# Enhancing Performance¶

## Cython (Writing C extensions for pandas)¶

For many use cases writing pandas in pure python and numpy is sufficient. In some computationally heavy applications however, it can be possible to achieve sizeable speed-ups by offloading work to cython.

This tutorial assumes you have refactored as much as possible in python, for example trying to remove for loops and making use of numpy vectorization, it’s always worth optimising in python first.

This tutorial walks through a “typical” process of cythonizing a slow computation. We use an example from the cython documentation but in the context of pandas. Our final cythonized solution is around 100 times faster than the pure python.

### Pure python¶

We have a DataFrame to which we want to apply a function row-wise.

```
In [1]: df = DataFrame({'a': randn(1000), 'b': randn(1000),'N': randint(100, 1000, (1000)), 'x': 'x'})
In [2]: df
N a b x
0 585 0.469112 -0.218470 x
1 841 -0.282863 -0.061645 x
2 251 -1.509059 -0.723780 x
3 972 -1.135632 0.551225 x
4 181 1.212112 -0.497767 x
5 458 -0.173215 0.837519 x
6 159 0.119209 1.103245 x
7 650 -1.044236 -1.118384 x
8 389 -0.861849 -0.542980 x
9 772 -2.104569 -0.994002 x
10 174 -0.494929 1.508742 x
11 394 1.071804 -0.328697 x
12 199 0.721555 -0.562235 x
13 318 -0.706771 0.001596 x
14 281 -1.039575 0.077546 x
... ... ... ..
[1000 rows x 4 columns]
```

Here’s the function in pure python:

```
In [3]: def f(x):
...: return x * (x - 1)
...:
In [4]: def integrate_f(a, b, N):
...: s = 0
...: dx = (b - a) / N
...: for i in range(N):
...: s += f(a + i * dx)
...: return s * dx
...:
```

We achieve our result by by using `apply` (row-wise):

```
In [5]: %timeit df.apply(lambda x: integrate_f(x['a'], x['b'], x['N']), axis=1)
1 loops, best of 3: 319 ms per loop
```

But clearly this isn’t fast enough for us. Let’s take a look and see where the time is spent during this operation (limited to the most time consuming four calls) using the prun ipython magic function:

```
In [6]: %prun -l 4 df.apply(lambda x: integrate_f(x['a'], x['b'], x['N']), axis=1)
650647 function calls in 0.475 seconds
Ordered by: internal time
List reduced from 110 to 4 due to restriction <4>
ncalls tottime percall cumtime percall filename:lineno(function)
1000 0.195 0.000 0.312 0.000 <ipython-input-4-a877a66f40a5>:1(integrate_f)
552423 0.109 0.000 0.109 0.000 <ipython-input-3-0b27f90c4c8a>:1(f)
1004 0.020 0.000 0.020 0.000 {method 'reduce' of 'numpy.ufunc' objects}
2001 0.013 0.000 0.013 0.000 {pandas.lib.infer_dtype}
```

By far the majority of time is spend inside either `integrate_f` or `f`,
hence we’ll concentrate our efforts cythonizing these two functions.

Note

In python 2 replacing the `range` with its generator counterpart (`xrange`)
would mean the `range` line would vanish. In python 3 range is already a generator.

### Plain cython¶

First we’re going to need to import the cython magic function to ipython:

```
In [7]: %load_ext cythonmagic
```

Now, let’s simply copy our functions over to cython as is (the suffix is here to distinguish between function versions):

```
In [8]: %%cython
...: def f_plain(x):
...: return x * (x - 1)
...: def integrate_f_plain(a, b, N):
...: s = 0
...: dx = (b - a) / N
...: for i in range(N):
...: s += f_plain(a + i * dx)
...: return s * dx
...:
```

Note

If you’re having trouble pasting the above into your ipython, you may need to be using bleeding edge ipython for paste to play well with cell magics.

```
In [9]: %timeit df.apply(lambda x: integrate_f_plain(x['a'], x['b'], x['N']), axis=1)
1 loops, best of 3: 214 ms per loop
```

Already this has shaved a third off, not too bad for a simple copy and paste.

