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.
The primitive types supported are tied closely to those in C:
Numpy type |
C type |
Description |
|---|---|---|
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Boolean (True or False) stored as a byte |
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Platform-defined |
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Platform-defined |
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|
Platform-defined |
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|
Platform-defined |
|
|
Platform-defined |
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Platform-defined |
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Platform-defined |
|
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Platform-defined |
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Platform-defined |
|
|
Platform-defined |
|
Half precision float: sign bit, 5 bits exponent, 10 bits mantissa |
||
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Platform-defined single precision float: typically sign bit, 8 bits exponent, 23 bits mantissa |
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Platform-defined double precision float: typically sign bit, 11 bits exponent, 52 bits mantissa. |
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Platform-defined extended-precision float |
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Complex number, represented by two single-precision floats (real and imaginary components) |
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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).
NumPy numerical types are instances of dtype (data-type) objects, each
having unique characteristics. Once you have imported NumPy using
>>> import numpy as np
the dtypes are available as np.bool_, np.float32, etc.
Advanced types, not listed above, are explored in section Structured arrays.
There are 5 basic numerical types representing booleans (bool), integers (int),
unsigned integers (uint) floating point (float) and complex. Those with numbers
in their name indicate the bitsize of the type (i.e. how many bits are needed
to represent a single value in memory). Some types, such as int and
intp, have differing bitsizes, dependent on the platforms (e.g. 32-bit
vs. 64-bit machines). 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 can be used as functions to convert python numbers to array scalars (see the array scalar section for an explanation), python sequences of numbers to arrays of that type, or as arguments to the dtype keyword that many numpy functions or methods accept. Some examples:
>>> import numpy as np
>>> x = np.float32(1.0)
>>> x
1.0
>>> y = np.int_([1,2,4])
>>> y
array([1, 2, 4])
>>> z = np.arange(3, dtype=np.uint8)
>>> z
array([0, 1, 2], dtype=uint8)
Array types can also be referred to by character codes, mostly to retain backward compatibility with older packages such as Numeric. Some documentation may still refer to these, for example:
>>> np.array([1, 2, 3], dtype='f')
array([ 1., 2., 3.], dtype=float32)
We recommend using dtype objects instead.
To convert the type of an array, use the .astype() method (preferred) or the type itself as a function. For example:
>>> z.astype(float)
array([ 0., 1., 2.])
>>> np.int8(z)
array([0, 1, 2], dtype=int8)
Note that, above, we use the Python float object as a dtype. NumPy knows
that int refers to np.int_, bool means np.bool_,
that float is np.float_ and complex is np.complex_.
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(int)
>>> d
dtype('int32')
>>> np.issubdtype(d, np.integer)
True
>>> np.issubdtype(d, np.floating)
False
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, unicode).
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 ** 8 correctly for 64-bit integers,
but gives 1874919424 (incorrect) for a 32-bit integer.
>>> np.power(100, 8, dtype=np.int64)
10000000000000000
>>> np.power(100, 8, dtype=np.int32)
1874919424
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 np.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 np.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, np.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 np.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.