Python数据分析

- PolarsBook中文版: https://www.pythondataanalysis.com/docs/polars_book_cn/
- Polars快速入门: https://www.pythondataanalysis.com/docs/polars_book_cn/quickstart/
- Polars表达式: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/
- Polars表达式: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/expressions/
- Polars上下文: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/contexts/
- Polars分组: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/groupby/
- Polars折叠: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/folds/
- Polars自定义函数: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/custom_functions/
- Polars实例: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/introduction_polars/
- Polars表达式方法: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/api/
- Polars视频介绍: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/video_intro/
- Polars与Numpy交互: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/numpy/
- Polars窗口函数: https://www.pythondataanalysis.com/docs/polars_book_cn/dsl/window_functions/
- Polars索引: https://www.pythondataanalysis.com/docs/polars_book_cn/indexing/
- Polars数据类型: https://www.pythondataanalysis.com/docs/polars_book_cn/datatypes/
- 来自Pandas: https://www.pythondataanalysis.com/docs/polars_book_cn/coming_from_pandas/
- 来自ApacheSpark: https://www.pythondataanalysis.com/docs/polars_book_cn/coming_from_spark/
- Polars性能: https://www.pythondataanalysis.com/docs/polars_book_cn/performance/
- 字符串: https://www.pythondataanalysis.com/docs/polars_book_cn/performance/strings/
- Polars优化: https://www.pythondataanalysis.com/docs/polars_book_cn/optimizations/
- Polars惰性方法: https://www.pythondataanalysis.com/docs/polars_book_cn/optimizations/lazy/
- 谓词下推: https://www.pythondataanalysis.com/docs/polars_book_cn/optimizations/lazy/predicate-pushdown/
- 投影下推: https://www.pythondataanalysis.com/docs/polars_book_cn/optimizations/lazy/projection-pushdown/
- 其它优化: https://www.pythondataanalysis.com/docs/polars_book_cn/optimizations/lazy/other-optimizations/
- Polars参考指南: https://www.pythondataanalysis.com/docs/polars_book_cn/references/
- Polars时间序列: https://www.pythondataanalysis.com/docs/polars_book_cn/timeseries/
- Polars时间序列实例: https://www.pythondataanalysis.com/docs/polars_book_cn/timeseries/time-series/
- Polars使用范围: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/
- IO: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/
- Polars操作CSV文件: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/csv/
- Polars操作Parquet文件: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/parquet/
- Polars处理多个文件: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/multiple_files/
- Polars读取数据库: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/read_db/
- Polars与AWS交互: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/aws/
- Polars与Google BigQuery交互: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/google-big-query/
- Polars与Postgres交互: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/io/postgres/
- 互通性: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/interop/
- Arrow: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/interop/arrow/
- Numpy: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/interop/numpy/
- 数据: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/data/
- 字符串: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/data/strings/
- 时间戳: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/data/timestamps/
- 数据帧: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/
- 选中行或列: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/row_col_selection/
- 常用操作: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/common-manipulations/
- 聚合: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/aggregate/
- 分组: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/groupby/
- 过滤: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/filter/
- 连接: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/join/
- 重塑: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/melt/
- 条件应用: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/conditionally-apply/
- 排序: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/sorting/
- 透视: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/df/pivot/
- 应用: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/apply/
- Polars自定义函数: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/apply/udfs/
- Polars窗口函数: https://www.pythondataanalysis.com/docs/polars_book_cn/howcani/apply/window-functions/
- Python数据分析 第二版: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/
- 第 1 章 准备工作: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-01/
- 第 2 章 Python 语法基础: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-02/
- 第 3 章 Python 的数据结构、函数和文件: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-03/
- 第 4 章 NumPy 基础：数组和向量计算: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-04/
- 第 5 章 Pandas 入门: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-05/
- 第 6 章 数据加载、存储与文件格式: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-06/
- 第 7 章 数据清洗和准备: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-07/
- 第 10 章 数据聚合与分组运算: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-10/
- 第 11 章 时间序列: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-11/
- 第 12 章 pandas 高级应用: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-12/
- 第 13 章 Python 建模库介绍: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-13/
-  第 14 章 数据分析案例: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-14/
-  附录 A NumPy 高级应用: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Appendix-A/
-  附录 B 更多关于 IPython 的内容: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Appendix-B/
- 第 8 章 数据规整：聚合、合并和重塑: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-08/
- 第 9 章 绘图和可视化: https://www.pythondataanalysis.com/docs/Python_Data_Analysis_2nd_Editon/Chapter-09/
- Polars用户指南: https://www.pythondataanalysis.com/docs/Polars_user_guide/
- Polars入门: https://www.pythondataanalysis.com/docs/Polars_user_guide/polars_getting_started/
- 安装Polars: https://www.pythondataanalysis.com/docs/Polars_user_guide/polars_installation/
- Polars核心概念: https://www.pythondataanalysis.com/docs/Polars_user_guide/concepts/
- Polars数据类型和结构: https://www.pythondataanalysis.com/docs/Polars_user_guide/concepts/data-types-and-structures/
- Polars表达式和上下文: https://www.pythondataanalysis.com/docs/Polars_user_guide/concepts/expressions-and-contexts/
- Polars延迟API: https://www.pythondataanalysis.com/docs/Polars_user_guide/concepts/lazy-api/
- Streaming: https://www.pythondataanalysis.com/docs/Polars_user_guide/concepts/_streaming/
- Polars表达式: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/
- Polars基本操作: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/basic-operations/
- Aggregation: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/aggregation/
- Casting: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/casting/
- Categorical Data and Enums: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/categorical-data-and-enums/
- Expression Expansion: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/expression-expansion/
- Folds: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/folds/
- Lists and Arrays: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/lists-and-arrays/
- Missing Data: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/missing-data/
- Numpy Functions: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/numpy-functions/
- Strings: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/strings/
- Structs: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/structs/
- User Defined Python Functions: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/user-defined-python-functions/
- Window Functions: https://www.pythondataanalysis.com/docs/Polars_user_guide/expressions/window-functions/
- Reference: https://www.pythondataanalysis.com/docs/Polars_user_guide/api/reference/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/development/contributing/
- Versioning: https://www.pythondataanalysis.com/docs/Polars_user_guide/development/versioning/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/polars-cloud/
- Ecosystem: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/ecosystem/
- Gpu Support: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/gpu-support/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/io/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/lazy/
- Pandas: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/migration/pandas/
- Spark: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/migration/spark/
- Arrow: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/arrow/
- Comparison: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/comparison/
- Multiprocessing: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/multiprocessing/
- Polars Llms: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/polars_llms/
- Styling: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/styling/
- Visualization: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/misc/visualization/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/plugins/
- Create: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/sql/create/
- Cte: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/sql/cte/
- Intro: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/sql/intro/
- Select: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/sql/select/
- Show: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/sql/show/
- Index: https://www.pythondataanalysis.com/docs/Polars_user_guide/user-guide/transformations/

