Standard array subclasses

The ndarray can be inherited from (in Python or in C) if desired. Therefore, it can form a foundation for many useful classes. Often whether to sub-class the array object or to simply use the core array component as an internal part of a new class is a difficult decision, and can be simply a matter of choice. NumPy has several tools for simplifying how your new object interacts with other array objects, and so the choice may not be significant in the end. One way to simplify the question is by asking yourself if the object you are interested in can be replaced as a single array or does it really require two or more arrays at its core.

Note that asarray always returns the base-class ndarray. If you are confident that your use of the array object can handle any subclass of an ndarray, then asanyarray can be used to allow subclasses to propagate more cleanly through your subroutine. In principal a subclass could redefine any aspect of the array and therefore, under strict guidelines, asanyarray would rarely be useful. However, most subclasses of the array object will not redefine certain aspects of the array object such as the buffer interface, or the attributes of the array. One important example, however, of why your subroutine may not be able to handle an arbitrary subclass of an array is that matrices redefine the “*” operator to be matrix-multiplication, rather than element-by-element multiplication.

Special attributes and methods

NumPy provides several hooks that classes can customize:

class.__array_ufunc__(ufunc, method, *inputs, **kwargs)

New in version 1.13.

Any class, ndarray subclass or not, can define this method or set it to None in order to override the behavior of NumPy’s ufuncs. This works quite similarly to Python’s __mul__ and other binary operation routines.

• ufunc is the ufunc object that was called.
• method is a string indicating which Ufunc method was called (one of "__call__", "reduce", "reduceat", "accumulate", "outer", "inner").
• inputs is a tuple of the input arguments to the ufunc.
• kwargs is a dictionary containing the optional input arguments of the ufunc. If given, any out arguments, both positional and keyword, are passed as a tuple in kwargs. See the discussion in Universal functions (ufunc) for details.

The method should return either the result of the operation, or NotImplemented if the operation requested is not implemented.

If one of the input or output arguments has a __array_ufunc__ method, it is executed instead of the ufunc. If more than one of the arguments implements __array_ufunc__, they are tried in the order: subclasses before superclasses, inputs before outputs, otherwise left to right. The first routine returning something other than NotImplemented determines the result. If all of the __array_ufunc__ operations return NotImplemented, a TypeError is raised.

Note

We intend to re-implement numpy functions as (generalized) Ufunc, in which case it will become possible for them to be overridden by the __array_ufunc__ method. A prime candidate is matmul, which currently is not a Ufunc, but could be relatively easily be rewritten as a (set of) generalized Ufuncs. The same may happen with functions such as median, min, and argsort.

Like with some other special methods in python, such as __hash__ and __iter__, it is possible to indicate that your class does not support ufuncs by setting __array_ufunc__ = None. Ufuncs always raise TypeError when called on an object that sets __array_ufunc__ = None.

The presence of __array_ufunc__ also influences how ndarray handles binary operations like arr + obj and arr < obj when arr is an ndarray and obj is an instance of a custom class. There are two possibilities. If obj.__array_ufunc__ is present and not None, then ndarray.__add__ and friends will delegate to the ufunc machinery, meaning that arr + obj becomes np.add(arr, obj), and then add invokes obj.__array_ufunc__. This is useful if you want to define an object that acts like an array.

Alternatively, if obj.__array_ufunc__ is set to None, then as a special case, special methods like ndarray.__add__ will notice this and unconditionally raise TypeError. This is useful if you want to create objects that interact with arrays via binary operations, but are not themselves arrays. For example, a units handling system might have an object m representing the “meters” unit, and want to support the syntax arr * m to represent that the array has units of “meters”, but not want to otherwise interact with arrays via ufuncs or otherwise. This can be done by setting __array_ufunc__ = None and defining __mul__ and __rmul__ methods. (Note that this means that writing an __array_ufunc__ that always returns NotImplemented is not quite the same as setting __array_ufunc__ = None: in the former case, arr + obj will raise TypeError, while in the latter case it is possible to define a __radd__ method to prevent this.)

The above does not hold for in-place operators, for which ndarray never returns NotImplemented. Hence, arr += obj would always lead to a TypeError. This is because for arrays in-place operations cannot generically be replaced by a simple reverse operation. (For instance, by default, arr += obj would be translated to arr = arr + obj, i.e., arr would be replaced, contrary to what is expected for in-place array operations.)

