.. highlight:: cython .. _memoryviews: ***************** Typed Memoryviews ***************** .. include:: ../two-syntax-variants-used Typed memoryviews allow efficient access to memory buffers, such as those underlying NumPy arrays, without incurring any Python overhead. Memoryviews are similar to the current NumPy array buffer support (``np.ndarray[np.float64_t, ndim=2]``), but they have more features and cleaner syntax. Memoryviews are more general than the old NumPy array buffer support, because they can handle a wider variety of sources of array data. For example, they can handle C arrays and the Cython array type (:ref:`view_cython_arrays`). A memoryview can be used in any context (function parameters, module-level, cdef class attribute, etc) and can be obtained from nearly any object that exposes writable buffer through the `PEP 3118`_ buffer interface. .. _`PEP 3118`: https://www.python.org/dev/peps/pep-3118/ .. _view_quickstart: Quickstart ========== If you are used to working with NumPy, the following examples should get you started with Cython memory views. .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/quickstart.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/quickstart.pyx This code should give the following output:: NumPy sum of the NumPy array before assignments: 351 NumPy sum of NumPy array after assignments: 81 Memoryview sum of NumPy array is 81 Memoryview sum of C array is 451 Memoryview sum of Cython array is 1351 Memoryview sum of C memoryview is 451 .. _using_memoryviews: Using memoryviews ================= Syntax ------ Memory views use Python slicing syntax in a similar way as NumPy. To create a complete view on a one-dimensional ``int`` buffer: .. tabs:: .. group-tab:: Pure Python .. code-block:: python view1D: cython.int[:] = exporting_object .. group-tab:: Cython .. code-block:: cython cdef int[:] view1D = exporting_object A complete 3D view: .. tabs:: .. group-tab:: Pure Python .. code-block:: python view3D: cython.int[:,:,:] = exporting_object .. group-tab:: Cython .. code-block:: cython cdef int[:,:,:] view3D = exporting_object They also work conveniently as function arguments: .. tabs:: .. group-tab:: Pure Python .. code-block:: python def process_3d_buffer(view: cython.int[:,:,:]): ... .. group-tab:: Cython .. code-block:: cython def process_3d_buffer(int[:,:,:] view not None): ... The Cython ``not None`` declaration for the argument automatically rejects ``None`` values as input, which would otherwise be allowed. The reason why ``None`` is allowed by default is that it is conveniently used for return arguments. On the other hand, when pure python mode is used, ``None`` value is rejected by default. It is allowed only when type is declared as ``Optional``: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/not_none.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/not_none.pyx Cython will reject incompatible buffers automatically, e.g. passing a three dimensional buffer into a function that requires a two dimensional buffer will raise a ``ValueError``. To use a memory view on a numpy array with a custom dtype, you'll need to declare an equivalent packed struct that mimics the dtype: .. literalinclude:: ../../examples/userguide/memoryviews/custom_dtype.pyx .. note:: Pure python mode currently does not support packed structs Indexing -------- In Cython, index access on memory views is automatically translated into memory addresses. The following code requests a two-dimensional memory view of C ``int`` typed items and indexes into it: .. tabs:: .. group-tab:: Pure Python .. code-block:: python buf: cython.int[:,:] = exporting_object print(buf[1,2]) .. group-tab:: Cython .. code-block:: cython cdef int[:,:] buf = exporting_object print(buf[1,2]) Negative indices work as well, counting from the end of the respective dimension:: print(buf[-1,-2]) The following function loops over each dimension of a 2D array and adds 1 to each item: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/add_one.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/add_one.pyx Indexing and slicing can be done with or without the GIL. It basically works like NumPy. If indices are specified for every dimension you will get an element of the base type (e.g. ``int``). Otherwise, you will get a new view. An Ellipsis means you get consecutive slices for every unspecified dimension: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/slicing.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/slicing.pyx Copying ------- Memory views can be copied in place: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/copy.