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data_algebra is a piped data wrangling system based on Codd's relational algebra and experience working with data manipulation languages at scale. The primary purpose of the package is to support an easy to compose and maintain grammar of data processing steps that in turn can be used to generate database specific SQL. The package also implements the same transforms for Pandas DataFrames.

A good introduction can be found here, and numerous examples are catalogued here. Additional documentation is here.

Currently the system is primarily adapted and testing for Pandas, Google BigQuery, PostgreSQL, SQLite, and Spark. Porting and extension is designed to be easy.

This is to be the Python equivalent of the R packages rquery, rqdatatable, and cdata. This package supplies piped Codd-transform style notation that can perform data engineering in Pandas and generate SQL queries from the same specification.


Install data_algebra with pip install data_algebra


This article introduces the data_algebra project: a data processing tool family available in R and Python. These tools are designed to transform data either in-memory or on remote databases. For an example (with video) of using data_algebra to re-arrange data layout please see here.

In particular, we will discuss the Python implementation (also called data_algebra) and its relation to the mature R implementations (rquery and rqdatatable).


The project intent is to realize a method chained data processing language based on Codd's relational operators that is easy to maintain, has helpful tooling, and has very similar realizations (or dialects) for:

  • SQL databases accessed from Python, useful working at scale with PostgreSQL or Apache Spark (Spark example here).
  • Pandas DataFrame objects in Python.
  • SQL databases access from R (implementation is here, and is mature and ready for production use).

The intent is the notation should look idiomatic in each language. Working in Python should feel like working in Python, and working in R should feel like working in R. The data semantics, however, are designed to be close to the SQL realizations (given the close connection of SQL to the relational algebra; in particular row numbering starts at 1 and row and column order is not preserved except at row-order steps or select-columns steps respectively). The intent is: it should be very easy to use the system in either Python or R (a boon to multi-language data science projects) and it is easy to port either code or experience from one system to another (a boon for porting projects, or for data scientists working with more than one code base or computer language).

Related work includes:

The data_algebra principles include:

  • Writing data transforms as a pipeline or method-chain of many simple transform steps.
  • Treating data transform pipelines or directed acyclic graphs (DAGs) as themselves being sharable data.
  • Being able to use the same transform specification many places (in memory, on databases, in R, in Python).

The data_algebra supplies two primary services:

  • Building composite data processing pipelines (which we demonstrate in this note).
  • Building record transforms (which we demonstrate here).


Let's start with a pipeline example in Python (for a record transform example, please see here).

For our example we will assume we have a data set of how many points different subjects score in a psychological survey. The goal is transform the data so that we see what fraction of the subjects answers are in each category (subject to an exponential transform, as often used in logistic regression). We then treat the per-subject renormalized data as a probability or diagnosis.

The exact meaning of such a scoring method are not the topic of this note. It is a notional example to show a non-trivial data transformation need. In particular: having to normalize per-subject (divide some set of scores per-subject by a per-subject total) is a classic pain point in data-processing. In classic SQL this can only be done by joining against a summary table, or in more modern SQL with a "window function." We want to show by working in small enough steps this can be done simply.

Set up

Let's start our Python example. First we import the packages we are going to use, and set a few options.

import pandas
from data_algebra.data_ops import *  #
import data_algebra.BigQuery


Now let's type in our example data. Notice this is an in-memory Pandas Data.Frame.

d_local = pandas.DataFrame({
    'subjectID':[1, 1, 2, 2],
    'surveyCategory': [ "withdrawal behavior", "positive re-framing", "withdrawal behavior", "positive re-framing"],
    'assessmentTotal': [5., 2., 3., 4.],
    'irrelevantCol1': ['irrel1']*4,
    'irrelevantCol2': ['irrel2']*4,

subjectID surveyCategory assessmentTotal irrelevantCol1 irrelevantCol2
0 1 withdrawal behavior 5.0 irrel1 irrel2
1 1 positive re-framing 2.0 irrel1 irrel2
2 2 withdrawal behavior 3.0 irrel1 irrel2
3 2 positive re-framing 4.0 irrel1 irrel2

Let's also copy this data to a database. Normally big data is already in the system one wants to work with, so the copying over is just to simulate the data already being there.

db_handle = data_algebra.BigQuery.example_handle()