### Adding type¶

We get another huge improvement simply by providing type information:

```
In [10]: %%cython
....: cdef double f_typed(double x) except? -2:
....: return x * (x - 1)
....: cpdef double integrate_f_typed(double a, double b, int N):
....: cdef int i
....: cdef double s, dx
....: s = 0
....: dx = (b - a) / N
....: for i in range(N):
....: s += f_typed(a + i * dx)
....: return s * dx
....:
```

```
In [11]: %timeit df.apply(lambda x: integrate_f_typed(x['a'], x['b'], x['N']), axis=1)
10 loops, best of 3: 116 ms per loop
```

Now, we’re talking! It’s now over ten times faster than the original python
implementation, and we haven’t *really* modified the code. Let’s have another
look at what’s eating up time:

```
In [12]: %prun -l 4 df.apply(lambda x: integrate_f_typed(x['a'], x['b'], x['N']), axis=1)
97224 function calls in 0.172 seconds
Ordered by: internal time
List reduced from 108 to 4 due to restriction <4>
ncalls tottime percall cumtime percall filename:lineno(function)
1004 0.021 0.000 0.021 0.000 {method 'reduce' of 'numpy.ufunc' objects}
2001 0.012 0.000 0.012 0.000 {pandas.lib.infer_dtype}
1001 0.010 0.000 0.108 0.000 series.py:124(__init__)
1001 0.010 0.000 0.054 0.000 internals.py:1864(make_block)
```

### Using ndarray¶

It’s calling series... a lot! It’s creating a Series from each row, and get-ting from both the index and the series (three times for each row). Function calls are expensive in python, so maybe we could minimise these by cythonizing the apply part.

Note

We are now passing ndarrays into the cython function, fortunately cython plays very nicely with numpy.

```
In [13]: %%cython
....: cimport numpy as np
....: import numpy as np
....: cdef double f_typed(double x) except? -2:
....: return x * (x - 1)
....: cpdef double integrate_f_typed(double a, double b, int N):
....: cdef int i
....: cdef double s, dx
....: s = 0
....: dx = (b - a) / N
....: for i in range(N):
....: s += f_typed(a + i * dx)
....: return s * dx
....: cpdef np.ndarray[double] apply_integrate_f(np.ndarray col_a, np.ndarray col_b, np.ndarray col_N):
....: assert (col_a.dtype == np.float and col_b.dtype == np.float and col_N.dtype == np.int)
....: cdef Py_ssize_t i, n = len(col_N)
....: assert (len(col_a) == len(col_b) == n)
....: cdef np.ndarray[double] res = np.empty(n)
....: for i in range(len(col_a)):
....: res[i] = integrate_f_typed(col_a[i], col_b[i], col_N[i])
....: return res
....:
```

The implementation is simple, it creates an array of zeros and loops over
the rows, applying our `integrate_f_typed`, and putting this in the zeros array.

Warning

In 0.13.0 since `Series` has internaly been refactored to no longer sub-class `ndarray`
but instead subclass `NDFrame`, you can **not pass** a `Series` directly as a `ndarray` typed parameter
to a cython function. Instead pass the actual `ndarray` using the `.values` attribute of the Series.

Prior to 0.13.0

```
apply_integrate_f(df['a'], df['b'], df['N'])
```

Use `.values` to get the underlying `ndarray`

```
apply_integrate_f(df['a'].values, df['b'].values, df['N'].values)
```

Note

Loops like this would be *extremely* slow in python, but in Cython looping
over numpy arrays is *fast*.

```
In [14]: %timeit apply_integrate_f(df['a'].values, df['b'].values, df['N'].values)
100 loops, best of 3: 2.52 ms per loop
```

We’ve gone another three times faster! Let’s check again where the time is spent:

```
In [15]: %prun -l 4 apply_integrate_f(df['a'].values, df['b'].values, df['N'].values)
33 function calls in 0.004 seconds
Ordered by: internal time
List reduced from 13 to 4 due to restriction <4>
ncalls tottime percall cumtime percall filename:lineno(function)
1 0.004 0.004 0.004 0.004 {_cython_magic_e90d139b668b225d575329a3043b5155.apply_integrate_f}
3 0.000 0.000 0.000 0.000 frame.py:1612(__getitem__)
1 0.000 0.000 0.004 0.004 <string>:1(<module>)
3 0.000 0.000 0.000 0.000 index.py:604(__contains__)
```

As one might expect, the majority of the time is now spent in `apply_integrate_f`,
so if we wanted to make anymore efficiencies we must continue to concentrate our
efforts here.

### More advanced techniques¶

There is still scope for improvement, here’s an example of using some more advanced cython techniques:

```
In [16]: %%cython
....: cimport cython
....: cimport numpy as np
....: import numpy as np
....: cdef double f_typed(double x) except? -2:
....: return x * (x - 1)
....: cpdef double integrate_f_typed(double a, double b, int N):
....: cdef int i
....: cdef double s, dx
....: s = 0
....: dx = (b - a) / N
....: for i in range(N):
....: s += f_typed(a + i * dx)
....: return s * dx
....: @cython.boundscheck(False)
....: @cython.wraparound(False)
....: cpdef np.ndarray[double] apply_integrate_f_wrap(np.ndarray[double] col_a, np.ndarray[double] col_b, np.ndarray[Py_ssize_t] col_N):
....: cdef Py_ssize_t i, n = len(col_N)
....: assert len(col_a) == len(col_b) == n
....: cdef np.ndarray[double] res = np.empty(n)
....: for i in range(n):
....: res[i] = integrate_f_typed(col_a[i], col_b[i], col_N[i])
....: return res
....:
```

```
In [17]: %timeit apply_integrate_f_wrap(df['a'].values, df['b'].values, df['N'].values)
100 loops, best of 3: 2.14 ms per loop
```

This shaves another third off!

