485628
DB 0.281070058049
F NaN
GOOG 0.112861123629
IBM 0.0496445829129
However, we often find it preferable to simply ignore the
state of data alignment:
>>> s1 + s2
AAPL 0.0686791008184
BAR 0.358165479807
C 0.16586702944
DB 0.367679872693
F NaN
GOOG 0.26666583847
IBM 0.0833057542385
SAP NaN
SCGLY NaN
VW NaN
Here, the data have been automatically aligned based on
their labels and added together. The result object contains
the union of the labels between the two objects so that no
information is lost. We will discuss the use of NaN (Not a
Number) to represent missing data in the next section.
Clearly, the user pays linear overhead whenever automatic
data alignment occurs and we seek to minimize that overhead
to the extent possible. Reindexing can be avoided when
Index objects are shared, which can be an effective strategy
in performance-sensitive applications. [Cython], a widely-
used tool for creating Python C extensions and interfacing
with C/C++ code, has been utilized to speed up these core
algorithms.
Data alignment using DataFrame occurs automatically
on both the column and row labels. This deeply integrated
data alignment differs from any other tools outside of Python
that we are aware of. Similar to the above, if the columns
themselves are different, the resulting object will contain the
union of the columns:
>>> df >>> df2
AAPL GOOG AAPL
2009-12-28 211.6 622.9 2009-12-28 2.3e+07
2009-12-29 209.1 619.4 2009-12-29 1.587e+07
2009-12-30 211.6 622.7 2009-12-30 1.47e+07
2009-12-31 210.7 620
>>> df / df2
AAPL GOOG
2009-12-28 9.199e-06 NaN
2009-12-29 1.318e-05 NaN
2009-12-30 1.44e-05 NaN
2009-12-31 NaN NaN
This may seem like a simple feature, but in practice it grants
immense freedom as there is no longer a need to sanitize
data from an untrusted source. For example, if you loaded
two data sets from a database and the columns and rows,
they can be added together, say, without having to do any
checking whether the labels are aligned. Of course, after doing
an operation between two data sets, you can perform an ad
hoc cleaning of the results using such functions as fillna
and dropna:
>>> (df / df2).fillna(0)
AAPL GOOG
2009-12-28 9.199e-06 0
2009-12-29 1.318e-05 0
2009-12-30 1.44e-05 0
2009-12-31 0 0
>>> (df / df2).dropna(axis=1, how=’all’)
AAPL
2009-12-28 9.199e-06
2009-12-29 1.318e-05
2009-12-30 1.44e-05
2009-12-31 NaN
Handling missing data
It is common for a data set to have missing observations.
For example, a group of related economic time series stored
in a DataFrame may start on different dates. Carrying
out calculations in the presence of missing data can lead
both to complicated code and considerable performance loss.
We chose to use NaN as opposed to using the NumPy
MaskedArray object for performance reasons (which are
beyond the scope of this paper), as NaN propagates in floating-
point operations in a natural way and can be easily detected
in algorithms. While this leads to good performance, it comes
with drawbacks: namely that NaN cannot be used in integer-
type arrays, and it is not an intuitive “null” value in object or
string arrays (though it is used in these arrays regardless).
