19. Polars
In addition to what’s in Anaconda, this lecture will need the following libraries:
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19.1Overview¶
Polars is a fast data manipulation library for Python written in Rust.
It has gained significant popularity as a modern alternative to Pandas due to its performance advantages.
Polars is designed with performance and memory efficiency in mind, leveraging:
Apache Arrow columnar format for fast data access
Lazy evaluation to optimize query execution
Parallel processing to utilize all available CPU cores
An expressive API built around column expressions
Throughout the lecture, we will assume that the following imports have taken place
import polars as pl
import numpy as np
import matplotlib.pyplot as pltLike Pandas, Polars defines two important data types: Series and DataFrame.
You can think of a Series as a column of data, such as a collection of observations on a single variable.
A DataFrame is a two-dimensional object for storing related columns of data.
19.2Series¶
Let’s start with Series.
We begin by creating a series of four random observations
rng = np.random.default_rng()
s = pl.Series(name='daily returns', values=rng.standard_normal(4))
sPolars Series are built on top of Apache Arrow arrays and support many familiar operations
s * 100Absolute values are available as a method
s.abs()We can also get quick summary statistics
s.describe()Since Polars has no row index, labelled data requires a DataFrame.
For example, to associate ticker symbols with returns:
df = pl.DataFrame({
'company': ['AMZN', 'AAPL', 'MSFT', 'GOOG'],
'daily returns': rng.standard_normal(4)
})
dfWe access a value by filtering on a column expression
df.filter(
pl.col('company') == 'AMZN'
).select('daily returns').item()-1.1169442297867929Updates also use expressions rather than index assignment
df = df.with_columns(
pl.when(pl.col('company') == 'AMZN')
.then(0)
.otherwise(pl.col('daily returns'))
.alias('daily returns')
)
dfWe can also check membership
'AAPL' in df['company']True19.3DataFrames¶
While a Series is a single column of data, a DataFrame is several columns, one for each variable.
As in Pandas, let’s work with data from the Penn World Tables.
We read this in using pl.read_csv
url = 'https://github.com/QuantEcon/data-lectures/raw/main/lectures/test_pwt.csv'
df = pl.read_csv(url)
df19.3.1Selecting data¶
We can select rows by slicing and columns by name
df[2:5]To select specific columns, pass a list of names to select
df.select(['country', 'tcgdp'])These can be combined
df[2:5].select(['country', 'tcgdp'])19.3.2Filtering by conditions¶
The filter method accepts boolean expressions built from pl.col
df.filter(pl.col('POP') >= 20000)Multiple conditions can be combined with & (and) and | (or)
df.filter(
(pl.col('country').is_in(['Argentina', 'India', 'South Africa'])) &
(pl.col('POP') > 40000)
)Expressions can involve arithmetic across columns
df.filter(
(pl.col('cc') + pl.col('cg') >= 80) & (pl.col('POP') <= 20000)
)Select the country with the largest household consumption share
df.filter(pl.col('cc') == pl.col('cc').max())19.3.3Column expressions¶
A key difference from pandas is that Polars uses column expressions for transformations rather than element-wise apply calls.
Here is an example computing the max of each numeric column
df.select(
pl.col(['year', 'POP', 'XRAT', 'tcgdp', 'cc', 'cg'])
.max()
.name.suffix('_max')
)Expressions can be used inside with_columns to add or modify columns
df.with_columns(
(pl.col('XRAT') / 10).alias('XRAT_scaled'),
pl.col(pl.Float64).round(2)
)Conditional logic uses pl.when(...).then(...).otherwise(...)
