text: """
  This is only meant to add docs to objects defined in C-extension modules.
  The purpose is to allow easier editing of the docstrings without
  requiring a re-compile.
  
  NOTE: Many of the methods of ndarray have corresponding functions.
        If you update these docstrings, please keep also the ones in
        core/fromnumeric.py, core/defmatrix.py up-to-date.
  
  """
  from __future__ import division, absolute_import, print_function
  
  import sys
  
  from numpy.core import numerictypes as _numerictypes
  from numpy.core import dtype
  from numpy.core.function_base import add_newdoc
  
  ###############################################################################
  #
  # flatiter
  #
  # flatiter needs a toplevel description
  #
  ###############################################################################
  
  add_newdoc('numpy.core', 'flatiter',
      """
      Flat iterator object to iterate over arrays.
  
      A `flatiter` iterator is returned by ``x.flat`` for any array `x`.
      It allows iterating over the array as if it were a 1-D array,
      either in a for-loop or by calling its `next` method.
  
      Iteration is done in row-major, C-style order (the last
      index varying the fastest). The iterator can also be indexed using
      basic slicing or advanced indexing.
  
      See Also
      --------
      ndarray.flat : Return a flat iterator over an array.
      ndarray.flatten : Returns a flattened copy of an array.
  
      Notes
      -----
      A `flatiter` iterator can not be constructed directly from Python code
      by calling the `flatiter` constructor.
  
      Examples
      --------
      >>> x = np.arange(6).reshape(2, 3)
      >>> fl = x.flat
      >>> type(fl)
      <type 'numpy.flatiter'>
      >>> for item in fl:
      ...     print(item)
      ...
      0
      1
      2
      3
      4
      5
  
      >>> fl[2:4]
      array([2, 3])
  
      """)
  
  # flatiter attributes
  
  add_newdoc('numpy.core', 'flatiter', ('base',
      """
      A reference to the array that is iterated over.
  
      Examples
      --------
      >>> x = np.arange(5)
      >>> fl = x.flat
      >>> fl.base is x
      True
  
      """))
  
  
  
  add_newdoc('numpy.core', 'flatiter', ('coords',
      """
      An N-dimensional tuple of current coordinates.
  
      Examples
      --------
      >>> x = np.arange(6).reshape(2, 3)
      >>> fl = x.flat
      >>> fl.coords
      (0, 0)
      >>> fl.next()
      0
      >>> fl.coords
      (0, 1)
  
      """))
  
  
  
  add_newdoc('numpy.core', 'flatiter', ('index',
      """
      Current flat index into the array.
  
      Examples
      --------
      >>> x = np.arange(6).reshape(2, 3)
      >>> fl = x.flat
      >>> fl.index
      0
      >>> fl.next()
      0
      >>> fl.index
      1
  
      """))
  
  # flatiter functions
  
  add_newdoc('numpy.core', 'flatiter', ('__array__',
      """__array__(type=None) Get array from iterator
  
      """))
  
  
  add_newdoc('numpy.core', 'flatiter', ('copy',
      """
      copy()
  
      Get a copy of the iterator as a 1-D array.
  
      Examples
      --------
      >>> x = np.arange(6).reshape(2, 3)
      >>> x
      array([[0, 1, 2],
             [3, 4, 5]])
      >>> fl = x.flat
      >>> fl.copy()
      array([0, 1, 2, 3, 4, 5])
  
      """))
  
  
  ###############################################################################
  #
  # nditer
  #
  ###############################################################################
  
  add_newdoc('numpy.core', 'nditer',
      """
      Efficient multi-dimensional iterator object to iterate over arrays.
      To get started using this object, see the
      :ref:`introductory guide to array iteration <arrays.nditer>`.
  
      Parameters
      ----------
      op : ndarray or sequence of array_like
          The array(s) to iterate over.
      flags : sequence of str, optional
          Flags to control the behavior of the iterator.
  
            * "buffered" enables buffering when required.
            * "c_index" causes a C-order index to be tracked.
            * "f_index" causes a Fortran-order index to be tracked.
            * "multi_index" causes a multi-index, or a tuple of indices
              with one per iteration dimension, to be tracked.
            * "common_dtype" causes all the operands to be converted to
              a common data type, with copying or buffering as necessary.
            * "copy_if_overlap" causes the iterator to determine if read
              operands have overlap with write operands, and make temporary
              copies as necessary to avoid overlap. False positives (needless
              copying) are possible in some cases.
            * "delay_bufalloc" delays allocation of the buffers until
              a reset() call is made. Allows "allocate" operands to
              be initialized before their values are copied into the buffers.
            * "external_loop" causes the `values` given to be
              one-dimensional arrays with multiple values instead of
              zero-dimensional arrays.
            * "grow_inner" allows the `value` array sizes to be made
              larger than the buffer size when both "buffered" and
              "external_loop" is used.
            * "ranged" allows the iterator to be restricted to a sub-range
              of the iterindex values.
            * "refs_ok" enables iteration of reference types, such as
              object arrays.
            * "reduce_ok" enables iteration of "readwrite" operands
              which are broadcasted, also known as reduction operands.
            * "zerosize_ok" allows `itersize` to be zero.
      op_flags : list of list of str, optional
          This is a list of flags for each operand. At minimum, one of
          "readonly", "readwrite", or "writeonly" must be specified.
  
            * "readonly" indicates the operand will only be read from.
            * "readwrite" indicates the operand will be read from and written to.
            * "writeonly" indicates the operand will only be written to.
            * "no_broadcast" prevents the operand from being broadcasted.
            * "contig" forces the operand data to be contiguous.
            * "aligned" forces the operand data to be aligned.
            * "nbo" forces the operand data to be in native byte order.
            * "copy" allows a temporary read-only copy if required.
            * "updateifcopy" allows a temporary read-write copy if required.
            * "allocate" causes the array to be allocated if it is None
              in the `op` parameter.
            * "no_subtype" prevents an "allocate" operand from using a subtype.
            * "arraymask" indicates that this operand is the mask to use
              for selecting elements when writing to operands with the
              'writemasked' flag set. The iterator does not enforce this,
              but when writing from a buffer back to the array, it only
              copies those elements indicated by this mask.
            * 'writemasked' indicates that only elements where the chosen
              'arraymask' operand is True will be written to.
            * "overlap_assume_elementwise" can be used to mark operands that are
              accessed only in the iterator order, to allow less conservative
              copying when "copy_if_overlap" is present.
      op_dtypes : dtype or tuple of dtype(s), optional
          The required data type(s) of the operands. If copying or buffering
          is enabled, the data will be converted to/from their original types.
      order : {'C', 'F', 'A', 'K'}, optional
          Controls the iteration order. 'C' means C order, 'F' means
          Fortran order, 'A' means 'F' order if all the arrays are Fortran
          contiguous, 'C' order otherwise, and 'K' means as close to the
          order the array elements appear in memory as possible. This also
          affects the element memory order of "allocate" operands, as they
          are allocated to be compatible with iteration order.
          Default is 'K'.
      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
          Controls what kind of data casting may occur when making a copy
          or buffering.  Setting this to 'unsafe' is not recommended,
          as it can adversely affect accumulations.
  