We regard the use of NaN as an implementation detail and
attempt to provide the user with appropriate API functions for
performing common operations on missing data points. From
the above example, we can use the dropna method to drop
missing data, or we could use fillna to replace missing data
with a specific value:
>>> (s1 + s2).dropna()
AAPL 0.0686791008184
BAR 0.358165479807
C 0.16586702944
DB 0.367679872693
GOOG 0.26666583847
IBM 0.0833057542385
>>> (s1 + s2).fillna(0)
AAPL 0.0686791008184
BAR 0.358165479807
5
C 0.16586702944
DB 0.367679872693
F 0.0
GOOG 0.26666583847
IBM 0.0833057542385
SAP 0.0
SCGLY 0.0
VW 0.0
The reindex and fillna methods are equipped with
a couple simple interpolation options to propagate values
forward and backward, which is especially useful for time
series data:
>>> ts >>> ts2
2000-01-03 0.03825 2000-01-03 0.03825
2000-01-04 -1.9884 2000-01-06 -0.0588
2000-01-05 0.73255 2000-01-11 0.04410
2000-01-06 -0.0588 2000-01-14 -0.1786
2000-01-07 -0.4767
2000-01-10 1.98008
2000-01-11 0.04410
>>> ts3 = ts + ts2
>>> ts3 >>> ts3.fillna(method=’ffill’)
2000-01-03 0.07649 2000-01-03 0.07649
2000-01-04 NaN 2000-01-04 0.07649
2000-01-05 NaN 2000-01-05 0.07649
2000-01-06 -0.1177 2000-01-06 -0.1177
2000-01-07 NaN 2000-01-07 -0.1177
2000-01-10 NaN 2000-01-10 -0.1177
2000-01-11 0.08821 2000-01-11 0.08821
2000-01-14 NaN 2000-01-14 0.08821
Series and DataFrame also have explicit arithmetic
methods with which a fill_value can be used to specify
a treatment of missing data in the computation. An occasional
choice is to treat missing values as 0 when adding two
Series objects:
>>> ts.add(ts2, fill_value=0)
2000-01-03 0.0764931953608
2000-01-04 -1.98842046359
2000-01-05 0.732553684194
2000-01-06 -0.117727627078
2000-01-07 -0.476754320696
2000-01-10 1.9800873096
2000-01-11 0.0882102892097
2000-01-14 -0.178640361674
Common ndarray methods have been rewritten to auto-
matically exclude missing data from calculations:
>>> (s1 + s2).sum()
1.3103630754662747
>>> (s1 + s2).count()
6
Similar to R’s is.na function, which detects NA (Not Avail-
able) values, pandas has special API functions isnull and
notnull for determining the validity of a data point. These
contrast with numpy.isnan in that they can be used with
dtypes other than float and also detect some other markers
for “missing” occurring in the wild, such as the Python None
value.
>>> isnull(s1 + s2)
AAPL False
BAR False
C False
DB False
F True
GOOG False
IBM False
SAP True
SCGLY True
VW True
Note that R’s NA value is distinct from NaN. NumPy core
developers are currently working on an NA value implementa-
tion that will hopefully suit the needs of libraries like pandas
in the future.
Hierarchical Indexing
A relatively recent addition to pandas is the ability for an
axis to have a hierarchical index, known in the library as a
MultiIndex. Semantically, this means that each a location
on a single axis can have multiple labels associated with it.
>>> hdf
ABC
foo one -0.9884 0.09406 1.263
two 1.29 0.08242 -0.05576
three 0.5366 -0.4897 0.3694
bar one -0.03457 -2.484 -0.2815
two 0.03071 0.1091 1.126
baz two -0.9773 1.474 -0.06403
three -1.283 0.7818 -1.071
qux one 0.4412 2.354 0.5838
two 0.2215 -0.7445 0.7585
three 1.73 -0.965 -0.8457
Hierarchical indexing can be viewed as a way to represent
higher-dimensional data in a lower-dimensional data structure
(here, a 2D DataFrame). For example, we can select rows
from the above DataFrame by specifying only a label from
the left-most level of the index:
>>> hdf.ix[’foo’]
ABC
one -0.9884 0.09406 1.263
two 1.29 0.08242 -0.05576
three 0.5366 -0.4897 0.3694
Of course, if all of the levels are specified, we can select a
row or column just as with a regular Index.
