Maximumelement = numpy.max (arr, 0) maximumelement = numpy.max (arr, 1) If we use 0 it will give us a list containing the maximum or minimum values from each column. Here we will get a list like 11 81 22 which have all the maximum numbers each column.

Return random integers from low (inclusive) to high (exclusive).

Return random integers from the “discrete uniform” distribution ofthe specified dtype in the “half-open” interval [low, high). Ifhigh is None (the default), then results are from [0, low).

• NumPy provides basic mathematical and statistical functions like mean, min, max, sum, prod, std, var, summation across different axes, transposing of a matrix, etc. A particular NumPy feature of interest is solving a system of linear equations. NumPy has a function to solve linear equations. For example, 2x + 6y = 6 5x + 3y = -9.
• The NumPy functions min and max can be used to return the smallest and largest values in the data sample; for example: datamin, datamax = data.min, data.max 1.

See also

random.random_integers

similar to randint, only for the closed interval [low, high], and 1 is the lowest value if high is omitted. In particular, this other one is the one to use to generate uniformly distributed discrete non-integers.

Examples

Generate a 2 x 4 array of ints between 0 and 4, inclusive:

This tutorial is aimed at NumPy users who have no experience with Cython atall. If you have some knowledge of Cython you may want to skip to the‘’Efficient indexing’’ section.

The main scenario considered is NumPy end-use rather than NumPy/SciPydevelopment. The reason is that Cython is not (yet) able to support functionsthat are generic with respect to the number of dimensions in ahigh-level fashion. This restriction is much more severe for SciPy developmentthan more specific, “end-user” functions. See the last section for moreinformation on this.

The style of this tutorial will not fit everybody, so you can also consider:

• Kurt Smith’s video tutorial of Cython at SciPy 2015.The slides and notebooks of this talk are on github.
• Basic Cython documentation (see Cython front page).

Cython at a glance¶

Cython is a compiler which compiles Python-like code files to C code. Still,‘’Cython is not a Python to C translator’’. That is, it doesn’t take your fullprogram and “turns it into C” – rather, the result makes full use of thePython runtime environment. A way of looking at it may be that your code isstill Python in that it runs within the Python runtime environment, but ratherthan compiling to interpreted Python bytecode one compiles to native machinecode (but with the addition of extra syntax for easy embedding of fasterC-like code).

This has two important consequences:

• Speed. How much depends very much on the program involved though. Typical Python numerical programs would tend to gain very little as most time is spent in lower-level C that is used in a high-level fashion. However for-loop-style programs can gain many orders of magnitude, when typing information is added (and is so made possible as a realistic alternative).
• Easy calling into C code. One of Cython’s purposes is to allow easy wrappingof C libraries. When writing code in Cython you can call into C code aseasily as into Python code.

Very few Python constructs are not yet supported, though making Cython compile allPython code is a stated goal, you can see the differences with Python inlimitations.

Your Cython environment¶

Using Cython consists of these steps:

1. Write a .pyx source file
2. Run the Cython compiler to generate a C file
3. Run a C compiler to generate a compiled library
4. Run the Python interpreter and ask it to import the module

However there are several options to automate these steps:

1. The SAGE mathematics software system providesexcellent support for using Cython and NumPy from an interactive commandline or through a notebook interface (likeMaple/Mathematica). See this documentation.
2. Cython can be used as an extension within a Jupyter notebook,making it easy to compile and use Cython code with just a %%cythonat the top of a cell. For more information seeUsing the Jupyter Notebook.
3. A version of pyximport is shipped with Cython,so that you can import pyx-files dynamically into Python andhave them compiled automatically (See Compiling with pyximport).
4. Cython supports setuptools so that you can very easily create build scriptswhich automate the process, this is the preferred method forCython implemented libraries and packages.See Basic setup.py.
5. Manual compilation (see below)

Note

If using another interactive command line environment than SAGE, likeIPython or Python itself, it is important that you restart the processwhen you recompile the module. It is not enough to issue an “import”statement again.

Installation¶

If you already have a C compiler, just do:

otherwise, see the installation page.

As of this writing SAGE comes with an older release of Cython than requiredfor this tutorial. So if using SAGE you should download the newest Cython andthen execute

This will install the newest Cython into SAGE.

Manual compilation¶

As it is always important to know what is going on, I’ll describe the manualmethod here. First Cython is run:

This creates yourmod.c which is the C source for a Python extensionmodule. A useful additional switch is -a which will generate a documentyourmod.html) that shows which Cython code translates to which C codeline by line.