            * 'no' means the data types should not be cast at all.
            * 'equiv' means only byte-order changes are allowed.
            * 'safe' means only casts which can preserve values are allowed.
            * 'same_kind' means only safe casts or casts within a kind,
              like float64 to float32, are allowed.
            * 'unsafe' means any data conversions may be done.
      op_axes : list of list of ints, optional
          If provided, is a list of ints or None for each operands.
          The list of axes for an operand is a mapping from the dimensions
          of the iterator to the dimensions of the operand. A value of
          -1 can be placed for entries, causing that dimension to be
          treated as "newaxis".
      itershape : tuple of ints, optional
          The desired shape of the iterator. This allows "allocate" operands
          with a dimension mapped by op_axes not corresponding to a dimension
          of a different operand to get a value not equal to 1 for that
          dimension.
      buffersize : int, optional
          When buffering is enabled, controls the size of the temporary
          buffers. Set to 0 for the default value.
  
      Attributes
      ----------
      dtypes : tuple of dtype(s)
          The data types of the values provided in `value`. This may be
          different from the operand data types if buffering is enabled.
          Valid only before the iterator is closed.
      finished : bool
          Whether the iteration over the operands is finished or not.
      has_delayed_bufalloc : bool
          If True, the iterator was created with the "delay_bufalloc" flag,
          and no reset() function was called on it yet.
      has_index : bool
          If True, the iterator was created with either the "c_index" or
          the "f_index" flag, and the property `index` can be used to
          retrieve it.
      has_multi_index : bool
          If True, the iterator was created with the "multi_index" flag,
          and the property `multi_index` can be used to retrieve it.
      index
          When the "c_index" or "f_index" flag was used, this property
          provides access to the index. Raises a ValueError if accessed
          and `has_index` is False.
      iterationneedsapi : bool
          Whether iteration requires access to the Python API, for example
          if one of the operands is an object array.
      iterindex : int
          An index which matches the order of iteration.
      itersize : int
          Size of the iterator.
      itviews
          Structured view(s) of `operands` in memory, matching the reordered
          and optimized iterator access pattern. Valid only before the iterator
          is closed.
      multi_index
          When the "multi_index" flag was used, this property
          provides access to the index. Raises a ValueError if accessed
          accessed and `has_multi_index` is False.
      ndim : int
          The iterator's dimension.
      nop : int
          The number of iterator operands.
      operands : tuple of operand(s)
          The array(s) to be iterated over. Valid only before the iterator is
          closed.
      shape : tuple of ints
          Shape tuple, the shape of the iterator.
      value
          Value of `operands` at current iteration. Normally, this is a
          tuple of array scalars, but if the flag "external_loop" is used,
          it is a tuple of one dimensional arrays.
  
      Notes
      -----
      `nditer` supersedes `flatiter`.  The iterator implementation behind
      `nditer` is also exposed by the NumPy C API.
  
      The Python exposure supplies two iteration interfaces, one which follows
      the Python iterator protocol, and another which mirrors the C-style
      do-while pattern.  The native Python approach is better in most cases, but
      if you need the iterator's coordinates or index, use the C-style pattern.
  
      Examples
      --------
      Here is how we might write an ``iter_add`` function, using the
      Python iterator protocol::
  
          def iter_add_py(x, y, out=None):
              addop = np.add
              it = np.nditer([x, y, out], [],
                          [['readonly'], ['readonly'], ['writeonly','allocate']])
              with it:
                  for (a, b, c) in it:
                      addop(a, b, out=c)
              return it.operands[2]
  
      Here is the same function, but following the C-style pattern::
  
          def iter_add(x, y, out=None):
              addop = np.add
  
              it = np.nditer([x, y, out], [],
                          [['readonly'], ['readonly'], ['writeonly','allocate']])
              with it:
                  while not it.finished:
                      addop(it[0], it[1], out=it[2])
                      it.iternext()
  
                  return it.operands[2]
  
      Here is an example outer product function::
  
          def outer_it(x, y, out=None):
              mulop = np.multiply
  
              it = np.nditer([x, y, out], ['external_loop'],
                      [['readonly'], ['readonly'], ['writeonly', 'allocate']],
                      op_axes=[list(range(x.ndim)) + [-1] * y.ndim,
                               [-1] * x.ndim + list(range(y.ndim)),
                               None])
              with it:
                  for (a, b, c) in it:
                      mulop(a, b, out=c)
                  return it.operands[2]
  
          >>> a = np.arange(2)+1
          >>> b = np.arange(3)+1
          >>> outer_it(a,b)
          array([[1, 2, 3],
                 [2, 4, 6]])
  
      Here is an example function which operates like a "lambda" ufunc::
  
          def luf(lamdaexpr, *args, **kwargs):
              "luf(lambdaexpr, op1, ..., opn, out=None, order='K', casting='safe', buffersize=0)"
              nargs = len(args)
              op = (kwargs.get('out',None),) + args
              it = np.nditer(op, ['buffered','external_loop'],
                      [['writeonly','allocate','no_broadcast']] +
                                      [['readonly','nbo','aligned']]*nargs,
                      order=kwargs.get('order','K'),
                      casting=kwargs.get('casting','safe'),
                      buffersize=kwargs.get('buffersize',0))
              while not it.finished:
                  it[0] = lamdaexpr(*it[1:])
                  it.iternext()
                  return it.operands[0]
  
          >>> a = np.arange(5)
          >>> b = np.ones(5)
          >>> luf(lambda i,j:i*i + j/2, a, b)
          array([  0.5,   1.5,   4.5,   9.5,  16.5])
  