>>> hdf.ix[’foo’, ’three’]
A 0.5366
B -0.4897
C 0.3694
# same result
>>> hdf.ix[’foo’].ix[’three’]
The hierarchical index can be used with any axis. From the
pivot example earlier in the paper we obtained:
>>> pivoted = data.pivot(’date’, ’item’)
>>> pivoted
price volume
AAPL GOOG AAPL GOOG
2009-12-28 211.6 622.9 2.3e+07 1.698e+06
2009-12-29 209.1 619.4 1.587e+07 1.425e+06
2009-12-30 211.6 622.7 1.47e+07 1.466e+06
2009-12-31 210.7 620 1.257e+07 1.22e+06
>>> pivoted[’volume’]
AAPL GOOG
2009-12-28 2.3e+07 1.698e+06
2009-12-29 1.587e+07 1.425e+06
2009-12-30 1.47e+07 1.466e+06
2009-12-31 1.257e+07 1.22e+06
There are several utility methods for manipulating a
MultiIndex such as swaplevel and sortlevel:
6
>>> swapped = pivoted.swaplevel(0, 1, axis=1)
>>> swapped
AAPL GOOG AAPL GOOG
price price volume volume
2009-12-28 211.6 622.9 2.3e+07 1.698e+06
2009-12-29 209.1 619.4 1.587e+07 1.425e+06
2009-12-30 211.6 622.7 1.47e+07 1.466e+06
2009-12-31 210.7 620 1.257e+07 1.22e+06
>>> swapped[’AAPL’]
price volume
2009-12-28 211.6 2.3e+07
2009-12-29 209.1 1.587e+07
2009-12-30 211.6 1.47e+07
2009-12-31 210.7 1.257e+07
Here is an example for sortlevel:
>>> pivoted.sortlevel(1, axis=1)
price volume price volume
AAPL AAPL GOOG GOOG
2009-12-28 211.6 2.3e+07 622.9 1.698e+06
2009-12-29 209.1 1.587e+07 619.4 1.425e+06
2009-12-30 211.6 1.47e+07 622.7 1.466e+06
2009-12-31 210.7 1.257e+07 620 1.22e+06
Advanced pivoting and reshaping
Closely related to hierarchical indexing and the earlier pivoting
example, we illustrate more advanced reshaping of data using
the stack and unstack methods. stack reshapes by
removing a level from the columns of a DataFrame object
and moving that level to the row labels, producing either a
1D Series or another DataFrame (if the columns were a
MultiIndex).
>>> df
AAPL GOOG
2009-12-28 211.6 622.9
2009-12-29 209.1 619.4
2009-12-30 211.6 622.7
2009-12-31 210.7 620
>>> df.stack()
2009-12-28 AAPL 211.61
GOOG 622.87
2009-12-29 AAPL 209.1
GOOG 619.4
2009-12-30 AAPL 211.64
GOOG 622.73
2009-12-31 AAPL 210.73
GOOG 619.98
>>> pivoted
price volume
AAPL GOOG AAPL GOOG
2009-12-28 211.6 622.9 2.3e+07 1.698e+06
2009-12-29 209.1 619.4 1.587e+07 1.425e+06
2009-12-30 211.6 622.7 1.47e+07 1.466e+06
2009-12-31 210.7 620 1.257e+07 1.22e+06
>>> pivoted.stack()
price volume
2009-12-28 AAPL 211.6 2.3e+07
GOOG 622.9 1.698e+06
2009-12-29 AAPL 209.1 1.587e+07
GOOG 619.4 1.425e+06
2009-12-30 AAPL 211.6 1.47e+07
GOOG 622.7 1.466e+06
2009-12-31 AAPL 210.7 1.257e+07
GOOG 620 1.22e+06
By default, the innermost level is stacked. The level to stack
can be specified explicitly:
>>> pivoted.stack(0)
AAPL GOOG
2009-12-28 price 211.6 622.9
volume 2.3e+07 1.698e+06
2009-12-29 price 209.1 619.4
volume 1.587e+07 1.425e+06
2009-12-30 price 211.6 622.7
volume 1.47e+07 1.466e+06
2009-12-31 price 210.7 620
volume 1.257e+07 1.22e+06
The unstack method is the inverse of stack:
>>> df.stack() >>> df.stack().unstack()
2009-12-28 AAPL 211.61 AAPL GOOG
GOOG 622.87 2009-12-28 211.6 622.9
2009-12-29 AAPL 209.1 2009-12-29 209.1 619.4
GOOG 619.4 2009-12-30 211.6 622.7
2009-12-30 AAPL 211.64 2009-12-31 210.7 620
GOOG 622.73
2009-12-31 AAPL 210.73
GOOG 619.98
These reshaping methods can be combined with built-in
DataFrame and Series method to select or aggregate data
at a level. Here we take the maximum among AAPL and GOOG
for each date / field pair:
>>> pivoted.stack(0)
AAPL GOOG
2009-12-28 price 211.6 622.9
volume 2.3e+07 1.698e+06
2009-12-29 price 209.1 619.4
volume 1.587e+07 1.425e+06
2009-12-30 price 211.6 622.7
volume 1.47e+07 1.466e+06
2009-12-31 price 210.7 620
volume 1.257e+07 1.22e+06
>>> pivoted.stack(0).max(1).unstack()
price volume
2009-12-28 622.9 2.3e+07
2009-12-29 619.4 1.587e+07
2009-12-30 622.7 1.47e+07
2009-12-31 620 1.257e+07
These kinds of aggregations are closely related to “group
by” operations which we discuss in the next section.