Then we compile the C file. This may vary according to your system, but the Cfile should be built like Python was built. Python documentation for writingextensions should have some details. On Linux this often means somethinglike:

gcc should have access to the NumPy C header files so if they are notinstalled at /usr/include/numpy or similar you may need to pass anotheroption for those. You only need to provide the NumPy headers if you write:

in your Cython code.

This creates yourmod.so in the same directory, which is importable byPython by using a normal importyourmod statement.

The first Cython program¶

You can easily execute the code of this tutorial bydownloading the Jupyter notebook.

The code below does the equivalent of this function in numpy:

We’ll say that array_1 and array_2 are 2D NumPy arrays of integer type anda, b and c are three Python integers.

This function uses NumPy and is already really fast, so it might be a bit overkillto do it again with Cython. This is for demonstration purposes. Nonetheless, wewill show that we achieve a better speed and memory efficiency than NumPy at the cost of more verbosity.

This code computes the function with the loops over the two dimensions being unrolled.It is both valid Python and valid Cython code. I’ll refer to it as bothcompute_py.py for the Python version and compute_cy.pyx for theCython version – Cython uses .pyx as its file suffix (but it can also compile.py files).

This should be compiled to produce compute_cy.so for Linux systems(on Windows systems, this will be a .pyd file). Werun a Python session to test both the Python version (imported from.py-file) and the compiled Cython module.

There’s not such a huge difference yet; because the C code still does exactlywhat the Python interpreter does (meaning, for instance, that a new object isallocated for each number used).

You can look at the Python interaction and the generated Ccode by using -a when calling Cython from the commandline, %%cython-a when using a Jupyter Notebook, or by usingcythonize('compute_cy.pyx',annotate=True) when using a setup.py.Look at the generated html file and see whatis needed for even the simplest statements. You get the point quickly. We needto give Cython more information; we need to add types.

Adding types¶

To add types we use custom Cython syntax, so we are now breaking Python sourcecompatibility. Here’s compute_typed.pyx. Read the comments!

At this point, have a look at the generated C code for compute_cy.pyx andcompute_typed.pyx. Click on the lines to expand them and see corresponding C.

Especially have a look at the for-loops: In compute_cy.c, these are ~20 linesof C code to set up while in compute_typed.c a normal C for loop is used.

After building this and continuing my (very informal) benchmarks, I get:

So adding types does make the code faster, but nowherenear the speed of NumPy?

What happened is that most of the time spend in this code is spent in the following lines,and those lines are slower to execute than in pure Python:

So what made those line so much slower than in the pure Python version?

array_1 and array_2 are still NumPy arrays, so Python objects, and expectPython integers as indexes. Here we pass C int values. So every timeCython reaches this line, it has to convert all the C integers to Pythonint objects. Since this line is called very often, it outweighs the speedbenefits of the pure C loops that were created from the range() earlier.

Furthermore, tmp*a+array_2[x,y]*b returns a Python integerand tmp is a C integer, so Cython has to do type conversions again.In the end those types conversions add up. And made our computation reallyslow. But this problem can be solved easily by using memoryviews.

Efficient indexing with memoryviews¶

There are still two bottlenecks that degrade the performance, and that is the array lookupsand assignments, as well as C/Python types conversion.The []-operator still uses full Python operations –what we would like to do instead is to access the data buffer directly at Cspeed.

What we need to do then is to type the contents of the ndarray objects.We do this with a memoryview. There is a page in the Cython documentation dedicated to it.

In short, memoryviews are C structures that can hold a pointer to the dataof a NumPy array and all the necessary buffer metadata to provide efficientand safe access: dimensions, strides, item size, item type information, etc…They also support slices, so they work even ifthe NumPy array isn’t contiguous in memory.They can be indexed by C integers, thus allowing fast access to theNumPy array data.

Here is how to declare a memoryview of integers:

No data is copied from the NumPy array to the memoryview in our example.As the name implies, it is only a “view” of the memory. So we can use theview result_view for efficient indexing and at the end return the real NumPyarray result that holds the data that we operated on.

Numpy Min Max Normalize

Here is how to use them in our code:

compute_memview.pyx

Let’s see how much faster accessing is now.

Note the importance of this change.We’re now 3081 times faster than an interpreted version of Python and 4.5 timesfaster than NumPy.

Memoryviews can be used with slices too, or evenwith Python arrays. Check out the memoryview page tosee what they can do for you.

