"""
=================
Structured Arrays
=================

Introduction
============

Structured arrays are ndarrays whose datatype is a composition of simpler
datatypes organized as a sequence of named :term:`fields <field>`. For example,
::

 >>> x = np.array([('Rex', 9, 81.0), ('Fido', 3, 27.0)],
 ...              dtype=[('name', 'U10'), ('age', 'i4'), ('weight', 'f4')])
 >>> x
 array([('Rex', 9, 81.0), ('Fido', 3, 27.0)],
       dtype=[('name', 'S10'), ('age', '<i4'), ('weight', '<f4')])

Here ``x`` is a one-dimensional array of length two whose datatype is a
structure with three fields: 1. A string of length 10 or less named 'name', 2.
a 32-bit integer named 'age', and 3. a 32-bit float named 'weight'.

If you index ``x`` at position 1 you get a structure::

 >>> x[1]
 ('Fido', 3, 27.0)

You can access and modify individual fields of a structured array by indexing
with the field name::

 >>> x['age']
 array([9, 3], dtype=int32)
 >>> x['age'] = 5
 >>> x
 array([('Rex', 5, 81.0), ('Fido', 5, 27.0)],
       dtype=[('name', 'S10'), ('age', '<i4'), ('weight', '<f4')])

Structured arrays are designed for low-level manipulation of structured data,
for example, for interpreting binary blobs. Structured datatypes are
designed to mimic 'structs' in the C language, making them also useful for
interfacing with C code. For these purposes, numpy supports specialized
features such as subarrays and nested datatypes, and allows manual control over
the memory layout of the structure.

For simple manipulation of tabular data other pydata projects, such as pandas,
xarray, or DataArray, provide higher-level interfaces that may be more
suitable. These projects may also give better performance for tabular data
analysis because the C-struct-like memory layout of structured arrays can lead
to poor cache behavior.

.. _defining-structured-types:

Structured Datatypes
====================

To use structured arrays one first needs to define a structured datatype.

A structured datatype can be thought of as a sequence of bytes of a certain
length (the structure's :term:`itemsize`) which is interpreted as a collection
of fields. Each field has a name, a datatype, and a byte offset within the
structure. The datatype of a field may be any numpy datatype including other
structured datatypes, and it may also be a :term:`sub-array` which behaves like
an ndarray of a specified shape. The offsets of the fields are arbitrary, and
fields may even overlap. These offsets are usually determined automatically by
numpy, but can also be manually specified.

Structured Datatype Creation
----------------------------

Structured datatypes may be created using the function :func:`numpy.dtype`.
There are 4 alternative forms of specification which vary in flexibility and
conciseness. These are further documented in the
:ref:`Data Type Objects <arrays.dtypes.constructing>` reference page, and in
summary they are:

1.   A list of tuples, one tuple per field

     Each tuple has the form ``(fieldname, datatype, shape)`` where shape is
     optional. ``fieldname`` is a string (or tuple if titles are used, see
     :ref:`Field Titles <titles>` below), ``datatype`` may be any object
     convertible to a datatype, and shape (optional) is a tuple of integers
     specifying subarray shape.

      >>> np.dtype([('x', 'f4'), ('y', np.float32), ('z', 'f4', (2,2))])
      dtype=[('x', '<f4'), ('y', '<f4'), ('z', '<f4', (2, 2))])

     If ``fieldname`` is the empty string ``''``, the field will be given a
     default name of the form ``f#``, where ``#`` is the integer index of the
     field, counting from 0 from the left::

      >>> np.dtype([('x', 'f4'),('', 'i4'),('z', 'i8')])
      dtype([('x', '<f4'), ('f1', '<i4'), ('z', '<i8')])

     The byte offsets of the fields within the structure and the total
     structure itemsize are determined automatically.

2.   A string of comma-separated dtype specifications

     In this shorthand notation any of the :ref:`string dtype specifications
     <arrays.dtypes.constructing>` may be used in a string and separated by
     commas. The itemsize and byte offsets of the fields are determined
     automatically, and the field names are given the default names ``f0``,
     ``f1``, etc. ::

      >>> np.dtype('i8,f4,S3')
      dtype([('f0', '<i8'), ('f1', '<f4'), ('f2', 'S3')])
      >>> np.dtype('3int8, float32, (2,3)float64')
      dtype([('f0', 'i1', 3), ('f1', '<f4'), ('f2', '<f8', (2, 3))])

3.   A dictionary of field parameter arrays

     This is the most flexible form of specification since it allows control
     over the byte-offsets of the fields and the itemsize of the structure.