Group By: grouping and aggregating data
A very common operation in SQL-like languages and gen-
erally in statistical data analysis is to group data by some
identifiers and perform either an aggregation or transformation
of the data. For example, suppose we had a simple data set
like this:
>>> df
A B C D
0 foo one -1.834 1.903
1 bar one 1.772 -0.7472
2 foo two -0.67 -0.309
3 bar three 0.04931 0.3939
4 foo two -0.5215 1.861
5 bar two -3.202 0.9365
6 foo one 0.7927 1.256
7 foo three 0.1461 -2.655
We could compute group means using the Acolumn like
so:
>>> df.groupby(’A’).mean()
C D
bar -0.4602 0.1944
7
foo -0.4173 0.4112
The object returned by groupby is a special intermediate
object with a lot of nice features. For example, you can use
it to iterate through the portions of the data set corresponding
to each group:
>>> for key, group in df.groupby(’A’):
... print key
... print group
bar
A B C D
1 bar one 1.772 -0.7472
3 bar three 0.04931 0.3939
5 bar two -3.202 0.9365
foo
A B C D
0 foo one -1.834 1.903
2 foo two -0.67 -0.309
4 foo two -0.5215 1.861
6 foo one 0.7927 1.256
7 foo three 0.1461 -2.65
Grouping by multiple columns is also possible:
df.groupby([’A’, ’B’]).mean()
C D
bar one 1.772 -0.7472
three 0.04931 0.3939
two -3.202 0.9365
foo one -0.5205 1.579
three 0.1461 -2.655
two -0.5958 0.7762
The default result of a multi-key groupby aggregation
is a hierarchical index. This can be disabled when calling
groupby which may be useful in some settings:
df.groupby([’A’, ’B’], as_index=False).mean()
A B C D
0 bar one 1.772 -0.7472
1 bar three 0.04931 0.3939
2 bar two -3.202 0.9365
3 foo one -0.5205 1.579
4 foo three 0.1461 -2.655
5 foo two -0.5958 0.7762
In a completely general setting, groupby operations are
about mapping axis labels to buckets. In the above examples,
when we pass column names we are simply establishing a cor-
respondence between the row labels and the group identifiers.
There are other ways to do this; the most general is to pass a
Python function (for single-key) or list of functions (for multi-
key) which will be invoked on each each label, producing a
group specification:
>>> dat
ABCD
2000-01-03 0.6371 0.672 0.9173 1.674
2000-01-04 -0.8178 -1.865 -0.23 0.5411
2000-01-05 0.314 0.2931 -0.6444 -0.9973
2000-01-06 1.913 -0.5867 0.273 0.4631
2000-01-07 1.308 0.426 -1.306 0.04358
>>> mapping
{’A’: ’Group 1’, ’B’: ’Group 2’,
’C’: ’Group 1’, ’D’: ’Group 2’}
>>> for name, group in dat.groupby(mapping.get,
... axis=1):
... print name; print group
Group 1
A C
2000-01-03 0.6371 0.9173
2000-01-04 -0.8178 -0.23
2000-01-05 0.314 -0.6444
2000-01-06 1.913 0.273
2000-01-07 1.308 -1.306
Group 2
B D
2000-01-03 0.672 1.674
2000-01-04 -1.865 0.5411
2000-01-05 0.2931 -0.9973
2000-01-06 -0.5867 0.4631
2000-01-07 0.426 0.04358
Some creativity with grouping functions will enable the
user to perform quite sophisticated operations. The object re-
turned by groupby can either iterate, aggregate (with an
arbitrary function), transform (compute a modified same-
size version of each data group), or do a general apply-by-
group. While we do not have space to go into great detail with
examples of each of these, the apply function is interesting in
that it attempts to combine the results of the aggregation into
a pandas object. For example, we could group the df object
above by column A, select just the Ccolumn, and apply the
describe function to each subgroup like so:
>>> df.groupby(’A’)[’C’].describe().T
bar foo
count 3 5
mean -0.4602 -0.4173
std 2.526 0.9827
min -3.202 -1.834
10% -2.552 -1.368
50% 0.04931 -0.5215
90% 1.427 0.5341
max 1.772 0.7927
Note that, under the hood, calling describe generates
and passes a dynamic function to apply which invokes
describe on each group and glues the results together. We
transposed the result with .T to make it more readable.
