From: Robert Bradshaw Date: Fri, 1 Apr 2011 18:44:51 +0000 (-0700) Subject: Merge docs repo X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=615b02ad52b6098589862b866ca4e3d277d89baa;p=cython.git Merge docs repo --HG-- extra : rebase_source : a14f3b57bc8404efb772183f14d9c3f58eec4e14 --- diff --git a/docs/src/userguide/numpy_tutorial.rst b/docs/src/userguide/numpy_tutorial.rst new file mode 100644 index 00000000..aafeea70 --- /dev/null +++ b/docs/src/userguide/numpy_tutorial.rst @@ -0,0 +1,496 @@ +.. highlight:: cython + +.. _numpy_tutorial: + +************************** +Cython for NumPy users +************************** + +This tutorial is aimed at NumPy users who have no experience with Cython at +all. If you have some knowledge of Cython you may want to skip to the +''Efficient indexing'' section which explains the new improvements made in +summer 2008. + +The main scenario considered is NumPy end-use rather than NumPy/SciPy +development. The reason is that Cython is not (yet) able to support functions +that are generic with respect to datatype and the number of dimensions in a +high-level fashion. This restriction is much more severe for SciPy development +than more specific, "end-user" functions. See the last section for more +information on this. + +The style of this tutorial will not fit everybody, so you can also consider: + +* Robert Bradshaw's `slides on cython for SciPy2008 + `_ + (a higher-level and quicker introduction) +* Basic Cython documentation (see `Cython front page `_). +* ``[:enhancements/buffer:Spec for the efficient indexing]`` + +.. Note:: + The fast array access documented below is a completely new feature, and + there may be bugs waiting to be discovered. It might be a good idea to do + a manual sanity check on the C code Cython generates before using this for + serious purposes, at least until some months have passed. + +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 full +program and "turns it into C" -- rather, the result makes full use of the +Python runtime environment. A way of looking at it may be that your code is +still Python in that it runs within the Python runtime environment, but rather +than compiling to interpreted Python bytecode one compiles to native machine +code (but with the addition of extra syntax for easy embedding of faster +C-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 wrapping + of C libraries. When writing code in Cython you can call into C code as + easily as into Python code. + +Some Python constructs are not yet supported, though making Cython compile all +Python code is a stated goal (among the more important omissions are inner +functions and generator functions). + +Your Cython environment +======================== + +Using Cython consists of these steps: + +1. Write a :file:`.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 provides + excellent support for using Cython and NumPy from an interactive command + line (like IPython) or through a notebook interface (like + Maple/Mathematica). See `this documentation + `_. +2. A version of `pyximport `_ is shipped + with Cython, so that you can import pyx-files dynamically into Python and + have them compiled automatically (See :ref:`pyximport`). +3. Cython supports distutils so that you can very easily create build scripts + which automate the process, this is the preferred method for full programs. +4. Manual compilation (see below) + +.. Note:: + If using another interactive command line environment than SAGE, like + IPython or Python itself, it is important that you restart the process + when you recompile the module. It is not enough to issue an "import" + statement again. + +Installation +============= + +Unless you are used to some other automatic method: +`download Cython `_ (0.9.8.1.1 or later), unpack it, +and run the usual ```python setup.py install``. This will install a +``cython`` executable on your system. It is also possible to use Cython from +the source directory without installing (simply launch :file:`cython.py` in the +root directory). + +As of this writing SAGE comes with an older release of Cython than required +for this tutorial. So if using SAGE you should download the newest Cython and +then execute :: + + $ cd path/to/cython-distro + $ path-to-sage/sage -python setup.py install + +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 manual +method here. First Cython is run:: + + $ cython yourmod.pyx + +This creates :file:`yourmod.c` which is the C source for a Python extension +module. A useful additional switch is ``-a`` which will generate a document +:file:`yourmod.html`) that shows which Cython code translates to which C code +line by line. + +Then we compile the C file. This may vary according to your system, but the C +file should be built like Python was built. Python documentation for writing +extensions should have some details. On Linux this often means something +like:: + + $ gcc -shared -pthread -fPIC -fwrapv -O2 -Wall -fno-strict-aliasing -I/usr/include/python2.5 -o yourmod.so yourmod.c + +``gcc`` should have access to the NumPy C header files so if they are not +installed at :file:`/usr/include/numpy` or similar you may need to pass another +option for those. + +This creates :file:`yourmod.so` in the same directory, which is importable by +Python by using a normal ``import yourmod`` statement. + +The first Cython program +========================== + +The code below does 2D discrete convolution of an image with a filter (and I'm +sure you can do better!, let it serve for demonstration purposes). It is both +valid Python and valid Cython code. I'll refer to it as both +:file:`convolve_py.py` for the Python version and :file:`convolve1.pyx` for the +Cython version -- Cython uses ".pyx" as its file suffix. + +.. code-block:: python + + from __future__ import division + import numpy as np + def naive_convolve(f, g): + # f is an image and is indexed by (v, w) + # g is a filter kernel and is indexed by (s, t), + # it needs odd dimensions + # h is the output image and is indexed by (x, y), + # it is not cropped + if g.shape[0] % 2 != 1 or g.shape[1] % 2 != 1: + raise ValueError("Only odd dimensions on filter supported") + # smid and tmid are number of pixels between the center pixel + # and the edge, ie for a 5x5 filter they will be 2. + # + # The output size is calculated by adding smid, tmid to each + # side of the dimensions of the input image. + vmax = f.shape[0] + wmax = f.shape[1] + smax = g.shape[0] + tmax = g.shape[1] + smid = smax // 2 + tmid = tmax // 2 + xmax = vmax + 2*smid + ymax = wmax + 2*tmid + # Allocate result image. + h = np.zeros([xmax, ymax], dtype=f.dtype) + # Do convolution + for x in range(xmax): + for y in range(ymax): + # Calculate pixel value for h at (x,y). Sum one component + # for each pixel (s, t) of the filter g. + s_from = max(smid - x, -smid) + s_to = min((xmax - x) - smid, smid + 1) + t_from = max(tmid - y, -tmid) + t_to = min((ymax - y) - tmid, tmid + 1) + value = 0 + for s in range(s_from, s_to): + for t in range(t_from, t_to): + v = x - smid + s + w = y - tmid + t + value += g[smid - s, tmid - t] * f[v, w] + h[x, y] = value + return h + +This should be compiled to produce :file:`yourmod.so` (for Linux systems). We +run a Python session to test both the Python version (imported from +``.py``-file) and the compiled Cython module. + +.. sourcecode:: ipython + + In [1]: import numpy as np + In [2]: import convolve_py + In [3]: convolve_py.naive_convolve(np.array([[1, 1, 1]], dtype=np.int), + ... np.array([[1],[2],[1]], dtype=np.int)) + Out [3]: + array([[1, 1, 1], + [2, 2, 2], + [1, 1, 1]]) + In [4]: import convolve1 + In [4]: convolve1.naive_convolve(np.array([[1, 1, 1]], dtype=np.int), + ... np.array([[1],[2],[1]], dtype=np.int)) + Out [4]: + array([[1, 1, 1], + [2, 2, 2], + [1, 1, 1]]) + In [11]: N = 100 + In [12]: f = np.arange(N*N, dtype=np.int).reshape((N,N)) + In [13]: g = np.arange(81, dtype=np.int).reshape((9, 9)) + In [19]: %timeit -n2 -r3 convolve_py.naive_convolve(f, g) + 2 loops, best of 3: 1.86 s per loop + In [20]: %timeit -n2 -r3 convolve1.naive_convolve(f, g) + 2 loops, best of 3: 1.41 s per loop + +There's not such a huge difference yet; because the C code still does exactly +what the Python interpreter does (meaning, for instance, that a new object is +allocated for each number used). Look at the generated html file and see what +is needed for even the simplest statements you get the point quickly. We need +to 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 source +compatibility. Here's :file:`convolve2.pyx`. *Read the comments!* :: + + from __future__ import division + import numpy as np + # "cimport" is used to import special compile-time information + # about the numpy module (this is stored in a file numpy.pxd which is + # currently part of the Cython distribution). + cimport numpy as np + # We now need to fix a datatype for our arrays. I've used the variable + # DTYPE for this, which is assigned to the usual NumPy runtime + # type info object. + DTYPE = np.int + # "ctypedef" assigns a corresponding compile-time type to DTYPE_t. For + # every type in the numpy module there's a corresponding compile-time + # type with a _t-suffix. + ctypedef np.int_t DTYPE_t + # The builtin min and max functions works with Python objects, and are + # so very slow. So we create our own. + # - "cdef" declares a function which has much less overhead than a normal + # def function (but it is not Python-callable) + # - "inline" is passed on to the C compiler which may inline the functions + # - The C type "int" is chosen as return type and argument types + # - Cython allows some newer Python constructs like "a if x else b", but + # the resulting C file compiles with Python 2.3 through to Python 3.0 beta. + cdef inline int int_max(int a, int b): return a if a >= b else b + cdef inline int int_min(int a, int b): return