# Folds

Polars provides many expressions to perform computations across columns, like `sum_horizontal`,
`mean_horizontal`, and `min_horizontal`. However, these are just special cases of a general
algorithm called a fold, and Polars provides a general mechanism for you to compute custom folds for
when the specialised versions of Polars are not enough.

Folds computed with the function `fold` operate on the full columns for maximum speed. They utilize
the data layout very efficiently and often have vectorized execution.

## Basic example

As a first example, we will reimplement `sum_horizontal` with the function `fold`:

{{code_block('user-guide/expressions/folds','mansum',['fold'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:mansum"
```

The function `fold` expects a function `f` as the parameter `function` and `f` should accept two
arguments. The first argument is the accumulated result, which we initialise as zero, and the second
argument takes the successive values of the expressions listed in the parameter `exprs`. In our
case, they're the two columns “a” and “b”.

The snippet below includes a third explicit expression that represents what the function `fold` is
doing above:

{{code_block('user-guide/expressions/folds','mansum-explicit',['fold'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:mansum-explicit"
```

??? tip "`fold` in Python"

    Most programming languages include a higher-order function that implements the algorithm that the function `fold` in Polars implements.
    The Polars `fold` is very similar to Python's `functools.reduce`.
    You can [learn more about the power of `functools.reduce` in this article](http://mathspp.com/blog/pydonts/the-power-of-reduce).

## The initial value `acc`

The initial value chosen for the accumulator `acc` is typically, but not always, the
[identity element](https://en.wikipedia.org/wiki/Identity_element) of the operation you want to
apply. For example, if we wanted to multiply across the columns, we would not get the correct result
if our accumulator was set to zero:

{{code_block('user-guide/expressions/folds','manprod',['fold'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:manprod"
```

To fix this, the accumulator `acc` should be set to `1`:

{{code_block('user-guide/expressions/folds','manprod-fixed',['fold'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:manprod-fixed"
```

## Conditional

In the case where you'd want to apply a condition/predicate across all columns in a dataframe, a
fold can be a very concise way to express this.

{{code_block('user-guide/expressions/folds','conditional',['fold'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:conditional"
```

The snippet above filters all rows where all columns are greater than 1.

## Folds and string data

Folds could be used to concatenate string data. However, due to the materialization of intermediate
columns, this operation will have squared complexity.

Therefore, we recommend using the function `concat_str` for this:

{{code_block('user-guide/expressions/folds','string',['concat_str'])}}

```python exec="on" result="text" session="user-guide/folds"
--8<-- "python/user-guide/expressions/folds.py:string"
```