     The dictionary has two required keys, 'names' and 'formats', and four
     optional keys, 'offsets', 'itemsize', 'aligned' and 'titles'. The values
     for 'names' and 'formats' should respectively be a list of field names and
     a list of dtype specifications, of the same length. The optional 'offsets'
     value should be a list of integer byte-offsets, one for each field within
     the structure. If 'offsets' is not given the offsets are determined
     automatically. The optional 'itemsize' value should be an integer
     describing the total size in bytes of the dtype, which must be large
     enough to contain all the fields.
     ::

      >>> np.dtype({'names': ['col1', 'col2'], 'formats': ['i4','f4']})
      dtype([('col1', '<i4'), ('col2', '<f4')])
      >>> np.dtype({'names': ['col1', 'col2'],
      ...           'formats': ['i4','f4'],
      ...           'offsets': [0, 4],
      ...           'itemsize': 12})
      dtype({'names':['col1','col2'], 'formats':['<i4','<f4'], 'offsets':[0,4], 'itemsize':12})

     Offsets may be chosen such that the fields overlap, though this will mean
     that assigning to one field may clobber any overlapping field's data. As
     an exception, fields of :class:`numpy.object` type .. (see 
     :ref:`object arrays <arrays.object>`) cannot overlap with other fields,
     because of the risk of clobbering the internal object pointer and then
     dereferencing it.

     The optional 'aligned' value can be set to ``True`` to make the automatic
     offset computation use aligned offsets (see :ref:`offsets-and-alignment`),
     as if the 'align' keyword argument of :func:`numpy.dtype` had been set to
     True.

     The optional 'titles' value should be a list of titles of the same length
     as 'names', see :ref:`Field Titles <titles>` below.

4.   A dictionary of field names

     The use of this form of specification is discouraged, but documented here
     because older numpy code may use it. The keys of the dictionary are the
     field names and the values are tuples specifying type and offset::

      >>> np.dtype=({'col1': ('i1',0), 'col2': ('f4',1)})
      dtype([(('col1'), 'i1'), (('col2'), '>f4')])

     This form is discouraged because Python dictionaries do not preserve order
     in Python versions before Python 3.6, and the order of the fields in a
     structured dtype has meaning. :ref:`Field Titles <titles>` may be
     specified by using a 3-tuple, see below.

Manipulating and Displaying Structured Datatypes
------------------------------------------------

The list of field names of a structured datatype can be found in the ``names``
attribute of the dtype object::

 >>> d = np.dtype([('x', 'i8'), ('y', 'f4')])
 >>> d.names
 ('x', 'y')

The field names may be modified by assigning to the ``names`` attribute using a
sequence of strings of the same length.

The dtype object also has a dictionary-like attribute, ``fields``, whose keys
are the field names (and :ref:`Field Titles <titles>`, see below) and whose
values are tuples containing the dtype and byte offset of each field. ::

 >>> d.fields
 mappingproxy({'x': (dtype('int64'), 0), 'y': (dtype('float32'), 8)})

Both the ``names`` and ``fields`` attributes will equal ``None`` for
unstructured arrays.

The string representation of a structured datatype is shown in the "list of
tuples" form if possible, otherwise numpy falls back to using the more general
dictionary form.

.. _offsets-and-alignment:

Automatic Byte Offsets and Alignment
------------------------------------

Numpy uses one of two methods to automatically determine the field byte offsets
and the overall itemsize of a structured datatype, depending on whether
``align=True`` was specified as a keyword argument to :func:`numpy.dtype`.

By default (with ``align=False``), numpy will pack the fields together tightly
such that each field starts at the byte offset the previous field ended, and the
fields are contiguous in memory. ::

 >>> def print_offsets(d):
 ...     print("offsets:", [d.fields[name][1] for name in d.names])
 ...     print("itemsize:", d.itemsize)
 >>> print_offsets(np.dtype('u1,u1,i4,u1,i8,u2'))
 offsets: [0, 1, 2, 6, 7, 15]
 itemsize: 17

If ``align=True`` is set, numpy will pad the structure in the same way many C
compilers would pad a C-struct. Aligned structures can give a performance
improvement in some cases, at the cost of increased datatype size. Padding
bytes are inserted between fields such that each field's byte offset will be a
multiple of that field's alignment (usually equal to the field's size in bytes
for simple datatypes, see :c:member:`PyArray_Descr.alignment`).
The structure will also have trailing padding added so that its itemsize is a
multiple of the largest field's alignment. ::

 >>> print_offsets(np.dtype('u1,u1,i4,u1,i8,u2', align=True))
 offsets: [0, 1, 4, 8, 16, 24]
 itemsize: 32

Note that although almost all modern C compilers pad in this way by default,
padding in C structs is C-implementation-dependent so this memory layout is not
guaranteed to exactly match that of a corresponding struct in a C program. Some
massaging may be needed either on the numpy side or the C side to obtain exact
correspondence.

