Scalars#

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 ndarrays. [1] 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 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 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 (str_, bytes_, void).

../_images/dtype-hierarchy.png

Figure: Hierarchy of type objects representing the array data types. Not shown are the two integer types intp and uintp which are used for indexing (the same as the default integer since NumPy 2).#

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?

int_

int

Python 2 only

double

float

yes

cdouble

complex

yes

bytes_

bytes

yes

str_

str

yes

bool_

bool

no

datetime64

datetime.datetime

no

timedelta64

datetime.timedelta

no

The bool_ data type is very similar to the Python bool but does not inherit from it because Python’s 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 int_ type does not inherit from the int built-in under Python 3, because type int is no longer a fixed-width integer type.

Tip

The default data type in NumPy is double.

class numpy.generic[source]#

Base class for numpy scalar types.

Class from which most (all?) numpy scalar types are derived. For consistency, exposes the same API as ndarray, despite many consequent attributes being either “get-only,” or completely irrelevant. This is the class from which it is strongly suggested users should derive custom scalar types.

class numpy.number[source]#

Abstract base class of all numeric scalar types.

Integer types#

class numpy.integer[source]#

Abstract base class of all integer scalar types.

Note

The numpy integer types mirror the behavior of C integers, and can therefore be subject to Overflow errors.

Signed integer types#

class numpy.signedinteger[source]#

Abstract base class of all signed integer scalar types.

class numpy.byte[source]#

Signed integer type, compatible with C char.

Character code:

'b'

Canonical name:

numpy.byte

Alias on this platform (Linux x86_64):

numpy.int8: 8-bit signed integer (-128 to 127).

class numpy.short[source]#

Signed integer type, compatible with C short.

Character code:

'h'

Canonical name:

numpy.short

Alias on this platform (Linux x86_64):

numpy.int16: 16-bit signed integer (-32_768 to 32_767).

class numpy.intc[source]#

Signed integer type, compatible with C int.

Character code:

'i'

Canonical name:

numpy.intc

Alias on this platform (Linux x86_64):

numpy.int32: 32-bit signed integer (-2_147_483_648 to 2_147_483_647).

class numpy.int_[source]#

Default signed integer type, 64bit on 64bit systems and 32bit on 32bit systems.

Character code:

'l'

Canonical name:

numpy.int_

Alias on this platform (Linux x86_64):

numpy.int64: 64-bit signed integer (-9_223_372_036_854_775_808 to 9_223_372_036_854_775_807).

Alias on this platform (Linux x86_64):

numpy.intp: Signed integer large enough to fit pointer, compatible with C intptr_t.

numpy.long[source]#

alias of int_

class numpy.longlong[source]#

Signed integer type, compatible with C long long.

Character code:

'q'

Unsigned integer types#

class numpy.unsignedinteger[source]#

Abstract base class of all unsigned integer scalar types.

class numpy.ubyte[source]#

Unsigned integer type, compatible with C unsigned char.

Character code:

'B'

Canonical name:

numpy.ubyte

Alias on this platform (Linux x86_64):

numpy.uint8: 8-bit unsigned integer (0 to 255).

class numpy.ushort[source]#

Unsigned integer type, compatible with C unsigned short.

Character code:

'H'

Canonical name:

numpy.ushort

Alias on this platform (Linux x86_64):

numpy.uint16: 16-bit unsigned integer (0 to 65_535).

class numpy.uintc[source]#

Unsigned integer type, compatible with C unsigned int.

Character code:

'I'

Canonical name:

numpy.uintc

Alias on this platform (Linux x86_64):

numpy.uint32: 32-bit unsigned integer (0 to 4_294_967_295).

class numpy.uint[source]#

Unsigned signed integer type, 64bit on 64bit systems and 32bit on 32bit systems.

Character code:

'L'

Canonical name:

numpy.uint

Alias on this platform (Linux x86_64):

numpy.uint64: 64-bit unsigned integer (0 to 18_446_744_073_709_551_615).

Alias on this platform (Linux x86_64):

numpy.uintp: Unsigned integer large enough to fit pointer, compatible with C uintptr_t.

numpy.ulong[source]#

alias of uint

class numpy.ulonglong[source]#

Signed integer type, compatible with C unsigned long long.

Character code:

'Q'

Inexact types#

class numpy.inexact[source]#

Abstract base class of all numeric scalar types with a (potentially) inexact representation of the values in its range, such as floating-point numbers.