## Expression Evaluation via `eval()` (Experimental)¶

New in version 0.13.

The top-level function `eval()` implements expression evaluation of
`Series` and `DataFrame` objects.

Note

To benefit from using `eval()` you need to
install `numexpr`. See the *recommended dependencies section* for more details.

The point of using `eval()` for expression evaluation rather than
plain Python is two-fold: 1) large `DataFrame` objects are
evaluated more efficiently and 2) large arithmetic and boolean expressions are
evaluated all at once by the underlying engine (by default `numexpr` is used
for evaluation).

Note

You should not use `eval()` for simple
expressions or for expressions involving small DataFrames. In fact,
`eval()` is many orders of magnitude slower for
smaller expressions/objects than plain ol’ Python. A good rule of thumb is
to only use `eval()` when you have a
`DataFrame` with more than 10,000 rows.

`eval()` supports all arithmetic expressions supported by the
engine in addition to some extensions available only in pandas.

Note

The larger the frame and the larger the expression the more speedup you will
see from using `eval()`.

### Supported Syntax¶

These operations are supported by `eval()`:

- Arithmetic operations except for the left shift (
`<<`) and right shift (`>>`) operators, e.g.,`df + 2 * pi / s ** 4 % 42 - the_golden_ratio` - Comparison operations, e.g.,
`2 < df < df2` - Boolean operations, e.g.,
`df < df2 and df3 < df4 or not df_bool` `list`and`tuple`literals, e.g.,`[1, 2]`or`(1, 2)`- Attribute access, e.g.,
`df.a` - Subscript expressions, e.g.,
`df[0]` - Simple variable evaluation, e.g.,
`pd.eval('df')`(this is not very useful)

This Python syntax is **not** allowed:

- Expressions
- Function calls
`is`/`is not`operations`if`expressions`lambda`expressions`list`/`set`/`dict`comprehensions- Literal
`dict`and`set`expressions `yield`expressions- Generator expressions
- Boolean expressions consisting of only scalar values

- Statements

`eval()` Examples¶

`eval()` works wonders for expressions containing large arrays

First let’s create 4 decent-sized arrays to play with:

```
In [18]: import pandas as pd
In [19]: from pandas import DataFrame, Series
In [20]: from numpy.random import randn
In [21]: import numpy as np
In [22]: nrows, ncols = 20000, 100
In [23]: df1, df2, df3, df4 = [DataFrame(randn(nrows, ncols)) for _ in xrange(4)]
```

Now let’s compare adding them together using plain ol’ Python versus
`eval()`:

```
In [24]: %timeit df1 + df2 + df3 + df4
10 loops, best of 3: 53.7 ms per loop
```

```
In [25]: %timeit pd.eval('df1 + df2 + df3 + df4')
100 loops, best of 3: 18.1 ms per loop
```

Now let’s do the same thing but with comparisons:

```
In [26]: %timeit (df1 > 0) & (df2 > 0) & (df3 > 0) & (df4 > 0)
10 loops, best of 3: 46.4 ms per loop
```

```
In [27]: %timeit pd.eval('(df1 > 0) & (df2 > 0) & (df3 > 0) & (df4 > 0)')
100 loops, best of 3: 15.1 ms per loop
```

`eval()` also works with unaligned pandas objects:

```
In [28]: s = Series(randn(50))
In [29]: %timeit df1 + df2 + df3 + df4 + s
10 loops, best of 3: 86.3 ms per loop
```

```
In [30]: %timeit pd.eval('df1 + df2 + df3 + df4 + s')
10 loops, best of 3: 18.8 ms per loop
```

Note

Operations such as

1 and 2 # would parse to 1 & 2, but should evaluate to 2 3 or 4 # would parse to 3 | 4, but should evaluate to 3 ~1 # this is okay, but slower when using eval

should be performed in Python. An exception will be raised if you try to
perform any boolean/bitwise operations with scalar operands that are not
of type `bool` or `np.bool_`. Again, you should perform these kinds of
operations in plain Python.