Easy spreadsheet-style pivot tables
An obvious application combining groupby and reshaping
operations is creating pivot tables, a common way of sum-
marizing data in spreadsheet applications such as Microsoft
Excel. We’ll take a brief look at a tipping data set collected
from a restaurant ([Bryant]):
>>> tips.head()
sex smoker time day size tip_pct
1 Female No Dinner Sun 2 0.05945
2 Male No Dinner Sun 3 0.1605
3 Male No Dinner Sun 3 0.1666
4 Male No Dinner Sun 2 0.1398
5 Female No Dinner Sun 4 0.1468
The pivot_table function in pandas takes a set of
column names to group on the pivot table rows, another set to
group on the columns, and optionally an aggregation function
for each group (which defaults to mean):
>>> import numpy as np
>>> from pandas import pivot_table
>>> pivot_table(tips, ’tip_pct’, rows=[’time’, ’sex’],
cols=’smoker’)
smoker No Yes
time sex
Dinner Female 0.1568 0.1851
8
Male 0.1594 0.1489
Lunch Female 0.1571 0.1753
Male 0.1657 0.1667
Conveniently, the returned object is a DataFrame, so it can
be further reshaped and manipulated by the user:
>>> table = pivot_table(tips, ’tip_pct’,
rows=[’sex’, ’day’],
cols=’smoker’, aggfunc=len)
>>> table
smoker No Yes
sex day
Female Fri 2 7
Sat 13 15
Sun 14 4
Thur 25 7
Male Fri 2 8
Sat 32 27
Sun 43 15
Thur 20 10
>>> table.unstack(’sex’)
smoker No Yes
sex Female Male Female Male
day
Fri 2 2 7 8
Sat 13 32 15 27
Sun 14 43 4 15
Thur 25 20 7 10
For many users, this will be an attractive alternative to
dumping a data set into a spreadsheet for the sole purpose
of creating a pivot table.
>>> pivot_table(tips, ’size’,
rows=[’time’, ’sex’, ’smoker’],
cols=’day’, aggfunc=np.sum,
fill_value=0)
day Fri Sat Sun Thur
time sex smoker
Dinner Female No 2 30 43 2
Yes 8 33 10 0
Dinner Male No 4 85 124 0
Yes 12 71 39 0
Lunch Female No 3 0 0 60
Yes 6 0 0 17
Lunch Male No 0 0 0 50
Yes 5 0 0 23
Combining or joining data sets
Combining, joining, or merging related data sets is a quite
common operation. In doing so we are interested in associating
observations from one data set with another via a merge key
of some kind. For similarly-indexed 2D data, the row labels
serve as a natural key for the join function:
>>> df1 >>> df2
AAPL GOOG MSFT YHOO
2009-12-24 209 618.5 2009-12-24 31 16.72
2009-12-28 211.6 622.9 2009-12-28 31.17 16.88
2009-12-29 209.1 619.4 2009-12-29 31.39 16.92
2009-12-30 211.6 622.7 2009-12-30 30.96 16.98
2009-12-31 210.7 620
>>> df1.join(df2)
AAPL GOOG MSFT YHOO
2009-12-24 209 618.5 31 16.72
2009-12-28 211.6 622.9 31.17 16.88
2009-12-29 209.1 619.4 31.39 16.92
2009-12-30 211.6 622.7 30.96 16.98
2009-12-31 210.7 620 NaN NaN
One might be interested in joining on something other than
the index as well, such as the categorical data we presented
in an earlier section:
>>> data.join(cats, on=’item’)
country date industry item value
0 US 2009-12-28 TECH GOOG 622.9
1 US 2009-12-29 TECH GOOG 619.4
2 US 2009-12-30 TECH GOOG 622.7
3 US 2009-12-31 TECH GOOG 620
4 US 2009-12-28 TECH AAPL 211.6
5 US 2009-12-29 TECH AAPL 209.1
6 US 2009-12-30 TECH AAPL 211.6
7 US 2009-12-31 TECH AAPL 210.7
This is akin to a SQL join operation between two tables
or a VLOOKUP operation in a spreadsheet such as Excel. It
is possible to join on multiple keys, in which case the table
being joined is currently required to have a hierarchical index
corresponding to those keys. We will be working on more
joining and merging methods in a future release of pandas.