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:

>>> 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 \(\frac{1}{10}\); 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#

class numpy.floating[source]#

Abstract base class of all floating-point scalar types.

class numpy.half[source]#

Half-precision floating-point number type.

Character code:

'e'

Canonical name:

numpy.half

Alias on this platform (Linux x86_64):

numpy.float16: 16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa.

class numpy.single[source]#

Single-precision floating-point number type, compatible with C float.

Character code:

'f'

Canonical name:

numpy.single

Alias on this platform (Linux x86_64):

numpy.float32: 32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa.

class numpy.double(x=0, /)[source]#

Double-precision floating-point number type, compatible with Python float and C double.

Character code:

'd'

Canonical name:

numpy.double

Alias on this platform (Linux x86_64):

numpy.float64: 64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa.

class numpy.longdouble[source]#

Extended-precision floating-point number type, compatible with C long double but not necessarily with IEEE 754 quadruple-precision.

Character code:

'g'

Alias on this platform (Linux x86_64):

numpy.float128: 128-bit extended-precision floating-point number type.

Complex floating-point types#

class numpy.complexfloating[source]#

Abstract base class of all complex number scalar types that are made up of floating-point numbers.

class numpy.csingle[source]#

Complex number type composed of two single-precision floating-point numbers.

Character code:

'F'

Canonical name:

numpy.csingle

Alias on this platform (Linux x86_64):

numpy.complex64: Complex number type composed of 2 32-bit-precision floating-point numbers.

class numpy.cdouble(real=0, imag=0)[source]#

Complex number type composed of two double-precision floating-point numbers, compatible with Python complex.

Character code:

'D'

Canonical name:

numpy.cdouble

Alias on this platform (Linux x86_64):

numpy.complex128: Complex number type composed of 2 64-bit-precision floating-point numbers.

class numpy.clongdouble[source]#

Complex number type composed of two extended-precision floating-point numbers.

Character code:

'G'

Alias on this platform (Linux x86_64):

numpy.complex256: Complex number type composed of 2 128-bit extended-precision floating-point numbers.

Other types#

numpy.bool_[source]#

alias of bool

class numpy.bool[source]#

Boolean type (True or False), stored as a byte.

Warning

The bool type is not a subclass of the int_ type (the bool is not even a number type). This is different than Python’s default implementation of bool as a sub-class of int.

Character code:

'?'

class numpy.datetime64[source]#

If created from a 64-bit integer, it represents an offset from 1970-01-01T00:00:00. If created from string, the string can be in ISO 8601 date or datetime format.

When parsing a string to create a datetime object, if the string contains a trailing timezone (A ‘Z’ or a timezone offset), the timezone will be dropped and a User Warning is given.

Datetime64 objects should be considered to be UTC and therefore have an offset of +0000.

>>> np.datetime64(10, 'Y')
np.datetime64('1980')
>>> np.datetime64('1980', 'Y')
np.datetime64('1980')
>>> np.datetime64(10, 'D')
np.datetime64('1970-01-11')

See Datetimes and timedeltas for more information.

Character code:

'M'

class numpy.timedelta64[source]#

A timedelta stored as a 64-bit integer.

See Datetimes and timedeltas for more information.

Character code:

'm'

class numpy.object_[source]#

Any Python object.

Character code:

'O'

Note

The data actually stored in object arrays (i.e., arrays having dtype object_) are references to Python objects, not the objects themselves. Hence, object arrays behave more like usual Python 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 object_ items does not return an object_ object on item access, but instead returns the actual object that the array item refers to.

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.)

class numpy.flexible[source]#

Abstract base class of all scalar types without predefined length. The actual size of these types depends on the specific numpy.dtype instantiation.

class numpy.character[source]#

Abstract base class of all character string scalar types.

class numpy.bytes_[source]#

A byte string.

When used in arrays, this type strips trailing null bytes.

Character code:

'S'

class numpy.str_[source]#

A unicode string.

This type strips trailing null codepoints.

>>> s = np.str_("abc\x00")
>>> s
'abc'

Unlike the builtin str, this supports the Buffer Protocol, exposing its contents as UCS4:

>>> m = memoryview(np.str_("abc"))
>>> m.format
'3w'
>>> m.tobytes()
b'a\x00\x00\x00b\x00\x00\x00c\x00\x00\x00'
Character code:

'U'

class numpy.void(length_or_data, /, dtype=None)[source]#

Create a new structured or unstructured void scalar.