      If operand flags `"writeonly"` or `"readwrite"` are used the operands may
      be views into the original data with the `WRITEBACKIFCOPY` flag. In this case
      nditer must be used as a context manager or the nditer.close
      method must be called before using the result. The temporary
      data will be written back to the original data when the `__exit__`
      function is called but not before:
  
          >>> a = np.arange(6, dtype='i4')[::-2]
          >>> with nditer(a, [],
          ...        [['writeonly', 'updateifcopy']],
          ...        casting='unsafe',
          ...        op_dtypes=[np.dtype('f4')]) as i:
          ...    x = i.operands[0]
          ...    x[:] = [-1, -2, -3]
          ...    # a still unchanged here
          >>> a, x
          array([-1, -2, -3]), array([-1, -2, -3])
  
      It is important to note that once the iterator is exited, dangling
      references (like `x` in the example) may or may not share data with
      the original data `a`. If writeback semantics were active, i.e. if
      `x.base.flags.writebackifcopy` is `True`, then exiting the iterator
      will sever the connection between `x` and `a`, writing to `x` will
      no longer write to `a`. If writeback semantics are not active, then
      `x.data` will still point at some part of `a.data`, and writing to
      one will affect the other.
  
      """)
  
  # nditer methods
  
  add_newdoc('numpy.core', 'nditer', ('copy',
      """
      copy()
  
      Get a copy of the iterator in its current state.
  
      Examples
      --------
      >>> x = np.arange(10)
      >>> y = x + 1
      >>> it = np.nditer([x, y])
      >>> it.next()
      (array(0), array(1))
      >>> it2 = it.copy()
      >>> it2.next()
      (array(1), array(2))
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('operands',
      """
      operands[`Slice`]
  
      The array(s) to be iterated over. Valid only before the iterator is closed.
      """))
  
  add_newdoc('numpy.core', 'nditer', ('debug_print',
      """
      debug_print()
  
      Print the current state of the `nditer` instance and debug info to stdout.
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('enable_external_loop',
      """
      enable_external_loop()
  
      When the "external_loop" was not used during construction, but
      is desired, this modifies the iterator to behave as if the flag
      was specified.
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('iternext',
      """
      iternext()
  
      Check whether iterations are left, and perform a single internal iteration
      without returning the result.  Used in the C-style pattern do-while
      pattern.  For an example, see `nditer`.
  
      Returns
      -------
      iternext : bool
          Whether or not there are iterations left.
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('remove_axis',
      """
      remove_axis(i)
  
      Removes axis `i` from the iterator. Requires that the flag "multi_index"
      be enabled.
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('remove_multi_index',
      """
      remove_multi_index()
  
      When the "multi_index" flag was specified, this removes it, allowing
      the internal iteration structure to be optimized further.
  
      """))
  
  add_newdoc('numpy.core', 'nditer', ('reset',
      """
      reset()
  
      Reset the iterator to its initial state.
  
      """))
  
  add_newdoc('numpy.core', 'nested_iters',
      """
      Create nditers for use in nested loops
  
      Create a tuple of `nditer` objects which iterate in nested loops over
      different axes of the op argument. The first iterator is used in the
      outermost loop, the last in the innermost loop. Advancing one will change
      the subsequent iterators to point at its new element.
  
      Parameters
      ----------
      op : ndarray or sequence of array_like
          The array(s) to iterate over.
  
      axes : list of list of int
          Each item is used as an "op_axes" argument to an nditer
  
      flags, op_flags, op_dtypes, order, casting, buffersize (optional)
          See `nditer` parameters of the same name
  
      Returns
      -------
      iters : tuple of nditer
          An nditer for each item in `axes`, outermost first
  
      See Also
      --------
      nditer
  
      Examples
      --------
  
      Basic usage. Note how y is the "flattened" version of
      [a[:, 0, :], a[:, 1, 0], a[:, 2, :]] since we specified
      the first iter's axes as [1]
  
      >>> a = np.arange(12).reshape(2, 3, 2)
      >>> i, j = np.nested_iters(a, [[1], [0, 2]], flags=["multi_index"])
      >>> for x in i:
      ...      print(i.multi_index)
      ...      for y in j:
      ...          print('', j.multi_index, y)
  
      (0,)
       (0, 0) 0
       (0, 1) 1
       (1, 0) 6
       (1, 1) 7
      (1,)
       (0, 0) 2
       (0, 1) 3
       (1, 0) 8
       (1, 1) 9
      (2,)
       (0, 0) 4
       (0, 1) 5
       (1, 0) 10
       (1, 1) 11
  
      """)
  
  add_newdoc('numpy.core', 'nditer', ('close',
      """
      close()
  
      Resolve all writeback semantics in writeable operands.
  
      See Also
      --------
  
      :ref:`nditer-context-manager`
  
      """))
  
  
  ###############################################################################
  #
  # broadcast
  #
  ###############################################################################
  
  add_newdoc('numpy.core', 'broadcast',
      """
      Produce an object that mimics broadcasting.
  
      Parameters
      ----------
      in1, in2, ... : array_like
          Input parameters.
  
      Returns
      -------
      b : broadcast object
          Broadcast the input parameters against one another, and
          return an object that encapsulates the result.
          Amongst others, it has ``shape`` and ``nd`` properties, and
          may be used as an iterator.
  
      See Also
      --------
      broadcast_arrays
      broadcast_to
  
      Examples
      --------
  
      Manually adding two vectors, using broadcasting:
  
      >>> x = np.array([[1], [2], [3]])
      >>> y = np.array([4, 5, 6])
      >>> b = np.broadcast(x, y)
  
      >>> out = np.empty(b.shape)
      >>> out.flat = [u+v for (u,v) in b]
      >>> out
      array([[ 5.,  6.,  7.],
             [ 6.,  7.,  8.],
             [ 7.,  8.,  9.]])
  
      Compare against built-in broadcasting:
  
      >>> x + y
      array([[5, 6, 7],
             [6, 7, 8],
             [7, 8, 9]])
  
      """)
  
  # attributes
  
  add_newdoc('numpy.core', 'broadcast', ('index',
      """
      current index in broadcasted result
  
      Examples
      --------
      >>> x = np.array([[1], [2], [3]])
      >>> y = np.array([4, 5, 6])
      >>> b = np.broadcast(x, y)
      >>> b.index
      0
      >>> b.next(), b.next(), b.next()
      ((1, 4), (1, 5), (1, 6))
      >>> b.index
      3
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('iters',
      """
      tuple of iterators along ``self``'s "components."
  