If offsets were specified manually using the optional ``offsets`` key in the
dictionary-based dtype specification, setting ``align=True`` will check that
each field's offset is a multiple of its size and that the itemsize is a
multiple of the largest field size, and raise an exception if not.

If the offsets of the fields and itemsize of a structured array satisfy the
alignment conditions, the array will have the ``ALIGNED`` :ref:`flag
<numpy.ndarray.flags>` set.

.. _titles:

Field Titles
------------

In addition to field names, fields may also have an associated :term:`title`,
an alternate name, which is sometimes used as an additional description or
mnemonic for the field. The title may be used to index an array, just like a
fieldname.

To add titles when using the list-of-tuples form of dtype specification, the
fieldname may be be specified as a tuple of two strings (instead of a single
string), which will be the field's title and field name respectively. For
example::

 >>> np.dtype([(('my title', 'name'), 'f4')])

When using the first form of dictionary-based specification, the titles may be
supplied as an extra ``'titles'`` key as described above. When using the second
(discouraged) dictionary-based specification, the title can be supplied by
providing a 3-element tuple ``(datatype, offset, title)`` instead of the usual
2-element tuple::

 >>> np.dtype({'name': ('i4', 0, 'my title')})

The ``dtype.fields`` dictionary will contain :term:`titles` as keys, if any
titles are used.  This means effectively that a field with a title will be
represented twice in the fields dictionary. The tuple values for these fields
will also have a third element, the field title.

Because of this, and because the ``names`` attribute preserves the field order
while the ``fields`` attribute may not, it is recommended to iterate through
the fields of a dtype using the ``names`` attribute of the dtype (which will
not list titles), as in::

 >>> for name in d.names:
 ...     print(d.fields[name][:2])

Union types
-----------

Structured datatypes are implemented in numpy to have base type
:class:`numpy.void` by default, but it is possible to interpret other numpy
types as structured types using the ``(base_dtype, dtype)`` form of dtype
specification described in
:ref:`Data Type Objects <arrays.dtypes.constructing>`.  Here, ``base_dtype`` is
the desired underlying dtype, and fields and flags will be copied from
``dtype``. This dtype is similar to a 'union' in C.

Indexing and Assignment to Structured arrays
=============================================

Assigning data to a Structured Array
------------------------------------

There are a number of ways to assign values to a structured array: Using python
tuples, using scalar values, or using other structured arrays.

Assignment from Python Native Types (Tuples)
```````````````````````````````````````````

The simplest way to assign values to a structured array is using python
tuples. Each assigned value should be a tuple (and not a list or array, as
these will trigger numpy's broadcasting rules) of length equal to the number of
fields in the array. The tuple's elements are assigned to the successive fields
of the array, from left to right::

 >>> x = np.array([(1,2,3),(4,5,6)], dtype='i8,f4,f8')
 >>> x[1] = (7,8,9)
 >>> x
 array([(1, 2., 3.), (7, 8., 9.)],
      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '<f8')])

Assignment from Scalars
```````````````````````

A scalar assigned to a structured element will be assigned to all fields. This
happens when a scalar is assigned to a structured array, or when a scalar array
is assigned to a structured array::

 >>> x = np.zeros(2, dtype='i8,f4,?,S1')
 >>> x[:] = 3
 >>> x
 array([(3, 3.0, True, b'3'), (3, 3.0, True, b'3')],
       dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])
 >>> x[:] = np.arange(2)
 >>> x
 array([(0, 0.0, False, b'0'), (1, 1.0, True, b'1')],
       dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])

Structured arrays can also be assigned to scalar arrays, but only if the
structured datatype has just a single field::

 >>> x = np.zeros(2, dtype=[('A', 'i4'), ('B', 'i4')])
 >>> y = np.zeros(2, dtype=[('A', 'i4')])
 >>> a = np.zeros(2, dtype='i4')
 >>> a[:] = x
 ValueError: Can't cast from structure to non-structure, except if the structure only has a single field.
 >>> a[:] = y
 >>> a
 array([0, 0], dtype=int32)