### The `DataFrame.eval` method (Experimental)¶

In addition to the top level `eval()` function you can also
evaluate an expression in the “context” of a `DataFrame`.

```
In [31]: df = DataFrame(randn(5, 2), columns=['a', 'b'])
In [32]: df.eval('a + b')
0 -0.246747
1 0.867786
2 -1.626063
3 -1.134978
4 -1.027798
dtype: float64
```

Any expression that is a valid `eval()` expression is also a valid
`DataFrame.eval` expression, with the added benefit that *you don’t have to
prefix the name of the* `DataFrame` *to the column you’re interested in
evaluating*.

In addition, you can perform in-line assignment of columns within an expression.
This can allow for *formulaic evaluation*. Only a signle assignement is permitted.
It can be a new column name or an existing column name. It must be a string-like.

```
In [33]: df = DataFrame(dict(a = range(5), b = range(5,10)))
In [34]: df.eval('c=a+b')
In [35]: df.eval('d=a+b+c')
In [36]: df.eval('a=1')
In [37]: df
a b c d
0 1 5 5 10
1 1 6 7 14
2 1 7 9 18
3 1 8 11 22
4 1 9 13 26
[5 rows x 4 columns]
```

### Local Variables¶

You can refer to local variables the same way you would in vanilla Python

```
In [38]: df = DataFrame(randn(5, 2), columns=['a', 'b'])
In [39]: newcol = randn(len(df))
In [40]: df.eval('b + newcol')
0 -0.173926
1 2.493083
2 -0.881831
3 -0.691045
4 1.334703
dtype: float64
```

Note

The one exception is when you have a local (or global) with the same name as
a column in the `DataFrame`

df = DataFrame(randn(5, 2), columns=['a', 'b']) a = randn(len(df)) df.eval('a + b') NameResolutionError: resolvers and locals overlap on names ['a']

To deal with these conflicts, a special syntax exists for referring variables with the same name as a column

In [41]: df.eval('@a + b') 0 0.291737 1 -0.073076 2 -2.259372 3 -1.513447 4 -0.222295 dtype: float64

The same is true for `query()`

In [42]: df.query('@a < b') a b 1 -1.215949 1.670837 3 -0.835893 0.315213 4 -1.337334 0.772364 [3 rows x 2 columns]

`eval()` Parsers¶

There are two different parsers and and two different engines you can use as the backend.

The default `'pandas'` parser allows a more intuitive syntax for expressing
query-like operations (comparisons, conjunctions and disjunctions). In
particular, the precedence of the `&` and `|` operators is made equal to
the precedence of the corresponding boolean operations `and` and `or`.

For example, the above conjunction can be written without parentheses.
Alternatively, you can use the `'python'` parser to enforce strict Python
semantics.

```
In [43]: expr = '(df1 > 0) & (df2 > 0) & (df3 > 0) & (df4 > 0)'
In [44]: x = pd.eval(expr, parser='python')
In [45]: expr_no_parens = 'df1 > 0 & df2 > 0 & df3 > 0 & df4 > 0'
In [46]: y = pd.eval(expr_no_parens, parser='pandas')
In [47]: np.all(x == y)
True
```

The same expression can be “anded” together with the word `and` as
well:

```
In [48]: expr = '(df1 > 0) & (df2 > 0) & (df3 > 0) & (df4 > 0)'
In [49]: x = pd.eval(expr, parser='python')
In [50]: expr_with_ands = 'df1 > 0 and df2 > 0 and df3 > 0 and df4 > 0'
In [51]: y = pd.eval(expr_with_ands, parser='pandas')
In [52]: np.all(x == y)
True
```

The `and` and `or` operators here have the same precedence that they would
in vanilla Python.

`eval()` Backends¶

There’s also the option to make `eval()` operate identical to plain
ol’ Python.

Note

Using the `'python'` engine is generally *not* useful, except for testing
other `eval()` engines against it. You will acheive **no**
performance benefits using `eval()` with `engine='python'`.

You can see this by using `eval()` with the `'python'` engine is
actually a bit slower (not by much) than evaluating the same expression in
Python:

```
In [53]: %timeit df1 + df2 + df3 + df4
10 loops, best of 3: 54.6 ms per loop
```

```
In [54]: %timeit pd.eval('df1 + df2 + df3 + df4', engine='python')
10 loops, best of 3: 56 ms per loop
```

`eval()` Performance¶

`eval()` is intended to speed up certain kinds of operations. In
particular, those operations involving complex expressions with large
`DataFrame`/`Series` objects should see a significant performance benefit.
Here is a plot showing the running time of `eval()` as function of
the size of the frame involved in the computation. The two lines are two
different engines.

Note

Operations with smallish objects (around 15k-20k rows) are faster using plain Python:

This plot was created using a `DataFrame` with 3 columns each containing
floating point values generated using `numpy.random.randn()`.