.. _arrays.scalars: ******* Scalars ******* .. currentmodule:: numpy Python defines only one type of a particular data class (there is only one integer type, one floating-point type, etc.). This can be convenient in applications that don't need to be concerned with all the ways data can be represented in a computer. For scientific computing, however, more control is often needed. In NumPy, there are 24 new fundamental Python types to describe different types of scalars. These type descriptors are mostly based on the types available in the C language that CPython is written in, with several additional types compatible with Python's types. Array scalars have the same attributes and methods as :class:`ndarrays `. [#]_ This allows one to treat items of an array partly on the same footing as arrays, smoothing out rough edges that result when mixing scalar and array operations. Array scalars live in a hierarchy (see the Figure below) of data types. They can be detected using the hierarchy: For example, ``isinstance(val, np.generic)`` will return :py:data:`True` if *val* is an array scalar object. Alternatively, what kind of array scalar is present can be determined using other members of the data type hierarchy. Thus, for example ``isinstance(val, np.complexfloating)`` will return :py:data:`True` if *val* is a complex valued type, while ``isinstance(val, np.flexible)`` will return true if *val* is one of the flexible itemsize array types (:class:`str_`, :class:`bytes_`, :class:`void`). .. figure:: figures/dtype-hierarchy.png **Figure:** Hierarchy of type objects representing the array data types. Not shown are the two integer types :class:`intp` and :class:`uintp` which are used for indexing (the same as the default integer since NumPy 2). .. TODO - use something like this instead of the diagram above, as it generates links to the classes and is a vector graphic. Unfortunately it looks worse and the html element providing the linked regions is misaligned. .. inheritance-diagram:: byte short intc int_ longlong ubyte ushort uintc uint ulonglong half single double longdouble csingle cdouble clongdouble bool_ datetime64 timedelta64 object_ bytes_ str_ void .. [#] However, array scalars are immutable, so none of the array scalar attributes are settable. .. _arrays.scalars.character-codes: .. _arrays.scalars.built-in: Built-in scalar types ===================== The built-in scalar types are shown below. The C-like names are associated with character codes, which are shown in their descriptions. Use of the character codes, however, is discouraged. Some of the scalar types are essentially equivalent to fundamental Python types and therefore inherit from them as well as from the generic array scalar type: ==================== =========================== ============= Array scalar type Related Python type Inherits? ==================== =========================== ============= :class:`int_` :class:`int` Python 2 only :class:`double` :class:`float` yes :class:`cdouble` :class:`complex` yes :class:`bytes_` :class:`bytes` yes :class:`str_` :class:`str` yes :class:`bool_` :class:`bool` no :class:`datetime64` :class:`datetime.datetime` no :class:`timedelta64` :class:`datetime.timedelta` no ==================== =========================== ============= The :class:`bool_` data type is very similar to the Python :class:`bool` but does not inherit from it because Python's :class:`bool` does not allow itself to be inherited from, and on the C-level the size of the actual bool data is not the same as a Python Boolean scalar. .. warning:: The :class:`int_` type does **not** inherit from the :class:`int` built-in under Python 3, because type :class:`int` is no longer a fixed-width integer type. .. tip:: The default data type in NumPy is :class:`double`. .. autoclass:: numpy.generic :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.number :members: __init__ :exclude-members: __init__ Integer types ------------- .. autoclass:: numpy.integer :members: __init__ :exclude-members: __init__ .. note:: The numpy integer types mirror the behavior of C integers, and can therefore be subject to :ref:`overflow-errors`. Signed integer types ~~~~~~~~~~~~~~~~~~~~ .. autoclass:: numpy.signedinteger :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.byte :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.short :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.intc :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.int_ :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.long :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.longlong :members: __init__ :exclude-members: __init__ Unsigned integer types ~~~~~~~~~~~~~~~~~~~~~~ .. autoclass:: numpy.unsignedinteger :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.ubyte :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.ushort :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.uintc :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.uint :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.ulong :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.ulonglong :members: __init__ :exclude-members: __init__ Inexact types ------------- .. autoclass:: numpy.inexact :members: __init__ :exclude-members: __init__ .. note:: Inexact scalars are printed using the fewest decimal digits needed to distinguish their value from other values of the same datatype, by judicious rounding. See the ``unique`` parameter of `format_float_positional` and `format_float_scientific`. This means that variables with equal binary values but whose datatypes are of different precisions may display differently: >>> import numpy as np >>> f16 = np.float16("0.1") >>> f32 = np.float32(f16) >>> f64 = np.float64(f32) >>> f16 == f32 == f64 True >>> f16, f32, f64 (0.1, 0.099975586, 0.0999755859375) Note that none of these floats hold the exact value :math:`\frac{1}{10}`; ``f16`` prints as ``0.1`` because it is as close to that value as possible, whereas the other types do not as they have more precision and therefore have closer values. Conversely, floating-point scalars of different precisions which approximate the same decimal value may compare unequal despite printing identically: >>> f16 = np.float16("0.1") >>> f32 = np.float32("0.1") >>> f64 = np.float64("0.1") >>> f16 == f32 == f64 False >>> f16, f32, f64 (0.1, 0.1, 0.1) Floating-point types ~~~~~~~~~~~~~~~~~~~~ .. autoclass:: numpy.floating :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.half :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.single :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.double :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.longdouble :members: __init__ :exclude-members: __init__ Complex floating-point types ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. autoclass:: numpy.complexfloating :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.csingle :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.cdouble :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.clongdouble :members: __init__ :exclude-members: __init__ Other types ----------- .. autoclass:: numpy.bool_ :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.bool :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.datetime64 :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.timedelta64 :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.object_ :members: __init__ :exclude-members: __init__ .. note:: The data actually stored in object arrays (*i.e.