What is a memoryview:
When you write in a function:
cdef double[:] a
you end up with a __Pyx_memviewslice object:
typedef struct {
struct __pyx_memoryview_obj *memview;
char *data;
Py_ssize_t shape[8];
Py_ssize_t strides[8];
Py_ssize_t suboffsets[8];
} __Pyx_memviewslice;
The memoryview contains a C pointer some some data which it (usually) doesn't directly own. It also contains a pointer to an underlying Python object (struct __pyx_memoryview_obj *memview;). If the data is owned by a Python object then memview holds a reference to that and ensures the Python object that holds the data is kept alive as long as the memoryview is around.
The combination of the pointer to the raw data, and information of how to index it (shape, strides and suboffsets) allows Cython to do indexing the using the raw data pointers and some simple C maths (which is very efficient). e.g.:
x=a[0]
gives something like:
(*((double *) ( /* dim=0 */ (__pyx_v_a.data + __pyx_t_2 * __pyx_v_a.strides[0]) )));
In contrast, if you work with untyped objects and write something like:
a = np.array([1,2,3]) # note no typedef
x = x[0]
the indexing is done as:
__Pyx_GetItemInt(__pyx_v_a, 0, long, 1, __Pyx_PyInt_From_long, 0, 0, 1);
which itself expands to a whole bunch of Python C-api calls (so is slow). Ultimately it calls a's __getitem__ method.
Compared to typed numpy arrays: there really isn't a huge difference.
If you do something like:
cdef np.ndarray[np.int32_t, ndim=1] new_arr
it works practically very like a memoryview, with access to raw pointers and the speed should be very similar.
The advantage to using memoryviews is that you can use a wider range of array types with them (such as the standard library array), so you're more flexible about the types your functions can be called with. This fits in with the general Python idea of "duck-typing" - that your code should work with any parameter that behaves the right way (rather than checking the type).
A second (small) advantage is that you don't need the numpy headers to build your module.
A third (possibly larger) advantage is that memoryviews can be initialised without the GIL while cdef np.ndarrays can't (http://docs.cython.org/src/userguide/memoryviews.html#comparison-to-the-old-buffer-support)
A slight disadvantage to memoryviews is that they seem to be slightly slower to set up.
Compared to just using malloced int pointers:
You won't get any speed advantage (but neither will you get too much speed loss). The minor advantages of converting using a memoryview are:
You can write functions that can be used either from Python or internally within Cython:
cpdef do_something_useful(double[:] x):
# can be called from Python with any array type or from Cython
# with something that's already a memoryview
....
You can let Cython handle the freeing of memory for this type of array, which could simplify your life for things that have an unknown lifetime. See http://docs.cython.org/src/userguide/memoryviews.html#cython-arrays and especially .callback_free_data.
You can pass your data back to python python code (it'll get the underlying __pyx_memoryview_obj or something similar). Be very careful of memory management here (i.e. see point 2!).
The other thing you can do is handle things like 2D arrays defined as pointer to pointer (e.g. double**). See http://docs.cython.org/src/userguide/memoryviews.html#specifying-more-general-memory-layouts. I generally don't like this type of array, but if you have existing C code that already uses if then you can interface with that (and pass it back to Python so your Python code can also use it).