# 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.

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.

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!

### Further topics¶

Read more in the cython docs.

## 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
• Neither simple nor compound statements are allowed. This includes things like for, while, and if.

### 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().