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 (string, unicode, 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. 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 (e.g. int8, float64, complex128). Two aliases (intp and uintp) pointing to the integer type that is sufficiently large to hold a C pointer are also provided. The C-like names are associated with character codes, which are shown in the table. 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
int_	IntType (Python 2 only)
float_	FloatType
complex_	ComplexType
bytes_	BytesType
unicode_	UnicodeType

The bool_ data type is very similar to the Python BooleanType but does not inherit from it because Python’s BooleanType 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.

In the tables below, platform? means that the type may not be available on all platforms. Compatibility with different C or Python types is indicated: two types are compatible if their data is of the same size and interpreted in the same way.

Booleans:

Type	Remarks	Character code
bool_	compatible: Python bool	'?'
bool8	8 bits

Integers:

byte	compatible: C char	'b'
short	compatible: C short	'h'
intc	compatible: C int	'i'
int_	compatible: Python int	'l'
longlong	compatible: C long long	'q'
intp	large enough to fit a pointer	'p'
int8	8 bits
int16	16 bits
int32	32 bits
int64	64 bits

Unsigned integers:

ubyte	compatible: C unsigned char	'B'
ushort	compatible: C unsigned short	'H'
uintc	compatible: C unsigned int	'I'
uint	compatible: Python int	'L'
ulonglong	compatible: C long long	'Q'
uintp	large enough to fit a pointer	'P'
uint8	8 bits
uint16	16 bits
uint32	32 bits
uint64	64 bits

Floating-point numbers:

half		'e'
single	compatible: C float	'f'
double	compatible: C double
float_	compatible: Python float	'd'
longfloat	compatible: C long float	'g'
float16	16 bits
float32	32 bits
float64	64 bits
float96	96 bits, platform?
float128	128 bits, platform?

Complex floating-point numbers:

csingle		'F'
complex_	compatible: Python complex	'D'
clongfloat		'G'
complex64	two 32-bit floats
complex128	two 64-bit floats
complex192	two 96-bit floats, platform?
complex256	two 128-bit floats, platform?

Any Python object:

object_

any Python object

'O'

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.)

bytes_	compatible: Python bytes	'S#'
unicode_	compatible: Python unicode/str	'U#'
void		'V#'

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	integer value of flags
generic.shape	tuple of array dimensions
generic.strides	tuple of bytes steps in each dimension
generic.ndim	number of array dimensions
generic.data	pointer to start of data
generic.size	number of elements in the gentype
generic.itemsize	length of one element in bytes
generic.base	base object
generic.dtype	get array data-descriptor
generic.real	real part of scalar
generic.imag	imaginary part of scalar
generic.flat	a 1-d view of scalar
generic.T	transpose
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	Base class for numpy scalar types.
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()	Not implemented (virtual attribute)
generic.byteswap()	Not implemented (virtual attribute)
generic.__reduce__()	Helper for pickle.
generic.__setstate__()
generic.setflags()	Not implemented (virtual attribute)

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.