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/copy.pyx They can also be copied with the ``copy()`` and ``copy_fortran()`` methods; see :ref:`view_copy_c_fortran`. .. _view_transposing: Transposing ----------- In most cases (see below), the memoryview can be transposed in the same way that NumPy slices can be transposed: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/transpose.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/transpose.pyx This gives a new, transposed, view on the data. Transposing requires that all dimensions of the memoryview have a direct access memory layout (i.e., there are no indirections through pointers). See :ref:`view_general_layouts` for details. Newaxis ------- As for NumPy, new axes can be introduced by indexing an array with ``None`` : .. tabs:: .. group-tab:: Pure Python .. code-block:: python myslice: cython.double[:] = np.linspace(0, 10, num=50) # 2D array with shape (1, 50) myslice[None] # or myslice[None, :] # 2D array with shape (50, 1) myslice[:, None] # 3D array with shape (1, 10, 1) myslice[None, 10:-20:2, None] .. group-tab:: Cython .. code-block:: cython cdef double[:] myslice = np.linspace(0, 10, num=50) # 2D array with shape (1, 50) myslice[None] # or myslice[None, :] # 2D array with shape (50, 1) myslice[:, None] # 3D array with shape (1, 10, 1) myslice[None, 10:-20:2, None] One may mix new axis indexing with all other forms of indexing and slicing. See also an example_. .. _readonly_views: Read-only views --------------- .. note:: Pure python mode currently does not support read-only views. Since Cython 0.28, the memoryview item type can be declared as ``const`` to support read-only buffers as input: .. literalinclude:: ../../examples/userguide/memoryviews/np_flag_const.pyx Using a non-const memoryview with a binary Python string produces a runtime error. You can solve this issue with a ``const`` memoryview: .. literalinclude:: ../../examples/userguide/memoryviews/view_string.pyx Note that this does not *require* the input buffer to be read-only:: a = np.linspace(0, 10, num=50) myslice = a # read-only view of a writable buffer Writable buffers are still accepted by ``const`` views, but read-only buffers are not accepted for non-const, writable views:: cdef double[:] myslice # a normal read/write memory view a = np.linspace(0, 10, num=50) a.setflags(write=False) myslice = a # ERROR: requesting writable memory view from read-only buffer! Comparison to the old buffer support ==================================== You will probably prefer memoryviews to the older syntax because: * The syntax is cleaner * Memoryviews do not usually need the GIL (see :ref:`view_needs_gil`) * Memoryviews are considerably faster For example, this is the old syntax equivalent of the ``sum3d`` function above: .. literalinclude:: ../../examples/userguide/memoryviews/old_sum3d.pyx Note that we can't use ``nogil`` for the buffer version of the function as we could for the memoryview version of ``sum3d`` above, because buffer objects are Python objects. However, even if we don't use ``nogil`` with the memoryview, it is significantly faster. This is a output from an IPython session after importing both versions:: In [2]: import numpy as np In [3]: arr = np.zeros((40, 40, 40), dtype=int) In [4]: timeit -r15 old_sum3d(arr) 1000 loops, best of 15: 298 us per loop In [5]: timeit -r15 sum3d(arr) 1000 loops, best of 15: 219 us per loop Python buffer support ===================== Cython memoryviews support nearly all objects exporting the interface of Python `new style buffers`_. This is the buffer interface described in `PEP 3118`_. NumPy arrays support this interface, as do :ref:`view_cython_arrays`. The "nearly all" is because the Python buffer interface allows the *elements* in the data array to themselves be pointers; Cython memoryviews do not yet support this. .. _`new style buffers`: https://docs.python.org/3/c-api/buffer.html .. _view_memory_layout: Memory layout ============= The buffer interface allows objects to identify the underlying memory in a variety of ways. With the exception of pointers for data elements, Cython memoryviews support all Python new-type buffer layouts. It can be useful to know or specify memory layout if the memory has to be in a particular format for an external routine, or for code optimization. Background ---------- The concepts are as follows: there is data access and data packing. Data access means either direct (no pointer) or indirect (pointer). Data