Note

If you define __array_ufunc__:

• If you are not a subclass of ndarray, we recommend your class define special methods like __add__ and __lt__ that delegate to ufuncs just like ndarray does. An easy way to do this is to subclass from NDArrayOperatorsMixin.
• If you subclass ndarray, we recommend that you put all your override logic in __array_ufunc__ and not also override special methods. This ensures the class hierarchy is determined in only one place rather than separately by the ufunc machinery and by the binary operation rules (which gives preference to special methods of subclasses; the alternative way to enforce a one-place only hierarchy, of setting __array_ufunc__ to None, would seem very unexpected and thus confusing, as then the subclass would not work at all with ufuncs).
• ndarray defines its own __array_ufunc__, which, evaluates the ufunc if no arguments have overrides, and returns NotImplemented otherwise. This may be useful for subclasses for which __array_ufunc__ converts any instances of its own class to ndarray: it can then pass these on to its superclass using super().__array_ufunc__(*inputs, **kwargs), and finally return the results after possible back-conversion. The advantage of this practice is that it ensures that it is possible to have a hierarchy of subclasses that extend the behaviour. See Subclassing ndarray for details.

Note

If a class defines the __array_ufunc__ method, this disables the __array_wrap__, __array_prepare__, __array_priority__ mechanism described below for ufuncs (which may eventually be deprecated).

class.__array_function__(func, types, args, kwargs)

New in version 1.16.

Note

• In NumPy 1.17, the protocol is enabled by default, but can be disabled with NUMPY_EXPERIMENTAL_ARRAY_FUNCTION=0.
• In NumPy 1.16, you need to set the environment variable NUMPY_EXPERIMENTAL_ARRAY_FUNCTION=1 before importing NumPy to use NumPy function overrides.
• Eventually, expect to __array_function__ to always be enabled.

• func is an arbitrary callable exposed by NumPy’s public API, which was called in the form func(*args, **kwargs).
• types is a collection of unique argument types from the original NumPy function call that implement __array_function__.
• The tuple args and dict kwargs are directly passed on from the original call.

As a convenience for __array_function__ implementors, types provides all argument types with an '__array_function__' attribute. This allows implementors to quickly identify cases where they should defer to __array_function__ implementations on other arguments. Implementations should not rely on the iteration order of types.

Most implementations of __array_function__ will start with two checks:

1. Is the given function something that we know how to overload?
2. Are all arguments of a type that we know how to handle?

If these conditions hold, __array_function__ should return the result from calling its implementation for func(*args, **kwargs). Otherwise, it should return the sentinel value NotImplemented, indicating that the function is not implemented by these types.

There are no general requirements on the return value from __array_function__, although most sensible implementations should probably return array(s) with the same type as one of the function’s arguments.

It may also be convenient to define a custom decorators (implements below) for registering __array_function__ implementations.

HANDLED_FUNCTIONS = {}

class MyArray:
    def __array_function__(self, func, types, args, kwargs):
        if func not in HANDLED_FUNCTIONS:
            return NotImplemented
        # Note: this allows subclasses that don't override
        # __array_function__ to handle MyArray objects
        if not all(issubclass(t, MyArray) for t in types):
            return NotImplemented
        return HANDLED_FUNCTIONS[func](*args, **kwargs)

def implements(numpy_function):
    """Register an __array_function__ implementation for MyArray objects."""
    def decorator(func):
        HANDLED_FUNCTIONS[numpy_function] = func
        return func
    return decorator

@implements(np.concatenate)
def concatenate(arrays, axis=0, out=None):
    ...  # implementation of concatenate for MyArray objects

@implements(np.broadcast_to)
def broadcast_to(array, shape):
    ...  # implementation of broadcast_to for MyArray objects

Note that it is not required for __array_function__ implementations to include all of the corresponding NumPy function’s optional arguments (e.g., broadcast_to above omits the irrelevant subok argument). Optional arguments are only passed in to __array_function__ if they were explicitly used in the NumPy function call.

Just like the case for builtin special methods like __add__, properly written __array_function__ methods should always return NotImplemented when an unknown type is encountered. Otherwise, it will be impossible to correctly override NumPy functions from another object if the operation also includes one of your objects.

For the most part, the rules for dispatch with __array_function__ match those for __array_ufunc__. In particular:

• NumPy will gather implementations of __array_function__ from all specified inputs and call them in order: subclasses before superclasses, and otherwise left to right. Note that in some edge cases involving subclasses, this differs slightly from the current behavior of Python.
• Implementations of __array_function__ indicate that they can handle the operation by returning any value other than NotImplemented.
• If all __array_function__ methods return NotImplemented, NumPy will raise TypeError.