Parameters:
length_or_dataint, array-like, bytes-like, object

One of multiple meanings (see notes). The length or bytes data of an unstructured void. Or alternatively, the data to be stored in the new scalar when dtype is provided. This can be an array-like, in which case an array may be returned.

dtypedtype, optional

If provided the dtype of the new scalar. This dtype must be “void” dtype (i.e. a structured or unstructured void, see also Structured datatypes).

New in version 1.24.

Notes

For historical reasons and because void scalars can represent both arbitrary byte data and structured dtypes, the void constructor has three calling conventions:

  1. np.void(5) creates a dtype="V5" scalar filled with five \0 bytes. The 5 can be a Python or NumPy integer.

  2. np.void(b"bytes-like") creates a void scalar from the byte string. The dtype itemsize will match the byte string length, here "V10".

  3. When a dtype= is passed the call is roughly the same as an array creation. However, a void scalar rather than array is returned.

Please see the examples which show all three different conventions.

Examples

>>> np.void(5)
np.void(b'\x00\x00\x00\x00\x00')
>>> np.void(b'abcd')
np.void(b'\x61\x62\x63\x64')
>>> np.void((3.2, b'eggs'), dtype="d,S5")
np.void((3.2, b'eggs'), dtype=[('f0', '<f8'), ('f1', 'S5')])
>>> np.void(3, dtype=[('x', np.int8), ('y', np.int8)])
np.void((3, 3), dtype=[('x', 'i1'), ('y', 'i1')])
Character code:

'V'

Warning

See 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 struct module.

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 (numpy.intp and numpy.uintp) pointing to the integer type that is sufficiently large to hold a C pointer are also provided.

numpy.int8[source]#
numpy.int16#
numpy.int32#
numpy.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.

numpy.uint8[source]#
numpy.uint16#
numpy.uint32#
numpy.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.

numpy.intp[source]#

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'

Changed in version 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.

numpy.uintp[source]#

Alias for the unsigned integer type that is the same size as intp.

Compatible with the C size_t.

Character code:

'N'

Changed in version 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.

numpy.float16[source]#

alias of half

numpy.float32[source]#

alias of single

numpy.float64[source]#

alias of double

numpy.float96#
numpy.float128[source]#

Alias for numpy.longdouble, named after its size in bits. The existence of these aliases depends on the platform.

numpy.complex64[source]#

alias of csingle

numpy.complex128[source]#

alias of cdouble

numpy.complex192#
numpy.complex256[source]#

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 array priority of NPY_SCALAR_PRIORITY (-1,000,000.0). They also do not (yet) have a ctypes attribute. Otherwise, they share the same attributes as arrays:

generic.flags

The integer value of flags.

generic.shape

Tuple of array dimensions.

generic.strides

Tuple of bytes steps in each dimension.

generic.ndim

The number of array dimensions.

generic.data

Pointer to start of data.

generic.size

The number of elements in the gentype.

generic.itemsize

The length of one element in bytes.

generic.base

Scalar attribute identical to the corresponding array attribute.

generic.dtype

Get array data-descriptor.

generic.real

The real part of the scalar.

generic.imag

The imaginary part of the scalar.

generic.flat

A 1-D view of the scalar.

generic.T

Scalar attribute identical to the corresponding array attribute.

generic.__array_interface__

Array protocol: Python side

generic.__array_struct__

Array protocol: struct

generic.__array_priority__

Array priority.

generic.__array_wrap__

sc.__array_wrap__(obj) return scalar from array

Indexing#

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 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 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:

generic.__array__

sc.__array__(dtype) return 0-dim array from scalar with specified dtype

generic.__array_wrap__

sc.__array_wrap__(obj) return scalar from array

generic.squeeze

Scalar method identical to the corresponding array attribute.

generic.byteswap

Scalar method identical to the corresponding array attribute.

generic.__reduce__

Helper for pickle.

generic.__setstate__

generic.setflags

Scalar method identical to the corresponding array attribute.

Utility method for typing:

number.__class_getitem__(item, /)

Return a parametrized wrapper around the number type.

Defining new types#

There are two ways to effectively define a new array scalar type (apart from composing structured types dtypes from the built-in scalar types): One way is to simply subclass the 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 NumPy C-API.