343 lines
11 KiB
Python
343 lines
11 KiB
Python
"""
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============
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Array basics
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============
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Array types and conversions between types
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=========================================
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NumPy supports a much greater variety of numerical types than Python does.
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This section shows which are available, and how to modify an array's data-type.
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The primitive types supported are tied closely to those in C:
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.. list-table::
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:header-rows: 1
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* - Numpy type
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- C type
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- Description
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* - `np.bool_`
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- ``bool``
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- Boolean (True or False) stored as a byte
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* - `np.byte`
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- ``signed char``
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- Platform-defined
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* - `np.ubyte`
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- ``unsigned char``
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- Platform-defined
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* - `np.short`
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- ``short``
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- Platform-defined
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* - `np.ushort`
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- ``unsigned short``
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- Platform-defined
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* - `np.intc`
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- ``int``
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- Platform-defined
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* - `np.uintc`
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- ``unsigned int``
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- Platform-defined
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* - `np.int_`
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- ``long``
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- Platform-defined
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* - `np.uint`
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- ``unsigned long``
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- Platform-defined
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* - `np.longlong`
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- ``long long``
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- Platform-defined
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* - `np.ulonglong`
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- ``unsigned long long``
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- Platform-defined
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* - `np.half` / `np.float16`
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-
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- Half precision float:
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sign bit, 5 bits exponent, 10 bits mantissa
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* - `np.single`
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- ``float``
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- Platform-defined single precision float:
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typically sign bit, 8 bits exponent, 23 bits mantissa
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* - `np.double`
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- ``double``
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- Platform-defined double precision float:
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typically sign bit, 11 bits exponent, 52 bits mantissa.
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* - `np.longdouble`
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- ``long double``
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- Platform-defined extended-precision float
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* - `np.csingle`
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- ``float complex``
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- Complex number, represented by two single-precision floats (real and imaginary components)
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* - `np.cdouble`
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- ``double complex``
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- Complex number, represented by two double-precision floats (real and imaginary components).
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* - `np.clongdouble`
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- ``long double complex``
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- Complex number, represented by two extended-precision floats (real and imaginary components).
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Since many of these have platform-dependent definitions, a set of fixed-size
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aliases are provided:
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.. list-table::
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:header-rows: 1
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* - Numpy type
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- C type
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- Description
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* - `np.int8`
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- ``int8_t``
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- Byte (-128 to 127)
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* - `np.int16`
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- ``int16_t``
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- Integer (-32768 to 32767)
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* - `np.int32`
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- ``int32_t``
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- Integer (-2147483648 to 2147483647)
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* - `np.int64`
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- ``int64_t``
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- Integer (-9223372036854775808 to 9223372036854775807)
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* - `np.uint8`
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- ``uint8_t``
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- Unsigned integer (0 to 255)
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* - `np.uint16`
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- ``uint16_t``
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- Unsigned integer (0 to 65535)
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* - `np.uint32`
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- ``uint32_t``
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- Unsigned integer (0 to 4294967295)
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* - `np.uint64`
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- ``uint64_t``
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- Unsigned integer (0 to 18446744073709551615)
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* - `np.intp`
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- ``intptr_t``
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- Integer used for indexing, typically the same as ``ssize_t``
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* - `np.uintp`
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- ``uintptr_t``
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- Integer large enough to hold a pointer
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* - `np.float32`
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- ``float``
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-
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* - `np.float64` / `np.float_`
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- ``double``
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- Note that this matches the precision of the builtin python `float`.
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* - `np.complex64`
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- ``float complex``
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- Complex number, represented by two 32-bit floats (real and imaginary components)
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* - `np.complex128` / `np.complex_`
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- ``double complex``
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- Note that this matches the precision of the builtin python `complex`.
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NumPy numerical types are instances of ``dtype`` (data-type) objects, each
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having unique characteristics. Once you have imported NumPy using
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::
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>>> import numpy as np
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the dtypes are available as ``np.bool_``, ``np.float32``, etc.
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Advanced types, not listed in the table above, are explored in
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section :ref:`structured_arrays`.
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There are 5 basic numerical types representing booleans (bool), integers (int),
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unsigned integers (uint) floating point (float) and complex. Those with numbers
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in their name indicate the bitsize of the type (i.e. how many bits are needed
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to represent a single value in memory). Some types, such as ``int`` and
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``intp``, have differing bitsizes, dependent on the platforms (e.g. 32-bit
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vs. 64-bit machines). This should be taken into account when interfacing
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with low-level code (such as C or Fortran) where the raw memory is addressed.
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Data-types can be used as functions to convert python numbers to array scalars
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(see the array scalar section for an explanation), python sequences of numbers
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to arrays of that type, or as arguments to the dtype keyword that many numpy
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functions or methods accept. Some examples::
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>>> import numpy as np
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>>> x = np.float32(1.0)
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>>> x
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1.0
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>>> y = np.int_([1,2,4])
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>>> y
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array([1, 2, 4])
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>>> z = np.arange(3, dtype=np.uint8)
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>>> z
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array([0, 1, 2], dtype=uint8)
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Array types can also be referred to by character codes, mostly to retain
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backward compatibility with older packages such as Numeric. Some
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documentation may still refer to these, for example::
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>>> np.array([1, 2, 3], dtype='f')
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array([ 1., 2., 3.], dtype=float32)
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We recommend using dtype objects instead.