Performance and use for Large Data Sets
Using DataFrame objects over homogeneous NumPy arrays
for computation incurs overhead from a number of factors:
•Computational functions like sum,mean, and std have
been overridden to omit missing data
•Most of the axis Index data structures are reliant on the
Python dict for performing lookups and data alignment.
This also results in a slightly larger memory footprint as
the dict containing the label mapping is created once
and then stored.
•The internal BlockManager data structure consolidates
the data of each type (floating point, integer, boolean,
object) into 2-dimensional arrays. However, this is an
upfront cost that speeds up row-oriented computations
and data alignment later.
•Performing repeated lookups of values by label passes
through much more Python code than simple integer-
based lookups on ndarray objects.
The savvy user will learn what operations are not very
efficient in DataFrame and Series and fall back on working
directly with the underlying ndarray objects (accessible
via the values attribute) in such cases. What DataFrame
sacrifices in performance it makes up for in flexibility and
expressiveness.
With 64-bit integers representing timestamps, pandas in
fact provides some of the fastest data alignment routines for
differently-indexed time series to be found in open source soft-
ware. As working with large, irregularly time series requires
having a timestamp index, pandas is well-positioned to become
the gold standard for high performance open source time series
processing.
With regard to memory usage and large data sets, pandas
is currently only designed for use with in-memory data sets.
We would like to expand its capability to work with data
sets that do not fit into memory, perhaps transparently using
the multiprocessing module or a parallel computing
backend to orchestrate large scale computations.
9
pandas for R users
Given the “DataFrame” name and feature overlap with the [R]
project and its 3rd party packages, pandas will draw inevitable
comparisons with R. pandas brings a robust, full-featured, and
integrated data analysis toolset to Python while maintaining a
simple and easy-to-use API. As nearly all data manipulations
involving data.frame objects in R can be easily expressed
using the pandas DataFrame, it is relatively straightforward
in most cases to port R functions to Python. It would be
useful to provide a migration guide for R users as we have
not copied R’s naming conventions or syntax in most places,
rather naming based on common-sense and making the syntax
and API as “Pythonic” as possible.
R does not provide indexing functionality in nearly such a
deeply integrated way as pandas does. For example, operations
between data.frame objects will proceed in R without
regard to whether the labels match as long as they are the
same length and width. Some R packages, such as zoo and
xts provides indexed data structures with data alignment,
but they are largely specialized to ordered time series data.
Hierarchical indexing with constant-time subset selection is
another significant feature missing from R’s data structures.
Outside of the scope of this paper is a rigorous performance
comparison of R and pandas. In almost all of the benchmarks
we have run comparing R and pandas, pandas significantly
outperforms R.
Other features of note
There are many other features in pandas worth exploring for
the interested users:
•Time series functionality: date range generation, shifting
and lagging, frequency conversion and forward/backward
filling
•Integration with [matplotlib] to concisely generate plots
with metadata
•Moving window statistics (e.g. moving standard devia-
tion, exponentially weighted moving average) and moving
window linear and panel regression
•3-dimensional Panel data structure for manipulating
collections of DataFrame objects
•Sparse versions of the data structures
•Robust IO tools for reading and writing pandas objects to
flat files (delimited text, CSV, Excel) and HDF5 format
Related packages
A number of other Python packages have some degree of
feature overlap with pandas. Among these, la ([Larry]) is
the most similar, as it implements a labeled ndarray object
intending to closely mimic NumPy arrays. Since ndarray
is only applicable many problems in its homogeneous (non-
structured dtype) form, in pandas we have distanced our-
selves from ndarray to instead provide a more flexible,
(potentially) heterogeneous, size-mutable data structure. The
references include a some other packages of interest.