df.with_columns(
pl.when(pl.col('POP') >= 20000)
.then(pl.col('POP'))
.otherwise(None)
.alias('POP_filtered')
).select(['country', 'POP', 'POP_filtered'])19.3.4Missing values¶
Let’s insert some null values to demonstrate imputation techniques
df_nulls = df.with_row_index().with_columns(
pl.when(pl.col('index') == 0)
.then(None).otherwise(pl.col('XRAT')).alias('XRAT'),
pl.when(pl.col('index') == 3)
.then(None).otherwise(pl.col('cc')).alias('cc'),
pl.when(pl.col('index') == 5)
.then(None).otherwise(pl.col('tcgdp')).alias('tcgdp'),
pl.when(pl.col('index') == 6)
.then(None).otherwise(pl.col('POP')).alias('POP'),
).drop('index')
df_nullsFill all nulls with zero
df_nulls.fill_null(0)Or fill with column means
cols = ['cc', 'tcgdp', 'POP', 'XRAT']
df_nulls.with_columns(
pl.col(cols).fill_null(pl.col(cols).mean())
)Polars also supports forward fill (fill_null(strategy='forward')) and interpolation.
There are more advanced imputation tools available in scikit-learn.
19.3.5Visualization¶
Let’s build a GDP per capita column and plot it
df = (df
.select(['country', 'POP', 'tcgdp'])
.rename({'POP': 'population', 'tcgdp': 'total GDP'})
.with_columns(
(pl.col('population') * 1e3).alias('population')
)
.with_columns(
(pl.col('total GDP') * 1e6 / pl.col('population'))
.alias('GDP percap')
)
.sort('GDP percap', descending=True)
)
dfWe can extract columns directly for matplotlib
fig, ax = plt.subplots()
ax.bar(df['country'].to_list(), df['GDP percap'].to_list())
ax.set_xlabel('country', fontsize=12)
ax.set_ylabel('GDP per capita', fontsize=12)
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()
19.4Lazy evaluation¶
One of Polars’ most powerful features is lazy evaluation.
Instead of executing each operation immediately, lazy mode collects the full query plan and optimizes it before running.
19.4.1Eager vs lazy¶
# Reload the dataset
url = 'https://github.com/QuantEcon/data-lectures/raw/main/lectures/test_pwt.csv'
df_full = pl.read_csv(url)The eager API executes immediately (like pandas)
result_eager = (df_full
.filter(pl.col('tcgdp') > 1000)
.select(['country', 'year', 'tcgdp'])
.sort('tcgdp', descending=True)
)
result_eager.head()The lazy API builds a query plan instead
lazy_query = (df_full.lazy()
.filter(pl.col('tcgdp') > 1000)
.select(['country', 'year', 'tcgdp'])
.sort('tcgdp', descending=True)
)
print(lazy_query.explain())SORT BY [descending: [true]] [col("tcgdp")]
FILTER col("tcgdp") > 1000.0
FROM
DF ["country", "country isocode", "year", "POP", ...]; PROJECT["country", "year", "tcgdp"] 3/8 COLUMNS
Call collect to execute the plan
result_lazy = lazy_query.collect()
result_lazy.head()19.4.2Query optimization¶
The lazy engine applies several optimizations automatically:
Predicate pushdown --- filters are applied as early as possible
Projection pushdown --- only required columns are read from the source
Common subexpression elimination --- duplicate calculations are merged
Let’s see how Polars rewrites a multi-step query
optimized = (df_full.lazy()
.select(['country', 'year', 'tcgdp', 'POP'])
.filter(pl.col('tcgdp') > 500)
.with_columns(
(pl.col('tcgdp') / pl.col('POP')).alias('gdp_per_capita')
)
.filter(pl.col('gdp_per_capita') > 10)
.select(['country', 'year', 'gdp_per_capita'])
)
print("Optimized plan:")
print(optimized.explain())Optimized plan:
FILTER col("gdp_per_capita") > 10.0
FROM
simple π 3/3 ["country", "year", ... 1 other column]
WITH_COLUMNS:
[(col("tcgdp") / col("POP")).alias("gdp_per_capita")]
FILTER col("tcgdp") > 500.0
FROM
DF ["country", "country isocode", "year", "POP", ...]; PROJECT["country", "year", "tcgdp", "POP"] 4/8 COLUMNS
Executing the plan gives us the final result
optimized.collect()19.4.3Performance comparison¶
Let’s compare pandas, Polars eager, and Polars lazy on the same task.