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To convert the type of an array, use the .astype() method (preferred) or
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the type itself as a function. For example: ::
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>>> z.astype(float) #doctest: +NORMALIZE_WHITESPACE
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array([ 0., 1., 2.])
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>>> np.int8(z)
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array([0, 1, 2], dtype=int8)
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Note that, above, we use the *Python* float object as a dtype. NumPy knows
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that ``int`` refers to ``np.int_``, ``bool`` means ``np.bool_``,
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that ``float`` is ``np.float_`` and ``complex`` is ``np.complex_``.
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The other data-types do not have Python equivalents.
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To determine the type of an array, look at the dtype attribute::
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>>> z.dtype
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dtype('uint8')
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dtype objects also contain information about the type, such as its bit-width
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and its byte-order. The data type can also be used indirectly to query
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properties of the type, such as whether it is an integer::
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>>> d = np.dtype(int)
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>>> d
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dtype('int32')
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>>> np.issubdtype(d, np.integer)
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True
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>>> np.issubdtype(d, np.floating)
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False
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Array Scalars
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=============
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NumPy generally returns elements of arrays as array scalars (a scalar
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with an associated dtype). Array scalars differ from Python scalars, but
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for the most part they can be used interchangeably (the primary
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exception is for versions of Python older than v2.x, where integer array
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scalars cannot act as indices for lists and tuples). There are some
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exceptions, such as when code requires very specific attributes of a scalar
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or when it checks specifically whether a value is a Python scalar. Generally,
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problems are easily fixed by explicitly converting array scalars
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to Python scalars, using the corresponding Python type function
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(e.g., ``int``, ``float``, ``complex``, ``str``, ``unicode``).
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The primary advantage of using array scalars is that
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they preserve the array type (Python may not have a matching scalar type
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available, e.g. ``int16``). Therefore, the use of array scalars ensures
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identical behaviour between arrays and scalars, irrespective of whether the
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value is inside an array or not. NumPy scalars also have many of the same
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methods arrays do.
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Overflow Errors
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===============
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The fixed size of NumPy numeric types may cause overflow errors when a value
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requires more memory than available in the data type. For example,
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`numpy.power` evaluates ``100 * 10 ** 8`` correctly for 64-bit integers,
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but gives 1874919424 (incorrect) for a 32-bit integer.
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>>> np.power(100, 8, dtype=np.int64)
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10000000000000000
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>>> np.power(100, 8, dtype=np.int32)
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1874919424
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The behaviour of NumPy and Python integer types differs significantly for
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integer overflows and may confuse users expecting NumPy integers to behave
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similar to Python's ``int``. Unlike NumPy, the size of Python's ``int`` is
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flexible. This means Python integers may expand to accommodate any integer and
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will not overflow.
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NumPy provides `numpy.iinfo` and `numpy.finfo` to verify the
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minimum or maximum values of NumPy integer and floating point values
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respectively ::
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>>> np.iinfo(int) # Bounds of the default integer on this system.
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iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
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>>> np.iinfo(np.int32) # Bounds of a 32-bit integer
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iinfo(min=-2147483648, max=2147483647, dtype=int32)
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>>> np.iinfo(np.int64) # Bounds of a 64-bit integer
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iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
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If 64-bit integers are still too small the result may be cast to a
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floating point number. Floating point numbers offer a larger, but inexact,
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range of possible values.
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>>> np.power(100, 100, dtype=np.int64) # Incorrect even with 64-bit int
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0
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>>> np.power(100, 100, dtype=np.float64)
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1e+200
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Extended Precision
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==================
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Python's floating-point numbers are usually 64-bit floating-point numbers,
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nearly equivalent to ``np.float64``. In some unusual situations it may be
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useful to use floating-point numbers with more precision. Whether this
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is possible in numpy depends on the hardware and on the development
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environment: specifically, x86 machines provide hardware floating-point
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with 80-bit precision, and while most C compilers provide this as their
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``long double`` type, MSVC (standard for Windows builds) makes
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``long double`` identical to ``double`` (64 bits). NumPy makes the
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compiler's ``long double`` available as ``np.longdouble`` (and
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``np.clongdouble`` for the complex numbers). You can find out what your
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numpy provides with ``np.finfo(np.longdouble)``.
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NumPy does not provide a dtype with more precision than C's
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``long double``\\; in particular, the 128-bit IEEE quad precision
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data type (FORTRAN's ``REAL*16``\\) is not available.
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For efficient memory alignment, ``np.longdouble`` is usually stored
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padded with zero bits, either to 96 or 128 bits. Which is more efficient
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depends on hardware and development environment; typically on 32-bit
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systems they are padded to 96 bits, while on 64-bit systems they are
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typically padded to 128 bits. ``np.longdouble`` is padded to the system
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default; ``np.float96`` and ``np.float128`` are provided for users who
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want specific padding. In spite of the names, ``np.float96`` and
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``np.float128`` provide only as much precision as ``np.longdouble``,
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that is, 80 bits on most x86 machines and 64 bits in standard
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Windows builds.
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Be warned that even if ``np.longdouble`` offers more precision than
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python ``float``, it is easy to lose that extra precision, since
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python often forces values to pass through ``float``. For example,
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the ``%`` formatting operator requires its arguments to be converted
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to standard python types, and it is therefore impossible to preserve
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extended precision even if many decimal places are requested. It can
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be useful to test your code with the value
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``1 + np.finfo(np.longdouble).eps``.
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"""
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from __future__ import division, absolute_import, print_function
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