Data types#
See also
Array types and conversions between types#
NumPy supports a much greater variety of numerical types than Python does. This section shows which are available, and how to modify an array’s data-type.
NumPy numerical types are instances of numpy.dtype (data-type) objects, each
having unique characteristics. Once you have imported NumPy using import
numpy as np you can create arrays with a specified dtype using the scalar
types in the numpy top-level API, e.g. numpy.bool, numpy.float32, etc.
These scalar types as arguments to the dtype keyword that many numpy functions or methods accept. For example:
>>> z = np.arange(3, dtype=np.uint8)
>>> z
array([0, 1, 2], dtype=uint8)
Array types can also be referred to by character codes, for example:
>>> np.array([1, 2, 3], dtype='f')
array([1., 2., 3.], dtype=float32)
>>> np.array([1, 2, 3], dtype='d')
array([1., 2., 3.], dtype=float64)
See Specifying and constructing data types for more information about specifying and constructing data type objects, including how to specify parameters like the byte order.
To convert the type of an array, use the .astype() method. For example:
>>> z.astype(np.float64)
array([0., 1., 2.])
Note that, above, we could have used the Python float object as a dtype
instead of numpy.float64. NumPy knows that
int refers to numpy.int_, bool means
numpy.bool, that float is numpy.float64 and
complex is numpy.complex128. The other data-types do not have
Python equivalents.
To determine the type of an array, look at the dtype attribute:
>>> z.dtype
dtype('uint8')
dtype objects also contain information about the type, such as its bit-width and its byte-order. The data type can also be used indirectly to query properties of the type, such as whether it is an integer:
>>> d = np.dtype(np.int64)
>>> d
dtype('int64')
>>> np.issubdtype(d, np.integer)
True
>>> np.issubdtype(d, np.floating)
False
Numerical Data Types#
There are 5 basic numerical types representing booleans (bool), integers
(int), unsigned integers (uint) floating point (float) and
complex. A basic numerical type name combined with a numeric bitsize defines
a concrete type. The bitsize is the number of bits that are needed to represent
a single value in memory. For example, numpy.float64 is a 64 bit
floating point data type. Some types, such as numpy.int_ and
numpy.intp, have differing bitsizes, dependent on the platforms
(e.g. 32-bit vs. 64-bit CPU architectures). This should be taken into account
when interfacing with low-level code (such as C or Fortran) where the raw memory
is addressed.
Data Types for Strings and Bytes#
In addition to numerical types, NumPy also supports storing unicode strings, via
the numpy.str_ dtype (U character code), null-terminated byte sequences via
numpy.bytes_ (S character code), and arbitrary byte sequences, via
numpy.void (V character code).
All of the above are fixed-width data types. They are parameterized by a width, in either bytes or unicode points, that a single data element in the array must fit inside. This means that storing an array of byte sequences or strings using this dtype requires knowing or calculating the sizes of the longest text or byte sequence in advance.
As an example, we can create an array storing the words "hello" and
"world!":
>>> np.array(["hello", "world!"])
array(['hello', 'world!'], dtype='<U6')
Here the data type is detected as a unicode string that is a maximum of 6 code points long, enough to store both entries without truncation. If we specify a shorter or longer data type, the string is either truncated or zero-padded to fit in the specified width:
>>> np.array(["hello", "world!"], dtype="U5")
array(['hello', 'world'], dtype='<U5')
>>> np.array(["hello", "world!"], dtype="U7")
array(['hello', 'world!'], dtype='<U7')
We can see the zero-padding a little more clearly if we use the bytes data type and ask NumPy to print out the bytes in the array buffer:
>>> np.array(["hello", "world"], dtype="S7").tobytes()
b'hello\x00\x00world\x00\x00'
Each entry is padded with two extra null bytes. Note however that NumPy cannot tell the difference between intentionally stored trailing nulls and padding nulls:
>>> x = [b"hello\0\0", b"world"]
>>> a = np.array(x, dtype="S7")
>>> print(a[0])
b"hello"
>>> a[0] == x[0]
False
If you need to store and round-trip any trailing null bytes, you will need to use an unstructured void data type:
>>> a = np.array(x, dtype="V7")
>>> a
array([b'\x68\x65\x6C\x6C\x6F\x00\x00', b'\x77\x6F\x72\x6C\x64\x00\x00'],
dtype='|V7')
>>> a[0] == np.void(x[0])
True
Advanced types, not listed above, are explored in section Structured arrays.
Relationship Between NumPy Data Types and C Data Types#
NumPy provides both bit sized type names and names based on the names of C types. Since the definition of C types are platform dependent, this means the explicitly bit sized should be preferred to avoid platform-dependent behavior in programs using NumPy.
To ease integration with C code, where it is more natural to refer to
platform-dependent C types, NumPy also provides type aliases that correspond
to the C types for the platform. Some dtypes have trailing underscore to avoid
confusion with builtin python type names, such as numpy.bool_.