a if a <= b else b + # "def" can type its arguments but not have a return type. The type of the + # arguments for a "def" function is checked at run-time when entering the + # function. + # + # The arrays f, g and h is typed as "np.ndarray" instances. The only effect + # this has is to a) insert checks that the function arguments really are + # NumPy arrays, and b) make some attribute access like f.shape[0] much + # more efficient. (In this example this doesn't matter though.) + def naive_convolve(np.ndarray f, np.ndarray g): + if g.shape[0] % 2 != 1 or g.shape[1] % 2 != 1: + raise ValueError("Only odd dimensions on filter supported") + assert f.dtype == DTYPE and g.dtype == DTYPE + # The "cdef" keyword is also used within functions to type variables. It + # can only be used at the top indendation level (there are non-trivial + # problems with allowing them in other places, though we'd love to see + # good and thought out proposals for it). + # + # For the indices, the "int" type is used. This corresponds to a C int, + # other C types (like "unsigned int") could have been used instead. + # Purists could use "Py_ssize_t" which is the proper Python type for + # array indices. + cdef int vmax = f.shape[0] + cdef int wmax = f.shape[1] + cdef int smax = g.shape[0] + cdef int tmax = g.shape[1] + cdef int smid = smax // 2 + cdef int tmid = tmax // 2 + cdef int xmax = vmax + 2*smid + cdef int ymax = wmax + 2*tmid + cdef np.ndarray h = np.zeros([xmax, ymax], dtype=DTYPE) + cdef int x, y, s, t, v, w + # It is very important to type ALL your variables. You do not get any + # warnings if not, only much slower code (they are implicitly typed as + # Python objects). + cdef int s_from, s_to, t_from, t_to + # For the value variable, we want to use the same data type as is + # stored in the array, so we use "DTYPE_t" as defined above. + # NB! An important side-effect of this is that if "value" overflows its + # datatype size, it will simply wrap around like in C, rather than raise + # an error like in Python. + cdef DTYPE_t value + for x in range(xmax): + for y in range(ymax): + s_from = int_max(smid - x, -smid) + s_to = int_min((xmax - x) - smid, smid + 1) + t_from = int_max(tmid - y, -tmid) + t_to = int_min((ymax - y) - tmid, tmid + 1) + value = 0 + for s in range(s_from, s_to): + for t in range(t_from, t_to): + v = x - smid + s + w = y - tmid + t + value += g[smid - s, tmid - t] * f[v, w] + h[x, y] = value + return h + +At this point, have a look at the generated C code for :file:`convolve1.pyx` and +:file:`convolve2.pyx`. Click on the lines to expand them and see corresponding C. +(Note that this code annotation is currently experimental and especially +"trailing" cleanup code for a block may stick to the last expression in the +block and make it look worse than it is -- use some common sense). + +* .. literalinclude: convolve1.html +* .. literalinclude: convolve2.html + +Especially have a look at the for loops: In :file:`convolve1.c`, these are ~20 lines +of C code to set up while in :file:`convolve2.c` a normal C for loop is used. + +After building this and continuing my (very informal) benchmarks, I get: + +.. sourcecode:: ipython + + In [21]: import convolve2 + In [22]: %timeit -n2 -r3 convolve2.naive_convolve(f, g) + 2 loops, best of 3: 828 ms per loop + +Efficient indexing +==================== + +There's still a bottleneck killing performance, and that is the array lookups +and assignments. The ``[]``-operator still uses full Python operations -- +what we would like to do instead is to access the data buffer directly at C +speed. + +What we need to do then is to type the contents of the :obj:`ndarray` objects. +We do this with a special "buffer" syntax which must be told the datatype +(first argument) and number of dimensions ("ndim" keyword-only argument, if +not provided then one-dimensional is assumed). + +More information on this syntax [:enhancements/buffer:can be found here]. + +Showing the changes needed to produce :file:`convolve3.pyx` only:: + + ... + def naive_convolve(np.ndarray[DTYPE_t, ndim=2] f, np.ndarray[DTYPE_t, ndim=2] g): + ... + cdef np.ndarray[DTYPE_t, ndim=2] h = ... + +Usage: + +.. sourcecode:: ipython + + In [18]: import convolve3 + In [19]: %timeit -n3 -r100 convolve3.naive_convolve(f, g) + 3 loops, best of 100: 11.6 ms per loop + +Note the importance of this change. + +*Gotcha*: This efficient indexing only affects certain index operations, +namely those with exactly ``ndim`` number of typed integer indices. So if +``v`` for instance isn't typed, then the lookup ``f[v, w]`` isn't +optimized. On the other hand this means that you can continue using Python +objects for sophisticated dynamic slicing etc. just as when the array is not +typed. + +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 is + explicitly coded so that it doesn't use negative indices, and it + (hopefully) always access within bounds. We can add a decorator to disable + bounds