BigQuery_DBHandle(db_model=BigQueryModel, conn=< object at 0x7fa6a0a4da30>)
remote_table_desciption = db_handle.insert_table(

subjectID surveyCategory assessmentTotal irrelevantCol1 irrelevantCol2
0 1 withdrawal behavior 5.0 irrel1 irrel2
1 1 positive re-framing 2.0 irrel1 irrel2
2 2 withdrawal behavior 3.0 irrel1 irrel2
3 2 positive re-framing 4.0 irrel1 irrel2

Normally one does not read data back from a database, but instead materializes results in the database with SQL commands such as CREATE TABLE tablename AS SELECT .... Also note: case in columns is a bit of nightmare. It is often best to lower-case them all.

Back to the data_algebra

Now we continue our example by importing the data_algebra components we need.

Now we use the data_algebra to define our processing pipeline: ops. We are writing this pipeline using a method chaining notation where we have placed Python method-dot at the end of lines using the .\ notation. This notation will look very much like a pipe to R/magrittr users.

scale = 0.237

ops = (
    data_algebra.data_ops.describe_table(d_local, 'd')
        .extend({'probability': f'(assessmentTotal * {scale}).exp()'})
        .extend({'total': 'probability.sum()'},
        .extend({'probability': 'probability / total'})
        .extend({'row_number': '(1).cumsum()'},
        .select_rows('row_number == 1')
        .select_columns(['subjectID', 'surveyCategory', 'probability'])
        .rename_columns({'diagnosis': 'surveyCategory'})

We are deliberately writing a longer pipeline of simple steps, so we can use the same pipeline locally with Pandas, and (potentially) great scale with PostgreSQL or Apache Spark. A more concise variation of this pipeline can be found in the R example here.

The intent is: the user can build up very sophisticated processing pipelines using a small number of primitive steps. The pipelines tend to be long, but can still be very efficient- as they are well suited for use with Pandas and with SQL query optimizers. Most of the heavy lifting is performed by the very powerful "window functions" (triggered by use of partition_by and order_by) available on the extend() step. Multiple statements can be combined into extend steps, but only when they have the same window-structure, and don't create and use the same value name in the same statement (except for replacement, which is shown in this example). Many conditions are checked and enforced during pipeline construction, making debugging very easy.

For a more Pythonic way of writing the same pipeline we can show how the code would have been formatted by black.

py_source = ops.to_python(pretty=True)

    .extend({"probability": "(assessmentTotal * 0.237).exp()"})
    .extend({"total": "probability.sum()"}, partition_by=["subjectID"])
    .extend({"probability": "probability / total"})
        {"row_number": "(1).cumsum()"},
    .select_rows("row_number == 1")
    .select_columns(["subjectID", "surveyCategory", "probability"])
    .rename_columns({"diagnosis": "surveyCategory"})

In either case, the pipeline is read as a sequence of operations (top to bottom, and left to right). What it is saying is:

  • We start with a table named "d" that is known to have columns "subjectID", "surveyCategory", "assessmentTotal", "irrelevantCol1", and "irrelevantCol2".

  • We produce a new table by transforming this table through a sequence of "extend" operations which add new columns.

    • The first extend computes probability = exp(scale*assessmentTotal), this is similar to the inverse-link step of a logistic regression. We assume when writing this pipeline we were given this math as a requirement.
    • The next few extend steps total the probability per-subject (this is controlled by the partition_by argument) and then rank the normalized probabilities per-subject (grouping again specified by the partition_by argument, and order controlled by the order_by clause).
  • We then select the per-subject top-ranked rows by the select_rows step.

  • And finally we clean up the results for presentation with the select_columns, rename_columns, and order_rows steps. The names of these methods are intended to evoke what they do.

The point is: each step is deliberately so trivial one can reason about it. However the many steps in sequence do quite a lot.