If no __array_function__ methods exists, NumPy will default to calling its own implementation, intended for use on NumPy arrays. This case arises, for example, when all array-like arguments are Python numbers or lists. (NumPy arrays do have a __array_function__ method, given below, but it always returns NotImplemented if any argument other than a NumPy array subclass implements __array_function__.)

One deviation from the current behavior of __array_ufunc__ is that NumPy will only call __array_function__ on the first argument of each unique type. This matches Python’s rule for calling reflected methods, and this ensures that checking overloads has acceptable performance even when there are a large number of overloaded arguments.

class.__array_finalize__(obj)

This method is called whenever the system internally allocates a new array from obj, where obj is a subclass (subtype) of the ndarray. It can be used to change attributes of self after construction (so as to ensure a 2-d matrix for example), or to update meta-information from the “parent.” Subclasses inherit a default implementation of this method that does nothing.

class.__array_prepare__(array, context=None)

At the beginning of every ufunc, this method is called on the input object with the highest array priority, or the output object if one was specified. The output array is passed in and whatever is returned is passed to the ufunc. Subclasses inherit a default implementation of this method which simply returns the output array unmodified. Subclasses may opt to use this method to transform the output array into an instance of the subclass and update metadata before returning the array to the ufunc for computation.

Note

For ufuncs, it is hoped to eventually deprecate this method in favour of __array_ufunc__.

class.__array_wrap__(array, context=None)

At the end of every ufunc, this method is called on the input object with the highest array priority, or the output object if one was specified. The ufunc-computed array is passed in and whatever is returned is passed to the user. Subclasses inherit a default implementation of this method, which transforms the array into a new instance of the object’s class. Subclasses may opt to use this method to transform the output array into an instance of the subclass and update metadata before returning the array to the user.

Note

For ufuncs, it is hoped to eventually deprecate this method in favour of __array_ufunc__.

class.__array_priority__

The value of this attribute is used to determine what type of object to return in situations where there is more than one possibility for the Python type of the returned object. Subclasses inherit a default value of 0.0 for this attribute.

Note

For ufuncs, it is hoped to eventually deprecate this method in favour of __array_ufunc__.

class.__array__([dtype])

If a class (ndarray subclass or not) having the __array__ method is used as the output object of an ufunc, results will be written to the object returned by __array__. Similar conversion is done on input arrays.

Matrix objects

matrix objects inherit from the ndarray and therefore, they have the same attributes and methods of ndarrays. There are six important differences of matrix objects, however, that may lead to unexpected results when you use matrices but expect them to act like arrays:

1. Matrix objects can be created using a string notation to allow Matlab-style syntax where spaces separate columns and semicolons (‘;’) separate rows.
2. Matrix objects are always two-dimensional. This has far-reaching implications, in that m.ravel() is still two-dimensional (with a 1 in the first dimension) and item selection returns two-dimensional objects so that sequence behavior is fundamentally different than arrays.
3. Matrix objects over-ride multiplication to be matrix-multiplication. Make sure you understand this for functions that you may want to receive matrices. Especially in light of the fact that asanyarray(m) returns a matrix when m is a matrix.
4. Matrix objects over-ride power to be matrix raised to a power. The same warning about using power inside a function that uses asanyarray(…) to get an array object holds for this fact.
5. The default __array_priority__ of matrix objects is 10.0, and therefore mixed operations with ndarrays always produce matrices.

6. Matrices have special attributes which make calculations easier. These are

   matrix.T	Returns the transpose of the matrix.
   matrix.H	Returns the (complex) conjugate transpose of self.
   matrix.I	Returns the (multiplicative) inverse of invertible self.
   matrix.A	Return self as an ndarray object.

The matrix class is a Python subclass of the ndarray and can be used as a reference for how to construct your own subclass of the ndarray. Matrices can be created from other matrices, strings, and anything else that can be converted to an ndarray . The name “mat “is an alias for “matrix “in NumPy.

Example 1: Matrix creation from a string

>>> a=mat('1 2 3; 4 5 3')
>>> print (a*a.T).I
[[ 0.2924 -0.1345]
 [-0.1345  0.0819]]

Example 2: Matrix creation from nested sequence

>>> mat([[1,5,10],[1.0,3,4j]])
matrix([[  1.+0.j,   5.+0.j,  10.+0.j],
        [  1.+0.j,   3.+0.j,   0.+4.j]])

Example 3: Matrix creation from an array

>>> mat(random.rand(3,3)).T
matrix([[ 0.7699,  0.7922,  0.3294],
        [ 0.2792,  0.0101,  0.9219],
        [ 0.3398,  0.7571,  0.8197]])

Memory-mapped file arrays

Memory-mapped files are useful for reading and/or modifying small segments of a large file with regular layout, without reading the entire file into memory. A simple subclass of the ndarray uses a memory-mapped file for the data buffer of the array. For small files, the over-head of reading the entire file into memory is typically not significant, however for large files using memory mapping can save considerable resources.

