mirror of
https://github.com/PiBrewing/craftbeerpi4.git
synced 2024-11-23 07:28:13 +01:00
341 lines
11 KiB
Python
341 lines
11 KiB
Python
"""
|
|
============
|
|
Array basics
|
|
============
|
|
|
|
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:
|
|
|
|
.. list-table::
|
|
:header-rows: 1
|
|
|
|
* - Numpy type
|
|
- C type
|
|
- Description
|
|
|
|
* - `np.bool_`
|
|
- ``bool``
|
|
- Boolean (True or False) stored as a byte
|
|
|
|
* - `np.byte`
|
|
- ``signed char``
|
|
- Platform-defined
|
|
|
|
* - `np.ubyte`
|
|
- ``unsigned char``
|
|
- Platform-defined
|
|
|
|
* - `np.short`
|
|
- ``short``
|
|
- Platform-defined
|
|
|
|
* - `np.ushort`
|
|
- ``unsigned short``
|
|
- Platform-defined
|
|
|
|
* - `np.intc`
|
|
- ``int``
|
|
- Platform-defined
|
|
|
|
* - `np.uintc`
|
|
- ``unsigned int``
|
|
- Platform-defined
|
|
|
|
* - `np.int_`
|
|
- ``long``
|
|
- Platform-defined
|
|
|
|
* - `np.uint`
|
|
- ``unsigned long``
|
|
- Platform-defined
|
|
|
|
* - `np.longlong`
|
|
- ``long long``
|
|
- Platform-defined
|
|
|
|
* - `np.ulonglong`
|
|
- ``unsigned long long``
|
|
- Platform-defined
|
|
|
|
* - `np.half` / `np.float16`
|
|
-
|
|
- Half precision float:
|
|
sign bit, 5 bits exponent, 10 bits mantissa
|
|
|
|
* - `np.single`
|
|
- ``float``
|
|
- Platform-defined single precision float:
|
|
typically sign bit, 8 bits exponent, 23 bits mantissa
|
|
|
|
* - `np.double`
|
|
- ``double``
|
|
- Platform-defined double precision float:
|
|
typically sign bit, 11 bits exponent, 52 bits mantissa.
|
|
|
|
* - `np.longdouble`
|
|
- ``long double``
|
|
- Platform-defined extended-precision float
|
|
|
|
* - `np.csingle`
|
|
- ``float complex``
|
|
- Complex number, represented by two single-precision floats (real and imaginary components)
|
|
|
|
* - `np.cdouble`
|
|
- ``double complex``
|
|
- Complex number, represented by two double-precision floats (real and imaginary components).
|
|
|
|
* - `np.clongdouble`
|
|
- ``long double complex``
|
|
- 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:
|
|
|
|
.. list-table::
|
|
:header-rows: 1
|
|
|
|
* - Numpy type
|
|
- C type
|
|
- Description
|
|
|
|
* - `np.int8`
|
|
- ``int8_t``
|
|
- Byte (-128 to 127)
|
|
|
|
* - `np.int16`
|
|
- ``int16_t``
|
|
- Integer (-32768 to 32767)
|
|
|
|
* - `np.int32`
|
|
- ``int32_t``
|
|
- Integer (-2147483648 to 2147483647)
|
|
|
|
* - `np.int64`
|
|
- ``int64_t``
|
|
- Integer (-9223372036854775808 to 9223372036854775807)
|
|
|
|
* - `np.uint8`
|
|
- ``uint8_t``
|
|
- Unsigned integer (0 to 255)
|
|
|
|
* - `np.uint16`
|
|
- ``uint16_t``
|
|
- Unsigned integer (0 to 65535)
|
|
|
|
* - `np.uint32`
|
|
- ``uint32_t``
|
|
- Unsigned integer (0 to 4294967295)
|
|
|
|
* - `np.uint64`
|
|
- ``uint64_t``
|
|
- Unsigned integer (0 to 18446744073709551615)
|
|
|
|
* - `np.intp`
|
|
- ``intptr_t``
|
|
- Integer used for indexing, typically the same as ``ssize_t``
|
|
|
|
* - `np.uintp`
|
|
- ``uintptr_t``
|
|
- Integer large enough to hold a pointer
|
|
|
|
* - `np.float32`
|
|
- ``float``
|
|
-
|
|
|
|
* - `np.float64` / `np.float_`
|
|
- ``double``
|
|
- Note that this matches the precision of the builtin python `float`.
|
|
|
|
* - `np.complex64`
|
|
- ``float complex``
|
|
- Complex number, represented by two 32-bit floats (real and imaginary components)
|
|
|
|
* - `np.complex128` / `np.complex_`
|
|
- ``double complex``
|
|
- Note that this matches the precision of the builtin python `complex`.
|
|
|
|
|
|
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 in the table above, are explored in
|
|
section :ref:`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) #doctest: +NORMALIZE_WHITESPACE
|
|
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 * 10 ** 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``.
|
|
|
|
"""
|