      Returns a tuple of `numpy.flatiter` objects, one for each "component"
      of ``self``.
  
      See Also
      --------
      numpy.flatiter
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> row, col = b.iters
      >>> row.next(), col.next()
      (1, 4)
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('ndim',
      """
      Number of dimensions of broadcasted result. Alias for `nd`.
  
      .. versionadded:: 1.12.0
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> b.ndim
      2
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('nd',
      """
      Number of dimensions of broadcasted result. For code intended for NumPy
      1.12.0 and later the more consistent `ndim` is preferred.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> b.nd
      2
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('numiter',
      """
      Number of iterators possessed by the broadcasted result.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> b.numiter
      2
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('shape',
      """
      Shape of broadcasted result.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> b.shape
      (3, 3)
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('size',
      """
      Total size of broadcasted result.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]])
      >>> b = np.broadcast(x, y)
      >>> b.size
      9
  
      """))
  
  add_newdoc('numpy.core', 'broadcast', ('reset',
      """
      reset()
  
      Reset the broadcasted result's iterator(s).
  
      Parameters
      ----------
      None
  
      Returns
      -------
      None
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> y = np.array([[4], [5], [6]]
      >>> b = np.broadcast(x, y)
      >>> b.index
      0
      >>> b.next(), b.next(), b.next()
      ((1, 4), (2, 4), (3, 4))
      >>> b.index
      3
      >>> b.reset()
      >>> b.index
      0
  
      """))
  
  ###############################################################################
  #
  # numpy functions
  #
  ###############################################################################
  
  add_newdoc('numpy.core.multiarray', 'array',
      """
      array(object, dtype=None, copy=True, order='K', subok=False, ndmin=0)
  
      Create an array.
  
      Parameters
      ----------
      object : array_like
          An array, any object exposing the array interface, an object whose
          __array__ method returns an array, or any (nested) sequence.
      dtype : data-type, optional
          The desired data-type for the array.  If not given, then the type will
          be determined as the minimum type required to hold the objects in the
          sequence.  This argument can only be used to 'upcast' the array.  For
          downcasting, use the .astype(t) method.
      copy : bool, optional
          If true (default), then the object is copied.  Otherwise, a copy will
          only be made if __array__ returns a copy, if obj is a nested sequence,
          or if a copy is needed to satisfy any of the other requirements
          (`dtype`, `order`, etc.).
      order : {'K', 'A', 'C', 'F'}, optional
          Specify the memory layout of the array. If object is not an array, the
          newly created array will be in C order (row major) unless 'F' is
          specified, in which case it will be in Fortran order (column major).
          If object is an array the following holds.
  
          ===== ========= ===================================================
          order  no copy                     copy=True
          ===== ========= ===================================================
          'K'   unchanged F & C order preserved, otherwise most similar order
          'A'   unchanged F order if input is F and not C, otherwise C order
          'C'   C order   C order
          'F'   F order   F order
          ===== ========= ===================================================
  
          When ``copy=False`` and a copy is made for other reasons, the result is
          the same as if ``copy=True``, with some exceptions for `A`, see the
          Notes section. The default order is 'K'.
      subok : bool, optional
          If True, then sub-classes will be passed-through, otherwise
          the returned array will be forced to be a base-class array (default).
      ndmin : int, optional
          Specifies the minimum number of dimensions that the resulting
          array should have.  Ones will be pre-pended to the shape as
          needed to meet this requirement.
  
      Returns
      -------
      out : ndarray
          An array object satisfying the specified requirements.
  
      See Also
      --------
      empty_like : Return an empty array with shape and type of input.
      ones_like : Return an array of ones with shape and type of input.
      zeros_like : Return an array of zeros with shape and type of input.
      full_like : Return a new array with shape of input filled with value.
      empty : Return a new uninitialized array.
      ones : Return a new array setting values to one.
      zeros : Return a new array setting values to zero.
      full : Return a new array of given shape filled with value.
  
  
      Notes
      -----
      When order is 'A' and `object` is an array in neither 'C' nor 'F' order,
      and a copy is forced by a change in dtype, then the order of the result is
      not necessarily 'C' as expected. This is likely a bug.
  
      Examples
      --------
      >>> np.array([1, 2, 3])
      array([1, 2, 3])
  
      Upcasting:
  
      >>> np.array([1, 2, 3.0])
      array([ 1.,  2.,  3.])
  
      More than one dimension:
  
      >>> np.array([[1, 2], [3, 4]])
      array([[1, 2],
             [3, 4]])
  
      Minimum dimensions 2:
  
      >>> np.array([1, 2, 3], ndmin=2)
      array([[1, 2, 3]])
  
      Type provided:
  
      >>> np.array([1, 2, 3], dtype=complex)
      array([ 1.+0.j,  2.+0.j,  3.+0.j])
  
      Data-type consisting of more than one element:
  
      >>> x = np.array([(1,2),(3,4)],dtype=[('a','<i4'),('b','<i4')])
      >>> x['a']
      array([1, 3])
  
      Creating an array from sub-classes:
  
      >>> np.array(np.mat('1 2; 3 4'))
      array([[1, 2],
             [3, 4]])
  
      >>> np.array(np.mat('1 2; 3 4'), subok=True)
      matrix([[1, 2],
              [3, 4]])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'empty',
      """
      empty(shape, dtype=float, order='C')
  
      Return a new array of given shape and type, without initializing entries.
  
      Parameters
      ----------
      shape : int or tuple of int
          Shape of the empty array, e.g., ``(2, 3)`` or ``2``.
      dtype : data-type, optional
          Desired output data-type for the array, e.g, `numpy.int8`. Default is
          `numpy.float64`.
      order : {'C', 'F'}, optional, default: 'C'
          Whether to store multi-dimensional data in row-major
          (C-style) or column-major (Fortran-style) order in
          memory.
  
      Returns
      -------
      out : ndarray
          Array of uninitialized (arbitrary) data of the given shape, dtype, and
          order.  Object arrays will be initialized to None.
  
      See Also
      --------
      empty_like : Return an empty array with shape and type of input.
      ones : Return a new array setting values to one.
      zeros : Return a new array setting values to zero.
      full : Return a new array of given shape filled with value.
  
  
      Notes
      -----
      `empty`, unlike `zeros`, does not set the array values to zero,
      and may therefore be marginally faster.  On the other hand, it requires
      the user to manually set all the values in the array, and should be
      used with caution.
  
      Examples
      --------
      >>> np.empty([2, 2])
      array([[ -9.74499359e+001,   6.69583040e-309],
             [  2.13182611e-314,   3.06959433e-309]])         #random
  
      >>> np.empty([2, 2], dtype=int)
      array([[-1073741821, -1067949133],
             [  496041986,    19249760]])                     #random
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'scalar',
      """
      scalar(dtype, obj)
  
      Return a new scalar array of the given type initialized with obj.
  
      This function is meant mainly for pickle support. `dtype` must be a
      valid data-type descriptor. If `dtype` corresponds to an object
      descriptor, then `obj` can be any object, otherwise `obj` must be a
      string. If `obj` is not given, it will be interpreted as None for object
      type and as zeros for all other types.
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'zeros',
      """
      zeros(shape, dtype=float, order='C')
  
      Return a new array of given shape and type, filled with zeros.
  
      Parameters
      ----------
      shape : int or tuple of ints
          Shape of the new array, e.g., ``(2, 3)`` or ``2``.
      dtype : data-type, optional
          The desired data-type for the array, e.g., `numpy.int8`.  Default is
          `numpy.float64`.
      order : {'C', 'F'}, optional, default: 'C'
          Whether to store multi-dimensional data in row-major
          (C-style) or column-major (Fortran-style) order in
          memory.
  
      Returns
      -------
      out : ndarray
          Array of zeros with the given shape, dtype, and order.
  
      See Also
      --------
      zeros_like : Return an array of zeros with shape and type of input.
      empty : Return a new uninitialized array.
      ones : Return a new array setting values to one.
      full : Return a new array of given shape filled with value.
  
      Examples
      --------
      >>> np.zeros(5)
      array([ 0.,  0.,  0.,  0.,  0.])
  
      >>> np.zeros((5,), dtype=int)
      array([0, 0, 0, 0, 0])
  
      >>> np.zeros((2, 1))
      array([[ 0.],
             [ 0.]])
  
      >>> s = (2,2)
      >>> np.zeros(s)
      array([[ 0.,  0.],
             [ 0.,  0.]])
  
      >>> np.zeros((2,), dtype=[('x', 'i4'), ('y', 'i4')]) # custom dtype
      array([(0, 0), (0, 0)],
            dtype=[('x', '<i4'), ('y', '<i4')])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'set_typeDict',
      """set_typeDict(dict)
  
      Set the internal dictionary that can look up an array type using a
      registered code.
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'fromstring',
      """
      fromstring(string, dtype=float, count=-1, sep='')
  
      A new 1-D array initialized from text data in a string.
  
      Parameters
      ----------
      string : str
          A string containing the data.
      dtype : data-type, optional
          The data type of the array; default: float.  For binary input data,
          the data must be in exactly this format.
      count : int, optional
          Read this number of `dtype` elements from the data.  If this is
          negative (the default), the count will be determined from the
          length of the data.
      sep : str, optional
          The string separating numbers in the data; extra whitespace between
          elements is also ignored.
  
          .. deprecated:: 1.14
              If this argument is not provided, `fromstring` falls back on the
              behaviour of `frombuffer` after encoding unicode string inputs as
              either utf-8 (python 3), or the default encoding (python 2).
  
      Returns
      -------
      arr : ndarray
          The constructed array.
  
      Raises
      ------
      ValueError
          If the string is not the correct size to satisfy the requested
          `dtype` and `count`.
  
      See Also
      --------
      frombuffer, fromfile, fromiter
  
      Examples
      --------
      >>> np.fromstring('1 2', dtype=int, sep=' ')
      array([1, 2])
      >>> np.fromstring('1, 2', dtype=int, sep=',')
      array([1, 2])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'compare_chararrays',
      """
      compare_chararrays(a, b, cmp_op, rstrip)
  
      Performs element-wise comparison of two string arrays using the
      comparison operator specified by `cmp_op`.
  
      Parameters
      ----------
      a, b : array_like
          Arrays to be compared.
      cmp_op : {"<", "<=", "==", ">=", ">", "!="}
          Type of comparison.
      rstrip : Boolean
          If True, the spaces at the end of Strings are removed before the comparison.
  
      Returns
      -------
      out : ndarray
          The output array of type Boolean with the same shape as a and b.
  
      Raises
      ------
      ValueError
          If `cmp_op` is not valid.
      TypeError
          If at least one of `a` or `b` is a non-string array
  
      Examples
      --------
      >>> a = np.array(["a", "b", "cde"])
      >>> b = np.array(["a", "a", "dec"])
      >>> np.compare_chararrays(a, b, ">", True)
      array([False,  True, False])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'fromiter',
      """
      fromiter(iterable, dtype, count=-1)
  
      Create a new 1-dimensional array from an iterable object.
  
      Parameters
      ----------
      iterable : iterable object
          An iterable object providing data for the array.
      dtype : data-type
          The data-type of the returned array.
      count : int, optional
          The number of items to read from *iterable*.  The default is -1,
          which means all data is read.
  
      Returns
      -------
      out : ndarray
          The output array.
  
      Notes
      -----
      Specify `count` to improve performance.  It allows ``fromiter`` to
      pre-allocate the output array, instead of resizing it on demand.
  
      Examples
      --------
      >>> iterable = (x*x for x in range(5))
      >>> np.fromiter(iterable, float)
      array([  0.,   1.,   4.,   9.,  16.])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'fromfile',
      """
      fromfile(file, dtype=float, count=-1, sep='')
  
      Construct an array from data in a text or binary file.
  
      A highly efficient way of reading binary data with a known data-type,
      as well as parsing simply formatted text files.  Data written using the
      `tofile` method can be read using this function.
  
      Parameters
      ----------
      file : file or str
          Open file object or filename.
      dtype : data-type
          Data type of the returned array.
          For binary files, it is used to determine the size and byte-order
          of the items in the file.
      count : int
          Number of items to read. ``-1`` means all items (i.e., the complete
          file).
      sep : str
          Separator between items if file is a text file.
          Empty ("") separator means the file should be treated as binary.
          Spaces (" ") in the separator match zero or more whitespace characters.
          A separator consisting only of spaces must match at least one
          whitespace.
  