Assignment from other Structured Arrays
```````````````````````````````````````

Assignment between two structured arrays occurs as if the source elements had
been converted to tuples and then assigned to the destination elements. That
is, the first field of the source array is assigned to the first field of the
destination array, and the second field likewise, and so on, regardless of
field names. Structured arrays with a different number of fields cannot be
assigned to each other. Bytes of the destination structure which are not
included in any of the fields are unaffected. ::

 >>> a = np.zeros(3, dtype=[('a', 'i8'), ('b', 'f4'), ('c', 'S3')])
 >>> b = np.ones(3, dtype=[('x', 'f4'), ('y', 'S3'), ('z', 'O')])
 >>> b[:] = a
 >>> b
 array([(0.0, b'0.0', b''), (0.0, b'0.0', b''), (0.0, b'0.0', b'')],
       dtype=[('x', '<f4'), ('y', 'S3'), ('z', 'O')])


Assignment involving subarrays
``````````````````````````````

When assigning to fields which are subarrays, the assigned value will first be
broadcast to the shape of the subarray.

Indexing Structured Arrays
--------------------------

Accessing Individual Fields
```````````````````````````

Individual fields of a structured array may be accessed and modified by indexing
the array with the field name. ::

 >>> x = np.array([(1,2),(3,4)], dtype=[('foo', 'i8'), ('bar', 'f4')])
 >>> x['foo']
 array([1, 3])
 >>> x['foo'] = 10
 >>> x
 array([(10, 2.), (10, 4.)],
       dtype=[('foo', '<i8'), ('bar', '<f4')])

The resulting array is a view into the original array. It shares the same
memory locations and writing to the view will modify the original array. ::

 >>> y = x['bar']
 >>> y[:] = 10
 >>> x
 array([(10, 5.), (10, 5.)],
       dtype=[('foo', '<i8'), ('bar', '<f4')])

This view has the same dtype and itemsize as the indexed field, so it is
typically a non-structured array (except in the case of nested structures).

 >>> y.dtype, y.shape, y.strides
 (dtype('float32'), (2,), (12,))

Accessing Multiple Fields
```````````````````````````

One can index a structured array with a multi-field index, where the index is a
list of field names::

 >>> a = np.zeros(3, dtype=[('a', 'i8'), ('b', 'i4'), ('c', 'f8')])
 >>> a[['a', 'c']]
 array([(0, 0.0), (0, 0.0), (0, 0.0)],
       dtype={'names':['a','c'], 'formats':['<i8','<f8'], 'offsets':[0,11], 'itemsize':19})
 >>> a[['a', 'c']] = (2, 3)
 >>> a
 array([(2, 0, 3.0), (2, 0, 3.0), (2, 0, 3.0)],
       dtype=[('a', '<i8'), ('b', '<i4'), ('c', '<f8')])

The resulting array is a view into the original array, such that assignment to
the view modifies the original array. This view's fields will be in the order
they were indexed. Note that unlike for single-field indexing, the view's dtype
has the same itemsize as the original array and has fields at the same offsets
as in the original array, and unindexed fields are merely missing.

Since this view is a structured array itself, it obeys the assignment rules
described above. For example, this means that one can swap the values of two
fields using appropriate multi-field indexes::

 >>> a[['a', 'c']] = a[['c', 'a']]