*, arrays having dtype :class:`object_`) are references to Python objects, not the objects themselves. Hence, object arrays behave more like usual Python :class:`lists `, in the sense that their contents need not be of the same Python type. The object type is also special because an array containing :class:`object_` items does not return an :class:`object_` object on item access, but instead returns the actual object that the array item refers to. .. index:: flexible The following data types are **flexible**: they have no predefined size and the data they describe can be of different length in different arrays. (In the character codes ``#`` is an integer denoting how many elements the data type consists of.) .. autoclass:: numpy.flexible :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.character :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.bytes_ :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.str_ :members: __init__ :exclude-members: __init__ .. autoclass:: numpy.void :members: __init__ :exclude-members: __init__ .. warning:: See :ref:`Note on string types`. Numeric Compatibility: If you used old typecode characters in your Numeric code (which was never recommended), you will need to change some of them to the new characters. In particular, the needed changes are ``c -> S1``, ``b -> B``, ``1 -> b``, ``s -> h``, ``w -> H``, and ``u -> I``. These changes make the type character convention more consistent with other Python modules such as the :mod:`struct` module. .. _sized-aliases: Sized aliases ------------- Along with their (mostly) C-derived names, the integer, float, and complex data-types are also available using a bit-width convention so that an array of the right size can always be ensured. Two aliases (:class:`numpy.intp` and :class:`numpy.uintp`) pointing to the integer type that is sufficiently large to hold a C pointer are also provided. .. note that these are documented with ..attribute because that is what autoclass does for aliases under the hood. .. attribute:: int8 int16 int32 int64 Aliases for the signed integer types (one of `numpy.byte`, `numpy.short`, `numpy.intc`, `numpy.int_`, `numpy.long` and `numpy.longlong`) with the specified number of bits. Compatible with the C99 ``int8_t``, ``int16_t``, ``int32_t``, and ``int64_t``, respectively. .. attribute:: uint8 uint16 uint32 uint64 Alias for the unsigned integer types (one of `numpy.ubyte`, `numpy.ushort`, `numpy.uintc`, `numpy.uint`, `numpy.ulong` and `numpy.ulonglong`) with the specified number of bits. Compatible with the C99 ``uint8_t``, ``uint16_t``, ``uint32_t``, and ``uint64_t``, respectively. .. attribute:: intp Alias for the signed integer type (one of `numpy.byte`, `numpy.short`, `numpy.intc`, `numpy.int_`, `numpy.long` and `numpy.longlong`) that is used as a default integer and for indexing. Compatible with the C ``Py_ssize_t``. :Character code: ``'n'`` .. versionchanged:: 2.0 Before NumPy 2, this had the same size as a pointer. In practice this is almost always identical, but the character code ``'p'`` maps to the C ``intptr_t``. The character code ``'n'`` was added in NumPy 2.0. .. attribute:: uintp Alias for the unsigned integer type that is the same size as ``intp``. Compatible with the C ``size_t``. :Character code: ``'N'`` .. versionchanged:: 2.0 Before NumPy 2, this had the same size as a pointer. In practice this is almost always identical, but the character code ``'P'`` maps to the C ``uintptr_t``. The character code ``'N'`` was added in NumPy 2.0. .. autoclass:: numpy.float16 .. autoclass:: numpy.float32 .. autoclass:: numpy.float64 .. attribute:: float96 float128 Alias for `numpy.longdouble`, named after its size in bits. The existence of these aliases depends on the platform. .. autoclass:: numpy.complex64 .. autoclass:: numpy.complex128 .. attribute:: complex192 complex256 Alias for `numpy.clongdouble`, named after its size in bits. The existence of these aliases depends on the platform. Attributes ========== The array scalar objects have an :obj:`array priority ` of :c:data:`NPY_SCALAR_PRIORITY` (-1,000,000.0). They also do not (yet) have a :attr:`ctypes ` attribute. Otherwise, they share the same attributes as arrays: .. autosummary:: :toctree: generated/ generic.flags generic.shape generic.strides generic.ndim generic.data generic.size generic.itemsize generic.base generic.dtype generic.real generic.imag generic.flat generic.T generic.__array_interface__ generic.__array_struct__ generic.__array_priority__ generic.__array_wrap__ Indexing ======== .. seealso:: :ref:`arrays.indexing`, :ref:`arrays.dtypes` Array scalars can be indexed like 0-dimensional arrays: if *x* is an array scalar, - ``x[()]`` returns a copy of array scalar - ``x[...]`` returns a 0-dimensional :class:`ndarray` - ``x['field-name']`` returns the array scalar in the field *field-name*. (*x* can have fields, for example, when it corresponds to a structured data type.) Methods ======= Array scalars have exactly the same methods as arrays. The default behavior of these methods is to internally convert the scalar to an equivalent 0-dimensional array and to call the corresponding array method. In addition, math operations on array scalars are defined so that the same hardware flags are set and used to interpret the results as for :ref:`ufunc `, so that the error state used for ufuncs also carries over to the math on array scalars. The exceptions to the above rules are given below: .. autosummary:: :toctree: generated/ generic.__array__ generic.__array_wrap__ generic.squeeze generic.byteswap generic.__reduce__ generic.__setstate__ generic.setflags Utility method for typing: .. autosummary:: :toctree: generated/ number.__class_getitem__ Defining new types ================== There are two ways to effectively define a new array scalar type (apart from composing structured types :ref:`dtypes ` from the built-in scalar types): One way is to simply subclass the :class:`ndarray` and overwrite the methods of interest. This will work to a degree, but internally certain behaviors are fixed by the data type of the array. To fully customize the data type of an array you need to define a new data-type, and register it with NumPy. Such new types can only be defined in C, using the :ref:`NumPy C-API `.