Tuning indexing further¶

The array lookups are still slowed down by two factors:

1. Bounds checking is performed.
2. Negative indices are checked for and handled correctly. The code above isexplicitly coded so that it doesn’t use negative indices, and it(hopefully) always access within bounds.

With decorators, we can deactivate those checks:

Now bounds checking is not performed (and, as a side-effect, if you ‘’do’’happen to access out of bounds you will in the best case crash your programand in the worst case corrupt data). It is possible to switch bounds-checkingmode in many ways, see Compiler directives for moreinformation.

We’re faster than the NumPy version (6.2x). NumPy is really well written,but does not performs operation lazily, resulting in a lotof intermediate copy operations in memory. Our version isvery memory efficient and cache friendly because wecan execute the operations in a single run over the data.

Warning

Speed comes with some cost. Especially it can be dangerous to set typedobjects (like array_1, array_2 and result_view in our sample code) to None.Setting such objects to None is entirely legal, but all you can do with themis check whether they are None. All other use (attribute lookup or indexing)can potentially segfault or corrupt data (rather than raising exceptions asthey would in Python).

The actual rules are a bit more complicated but the main message is clear: Donot use typed objects without knowing that they are not set to None.

Declaring the NumPy arrays as contiguous¶

For extra speed gains, if you know that the NumPy arrays you areproviding are contiguous in memory, you can declare thememoryview as contiguous.

We give an example on an array that has 3 dimensions.If you want to give Cython the information that the data is C-contiguousyou have to declare the memoryview like this:

If you want to give Cython the information that the data is Fortran-contiguousyou have to declare the memoryview like this:

If all this makes no sense to you, you can skip this part, declaringarrays as contiguous constrains the usage of your functions as it rejects array slices as input.If you still want to understand what contiguous arrays areall about, you can see this answer on StackOverflow.

For the sake of giving numbers, here are the speed gains that you shouldget by declaring the memoryviews as contiguous:

Numpy Min Max Axis

We’re now around nine times faster than the NumPy version, and 6300 timesfaster than the pure Python version!

Making the function cleaner¶

Numpy Min Max Scaler

Declaring types can make your code quite verbose. If you don’t mindCython inferring the C types of your variables, you can usethe infer_types=True compiler directive at the top of the file.It will save you quite a bit of typing.

Note that since type declarations must happen at the top indentation level,Cython won’t infer the type of variables declared for the first timein other indentation levels. It would change too much the meaning ofour code. This is why, we must still declare manually the type of thetmp, x and y variable.

And actually, manually giving the type of the tmp variable willbe useful when using fused types.

We now do a speed test:

Lo and behold, the speed has not changed.

More generic code¶

All those speed gains are nice, but adding types constrains our code.At the moment, it would mean that our function can only work withNumPy arrays with the np.intc type. Is it possible to make ourcode work for multiple NumPy data types?

Yes, with the help of a new feature called fused types.You can learn more about it at this section of the documentation.It is similar to C++ ‘s templates. It generates multiple function declarationsat compile time, and then chooses the right one at run-time based on thetypes of the arguments provided. By comparing types in if-conditions, itis also possible to execute entirely different code paths dependingon the specific data type.

In our example, since we don’t have access anymore to the NumPy’s dtypeof our input arrays, we use those if-else statements toknow what NumPy data type we should use for our output array.

In this case, our function now works for ints, doubles and floats.

We can check that the output type is the right one:

We now do a speed test:

More versions of the function are created at compile time. So it makessense that the speed doesn’t change for executing this function withintegers as before.

Using multiple threads¶

Cython has support for OpenMP. It also has some nice wrappers around it,like the function prange(). You can see more information about Cython andparallelism in Using Parallelism. Since we do elementwise operations, we can easilydistribute the work among multiple threads. It’s important not to forget to pass thecorrect arguments to the compiler to enable OpenMP. When using the Jupyter notebook,you should use the cell magic like this:

The GIL must be released (see Releasing the GIL), so this is why wedeclare our clip() function nogil.

Python Numpy Min

We can have substantial speed gains for minimal effort:

We’re now 7558 times faster than the pure Python version and 11.1 times fasterthan NumPy!

Where to go from here?¶

Numpy Min Max

• If you want to learn how to make use of BLASor LAPACK with Cython, you can watchthe presentation of Ian Henriksen at SciPy 2015.
• If you want to learn how to use Pythran as backend in Cython, youcan see how in Pythran as a NumPy backend.Note that using Pythran only works with theold buffer syntax and not yet with memoryviews.