      See also
      --------
      load, save
      ndarray.tofile
      loadtxt : More flexible way of loading data from a text file.
  
      Notes
      -----
      Do not rely on the combination of `tofile` and `fromfile` for
      data storage, as the binary files generated are are not platform
      independent.  In particular, no byte-order or data-type information is
      saved.  Data can be stored in the platform independent ``.npy`` format
      using `save` and `load` instead.
  
      Examples
      --------
      Construct an ndarray:
  
      >>> dt = np.dtype([('time', [('min', int), ('sec', int)]),
      ...                ('temp', float)])
      >>> x = np.zeros((1,), dtype=dt)
      >>> x['time']['min'] = 10; x['temp'] = 98.25
      >>> x
      array([((10, 0), 98.25)],
            dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')])
  
      Save the raw data to disk:
  
      >>> import os
      >>> fname = os.tmpnam()
      >>> x.tofile(fname)
  
      Read the raw data from disk:
  
      >>> np.fromfile(fname, dtype=dt)
      array([((10, 0), 98.25)],
            dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')])
  
      The recommended way to store and load data:
  
      >>> np.save(fname, x)
      >>> np.load(fname + '.npy')
      array([((10, 0), 98.25)],
            dtype=[('time', [('min', '<i4'), ('sec', '<i4')]), ('temp', '<f8')])
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'frombuffer',
      """
      frombuffer(buffer, dtype=float, count=-1, offset=0)
  
      Interpret a buffer as a 1-dimensional array.
  
      Parameters
      ----------
      buffer : buffer_like
          An object that exposes the buffer interface.
      dtype : data-type, optional
          Data-type of the returned array; default: float.
      count : int, optional
          Number of items to read. ``-1`` means all data in the buffer.
      offset : int, optional
          Start reading the buffer from this offset (in bytes); default: 0.
  
      Notes
      -----
      If the buffer has data that is not in machine byte-order, this should
      be specified as part of the data-type, e.g.::
  
        >>> dt = np.dtype(int)
        >>> dt = dt.newbyteorder('>')
        >>> np.frombuffer(buf, dtype=dt)
  
      The data of the resulting array will not be byteswapped, but will be
      interpreted correctly.
  
      Examples
      --------
      >>> s = 'hello world'
      >>> np.frombuffer(s, dtype='S1', count=5, offset=6)
      array(['w', 'o', 'r', 'l', 'd'],
            dtype='|S1')
  
      >>> np.frombuffer(b'\\x01\\x02', dtype=np.uint8)
      array([1, 2], dtype=uint8)
      >>> np.frombuffer(b'\\x01\\x02\\x03\\x04\\x05', dtype=np.uint8, count=3)
      array([1, 2, 3], dtype=uint8)
  
      """)
  
  add_newdoc('numpy.core', 'fastCopyAndTranspose',
      """_fastCopyAndTranspose(a)""")
  
  add_newdoc('numpy.core.multiarray', 'correlate',
      """cross_correlate(a,v, mode=0)""")
  
  add_newdoc('numpy.core.multiarray', 'arange',
      """
      arange([start,] stop[, step,], dtype=None)
  
      Return evenly spaced values within a given interval.
  
      Values are generated within the half-open interval ``[start, stop)``
      (in other words, the interval including `start` but excluding `stop`).
      For integer arguments the function is equivalent to the Python built-in
      `range` function, but returns an ndarray rather than a list.
  
      When using a non-integer step, such as 0.1, the results will often not
      be consistent.  It is better to use `numpy.linspace` for these cases.
  
      Parameters
      ----------
      start : number, optional
          Start of interval.  The interval includes this value.  The default
          start value is 0.
      stop : number
          End of interval.  The interval does not include this value, except
          in some cases where `step` is not an integer and floating point
          round-off affects the length of `out`.
      step : number, optional
          Spacing between values.  For any output `out`, this is the distance
          between two adjacent values, ``out[i+1] - out[i]``.  The default
          step size is 1.  If `step` is specified as a position argument,
          `start` must also be given.
      dtype : dtype
          The type of the output array.  If `dtype` is not given, infer the data
          type from the other input arguments.
  
      Returns
      -------
      arange : ndarray
          Array of evenly spaced values.
  
          For floating point arguments, the length of the result is
          ``ceil((stop - start)/step)``.  Because of floating point overflow,
          this rule may result in the last element of `out` being greater
          than `stop`.
  
      See Also
      --------
      linspace : Evenly spaced numbers with careful handling of endpoints.
      ogrid: Arrays of evenly spaced numbers in N-dimensions.
      mgrid: Grid-shaped arrays of evenly spaced numbers in N-dimensions.
  
      Examples
      --------
      >>> np.arange(3)
      array([0, 1, 2])
      >>> np.arange(3.0)
      array([ 0.,  1.,  2.])
      >>> np.arange(3,7)
      array([3, 4, 5, 6])
      >>> np.arange(3,7,2)
      array([3, 5])
  
      """)
  
  add_newdoc('numpy.core.multiarray', '_get_ndarray_c_version',
      """_get_ndarray_c_version()
  
      Return the compile time NDARRAY_VERSION number.
  
      """)
  
  add_newdoc('numpy.core.multiarray', '_reconstruct',
      """_reconstruct(subtype, shape, dtype)
  
      Construct an empty array. Used by Pickles.
  
      """)
  
  
  add_newdoc('numpy.core.multiarray', 'set_string_function',
      """
      set_string_function(f, repr=1)
  
      Internal method to set a function to be used when pretty printing arrays.
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'set_numeric_ops',
      """
      set_numeric_ops(op1=func1, op2=func2, ...)
  
      Set numerical operators for array objects.
  
      .. deprecated:: 1.16
  
          For the general case, use :c:func:`PyUFunc_ReplaceLoopBySignature`.
          For ndarray subclasses, define the ``__array_ufunc__`` method and
          override the relevant ufunc.
  
      Parameters
      ----------
      op1, op2, ... : callable
          Each ``op = func`` pair describes an operator to be replaced.
          For example, ``add = lambda x, y: np.add(x, y) % 5`` would replace
          addition by modulus 5 addition.
  
      Returns
      -------
      saved_ops : list of callables
          A list of all operators, stored before making replacements.
  
      Notes
      -----
      .. WARNING::
         Use with care!  Incorrect usage may lead to memory errors.
  
      A function replacing an operator cannot make use of that operator.
      For example, when replacing add, you may not use ``+``.  Instead,
      directly call ufuncs.
  
      Examples
      --------
      >>> def add_mod5(x, y):
      ...     return np.add(x, y) % 5
      ...
      >>> old_funcs = np.set_numeric_ops(add=add_mod5)
  
      >>> x = np.arange(12).reshape((3, 4))
      >>> x + x
      array([[0, 2, 4, 1],
             [3, 0, 2, 4],
             [1, 3, 0, 2]])
  
      >>> ignore = np.set_numeric_ops(**old_funcs) # restore operators
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'promote_types',
      """
      promote_types(type1, type2)
  
      Returns the data type with the smallest size and smallest scalar
      kind to which both ``type1`` and ``type2`` may be safely cast.
      The returned data type is always in native byte order.
  
      This function is symmetric, but rarely associative.
  
      Parameters
      ----------
      type1 : dtype or dtype specifier
          First data type.
      type2 : dtype or dtype specifier
          Second data type.
  
      Returns
      -------
      out : dtype
          The promoted data type.
  
      Notes
      -----
      .. versionadded:: 1.6.0
  
      Starting in NumPy 1.9, promote_types function now returns a valid string
      length when given an integer or float dtype as one argument and a string
      dtype as another argument. Previously it always returned the input string
      dtype, even if it wasn't long enough to store the max integer/float value
      converted to a string.
  
      See Also
      --------
      result_type, dtype, can_cast
  
      Examples
      --------
      >>> np.promote_types('f4', 'f8')
      dtype('float64')
  
      >>> np.promote_types('i8', 'f4')
      dtype('float64')
  
      >>> np.promote_types('>i8', '<c8')
      dtype('complex128')
  
      >>> np.promote_types('i4', 'S8')
      dtype('S11')
  
      An example of a non-associative case:
  
      >>> p = np.promote_types
      >>> p('S', p('i1', 'u1'))
      dtype('S6')
      >>> p(p('S', 'i1'), 'u1')
      dtype('S4')
  
      """)
  
  if sys.version_info.major < 3:
      add_newdoc('numpy.core.multiarray', 'newbuffer',
          """
          newbuffer(size)
  
          Return a new uninitialized buffer object.
  
          Parameters
          ----------
          size : int
              Size in bytes of returned buffer object.
  
          Returns
          -------
          newbuffer : buffer object
              Returned, uninitialized buffer object of `size` bytes.
  
          """)
  
      add_newdoc('numpy.core.multiarray', 'getbuffer',
          """
          getbuffer(obj [,offset[, size]])
  
          Create a buffer object from the given object referencing a slice of
          length size starting at offset.
  
          Default is the entire buffer. A read-write buffer is attempted followed
          by a read-only buffer.
  
          Parameters
          ----------
          obj : object
  
          offset : int, optional
  
          size : int, optional
  
          Returns
          -------
          buffer_obj : buffer
  
          Examples
          --------
          >>> buf = np.getbuffer(np.ones(5), 1, 3)
          >>> len(buf)
          3
          >>> buf[0]
          '\\x00'
          >>> buf
          <read-write buffer for 0x8af1e70, size 3, offset 1 at 0x8ba4ec0>
  
          """)
  
  add_newdoc('numpy.core.multiarray', 'c_einsum',
      """
      c_einsum(subscripts, *operands, out=None, dtype=None, order='K',
             casting='safe')
  
      *This documentation shadows that of the native python implementation of the `einsum` function,
      except all references and examples related to the `optimize` argument (v 0.12.0) have been removed.*
  
      Evaluates the Einstein summation convention on the operands.
  
      Using the Einstein summation convention, many common multi-dimensional,
      linear algebraic array operations can be represented in a simple fashion.
      In *implicit* mode `einsum` computes these values.
  
      In *explicit* mode, `einsum` provides further flexibility to compute
      other array operations that might not be considered classical Einstein
      summation operations, by disabling, or forcing summation over specified
      subscript labels.
  
      See the notes and examples for clarification.
  
      Parameters
      ----------
      subscripts : str
          Specifies the subscripts for summation as comma separated list of
          subscript labels. An implicit (classical Einstein summation)
          calculation is performed unless the explicit indicator '->' is
          included as well as subscript labels of the precise output form.
      operands : list of array_like
          These are the arrays for the operation.
      out : ndarray, optional
          If provided, the calculation is done into this array.
      dtype : {data-type, None}, optional
          If provided, forces the calculation to use the data type specified.
          Note that you may have to also give a more liberal `casting`
          parameter to allow the conversions. Default is None.
      order : {'C', 'F', 'A', 'K'}, optional
          Controls the memory layout of the output. 'C' means it should
          be C contiguous. 'F' means it should be Fortran contiguous,
          'A' means it should be 'F' if the inputs are all 'F', 'C' otherwise.
          'K' means it should be as close to the layout as the inputs as
          is possible, including arbitrarily permuted axes.
          Default is 'K'.
      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
          Controls what kind of data casting may occur.  Setting this to
          'unsafe' is not recommended, as it can adversely affect accumulations.
  
            * 'no' means the data types should not be cast at all.
            * 'equiv' means only byte-order changes are allowed.
            * 'safe' means only casts which can preserve values are allowed.
            * 'same_kind' means only safe casts or casts within a kind,
              like float64 to float32, are allowed.
            * 'unsafe' means any data conversions may be done.
  
          Default is 'safe'.
      optimize : {False, True, 'greedy', 'optimal'}, optional
          Controls if intermediate optimization should occur. No optimization
          will occur if False and True will default to the 'greedy' algorithm.
          Also accepts an explicit contraction list from the ``np.einsum_path``
          function. See ``np.einsum_path`` for more details. Defaults to False.
  
      Returns
      -------
      output : ndarray
          The calculation based on the Einstein summation convention.
  
      See Also
      --------
      einsum_path, dot, inner, outer, tensordot, linalg.multi_dot
  
      Notes
      -----
      .. versionadded:: 1.6.0
  
      The Einstein summation convention can be used to compute
      many multi-dimensional, linear algebraic array operations. `einsum`
      provides a succinct way of representing these.
  