Indexing with an Integer to get a Structured Scalar
```````````````````````````````````````````````````

Indexing a single element of a structured array (with an integer index) returns
a structured scalar::

 >>> x = np.array([(1, 2., 3.)], dtype='i,f,f')
 >>> scalar = x[0]
 >>> scalar
 (1, 2., 3.)
 >>> type(scalar)
 numpy.void

Importantly, unlike other numpy scalars, structured scalars are mutable and act
like views into the original array, such that modifying the scalar will modify
the original array. Structured scalars also support access and assignment by
field name::

 >>> x = np.array([(1,2),(3,4)], dtype=[('foo', 'i8'), ('bar', 'f4')])
 >>> s = x[0]
 >>> s['bar'] = 100
 >>> x
 array([(1, 100.), (3, 4.)],
       dtype=[('foo', '<i8'), ('bar', '<f4')])

Similarly to tuples, structured scalars can also be indexed with an integer::

 >>> scalar = np.array([(1, 2., 3.)], dtype='i,f,f')[0]
 >>> scalar[0]
 1
 >>> scalar[1] = 4

Thus, tuples might be though of as the native Python equivalent to numpy's
structured types, much like native python integers are the equivalent to
numpy's integer types. Structured scalars may be converted to a tuple by
calling :func:`ndarray.item`::

 >>> scalar.item(), type(scalar.item())
 ((1, 2.0, 3.0), tuple)

Viewing Structured Arrays Containing Objects
--------------------------------------------

In order to prevent clobbering of object pointers in fields of
:class:`numpy.object` type, numpy currently does not allow views of structured
arrays containing objects.

Structure Comparison
--------------------

If the dtypes of two structured arrays are equivalent, testing the equality of
the arrays will result in a boolean array with the dimension of the original
arrays, with elements set to True where all fields of the corresponding
structures are equal. Structured dtypes are equivalent if the field names,
dtypes and titles are the same, ignoring endianness, and the fields are in
the same order::

 >>> a = np.zeros(2, dtype=[('a', 'i4'), ('b', 'i4')])
 >>> b = np.ones(2, dtype=[('a', 'i4'), ('b', 'i4')])
 >>> a == b
 array([False, False], dtype=bool)

Currently, if the dtypes of two arrays are not equivalent all comparisons will
return ``False``. This behavior is deprecated as of numpy 1.10 and may change
in the future.

Currently, the ``<`` and ``>`` operators will always return ``False`` when
comparing structured arrays. Many other pairwise operators are not supported.

Record Arrays
=============

As an optional convenience numpy provides an ndarray subclass,
:class:`numpy.recarray`, and associated helper functions in the
:mod:`numpy.rec` submodule, which allows access to fields of structured arrays
by attribute, instead of only by index. Record arrays also use a special
datatype, :class:`numpy.record`, which allows field access by attribute on the
structured scalars obtained from the array.

The simplest way to create a record array is with :func:`numpy.rec.array`::

 >>> recordarr = np.rec.array([(1,2.,'Hello'),(2,3.,"World")],
 ...                    dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'S10')])
 >>> recordarr.bar
 array([ 2.,  3.], dtype=float32)
 >>> recordarr[1:2]
 rec.array([(2, 3.0, 'World')],
       dtype=[('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')])
 >>> recordarr[1:2].foo
 array([2], dtype=int32)
 >>> recordarr.foo[1:2]
 array([2], dtype=int32)
 >>> recordarr[1].baz
 'World'

:func:`numpy.rec.array` can convert a wide variety of arguments into record
arrays, including structured arrays::

 >>> arr = array([(1,2.,'Hello'),(2,3.,"World")],
 ...             dtype=[('foo', 'i4'), ('bar', 'f4'), ('baz', 'S10')])
 >>> recordarr = np.rec.array(arr)

The :mod:`numpy.rec` module provides a number of other convenience functions for
creating record arrays, see :ref:`record array creation routines
<routines.array-creation.rec>`.

A record array representation of a structured array can be obtained using the
appropriate :ref:`view`::

 >>> arr = np.array([(1,2.,'Hello'),(2,3.,"World")],
 ...                dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'a10')])
 >>> recordarr = arr.view(dtype=dtype((np.record, arr.dtype)),
 ...                      type=np.recarray)

For convenience, viewing an ndarray as type :class:`np.recarray` will
automatically convert to :class:`np.record` datatype, so the dtype can be left
out of the view::

 >>> recordarr = arr.view(np.recarray)
 >>> recordarr.dtype
 dtype((numpy.record, [('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')]))

To get back to a plain ndarray both the dtype and type must be reset. The
following view does so, taking into account the unusual case that the
recordarr was not a structured type::

 >>> arr2 = recordarr.view(recordarr.dtype.fields or recordarr.dtype, np.ndarray)

Record array fields accessed by index or by attribute are returned as a record
array if the field has a structured type but as a plain ndarray otherwise. ::

 >>> recordarr = np.rec.array([('Hello', (1,2)),("World", (3,4))],
 ...                 dtype=[('foo', 'S6'),('bar', [('A', int), ('B', int)])])
 >>> type(recordarr.foo)
 <type 'numpy.ndarray'>
 >>> type(recordarr.bar)
 <class 'numpy.core.records.recarray'>

Note that if a field has the same name as an ndarray attribute, the ndarray
attribute takes precedence. Such fields will be inaccessible by attribute but
will still be accessible by index.

"""
from __future__ import division, absolute_import, print_function