packing means your data may be contiguous or not contiguous in memory, and may use *strides* to identify the jumps in memory consecutive indices need to take for each dimension. NumPy arrays provide a good model of strided direct data access, so we'll use them for a refresher on the concepts of C and Fortran contiguous arrays, and data strides. Brief recap on C, Fortran and strided memory layouts ---------------------------------------------------- The simplest data layout might be a C contiguous array. This is the default layout in NumPy and Cython arrays. C contiguous means that the array data is continuous in memory (see below) and that neighboring elements in the first dimension of the array are furthest apart in memory, whereas neighboring elements in the last dimension are closest together. For example, in NumPy:: In [2]: arr = np.array([['0', '1', '2'], ['3', '4', '5']], dtype='S1') Here, ``arr[0, 0]`` and ``arr[0, 1]`` are one byte apart in memory, whereas ``arr[0, 0]`` and ``arr[1, 0]`` are 3 bytes apart. This leads us to the idea of *strides*. Each axis of the array has a stride length, which is the number of bytes needed to go from one element on this axis to the next element. In the case above, the strides for axes 0 and 1 will obviously be:: In [3]: arr.strides Out[4]: (3, 1) For a 3D C contiguous array:: In [5]: c_contig = np.arange(24, dtype=np.int8).reshape((2,3,4)) In [6] c_contig.strides Out[6]: (12, 4, 1) A Fortran contiguous array has the opposite memory ordering, with the elements on the first axis closest together in memory:: In [7]: f_contig = np.array(c_contig, order='F') In [8]: np.all(f_contig == c_contig) Out[8]: True In [9]: f_contig.strides Out[9]: (1, 2, 6) A contiguous array is one for which a single continuous block of memory contains all the data for the elements of the array, and therefore the memory block length is the product of number of elements in the array and the size of the elements in bytes. In the example above, the memory block is 2 * 3 * 4 * 1 bytes long, where 1 is the length of an ``np.int8``. An array can be contiguous without being C or Fortran order:: In [10]: c_contig.transpose((1, 0, 2)).strides Out[10]: (4, 12, 1) Slicing an NumPy array can easily make it not contiguous:: In [11]: sliced = c_contig[:,1,:] In [12]: sliced.strides Out[12]: (12, 1) In [13]: sliced.flags Out[13]: C_CONTIGUOUS : False F_CONTIGUOUS : False OWNDATA : False WRITEABLE : True ALIGNED : True UPDATEIFCOPY : False Default behavior for memoryview layouts --------------------------------------- As you'll see in :ref:`view_general_layouts`, you can specify memory layout for any dimension of an memoryview. For any dimension for which you don't specify a layout, then the data access is assumed to be direct, and the data packing assumed to be strided. For example, that will be the assumption for memoryviews like: .. tabs:: .. group-tab:: Pure Python .. code-block:: python my_memoryview: cython.int[:, :, :] = obj .. group-tab:: Cython .. code-block:: cython int [:, :, :] my_memoryview = obj .. _c_and_fortran_contiguous_memoryviews: C and Fortran contiguous memoryviews ------------------------------------ You can specify C and Fortran contiguous layouts for the memoryview by using the ``::1`` step syntax at definition. For example, if you know for sure your memoryview will be on top of a 3D C contiguous layout, you could write: .. tabs:: .. group-tab:: Pure Python .. code-block:: python c_contiguous: cython.int[:, :, ::1] = c_contig .. group-tab:: Cython .. code-block:: cython cdef int[:, :, ::1] c_contiguous = c_contig where ``c_contig`` could be a C contiguous NumPy array. The ``::1`` at the 3rd position means that the elements in this 3rd dimension will be one element apart in memory. If you know you will have a 3D Fortran contiguous array: .. tabs:: .. group-tab:: Pure Python .. code-block:: python f_contiguous: cython.int[::1, :, :] = f_contig .. group-tab:: Cython .. code-block:: cython cdef int[::1, :, :] f_contiguous = f_contig If you pass a non-contiguous buffer, for example: .. tabs:: .. group-tab:: Pure Python .. code-block:: python # This array is C contiguous c_contig = np.arange(24).reshape((2,3,4)) c_contiguous: cython.int[:, :, ::1] = c_contig # But this isn't c_contiguous = np.array(c_contig, order='F') .. group-tab:: Cython .. code-block:: cython # This array is C contiguous c_contig = np.arange(24).reshape((2,3,4)) cdef int[:, :, ::1] c_contiguous = c_contig # But this isn't c_contiguous = np.array(c_contig, order='F') you will get a ``ValueError`` at runtime:: /Users/mb312/dev_trees/minimal-cython/mincy.pyx in init mincy (mincy.c:17267)() 69 70 # But this isn't ---> 71 c_contiguous = np.array(c_contig, order='F') 72 73 # Show the sum of all the arrays before altering it /Users/mb312/dev_trees/minimal-cython/stringsource in View.MemoryView.memoryview_cwrapper (mincy.c:9995)() /Users/mb312/dev_trees/minimal-cython/stringsource in View.MemoryView.memoryview.