Standard array subclasses¶
ndarray in NumPy is a “new-style” Python
built-in-type. Therefore, it 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.
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:
__array_ufunc__(ufunc, method, *inputs, **kwargs)¶
New in version 1.13.
The API is provisional, i.e., we do not yet guarantee backward compatibility.
Any class, ndarray subclass or not, can define this method or set it to
Nonein 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
- inputs is a tuple of the input arguments to the
- kwargs is a dictionary containing the optional input arguments
of the ufunc. If given, any
outarguments, both positional and keyword, are passed as a
tuplein kwargs. See the discussion in Universal functions (ufunc) for details.
The method should return either the result of the operation, or
NotImplementedif 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
NotImplementeddetermines the result. If all of the
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
Like with some other special methods in python, such as
__iter__, it is possible to indicate that your class does not support ufuncs by setting
__array_ufunc__ = None. Ufuncs always raise
TypeErrorwhen called on an object that sets
__array_ufunc__ = None.
The presence of
__array_ufunc__also influences how
ndarrayhandles binary operations like
arr + objand
arr < objwhen
objis an instance of a custom class. There are two possibilities. If
obj.__array_ufunc__is present and not
ndarray.__add__and friends will delegate to the ufunc machinery, meaning that
arr + objbecomes
np.add(arr, obj), and then
obj.__array_ufunc__. This is useful if you want to define an object that acts like an array.
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
mrepresenting the “meters” unit, and want to support the syntax
arr * mto 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__ = Noneand defining
__rmul__methods. (Note that this means that writing an
__array_ufunc__that always returns
NotImplementedis not quite the same as setting
__array_ufunc__ = None: in the former case,
arr + objwill 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
arr += objwould 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 += objwould be translated to
arr = arr + obj, i.e.,
arrwould be replaced, contrary to what is expected for in-place array operations.)
If you define
- If you are not a subclass of
ndarray, we recommend your class define special methods like
__lt__that delegate to ufuncs just like ndarray does. An easy way to do this is to subclass from
- 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
None, would seem very unexpected and thus confusing, as then the subclass would not work at all with ufuncs).
ndarraydefines its own
__array_ufunc__, which, evaluates the ufunc if no arguments have overrides, and returns
NotImplementedotherwise. 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.
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.
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.
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.
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.
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
Matrix objects can be created using a string notation to allow Matlab-style syntax where spaces separate columns and semicolons (‘;’) separate rows.
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.
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.
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.
The default __array_priority__ of matrix objects is 10.0, and therefore mixed operations with ndarrays always produce matrices.
Matrices have special attributes which make calculations easier. These are
Returns the transpose of the matrix.
Returns the (complex) conjugate transpose of self.
Returns the (multiplicative) inverse of invertible self.
Return self as an
Matrix objects over-ride multiplication, ‘*’, and power, ‘**’, to be matrix-multiplication and matrix power, respectively. If your subroutine can accept sub-classes and you do not convert to base- class arrays, then you must use the ufuncs multiply and power to be sure that you are performing the correct operation for all inputs.
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.
||Returns a matrix from an array-like object, or from a string of data.|
||Interpret the input as a matrix.|
||Build a matrix object from a string, nested sequence, or array.|
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):
must be called manually by the user to ensure that any changes to the
array actually get written to disk.
||Create a memory-map to an array stored in a binary file on disk.|
||Write any changes in the array to the file on disk.|
>>> a = memmap('newfile.dat', dtype=float, mode='w+', shape=1000) >>> a = 10.0 >>> a = 30.0 >>> del a >>> b = fromfile('newfile.dat', dtype=float) >>> print b, b 10.0 30.0 >>> a = memmap('newfile.dat', dtype=float) >>> print a, a 10.0 30.0
Character arrays (
chararray class exists for backwards compatibility with
Numarray, it is not recommended for new development. Starting from numpy
1.4, if one needs arrays of strings, it is recommended to use arrays of
unicode_, and use the free functions
numpy.char module for fast vectorized string operations.
These are enhanced arrays of either
string_ type or
unicode_ type. These arrays inherit from the
ndarray, but specially-define the operations
% on a (broadcasting) element-by-element basis. These
operations are not available on the standard
character type. In addition, the
chararray has all of the
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
||Provides a convenient view on arrays of string and unicode values.|
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 (
||Construct an ndarray that allows field access using attributes.|
||A data-type scalar that allows field access as attribute lookup.|
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.
||Standard container-class for easy multiple-inheritance.|
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 ...
val = myiter.next() repeatedly until
raised by the iterator. There are several ways to iterate over an
array that may be useful: default iteration, flat iteration, and
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): 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]]
||A 1-D iterator over the array.|
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.
||Multidimensional index iterator.|
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¶
||Produce an object that mimics broadcasting.|
The general concept of broadcasting is also available from Python
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
>>> for val in broadcast([[1,0],[2,3]],[0,1]): ... print val (1, 0) (0, 1) (2, 0) (3, 1)