pandas will soon become a dependency of statsmodels
([StaM]), the main statistics and econometric library in Python,
to make statistical modeling and data analysis tools in Python
more cohesive and integrated. We plan to combine pandas
with a formula framework to make specifying statistical mod-
els easy and intuitive when working with a DataFrame of
data, for example.
Conclusions
We believe that in the coming years there will be great oppor-
tunity to attract users in need of statistical data analysis tools
to Python who might have previously chosen R, MATLAB,
or another research environment. By designing robust, easy-
to-use data structures that cohere with the rest of the scientific
Python stack, we can make Python a compelling choice for
data analysis applications. In our opinion, pandas provides
a solid foundation upon which a very powerful data analysis
ecosystem can be established.
REFERENCES
[pandas] W. McKinney, pandas: a python data analysis library,http:
//pandas.sourceforge.net
[scipy2010] W. McKinney, Data Structures for Statistical Computing in
Python Proceedings of the 9th Python in Science Conference,
http://http://conference.scipy.org/. 2010
[Larry] K. Goodman. la / larry: ndarray with labeled axes,http://larry.
sourceforge.net/
[SciTS] M. Knox, P. Gerard-Marchant, scikits.timeseries: python time
series analysis,http://pytseries.sourceforge.net/
[StaM] S. Seabold, J. Perktold, J. Taylor, statsmodels: statistical
modeling in Python,http://statsmodels.sourceforge.net
[SciL] D. Cournapeau, et al., scikit-learn: machine learning in
Python,http://scikit-learn.sourceforge.net
[PyMC] C. Fonnesbeck, A. Patil, D. Huard, PyMC: Markov Chain
Monte Carlo for Python,http://code.google.com/p/pymc/
[Tab] D. Yamins, E. Angelino, tabular: tabarray data structure for
2D data,http://parsemydata.com/tabular/
[NumPy] T. Oliphant, http://numpy.scipy.org
[SciPy] E. Jones, T. Oliphant, P. Peterson, http://scipy.org
[matplotlib] J. Hunter, et al., matplotlib: Python plotting,http://matplotlib.
sourceforge.net/
[EPD] Enthought, Inc., EPD: Enthought Python Distribution,http:
//www.enthought.com/products/epd.php
[Pythonxy] P. Raybaut, Python(x,y): Scientific-oriented Python distribu-
tion,http://www.pythonxy.com/
[CRAN] The R Project for Statistical Computing,http://cran.r-project.
org/
[Cython] G. Ewing, R. W. Bradshaw, S. Behnel, D. S. Seljebotn, et al.,
The Cython compiler,http://cython.org
[IPython] Fernando Pérez, Brian E. Granger, IPython: A System for
Interactive Scientific Computing, Computing in Science and
Engineering, vol. 9, no. 3, pp. 21-29, May/June 2007,
doi:10.1109/MCSE.2007.53. http://ipython.org
[Grun] Batalgi, Grunfeld data set,http://www.wiley.com/legacy/
wileychi/baltagi/
[nipy] J. Taylor, F. Perez, et al., nipy: Neuroimaging in Python,http:
//nipy.sourceforge.net
[pydataframe] A. Straw, F. Finkernagel, pydataframe,http://code.google.com/
p/pydataframe/
[R] R Development Core Team. 2010, R: A Language and Envi-
ronment for Statistical Computing,http://www.R-project.org
[MATLAB] The MathWorks Inc. 2010, MATLAB,http://www.mathworks.
com
[Stata] StatCorp. 2010, Stata Statistical Software: Release 11 http:
//www.stata.com
[SAS] SAS Institute Inc., SAS System,http://www.sas.com
[Bryant] Bryant, P. G. and Smith, M (1995) Practical Data Analysis:
Case Studies in Business Statistics. Homewood, IL: Richard
D. Irwin Publishing:
