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								:mod:`array` --- Efficient arrays of numeric values
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								===================================================
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								.. module:: array
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												Merged revisions 62021,62029,62035-62038,62043-62044,62052-62053 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
  r62021 | benjamin.peterson | 2008-03-28 18:11:01 -0500 (Fri, 28 Mar 2008) | 2 lines
  NIL => NULL
........
  r62029 | amaury.forgeotdarc | 2008-03-28 20:42:31 -0500 (Fri, 28 Mar 2008) | 3 lines
  Correctly call the base class tearDown();
  otherwise running test_logging twice produce the errors we see on all buildbots
........
  r62035 | raymond.hettinger | 2008-03-29 05:42:07 -0500 (Sat, 29 Mar 2008) | 1 line
  Be explicit about what efficient means.
........
  r62036 | georg.brandl | 2008-03-29 06:46:18 -0500 (Sat, 29 Mar 2008) | 2 lines
  Fix capitalization.
........
  r62037 | amaury.forgeotdarc | 2008-03-29 07:42:54 -0500 (Sat, 29 Mar 2008) | 5 lines
  lib2to3 should install a logging handler only when run as a main program,
  not when used as a library.
  This may please the buildbots, which fail when test_lib2to3 is run before test_logging.
........
  r62043 | benjamin.peterson | 2008-03-29 10:24:25 -0500 (Sat, 29 Mar 2008) | 3 lines
  #2503 make singletons compared with "is" not == or !=
  Thanks to Wummel for the patch
........
  r62044 | gerhard.haering | 2008-03-29 14:11:52 -0500 (Sat, 29 Mar 2008) | 2 lines
  Documented the lastrowid attribute.
........
  r62052 | benjamin.peterson | 2008-03-30 14:35:10 -0500 (Sun, 30 Mar 2008) | 2 lines
  Updated README regarding doc formats
........
  r62053 | georg.brandl | 2008-03-30 14:41:39 -0500 (Sun, 30 Mar 2008) | 2 lines
  The other download formats will be available for 2.6 too.
........
											
										 
										
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								   :synopsis: Space efficient arrays of uniformly typed numeric values.
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								.. index:: single: arrays
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												Merged revisions 62021,62029,62035-62038,62043-62044,62052-62053 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
........
  r62021 | benjamin.peterson | 2008-03-28 18:11:01 -0500 (Fri, 28 Mar 2008) | 2 lines
  NIL => NULL
........
  r62029 | amaury.forgeotdarc | 2008-03-28 20:42:31 -0500 (Fri, 28 Mar 2008) | 3 lines
  Correctly call the base class tearDown();
  otherwise running test_logging twice produce the errors we see on all buildbots
........
  r62035 | raymond.hettinger | 2008-03-29 05:42:07 -0500 (Sat, 29 Mar 2008) | 1 line
  Be explicit about what efficient means.
........
  r62036 | georg.brandl | 2008-03-29 06:46:18 -0500 (Sat, 29 Mar 2008) | 2 lines
  Fix capitalization.
........
  r62037 | amaury.forgeotdarc | 2008-03-29 07:42:54 -0500 (Sat, 29 Mar 2008) | 5 lines
  lib2to3 should install a logging handler only when run as a main program,
  not when used as a library.
  This may please the buildbots, which fail when test_lib2to3 is run before test_logging.
........
  r62043 | benjamin.peterson | 2008-03-29 10:24:25 -0500 (Sat, 29 Mar 2008) | 3 lines
  #2503 make singletons compared with "is" not == or !=
  Thanks to Wummel for the patch
........
  r62044 | gerhard.haering | 2008-03-29 14:11:52 -0500 (Sat, 29 Mar 2008) | 2 lines
  Documented the lastrowid attribute.
........
  r62052 | benjamin.peterson | 2008-03-30 14:35:10 -0500 (Sun, 30 Mar 2008) | 2 lines
  Updated README regarding doc formats
........
  r62053 | georg.brandl | 2008-03-30 14:41:39 -0500 (Sun, 30 Mar 2008) | 2 lines
  The other download formats will be available for 2.6 too.
........
											
										 
										
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								This module defines an object type which can compactly represent an array of
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								basic values: characters, integers, floating point numbers.  Arrays are sequence
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								types and behave very much like lists, except that the type of objects stored in
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								them is constrained.  The type is specified at object creation time by using a
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								:dfn:`type code`, which is a single character.  The following type codes are
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								defined:
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								+-----------+----------------+-------------------+-----------------------+
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								| Type code | C Type         | Python Type       | Minimum size in bytes |
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								+===========+================+===================+=======================+
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								| ``'b'``   | signed char    | int               | 1                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'B'``   | unsigned char  | int               | 1                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'u'``   | Py_UNICODE     | Unicode character | 2                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'h'``   | signed short   | int               | 2                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'H'``   | unsigned short | int               | 2                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'i'``   | signed int     | int               | 2                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'I'``   | unsigned int   | int               | 2                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'l'``   | signed long    | int               | 4                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'L'``   | unsigned long  | int               | 4                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'f'``   | float          | float             | 4                     |
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								+-----------+----------------+-------------------+-----------------------+
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								| ``'d'``   | double         | float             | 8                     |
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								+-----------+----------------+-------------------+-----------------------+
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								The actual representation of values is determined by the machine architecture
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								(strictly speaking, by the C implementation).  The actual size can be accessed
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								through the :attr:`itemsize` attribute.
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								The module defines the following type:
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								.. function:: array(typecode[, initializer])
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								   Return a new array whose items are restricted by *typecode*, and initialized
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								   from the optional *initializer* value, which must be a list, object
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								   supporting the buffer interface, or iterable over elements of the
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								   appropriate type.
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								   If given a list or string, the initializer is passed to the new array's
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								   :meth:`fromlist`, :meth:`fromstring`, or :meth:`fromunicode` method (see below)
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								   to add initial items to the array.  Otherwise, the iterable initializer is
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								   passed to the :meth:`extend` method.
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								.. data:: ArrayType
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								   Obsolete alias for :func:`array`.
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								.. data:: typecodes
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								   A string with all available type codes.
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								Array objects support the ordinary sequence operations of indexing, slicing,
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								concatenation, and multiplication.  When using slice assignment, the assigned
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								value must be an array object with the same type code; in all other cases,
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								:exc:`TypeError` is raised. Array objects also implement the buffer interface,
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								and may be used wherever buffer objects are supported.
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								The following data items and methods are also supported:
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								.. attribute:: array.typecode
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								   The typecode character used to create the array.
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								.. attribute:: array.itemsize
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								   The length in bytes of one array item in the internal representation.
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								.. method:: array.append(x)
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								   Append a new item with value *x* to the end of the array.
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								.. method:: array.buffer_info()
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								   Return a tuple ``(address, length)`` giving the current memory address and the
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								   length in elements of the buffer used to hold array's contents.  The size of the
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								   memory buffer in bytes can be computed as ``array.buffer_info()[1] *
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								   array.itemsize``.  This is occasionally useful when working with low-level (and
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								   inherently unsafe) I/O interfaces that require memory addresses, such as certain
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								   :cfunc:`ioctl` operations.  The returned numbers are valid as long as the array
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								   exists and no length-changing operations are applied to it.
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								   .. note::
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								      When using array objects from code written in C or C++ (the only way to
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								      effectively make use of this information), it makes more sense to use the buffer
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								      interface supported by array objects.  This method is maintained for backward
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								      compatibility and should be avoided in new code.  The buffer interface is
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								      documented in :ref:`bufferobjects`.
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								.. method:: array.byteswap()
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								   "Byteswap" all items of the array.  This is only supported for values which are
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								   1, 2, 4, or 8 bytes in size; for other types of values, :exc:`RuntimeError` is
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								   raised.  It is useful when reading data from a file written on a machine with a
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								   different byte order.
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								.. method:: array.count(x)
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							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Return the number of occurrences of *x* in the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.extend(iterable)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Append items from *iterable* to the end of the array.  If *iterable* is another
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   array, it must have *exactly* the same type code; if not, :exc:`TypeError` will
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   be raised.  If *iterable* is not an array, it must be iterable and its elements
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   must be the right type to be appended to the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.fromfile(f, n)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Read *n* items (as machine values) from the file object *f* and append them to
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   the end of the array.  If less than *n* items are available, :exc:`EOFError` is
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   raised, but the items that were available are still inserted into the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   *f* must be a real built-in file object; something else with a :meth:`read`
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   method won't do.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.fromlist(list)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Append items from the list.  This is equivalent to ``for x in list:
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   a.append(x)`` except that if there is a type error, the array is unchanged.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.fromstring(s)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Appends items from the string, interpreting the string as an array of machine
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   values (as if it had been read from a file using the :meth:`fromfile` method).
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.fromunicode(s)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Extends this array with data from the given unicode string.  The array must
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   be a type ``'u'`` array; otherwise a :exc:`ValueError` is raised.  Use
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   ``array.fromstring(unicodestring.encode(enc))`` to append Unicode data to an
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   array of some other type.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.index(x)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Return the smallest *i* such that *i* is the index of the first occurrence of
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   *x* in the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.insert(i, x)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Insert a new item with value *x* in the array before position *i*. Negative
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   values are treated as being relative to the end of the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.pop([i])
							 | 
						
