# 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).

1

However, array scalars are immutable, so none of the array scalar attributes are settable.

## 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

float_

float

yes

complex_

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 float_.

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'

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'

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'

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]#

Signed integer type, compatible with Python int and C long.

Character code

'l'

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.

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'

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'

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'

Alias on this platform (Linux x86_64)

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

class numpy.uint[source]#

Unsigned integer type, compatible with C unsigned long.

Character code

'L'

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.

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'

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'

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'

Alias

numpy.float_

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

numpy.longfloat

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'

Alias

numpy.singlecomplex

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'

Alias

numpy.cfloat

Alias

numpy.complex_

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

numpy.clongfloat

Alias

numpy.longcomplex

Alias on this platform (Linux x86_64)

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

### Other types#

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

'?'

Alias

numpy.bool8

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.

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


Character code

'M'

class numpy.timedelta64[source]#

A timedelta stored as a 64-bit integer.

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 np.dtype instantiation.

class numpy.bytes_[source]#

A byte string.

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

Character code

'S'

Alias

numpy.string_

class numpy.str_[source]#

A unicode string.

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

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'

Alias

numpy.unicode_

class numpy.void[source]#

Either an opaque sequence of bytes, or a structure.

>>> np.void(b'abcd')
void(b'\x61\x62\x63\x64')


Structured void scalars can only be constructed via extraction from Structured arrays:

>>> arr = np.array((1, 2), dtype=[('x', np.int8), ('y', np.int8)])
>>> arr[()]
(1, 2)  # looks like a tuple, but is np.void

Character code

'V'

Warning

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.bool8[source]#

alias of numpy.bool_

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_ 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 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_ and np.longlong) that is the same size as a pointer.

Compatible with the C intptr_t.

Character code

'p'

numpy.uintp[source]#

Alias for the unsigned integer type (one of numpy.ubyte, numpy.ushort, numpy.uintc, numpy.uint and np.ulonglong) that is the same size as a pointer.

Compatible with the C uintptr_t.

Character code

'P'

numpy.float16[source]#

alias of numpy.half

numpy.float32[source]#

alias of numpy.single

numpy.float64[source]#

alias of numpy.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 numpy.csingle

numpy.complex128[source]#

alias of numpy.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.

### Other aliases#

The first two of these are conveniences which resemble the names of the builtin types, in the same style as bool_, int_, str_, bytes_, and object_:

numpy.float_[source]#

alias of numpy.double

numpy.complex_[source]#

alias of numpy.cdouble

Some more use alternate naming conventions for extended-precision floats and complex numbers:

numpy.longfloat[source]#

alias of numpy.longdouble

numpy.singlecomplex[source]#

alias of numpy.csingle

numpy.cfloat[source]#

alias of numpy.cdouble

numpy.longcomplex[source]#

alias of numpy.clongdouble

numpy.clongfloat[source]#

alias of numpy.clongdouble

The following aliases originate from Python 2, and it is recommended that they not be used in new code.

numpy.string_[source]#

alias of numpy.bytes_

numpy.unicode_[source]#

alias of numpy.str_

## 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.