# 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`).

Figure: Hierarchy of type objects representing the array data types. Not shown are the two integer types `intp` and `uintp` which just point to the integer type that holds a pointer for the platform. All the number types can be obtained using bit-width names as well.

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

  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

  Abstract base class of all numeric scalar types.

### Integer types

class numpy.integer

  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

  Abstract base class of all signed integer scalar types.

class numpy.byte

  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

  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

  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_

  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

  Signed integer type, compatible with C `long long`.

  Character code

    `'q'`

#### Unsigned integer types

class numpy.unsignedinteger

  Abstract base class of all unsigned integer scalar types.

class numpy.ubyte

  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

  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

  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

  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

  Signed integer type, compatible with C `unsigned long long`.

  Character code

    `'Q'`

### Inexact types

class numpy.inexact

  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

  Abstract base class of all floating-point scalar types.

class numpy.half

  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

  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, /)

  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

  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

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

class numpy.csingle

  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)

  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

  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_

  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

  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')

  See Datetimes and Timedeltas for more information.

  Character code

    `'M'`

class numpy.timedelta64

  A timedelta stored as a 64-bit integer.

  See Datetimes and Timedeltas for more information.

  Character code

    `'m'`

class numpy.object_

  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

  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_

  A byte string.

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

  Character code

    `'S'`

  Alias

    `numpy.string_`

class numpy.str_

  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

  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

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.bool8

  alias of `numpy.bool_`

numpy.int8
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
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

  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

  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

  alias of `numpy.half`

numpy.float32

  alias of `numpy.single`

numpy.float64

  alias of `numpy.double`

numpy.float96
numpy.float128

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

numpy.complex64

  alias of `numpy.csingle`

numpy.complex128

  alias of `numpy.cdouble`

numpy.complex192
numpy.complex256

  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_

  alias of `numpy.double`

numpy.complex_

  alias of `numpy.cdouble`

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

numpy.longfloat

  alias of `numpy.longdouble`

numpy.singlecomplex

  alias of `numpy.csingle`

numpy.cfloat

  alias of `numpy.cdouble`

numpy.longcomplex

  alias of `numpy.clongdouble`

numpy.clongfloat

  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_

  alias of `numpy.bytes_`

numpy.unicode_

  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

See also

Indexing routines, Data type objects (dtype)

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.

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