__cinit__ (mincy.c:6799)() ValueError: ndarray is not C-contiguous Thus the ``::1`` in the slice type specification indicates in which dimension the data is contiguous. It can only be used to specify full C or Fortran contiguity. .. _view_copy_c_fortran: C and Fortran contiguous copies ------------------------------- .. Mark : I could not make this work - should it? # This slice is C contiguous c_contig = np.arange(24).reshape((2,3,4)) f_contig = np.array(c_contig, order='F') cdef int [:, :, ::1] c_contig_view = c_contig cdef int [::1, :, :] f_contig_view = f_contig cdef int[:, :, ::1] f2c = f_contig_view.copy() cdef int[::1, :, :] c2f = c_contig_view.copy_fortran() Copies can be made C or Fortran contiguous using the ``.copy()`` and ``.copy_fortran()`` methods: .. tabs:: .. group-tab:: Pure Python .. code-block:: python # This view is C contiguous c_contiguous: cython.int[:, :, ::1] = myview.copy() # This view is Fortran contiguous f_contiguous_slice: cython.int[::1, :] = myview.copy_fortran() .. group-tab:: Cython .. code-block:: cython # This view is C contiguous cdef int[:, :, ::1] c_contiguous = myview.copy() # This view is Fortran contiguous cdef int[::1, :] f_contiguous_slice = myview.copy_fortran() .. _view_general_layouts: Specifying more general memory layouts -------------------------------------- Data layout can be specified using the previously seen ``::1`` slice syntax, or by using any of the constants in ``cython.view``. If no specifier is given in any dimension, then the data access is assumed to be direct, and the data packing assumed to be strided. If you don't know whether a dimension will be direct or indirect (because you're getting an object with a buffer interface from some library perhaps), then you can specify the ``generic`` flag, in which case it will be determined at runtime. The flags are as follows: * ``generic`` - strided and direct or indirect * ``strided`` - strided and direct (this is the default) * ``indirect`` - strided and indirect * ``contiguous`` - contiguous and direct * ``indirect_contiguous`` - the list of pointers is contiguous and they can be used like this: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/memory_layout.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/memory_layout.pyx Only the first, last or the dimension following an indirect dimension may be specified contiguous: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/memory_layout_2.py :lines: 2-13 .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/memory_layout_2.pyx :lines: 2-12 The difference between the ``contiguous`` flag and the ``::1`` specifier is that the former specifies contiguity for only one dimension, whereas the latter specifies contiguity for all following (Fortran) or preceding (C) dimensions: .. tabs:: .. group-tab:: Pure Python .. code-block:: python c_contig: cython.int[:, ::1] = ... # VALID myslice: cython.int[:, ::view.contiguous] = c_contig[::2] # INVALID myslice: cython.int[:, ::1] = c_contig[::2] .. group-tab:: Cython .. code-block:: cython cdef int[:, ::1] c_contig = ... # VALID cdef int[:, ::view.contiguous] myslice = c_contig[::2] # INVALID cdef int[:, ::1] myslice = c_contig[::2] The former case is valid because the last dimension remains contiguous, but the first dimension does not "follow" the last one anymore (meaning, it was strided already, but it is not C or Fortran contiguous any longer), since it was sliced. .. _view_needs_gil: Memoryviews and the GIL ======================= As you will see from the :ref:`view_quickstart` section, memoryviews often do not need the GIL: .. tabs:: .. group-tab:: Pure Python .. code-block:: python @cython.nogil @cython.ccall def sum3d(arr: cython.int[:, :, :]) -> cython.int: ... .. group-tab:: Cython .. code-block:: cython cpdef int sum3d(int[:, :, :] arr) nogil: ... In particular, you do not need the GIL for memoryview indexing, slicing or transposing. Memoryviews require the GIL for the copy methods (:ref:`view_copy_c_fortran`), or when the dtype is object and an object element is read or written. Memoryview Objects and Cython Arrays ==================================== These typed memoryviews can be converted to Python memoryview objects (``cython.view.memoryview``). These Python objects are indexable, sliceable and transposable in the same way that the original memoryviews are. They can also be converted back to Cython-space memoryviews at any time. They have the following attributes: * ``shape``: size in each dimension, as a tuple. * ``strides``: stride along each dimension, in bytes. * ``suboffsets`` * ``ndim``: number of dimensions. * ``size``: total number of items in the view (product of the shape). * ``itemsize``: size, in bytes, of the items in the view. * ``nbytes``: equal to ``size`` times ``itemsize``. * ``base`` And of course the aforementioned ``T`` attribute (:ref:`view_transposing`). These attributes have the same semantics as in NumPy_. For instance, to retrieve the original object: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/cython_array.py :lines: 2- .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/cython_array.pyx :lines: 2- Note that this example returns the original object from which the view was obtained, and that the view was resliced in the meantime. .. _view_cython_arrays: Cython arrays ============= Whenever a Cython memoryview is copied (using any of the ``copy()`` or ``copy_fortran()`` methods), you get a new memoryview slice of a newly created ``cython.view.array`` object. This array can also be used manually, and will automatically allocate a block of data. It can later be assigned to a C or Fortran contiguous slice (or a strided slice). It can be used like: .. tabs:: .. group-tab:: Pure Python .. code-block:: python from cython.cimports.cython import view my_array = view.array(shape=(10, 2), itemsize=cython.sizeof(cython.int), format="i") my_slice: cython.int[:, :] = my_array .. group-tab:: Cython .. code-block:: cython from cython cimport view my_array = view.array(shape=(10, 2), itemsize=sizeof(int), format="i") cdef int[:, :] my_slice = my_array It also takes an optional argument ``mode`` ('c' or 'fortran') and a boolean ``allocate_buffer``, that indicates whether a buffer should be allocated and freed when it goes out of scope: .. tabs:: .. group-tab:: Pure Python .. code-block:: python my_array: view.array = view.array(..., mode="fortran", allocate_buffer=False) my_array.data = cython.cast(cython.p_char, my_data_pointer) # define a function that can deallocate the data (if needed) my_array.callback_free_data = free .. group-tab:: Cython .. code-block:: cython cdef view.array my_array = view.array(..., mode="fortran", allocate_buffer=False) my_array.data = my_data_pointer # define a function that can deallocate the data (if needed) my_array.callback_free_data = free You can also cast pointers to array, or C arrays to arrays: .. tabs:: .. group-tab:: Pure Python .. code-block:: python my_array: view.array = cython.cast(cython.int[:10, :2], my_data_pointer) my_array: view.array = cython.cast(cython.int[:, :], my_c_array) .. group-tab:: Cython .. code-block:: cython cdef view.array my_array = my_data_pointer cdef view.array my_array = my_c_array Of course, you can also immediately assign a cython.view.array to a typed memoryview slice. A C array may be assigned directly to a memoryview slice: .. tabs:: .. group-tab:: Pure Python .. code-block:: python myslice: cython.int[:, ::1] = my_2d_c_array .. group-tab:: Cython .. code-block:: cython cdef int[:, ::1] myslice = my_2d_c_array The arrays are indexable and sliceable from Python space just like memoryview objects, and have the same attributes as memoryview objects. CPython array module ==================== An alternative to ``cython.view.array`` is the ``array`` module in the Python standard library. In Python 3, the ``array.array`` type supports the buffer interface natively, so memoryviews work on top of it without additional setup. Starting with Cython 0.17, however, it is possible to use these arrays as buffer providers also in Python 2. This is done through explicitly cimporting the ``cpython.array`` module as follows: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/cpython_array.py .