We start with a small dataset (the Penn World Tables we used above) to show that for small data the differences are negligible
import pandas as pd
import time
# Small dataset -- Penn World Tables (~8 rows)
url = 'https://github.com/QuantEcon/data-lectures/raw/main/lectures/test_pwt.csv'
small_pd = pd.read_csv(url)
small_pl = pl.read_csv(url)Now we time the same filter-select-sort operation in each library
# pandas
start = time.perf_counter()
_ = (small_pd
.query('tcgdp > 500')
[['country', 'year', 'tcgdp', 'POP']]
.assign(gdp_pc=lambda d: d['tcgdp'] / d['POP'])
.sort_values('gdp_pc', ascending=False))
pd_small = time.perf_counter() - start
# Polars eager
start = time.perf_counter()
_ = (small_pl
.filter(pl.col('tcgdp') > 500)
.select(['country', 'year', 'tcgdp', 'POP'])
.with_columns((pl.col('tcgdp') / pl.col('POP')).alias('gdp_pc'))
.sort('gdp_pc', descending=True))
pl_small = time.perf_counter() - start
print(f"Small data -- pandas: {pd_small:.4f}s | Polars eager: {pl_small:.4f}s")Small data -- pandas: 0.0073s | Polars eager: 0.0031s
On a handful of rows the speed difference is immaterial --- use whichever API you find more convenient.
Now let’s scale up to 5 million rows where the difference becomes clear.
The task is: filter rows where value > 0, compute a weighted product
value * weight, then take the mean of that product within each group ---
a grouped weighted average.
n = 5_000_000
rng = np.random.default_rng(42)
groups = rng.choice(['A', 'B', 'C', 'D'], n)
values = rng.standard_normal(n)
weights = rng.random(n)
extra1 = rng.standard_normal(n)
extra2 = rng.standard_normal(n)
big_pd = pd.DataFrame({
'group': groups, 'value': values,
'weight': weights, 'extra1': extra1, 'extra2': extra2
})
big_pl = pl.DataFrame({
'group': groups, 'value': values,
'weight': weights, 'extra1': extra1, 'extra2': extra2
})First, the pandas baseline
start = time.perf_counter()
tmp = big_pd[big_pd['value'] > 0][['group', 'value', 'weight']].copy()
tmp['weighted'] = tmp['value'] * tmp['weight']
_ = tmp.groupby('group')['weighted'].mean()
pd_time = time.perf_counter() - start
print(f"pandas: {pd_time:.4f}s")pandas: 0.5586s
Next, Polars in eager mode
start = time.perf_counter()
_ = (big_pl
.filter(pl.col('value') > 0)
.select(['group', 'value', 'weight'])
.with_columns(
(pl.col('value') * pl.col('weight')).alias('weighted'))
.group_by('group')
.agg(pl.col('weighted').mean()))
eager_time = time.perf_counter() - start
print(f"Polars eager: {eager_time:.4f}s")Polars eager: 0.0865s
And finally, Polars in lazy mode
start = time.perf_counter()
_ = (big_pl.lazy()
.filter(pl.col('value') > 0)
.select(['group', 'value', 'weight'])
.with_columns(
(pl.col('value') * pl.col('weight')).alias('weighted'))
.group_by('group')
.agg(pl.col('weighted').mean())
.collect())
lazy_time = time.perf_counter() - start
print(f"Polars lazy: {lazy_time:.4f}s")Polars lazy: 0.0477s
The take-away:
For small data (thousands of rows), pandas and Polars perform similarly --- choose based on API preference and ecosystem fit.
For medium to large data (hundreds of thousands of rows and above), Polars can be significantly faster thanks to its Rust engine, parallel execution, and (in lazy mode) query optimization.
The lazy API is particularly powerful when reading from disk --- scan_csv returns a LazyFrame directly, so filters and projections are pushed down to the file reader.
19.5On-line data sources¶
As in Pandas, Python makes it straightforward to query online databases.
An important database for economists is FRED --- a vast collection of time series data maintained by the St. Louis Fed.
Polars’ read_csv can fetch data from a URL directly.
We use try_parse_dates=True to parse the date column automatically
fred_url = ('https://fred.stlouisfed.org/graph/fredgraph.csv?'
'bgcolor=%23e1e9f0&chart_type=line&drp=0&'
'fo=open%20sans&graph_bgcolor=%23ffffff&'
'height=450&mode=fred&recession_bars=on&'
'txtcolor=%23444444&ts=12&tts=12&width=1318&'
'nt=0&thu=0&trc=0&show_legend=yes&'
'show_axis_titles=yes&show_tooltip=yes&'
'id=UNRATE&scale=left&cosd=1948-01-01&'
'coed=2024-06-01&line_color=%234572a7&'
'link_values=false&line_style=solid&'
'mark_type=none&mw=3&lw=2&ost=-99999&'
'oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&'
'fgst=lin&fgsnd=2020-02-01&line_index=1&'
'transformation=lin&vintage_date=2024-07-29&'
'revision_date=2024-07-29&nd=1948-01-01')
data = pl.read_csv(fred_url, try_parse_dates=True)---------------------------------------------------------------------------
TimeoutError Traceback (most recent call last)
Cell In[39], line 16
12 'oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&'
13 'fgst=lin&fgsnd=2020-02-01&line_index=1&'
14 'transformation=lin&vintage_date=2024-07-29&'
15 'revision_date=2024-07-29&nd=1948-01-01')
---> 16 data = pl.read_csv(fred_url, try_parse_dates=True)
File /opt/hostedtoolcache/Python/3.12.16/x64/lib/python3.12/site-packages/polars/_utils/expired.py:114, in removed_parameters.<locals>.decorate.<locals>.wrapper(*args, **kwargs)
108 if name in params_dict:
109 _raise_removed_argument_error(
110 params_dict[name],
111 func_name=function.__qualname__,
112 kwargs=kwargs,
113 )
--> 114 return function(*args, **kwargs)
File /opt/hostedtoolcache/Python/3.12.16/x64/lib/python3.12/site-packages/polars/io/csv/functions.py:530, in read_csv(***failed resolving arguments***)
527 name, offset = row_index
528 lf = lf.with_row_index(name, offset)
--> 530 return lf._collect_eager()
File /opt/hostedtoolcache/Python/3.12.16/x64/lib/python3.12/site-packages/polars/lazyframe/frame.py:1949, in LazyFrame._collect_eager(self, optimizations)
1945 def _collect_eager(
1946 self, *, optimizations: QueryOptFlags = DEFAULT_QUERY_OPT_FLAGS
1947 ) -> DataFrame:
1948 """Collect an internal eager operation locally."""
-> 1949 return _eager_engine().collect(
1950 self, optimizations=optimizations, background=False
1951 )
File /opt/hostedtoolcache/Python/3.12.16/x64/lib/python3.12/site-packages/polars/lazyframe/engine.py:410, in _LocalEngine.collect(self, lf, optimizations, background, post_opt_callback)
408 if post_opt_callback is not None:
409 callback = post_opt_callback
--> 410 return wrap_df(ldf.collect(self.name, callback))
TimeoutError: object-store error: Generic HTTP error: Error performing HEAD https://fred.stlouisfed.org/graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1318&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=UNRATE&scale=left&cosd=1948-01-01&coed=2024-06-01&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&fgst=lin&fgsnd=2020-02-01&line_index=1&transformation=lin&vintage_date=2024-07-29&revision_date=2024-07-29&nd=1948-01-01 in 184.31999042s, after 5 retries, max_retries: 10, retry_timeout: 180s - HTTP error: error sending request (location: graph/fredgraph.csv?bgcolor=%23e1e9f0&chart_type=line&drp=0&fo=open%20sans&graph_bgcolor=%23ffffff&height=450&mode=fred&recession_bars=on&txtcolor=%23444444&ts=12&tts=12&width=1318&nt=0&thu=0&trc=0&show_legend=yes&show_axis_titles=yes&show_tooltip=yes&id=UNRATE&scale=left&cosd=1948-01-01&coed=2024-06-01&line_color=%234572a7&link_values=false&line_style=solid&mark_type=none&mw=3&lw=2&ost=-99999&oet=99999&mma=0&fml=a&fq=Monthly&fam=avg&fgst=lin&fgsnd=2020-02-01&line_index=1&transformation=lin&vintage_date=2024-07-29&revision_date=2024-07-29&nd=1948-01-01) (path: https://fred.stlouisfed.org)
Caused by:
0: client error (SendRequest)
1: connection error
2: Connection timed out (os error 110)Let’s inspect the first few rows
data.head()And get summary statistics
data.describe()Plot the unemployment rate from 2006 to 2012
filtered = data.filter(
(pl.col('observation_date') >= pl.date(2006, 1, 1)) &
(pl.col('observation_date') <= pl.date(2012, 12, 31))
)
fig, ax = plt.subplots()
ax.plot(filtered['observation_date'].to_list(),
filtered['UNRATE'].to_list())
ax.set_title('US Unemployment Rate')
ax.set_xlabel('year', fontsize=12)
ax.set_ylabel('%', fontsize=12)
plt.show()Polars supports many file formats including Excel, JSON, Parquet, and direct database connections.
19.6Exercises¶
Solution to Exercise 1
Calculate percentage changes using Polars expressions:
price_change = ticker.select([
((pl.col(tick).drop_nulls().last() / pl.col(tick).drop_nulls().first() - 1) * 100)
.alias(tick)
for tick in ticker_list.keys()
]).transpose(
include_header=True,
header_name='ticker',
column_names=['pct_change']
).with_columns(
pl.col('ticker')
.replace_strict(ticker_list, default=pl.col('ticker'))
.alias('company')
).sort('pct_change')
print(price_change)Plot the results using matplotlib directly:
companies = price_change['company'].to_list()
changes = price_change['pct_change'].to_list()
colors = ['red' if x < 0 else 'blue' for x in changes]
fig, ax = plt.subplots(figsize=(10, 8))
ax.bar(companies, changes, color=colors)
ax.set_xlabel('stock', fontsize=12)
ax.set_ylabel('percentage change in price', fontsize=12)
plt.xticks(rotation=45, ha='right')
plt.tight_layout()
plt.show()Using read_data_polars from Exercise 1, obtain year-on-year percentage change for these indices:
indices_list = {'^GSPC': 'S&P 500',
'^IXIC': 'NASDAQ',
'^DJI': 'Dow Jones',
'^N225': 'Nikkei'}Plot the result as a time series graph.
Solution to Exercise 2
indices_data = read_data_polars(
indices_list,
start=dt.datetime(1971, 1, 1),
end=dt.datetime(2021, 12, 31)
)
indices_data = indices_data.with_columns(
pl.col('Date').dt.year().alias('year')
)Calculate yearly returns using group-by operations:
yearly_returns = indices_data.group_by('year').agg([
*[pl.col(idx).drop_nulls().first().alias(f'{idx}_first')
for idx in indices_list],
*[pl.col(idx).drop_nulls().last().alias(f'{idx}_last')
for idx in indices_list]
])
for idx, name in indices_list.items():
yearly_returns = yearly_returns.with_columns(
((pl.col(f'{idx}_last') - pl.col(f'{idx}_first'))
/ pl.col(f'{idx}_first') * 100).alias(name)
)
yearly_returns = (yearly_returns
.select(['year', *indices_list.values()])
.sort('year')
)
print(yearly_returns)Summary statistics:
yearly_returns.select(list(indices_list.values())).describe()Plot each index in a subplot:
fig, axes = plt.subplots(2, 2, figsize=(12, 10))
years = yearly_returns['year'].to_list()
for iter_, ax in enumerate(axes.flatten()):
name = list(indices_list.values())[iter_]
values = yearly_returns[name].to_list()
ax.plot(years, values, 'o-', linewidth=2, markersize=4)
ax.axhline(y=0, color='k', linestyle='--', alpha=0.3)
ax.set_ylabel('yearly return (%)', fontsize=12)
ax.set_xlabel('year', fontsize=12)
ax.set_title(name, fontsize=12)
plt.tight_layout()
plt.show()