Once we have the ops object we can do quite a lot with it. We have already exhibited the pretty-printing of the pipeline. Next we demonstrate translating the operator pipeline into SQL.

sql = db_handle.to_sql(ops)

-- data_algebra SQL
--  dialect: BigQueryModel
--       string quote: "
--   identifier quote: `
 `table_reference_0` AS (
   `surveyCategory` ,
   `subjectID` ,
 `extend_1` AS (
  SELECT  -- .extend({ 'probability': '(assessmentTotal * 0.237).exp()'})
   `surveyCategory` ,
   `subjectID` ,
   EXP(`assessmentTotal` * 0.237) AS `probability`
 `extend_2` AS (
  SELECT  -- .extend({ 'total': 'probability.sum()'}, partition_by=['subjectID'])
   `surveyCategory` ,
   `subjectID` ,
   `probability` ,
   SUM(`probability`) OVER ( PARTITION BY `subjectID`  )  AS `total`
 `extend_3` AS (
  SELECT  -- .extend({ 'probability': 'probability / total'})
   `probability` / `total` AS `probability` ,
   `surveyCategory` ,
 `extend_4` AS (
  SELECT  -- .extend({ 'row_number': '(1).cumsum()'}, partition_by=['subjectID'], order_by=['probability'], reverse=['probability'])
   `probability` ,
   `surveyCategory` ,
   `subjectID` ,
   SUM(1) OVER ( PARTITION BY `subjectID` ORDER BY `probability` DESC  )  AS `row_number`
 `select_rows_5` AS (
  SELECT  -- .select_rows('row_number == 1')
   `probability` ,
   `surveyCategory` ,
   `row_number` = 1
SELECT  -- .rename_columns({'diagnosis': 'surveyCategory'})
 `surveyCategory` AS `diagnosis` ,
 `probability` ,

Older SQL (with use of with or common table expressions) can be hard to read, as SQL expresses composition by inner-nesting (inside SELECT statements happen first). The operator pipeline expresses composition by sequencing or method-chaining, which can be a lot more legible. In this example we use the SQL-99 common table expression (WITH) notation to manage the composition in a more legible manner. A huge advantage of the SQL is: we can send it to the database for execution, as we do now.

Also notice the generated SQL has applied query narrowing: columns not used in the outer queries are removed from the inner queries. The "irrelevant" columns are not carried into the calculation as they would be with a SELECT *. This early optimization comes in quite handy.

diagnosis probability subjectID
0 positive re-framing 0.558974 2
1 withdrawal behavior 0.670622 1

What comes back is: one row per subject, with the highest per-subject diagnosis and the estimated probability. Again, the math of this is outside the scope of this note (think of that as something coming from a specification)- the ability to write such a pipeline is our actual topic.

The hope is that the data_algebra pipeline is easier to read, write, and maintain than the SQL query. If we wanted to change the calculation we would just add a stage to the data_algebra pipeline and then regenerate the SQL query.


An advantage of the pipeline is it can also be directly used on Pandas DataFrames. Let's see how that is achieved.

ops.eval({'d': d_local})
subjectID diagnosis probability
0 1 withdrawal behavior 0.670622
1 2 positive re-framing 0.558974

There is also a shorthand notation for single table source pipelines:

subjectID diagnosis probability
0 1 withdrawal behavior 0.670622
1 2 positive re-framing 0.558974

eval takes a dictionary of Pandas DataFrames (names matching names specified in the pipeline) and returns the result of applying the pipeline to the data using Pandas commands. Currently our Pandas implementation only allows very simple window functions. This is why we didn't write probability = probability/sum(probability), but instead broken the calculation into multiple steps by introducing the total column (the SQL realization does in fact support more complex window functions). This is a small issue with the grammar: but our feeling encourage simple steps is in fact a good thing (improves debuggability), and in SQL the query optimizers likely optimize the different query styles into very similar realizations anyway.


Because our operator pipeline is a Python object with no references to external objects (such as the database connection), it can be saved through standard methods such as "pickling."

Advantages of data_algebra

A data_algebra operator pipeline carries around usable knowledge of the data transform.

For example:

# report all source table columns used by the query
{'d': {'assessmentTotal', 'subjectID', 'surveyCategory'}}
# what columns does this operation produce?
['subjectID', 'diagnosis', 'probability']


The data_algebra is part of a powerful cross-language and mutli-implementaiton family data manipulation tools. These tools can greatly reduce the development and maintenance cost of data science projects, while improving the documentation of project intent.

Win Vector LLC is looking for sponsors and partners to further the package. In particular if your group is using both R and Python in big-data projects (where SQL is a need, including Apache Spark), or are porting a project from one of these languages to another- please get in touch.

# be neat

Note: as with SQL the data_algebra assumes the processing pipeline is a DAG with only table-nodes used more than once.


Codd method-chained SQL generator and Pandas data processing in Python.





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