					
						
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							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Removes the item with the index *i* from the array and returns it. The optional
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   argument defaults to ``-1``, so that by default the last item is removed and
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   returned.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.remove(x)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Remove the first occurrence of *x* from the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
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							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.reverse()
							 | 
						
					
						
							| 
								
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							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Reverse the order of the items in the array.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.tofile(f)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
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								   Write all items (as machine values) to the file object *f*.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.tolist()
							 | 
						
					
						
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							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Convert the array to an ordinary list with the same items.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.tostring()
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Convert the array to an array of machine values and return the string
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   representation (the same sequence of bytes that would be written to a file by
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   the :meth:`tofile` method.)
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. method:: array.tounicode()
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Convert the array to a unicode string.  The array must be a type ``'u'`` array;
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   otherwise a :exc:`ValueError` is raised. Use ``array.tostring().decode(enc)`` to
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   obtain a unicode string from an array of some other type.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								When an array object is printed or converted to a string, it is represented as
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								``array(typecode, initializer)``.  The *initializer* is omitted if the array is
							 | 
						
					
						
							
								
									
										
										
										
											2008-12-06 08:12:11 +00:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								empty, otherwise it is a string if the *typecode* is ``'u'``, otherwise it is a
							 | 
						
					
						
							
								
									
										
										
										
											2007-08-15 14:28:22 +00:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								list of numbers.  The string is guaranteed to be able to be converted back to an
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								array with the same type and value using :func:`eval`, so long as the
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								:func:`array` function has been imported using ``from array import array``.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								Examples::
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   array('l')
							 | 
						
					
						
							
								
									
										
										
										
											2008-12-06 08:12:11 +00:00
										 
									 
								 
							 | 
							
								
									
										
									
								
							 | 
							
								
							 | 
							
							
								   array('u', 'hello \u2641')
							 | 
						
					
						
							
								
									
										
										
										
											2007-08-15 14:28:22 +00:00
										 
									 
								 
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   array('l', [1, 2, 3, 4, 5])
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   array('d', [1.0, 2.0, 3.14])
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								.. seealso::
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Module :mod:`struct`
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      Packing and unpacking of heterogeneous binary data.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   Module :mod:`xdrlib`
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      Packing and unpacking of External Data Representation (XDR) data as used in some
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      remote procedure call systems.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								   `The Numerical Python Manual <http://numpy.sourceforge.net/numdoc/HTML/numdoc.htm>`_
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      The Numeric Python extension (NumPy) defines another array type; see
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      http://numpy.sourceforge.net/ for further information about Numerical Python.
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      (A PDF version of the NumPy manual is available at
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								      http://numpy.sourceforge.net/numdoc/numdoc.pdf).
							 | 
						
					
						
							| 
								
							 | 
							
								
							 | 
							
								
							 | 
							
							
								
							 |