checking:: + + ... + cimport cython + @cython.boundscheck(False) # turn of bounds-checking for entire function + def naive_convolve(np.ndarray[DTYPE_t, ndim=2] f, np.ndarray[DTYPE_t, ndim=2] g): + ... + +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 program +and in the worst case corrupt data). It is possible to switch bounds-checking +mode in many ways, see [:docs/compilerdirectives:compiler directives] for more +information. + +Negative indices are dealt with by ensuring Cython that the indices will be +positive, by casting the variables to unsigned integer types (if you do have +negative values, then this casting will create a very large positive value +instead and you will attempt to access out-of-bounds values). Casting is done +with a special ``<>``-syntax. The code below is changed to use either +unsigned ints or casting as appropriate:: + + ... + cdef int s, t # changed + cdef unsigned int x, y, v, w # changed + cdef int s_from, s_to, t_from, t_to + cdef DTYPE_t value + for x in range(xmax): + for y in range(ymax): + s_from = max(smid - x, -smid) + s_to = min((xmax - x) - smid, smid + 1) + t_from = max(tmid - y, -tmid) + t_to = min((ymax - y) - tmid, tmid + 1) + value = 0 + for s in range(s_from, s_to): + for t in range(t_from, t_to): + v = (x - smid + s) # changed + w = (y - tmid + t) # changed + value += g[(smid - s), (tmid - t)] * f[v, w] # changed + h[x, y] = value + ... + +(In the next Cython release we will likely add a compiler directive or +argument to the ``np.ndarray[]``-type specifier to disable negative indexing +so that casting so much isn't necessary; feedback on this is welcome.) + +The function call overhead now starts to play a role, so we compare the latter +two examples with larger N: + +.. sourcecode:: ipython + + In [11]: %timeit -n3 -r100 convolve4.naive_convolve(f, g) + 3 loops, best of 100: 5.97 ms per loop + In [12]: N = 1000 + In [13]: f = np.arange(N*N, dtype=np.int).reshape((N,N)) + In [14]: g = np.arange(81, dtype=np.int).reshape((9, 9)) + In [17]: %timeit -n1 -r10 convolve3.naive_convolve(f, g) + 1 loops, best of 10: 1.16 s per loop + In [18]: %timeit -n1 -r10 convolve4.naive_convolve(f, g) + 1 loops, best of 10: 597 ms per loop + +(Also this is a mixed benchmark as the result array is allocated within the +function call.) + +.. Warning:: + + Speed comes with some cost. Especially it can be dangerous to set typed + objects (like ``f``, ``g`` and ``h`` in our sample code) to :keyword:`None`. + Setting such objects to :keyword:`None` is entirely legal, but all you can do with them + is check whether they are None. All other use (attribute lookup or indexing) + can potentially segfault or corrupt data (rather than raising exceptions as + they would in Python). + + The actual rules are a bit more complicated but the main message is clear: Do + not use typed objects without knowing that they are not set to None. + +More generic code +================== + +It would be possible to do:: + + def naive_convolve(object[DTYPE_t, ndim=2] f, ...): + +i.e. use :obj:`object` rather than :obj:`np.ndarray`. Under Python 3.0 this +can allow your algorithm to work with any libraries supporting the buffer +interface; and support for e.g. the Python Imaging Library may easily be added +if someone is interested also under Python 2.x. + +There is some speed penalty to this though (as one makes more assumptions +compile-time if the type is set to :obj:`np.ndarray`, specifically it is +assumed that the data is stored in pure strided more and not in indirect +mode). + +[:enhancements/buffer:More information] + +The future +============ + +These are some points to consider for further development. All points listed +here has gone through a lot of thinking and planning already; still they may +or may not happen depending on available developer time and resources for +Cython. + +1. Support for efficient access to structs/records stored in arrays; currently + only primitive types are allowed. +2. Support for efficient access to complex floating point types in arrays. The + main obstacle here is getting support for efficient complex datatypes in + Cython. +3. Calling NumPy/SciPy functions currently has a Python call overhead; it + would be possible to take a short-cut from Cython directly to C. (This does + however require some isolated and incremental changes to those libraries; + mail the Cython mailing list for details). +4. Efficient code that is generic with respect to the number of dimensions. + This can probably be done today by calling the NumPy C multi-dimensional + iterator API directly; however it would be nice to have for-loops over + :func:`enumerate` and :func:`ndenumerate` on NumPy arrays create efficient + code. +5. A high-level construct for writing type-generic code, so that one can write + functions that work simultaneously with many datatypes. Note however that a + macro preprocessor language can help with doing this for now. +