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 (*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.

```
from cython.view cimport array as cvarray
import numpy as np
# Memoryview on a NumPy array
narr = np.arange(27, dtype=np.dtype("i")).reshape((3, 3, 3))
cdef int [:, :, :] narr_view = narr
# Memoryview on a C array
cdef int carr[3][3][3]
cdef int [:, :, :] carr_view = carr
# Memoryview on a Cython array
cyarr = cvarray(shape=(3, 3, 3), itemsize=sizeof(int), format="i")
cdef int [:, :, :] cyarr_view = cyarr
# Show the sum of all the arrays before altering it
print "NumPy sum of the NumPy array before assignments:", narr.sum()
# We can copy the values from one memoryview into another using a single
# statement, by either indexing with ... or (NumPy-style) with a colon.
carr_view[...] = narr_view
cyarr_view[:] = narr_view
# NumPy-style syntax for assigning a single value to all elements.
narr_view[:, :, :] = 3
# Just to distinguish the arrays
carr_view[0, 0, 0] = 100
cyarr_view[0, 0, 0] = 1000
# Assigning into the memoryview on the NumPy array alters the latter
print "NumPy sum of NumPy array after assignments:", narr.sum()
# A function using a memoryview does not usually need the GIL
cpdef int sum3d(int[:, :, :] arr) nogil:
cdef int total = 0
I = arr.shape[0]
J = arr.shape[1]
K = arr.shape[2]
for i in range(I):
for j in range(J):
for k in range(K):
total += arr[i, j, k]
return total
# A function accepting a memoryview knows how to use a NumPy array,
# a C array, a Cython array...
print "Memoryview sum of NumPy array is", sum3d(narr)
print "Memoryview sum of C array is", sum3d(carr)
print "Memoryview sum of Cython array is", sum3d(cyarr)
# ... and of course, a memoryview.
print "Memoryview sum of C memoryview is", sum3d(carr_view)
```

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
```

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:

```
cdef int[:, :, :] my_view = ...
# These are all equivalent
my_view[10]
my_view[10, :, :]
my_view[10, ...]
```

Memoryviews can be copied inplace:

```
cdef int[:, :, :] to_view, from_view
...
# copy the elements in from_view to to_view
to_view[...] = from_view
# or
to_view[:] = from_view
# or
to_view[:, :, :] = from_view
```

They can also be copied with the `copy()` and `copy_fortran()` methods; see
*C and Fortran contiguous copies*.

In most cases (see below), the memoryview can be transposed in the same way that NumPy slices can be transposed:

```
cdef int[:, ::1] c_contig = ...
cdef int[::1, :] f_contig = c_contig.T
```

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 *Specifying more general memory layouts* for details.

As for NumPy, new axes can be introduced by indexing an array with `None`

```
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]
```

One may mix new axis indexing with all other forms of indexing and slicing. See also an example.

You will probably prefer memoryviews to the older syntax because:

- The syntax is cleaner
- Memoryviews do not usually need the GIL (see
*Memoryviews and the GIL*) - Memoryviews are considerably faster

For example, this is the old syntax equivalent of the `sum3d` function above:

```
cpdef int old_sum3d(object[int, ndim=3, mode='strided'] arr):
cdef int I, J, K, total = 0
I = arr.shape[0]
J = arr.shape[1]
K = arr.shape[2]
for i in range(I):
for j in range(J):
for k in range(K):
total += arr[i, j, k]
return total
```

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
```

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 *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.

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.

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.

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 togther 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 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
```

As you’ll see in *Specifying more general memory 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:

```
int [:, :, :] my_memoryview = obj
```

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:

```
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:

```
cdef int[::1, :, :] f_contiguous = f_contig
```

If you try to do this kind of thing:

```
# 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` like this 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.

Copies can be made C or Fortran contiguous using the `.copy()` and
`.copy_fortran()` methods:

```
# 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()
```

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:

```
from cython cimport view
# direct access in both dimensions, strided in the first dimension, contiguous in the last
cdef int[:, ::view.contiguous] a
# contiguous list of pointers to contiguous lists of ints
cdef int[::view.indirect_contiguous, ::1] b
# direct or indirect in the first dimension, direct in the second dimension
# strided in both dimensions
cdef int[::view.generic, :] c
```

Only the first, last or the dimension following an indirect dimension may be specified contiguous:

```
# INVALID
cdef int[::view.contiguous, ::view.indirect, :] a
cdef int[::1, ::view.indirect, :] b
# VALID
cdef int[::view.indirect, ::1, :] a
cdef int[::view.indirect, :, ::1] b
cdef int[::view.indirect_contiguous, ::1, :]
```

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:

```
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.

As you will see from the *Quickstart* section, memoryviews often do
not need the GIL:

```
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
(*C and Fortran contiguous copies*), or when the dtype is object and an object
element is read or written.

These typed memoryviews can be converted to Python memoryview objects (cython.view.memoryview). These Python objects are indexable, slicable 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.suboffsetsndim: 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 tosizetimesitemsize.base

And of course the aforementioned `T` attribute (*Transposing*).
These attributes have the same semantics as in NumPy. For instance, to
retrieve the original object:

```
import numpy
cimport numpy as cnp
cdef cnp.int32_t[:] a = numpy.arange(10, dtype=numpy.int32)
a = a[::2]
print a, numpy.asarray(a), a.base
# this prints: <MemoryView of 'ndarray' object> [0 2 4 6 8] [0 1 2 3 4 5 6 7 8 9]
```

Note that this example returns the original object from which the view was obtained, and that the view was resliced in the meantime.

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:

```
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:

```
cdef view.array my_array = view.array(..., mode="fortran", allocate_buffer=False)
my_array.data = <char *> 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:

```
cdef view.array my_array = <int[:10, :2]> my_data_pointer
cdef view.array my_array = <int[:, :]> 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:

```
cdef int[:, ::1] myslice = my_2d_c_array
```

The arrays are indexable and slicable from Python space just like memoryview objects, and have the same attributes as memoryview objects.

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:

```
cimport cpython.array
def sum_array(int[:] view):
"""
>>> from array import array
>>> sum_array( array('i', [1,2,3]) )
6
"""
cdef int total
for i in range(view.shape[0]):
total += view[i]
return total
```

Note that the cimport also enables the old buffer syntax for the array type. Therefore, the following also works:

```
from cpython cimport array
def sum_array(array.array[int] arr): # using old buffer syntax
...
```

Memoryview (and array) objects can be coerced to a NumPy ndarray, without having to copy the data. You can e.g. do:

```
cimport numpy as np
import numpy as np
numpy_array = np.asarray(<np.int32_t[:10, :10]> my_pointer)
```

Of course, you are not restricted to using NumPy’s type (such as `np.int32_t`
here), you can use any usable type.

Although memoryview slices are not objects they can be set to None and they can be be checked for being None as well:

```
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, which is supported in Cython 0.17 and later as follows:

```
def func(double[:] myarray not None):
...
```

Unlike object attributes of extension classes, memoryview slices are not initialized to None.