Canonical Python API name |
Python API “C-like” name |
Actual C type |
Description |
|---|---|---|---|
N/A |
|
Boolean (True or False) stored as a byte. |
|
|
Platform-defined integer type with 8 bits. |
||
|
Platform-defined integer type with 8 bits without sign. |
||
|
Platform-defined integer type with 16 bits. |
||
|
Platform-defined integer type with 16 bits without sign. |
||
|
Platform-defined integer type with 32 bits. |
||
|
Platform-defined integer type with 32 bits without sign. |
||
N/A |
|
Platform-defined integer of size |
|
N/A |
|
Platform-defined integer type capable of storing the maximum allocation size. |
|
N/A |
|
|
Guaranteed to hold pointers. Character code only (Python and C). |
N/A |
|
|
Guaranteed to hold pointers. Character code only (Python and C). |
|
Platform-defined integer type with at least 32 bits. |
||
|
Platform-defined integer type with at least 32 bits without sign. |
||
N/A |
|
Platform-defined integer type with at least 64 bits. |
|
N/A |
|
Platform-defined integer type with at least 64 bits without sign. |
|
N/A |
Half precision float: sign bit, 5 bits exponent, 10 bits mantissa. |
||
|
Platform-defined single precision float: typically sign bit, 8 bits exponent, 23 bits mantissa. |
||
|
Platform-defined double precision float: typically sign bit, 11 bits exponent, 52 bits mantissa. |
||
|
|
Platform-defined extended-precision float. |
|
|
Complex number, represented by two single-precision floats (real and imaginary components). |
||
|
Complex number, represented by two double-precision floats (real and imaginary components). |
||
|
|
Complex number, represented by two extended-precision floats (real and imaginary components). |
Since many of these have platform-dependent definitions, a set of fixed-size aliases are provided (See Sized aliases).
Array scalars#
NumPy generally returns elements of arrays as array scalars (a scalar
with an associated dtype). Array scalars differ from Python scalars, but
for the most part they can be used interchangeably (the primary
exception is for versions of Python older than v2.x, where integer array
scalars cannot act as indices for lists and tuples). There are some
exceptions, such as when code requires very specific attributes of a scalar
or when it checks specifically whether a value is a Python scalar. Generally,
problems are easily fixed by explicitly converting array scalars
to Python scalars, using the corresponding Python type function
(e.g., int, float, complex, str).
The primary advantage of using array scalars is that
they preserve the array type (Python may not have a matching scalar type
available, e.g. int16). Therefore, the use of array scalars ensures
identical behaviour between arrays and scalars, irrespective of whether the
value is inside an array or not. NumPy scalars also have many of the same
methods arrays do.
Overflow errors#
The fixed size of NumPy numeric types may cause overflow errors when a value
requires more memory than available in the data type. For example,
numpy.power evaluates 100 ** 9 correctly for 64-bit integers,
but gives -1486618624 (incorrect) for a 32-bit integer.
>>> np.power(100, 9, dtype=np.int64)
1000000000000000000
>>> np.power(100, 9, dtype=np.int32)
-1486618624
The behaviour of NumPy and Python integer types differs significantly for
integer overflows and may confuse users expecting NumPy integers to behave
similar to Python’s int. Unlike NumPy, the size of Python’s
int is flexible. This means Python integers may expand to accommodate
any integer and will not overflow.
NumPy provides numpy.iinfo and numpy.finfo to verify the
minimum or maximum values of NumPy integer and floating point values
respectively
>>> np.iinfo(int) # Bounds of the default integer on this system.
iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
>>> np.iinfo(np.int32) # Bounds of a 32-bit integer
iinfo(min=-2147483648, max=2147483647, dtype=int32)
>>> np.iinfo(np.int64) # Bounds of a 64-bit integer
iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
If 64-bit integers are still too small the result may be cast to a floating point number. Floating point numbers offer a larger, but inexact, range of possible values.
>>> np.power(100, 100, dtype=np.int64) # Incorrect even with 64-bit int
0
>>> np.power(100, 100, dtype=np.float64)
1e+200
Extended precision#
Python’s floating-point numbers are usually 64-bit floating-point numbers,
nearly equivalent to numpy.float64. In some unusual situations it may be
useful to use floating-point numbers with more precision. Whether this
is possible in numpy depends on the hardware and on the development
environment: specifically, x86 machines provide hardware floating-point
with 80-bit precision, and while most C compilers provide this as their
long double type, MSVC (standard for Windows builds) makes
long double identical to double (64 bits). NumPy makes the
compiler’s long double available as numpy.longdouble (and
np.clongdouble for the complex numbers). You can find out what your
numpy provides with np.finfo(np.longdouble).
NumPy does not provide a dtype with more precision than C’s
long double; in particular, the 128-bit IEEE quad precision
data type (FORTRAN’s REAL*16) is not available.
For efficient memory alignment, numpy.longdouble is usually stored
padded with zero bits, either to 96 or 128 bits. Which is more efficient
depends on hardware and development environment; typically on 32-bit
systems they are padded to 96 bits, while on 64-bit systems they are
typically padded to 128 bits. np.longdouble is padded to the system
default; np.float96 and np.float128 are provided for users who
want specific padding. In spite of the names, np.float96 and
np.float128 provide only as much precision as np.longdouble,
that is, 80 bits on most x86 machines and 64 bits in standard
Windows builds.
Be warned that even if numpy.longdouble offers more precision than
python float, it is easy to lose that extra precision, since
python often forces values to pass through float. For example,
the % formatting operator requires its arguments to be converted
to standard python types, and it is therefore impossible to preserve
extended precision even if many decimal places are requested. It can
be useful to test your code with the value
1 + np.finfo(np.longdouble).eps.