Memory-mapped-file arrays have one additional method (besides those they inherit from the ndarray): .flush() which must be called manually by the user to ensure that any changes to the array actually get written to disk.

Example:

>>> a = memmap('newfile.dat', dtype=float, mode='w+', shape=1000)
>>> a[10] = 10.0
>>> a[30] = 30.0
>>> del a
>>> b = fromfile('newfile.dat', dtype=float)
>>> print b[10], b[30]
10.0 30.0
>>> a = memmap('newfile.dat', dtype=float)
>>> print a[10], a[30]
10.0 30.0

Character arrays (numpy.char)

These are enhanced arrays of either string_ type or unicode_ type. These arrays inherit from the ndarray, but specially-define the operations +, *, and % on a (broadcasting) element-by-element basis. These operations are not available on the standard ndarray of character type. In addition, the chararray has all of the standard string (and unicode) methods, executing them on an element-by-element basis. Perhaps the easiest way to create a chararray is to use self.view(chararray) where self is an ndarray of str or unicode data-type. However, a chararray can also be created using the numpy.chararray constructor, or via the numpy.char.array function:

Another difference with the standard ndarray of str data-type is that the chararray inherits the feature introduced by Numarray that white-space at the end of any element in the array will be ignored on item retrieval and comparison operations.

Record arrays (numpy.rec)

NumPy provides the recarray class which allows accessing the fields of a structured array as attributes, and a corresponding scalar data type object record.

Masked arrays (numpy.ma)

Standard container class

For backward compatibility and as a standard “container “class, the UserArray from Numeric has been brought over to NumPy and named numpy.lib.user_array.container The container class is a Python class whose self.array attribute is an ndarray. Multiple inheritance is probably easier with numpy.lib.user_array.container than with the ndarray itself and so it is included by default. It is not documented here beyond mentioning its existence because you are encouraged to use the ndarray class directly if you can.

Array Iterators

Iterators are a powerful concept for array processing. Essentially, iterators implement a generalized for-loop. If myiter is an iterator object, then the Python code:

for val in myiter:
    ...
    some code involving val
    ...

calls val = myiter.next() repeatedly until StopIteration is raised by the iterator. There are several ways to iterate over an array that may be useful: default iteration, flat iteration, and -dimensional enumeration.

Default iteration

The default iterator of an ndarray object is the default Python iterator of a sequence type. Thus, when the array object itself is used as an iterator. The default behavior is equivalent to:

for i in range(arr.shape[0]):
    val = arr[i]

This default iterator selects a sub-array of dimension from the array. This can be a useful construct for defining recursive algorithms. To loop over the entire array requires for-loops.

>>> a = arange(24).reshape(3,2,4)+10
>>> for val in a:
...     print 'item:', val
item: [[10 11 12 13]
 [14 15 16 17]]
item: [[18 19 20 21]
 [22 23 24 25]]
item: [[26 27 28 29]
 [30 31 32 33]]

Flat iteration

As mentioned previously, the flat attribute of ndarray objects returns an iterator that will cycle over the entire array in C-style contiguous order.

>>> for i, val in enumerate(a.flat):
...     if i%5 == 0: print i, val
0 10
5 15
10 20
15 25
20 30

Here, I’ve used the built-in enumerate iterator to return the iterator index as well as the value.

N-dimensional enumeration

Sometimes it may be useful to get the N-dimensional index while iterating. The ndenumerate iterator can achieve this.

>>> for i, val in ndenumerate(a):
...     if sum(i)%5 == 0: print i, val
(0, 0, 0) 10
(1, 1, 3) 25
(2, 0, 3) 29
(2, 1, 2) 32

Iterator for broadcasting

The general concept of broadcasting is also available from Python using the broadcast iterator. This object takes objects as inputs and returns an iterator that returns tuples providing each of the input sequence elements in the broadcasted result.

>>> for val in broadcast([[1,0],[2,3]],[0,1]):
...     print val
(1, 0)
(0, 1)
(2, 0)
(3, 1)