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/cpython_array.pyx Note that the cimport also enables the old buffer syntax for the array type. Therefore, the following also works: .. tabs:: .. group-tab:: Pure Python .. code-block:: python from cython.cimports.cpython import array def sum_array(arr: array.array[cython.int]): # using old buffer syntax ... .. group-tab:: Cython .. code-block:: cython from cpython cimport array def sum_array(array.array[int] arr): # using old buffer syntax ... Coercion to NumPy ================= Memoryview (and array) objects can be coerced to a NumPy ndarray, without having to copy the data. You can e.g. do: .. tabs:: .. group-tab:: Pure Python .. code-block:: python from cython.cimports.numpy import int32_t import numpy as np numpy_array = np.asarray(cython.cast(int32_t[:10, :10], my_pointer)) .. group-tab:: Cython .. code-block:: cython cimport numpy as cnp import numpy as np numpy_array = np.asarray( my_pointer) Of course, you are not restricted to using NumPy's type (such as ``cnp.int32_t`` here), you can use any usable type. None Slices =========== Although memoryview slices are not objects they can be set to ``None`` and they can be checked for being ``None`` as well: .. tabs:: .. group-tab:: Pure Python .. code-block:: python def func(myarray: typing.Optional[cython.double[:]] = None): print(myarray is None) .. group-tab:: Cython .. code-block:: cython def func(double[:] myarray = None): print(myarray is None) If the function requires real memory views as input, it is therefore best to reject ``None`` input straight away in the signature: .. tabs:: .. group-tab:: Pure Python .. code-block:: python def func(myarray: cython.double[:]): ... .. group-tab:: Cython .. code-block:: cython def func(double[:] myarray not None): ... Unlike object attributes of extension classes, memoryview slices are not initialized to ``None``. Pass data from a C function via pointer ======================================= Since use of pointers in C is ubiquitous, here we give a quick example of how to call C functions whose arguments contain pointers. Let's suppose you want to manage an array (allocate and deallocate) with NumPy (it can also be Python arrays, or anything that supports the buffer interface), but you want to perform computation on this array with an external C function implemented in :file:`C_func_file.c`: .. literalinclude:: ../../examples/userguide/memoryviews/C_func_file.c :caption: C_func_file.c :linenos: This file comes with a header file called :file:`C_func_file.h` containing: .. literalinclude:: ../../examples/userguide/memoryviews/C_func_file.h :caption: C_func_file.h :linenos: where ``arr`` points to the array and ``n`` is its size. You can call the function in a Cython file in the following way: .. tabs:: .. group-tab:: Pure Python .. literalinclude:: ../../examples/userguide/memoryviews/memview_to_c.pxd :caption: memview_to_c.pxd :linenos: .. literalinclude:: ../../examples/userguide/memoryviews/memview_to_c.py :caption: memview_to_c.py :linenos: .. group-tab:: Cython .. literalinclude:: ../../examples/userguide/memoryviews/memview_to_c.pyx :caption: memview_to_c.pyx :linenos: Several things to note: - ``::1`` requests a C contiguous view, and fails if the buffer is not C contiguous. See :ref:`c_and_fortran_contiguous_memoryviews`. - ``&arr_memview[0]`` and ``cython.address(arr_memview[0]`` can be understood as 'the address of the first element of the memoryview'. For contiguous arrays, this is equivalent to the start address of the flat memory buffer. - ``arr_memview.shape[0]`` could have been replaced by ``arr_memview.size``, ``arr.shape[0]`` or ``arr.size``. But ``arr_memview.shape[0]`` is more efficient because it doesn't require any Python interaction. - ``multiply_by_10`` will perform computation in-place if the array passed is contiguous, and will return a new numpy array if ``arr`` is not contiguous. - If you are using Python arrays instead of numpy arrays, you don't need to check if the data is stored contiguously as this is always the case. See :ref:`array-array`. This way, you can call the C function similar to a normal Python function, and leave all the memory management and cleanup to NumPy arrays and Python's object handling. For the details of how to compile and call functions in C files, see :ref:`using_c_libraries`. Performance: Disabling initialization checks ============================================ Every time the memoryview is accessed, Cython adds a check to make sure that it has been initialized. If you are looking for performance, you can disable them by setting the ``initializedcheck`` directive to ``False``. See: :ref:`compiler-directives` for more information about this directive. .. _GIL: https://docs.python.org/dev/glossary.html#term-global-interpreter-lock .. _NumPy: https://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html#memory-layout .. _example: https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html