      A non-exhaustive list of these operations,
      which can be computed by `einsum`, is shown below along with examples:
  
      * Trace of an array, :py:func:`numpy.trace`.
      * Return a diagonal, :py:func:`numpy.diag`.
      * Array axis summations, :py:func:`numpy.sum`.
      * Transpositions and permutations, :py:func:`numpy.transpose`.
      * Matrix multiplication and dot product, :py:func:`numpy.matmul` :py:func:`numpy.dot`.
      * Vector inner and outer products, :py:func:`numpy.inner` :py:func:`numpy.outer`.
      * Broadcasting, element-wise and scalar multiplication, :py:func:`numpy.multiply`.
      * Tensor contractions, :py:func:`numpy.tensordot`.
      * Chained array operations, in efficient calculation order, :py:func:`numpy.einsum_path`.
  
      The subscripts string is a comma-separated list of subscript labels,
      where each label refers to a dimension of the corresponding operand.
      Whenever a label is repeated it is summed, so ``np.einsum('i,i', a, b)``
      is equivalent to :py:func:`np.inner(a,b) <numpy.inner>`. If a label
      appears only once, it is not summed, so ``np.einsum('i', a)`` produces a
      view of ``a`` with no changes. A further example ``np.einsum('ij,jk', a, b)``
      describes traditional matrix multiplication and is equivalent to
      :py:func:`np.matmul(a,b) <numpy.matmul>`. Repeated subscript labels in one
      operand take the diagonal. For example, ``np.einsum('ii', a)`` is equivalent
      to :py:func:`np.trace(a) <numpy.trace>`.
  
      In *implicit mode*, the chosen subscripts are important
      since the axes of the output are reordered alphabetically.  This
      means that ``np.einsum('ij', a)`` doesn't affect a 2D array, while
      ``np.einsum('ji', a)`` takes its transpose. Additionally,
      ``np.einsum('ij,jk', a, b)`` returns a matrix multiplication, while,
      ``np.einsum('ij,jh', a, b)`` returns the transpose of the
      multiplication since subscript 'h' precedes subscript 'i'.
  
      In *explicit mode* the output can be directly controlled by
      specifying output subscript labels.  This requires the
      identifier '->' as well as the list of output subscript labels.
      This feature increases the flexibility of the function since
      summing can be disabled or forced when required. The call
      ``np.einsum('i->', a)`` is like :py:func:`np.sum(a, axis=-1) <numpy.sum>`,
      and ``np.einsum('ii->i', a)`` is like :py:func:`np.diag(a) <numpy.diag>`.
      The difference is that `einsum` does not allow broadcasting by default.
      Additionally ``np.einsum('ij,jh->ih', a, b)`` directly specifies the
      order of the output subscript labels and therefore returns matrix
      multiplication, unlike the example above in implicit mode.
  
      To enable and control broadcasting, use an ellipsis.  Default
      NumPy-style broadcasting is done by adding an ellipsis
      to the left of each term, like ``np.einsum('...ii->...i', a)``.
      To take the trace along the first and last axes,
      you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
      product with the left-most indices instead of rightmost, one can do
      ``np.einsum('ij...,jk...->ik...', a, b)``.
  
      When there is only one operand, no axes are summed, and no output
      parameter is provided, a view into the operand is returned instead
      of a new array.  Thus, taking the diagonal as ``np.einsum('ii->i', a)``
      produces a view (changed in version 1.10.0).
  
      `einsum` also provides an alternative way to provide the subscripts
      and operands as ``einsum(op0, sublist0, op1, sublist1, ..., [sublistout])``.
      If the output shape is not provided in this format `einsum` will be
      calculated in implicit mode, otherwise it will be performed explicitly.
      The examples below have corresponding `einsum` calls with the two
      parameter methods.
  
      .. versionadded:: 1.10.0
  
      Views returned from einsum are now writeable whenever the input array
      is writeable. For example, ``np.einsum('ijk...->kji...', a)`` will now
      have the same effect as :py:func:`np.swapaxes(a, 0, 2) <numpy.swapaxes>`
      and ``np.einsum('ii->i', a)`` will return a writeable view of the diagonal
      of a 2D array.
  
      Examples
      --------
      >>> a = np.arange(25).reshape(5,5)
      >>> b = np.arange(5)
      >>> c = np.arange(6).reshape(2,3)
  
      Trace of a matrix:
  
      >>> np.einsum('ii', a)
      60
      >>> np.einsum(a, [0,0])
      60
      >>> np.trace(a)
      60
  
      Extract the diagonal (requires explicit form):
  
      >>> np.einsum('ii->i', a)
      array([ 0,  6, 12, 18, 24])
      >>> np.einsum(a, [0,0], [0])
      array([ 0,  6, 12, 18, 24])
      >>> np.diag(a)
      array([ 0,  6, 12, 18, 24])
  
      Sum over an axis (requires explicit form):
  
      >>> np.einsum('ij->i', a)
      array([ 10,  35,  60,  85, 110])
      >>> np.einsum(a, [0,1], [0])
      array([ 10,  35,  60,  85, 110])
      >>> np.sum(a, axis=1)
      array([ 10,  35,  60,  85, 110])
  
      For higher dimensional arrays summing a single axis can be done with ellipsis:
  
      >>> np.einsum('...j->...', a)
      array([ 10,  35,  60,  85, 110])
      >>> np.einsum(a, [Ellipsis,1], [Ellipsis])
      array([ 10,  35,  60,  85, 110])
  
      Compute a matrix transpose, or reorder any number of axes:
  
      >>> np.einsum('ji', c)
      array([[0, 3],
             [1, 4],
             [2, 5]])
      >>> np.einsum('ij->ji', c)
      array([[0, 3],
             [1, 4],
             [2, 5]])
      >>> np.einsum(c, [1,0])
      array([[0, 3],
             [1, 4],
             [2, 5]])
      >>> np.transpose(c)
      array([[0, 3],
             [1, 4],
             [2, 5]])
  
      Vector inner products:
  
      >>> np.einsum('i,i', b, b)
      30
      >>> np.einsum(b, [0], b, [0])
      30
      >>> np.inner(b,b)
      30
  
      Matrix vector multiplication:
  
      >>> np.einsum('ij,j', a, b)
      array([ 30,  80, 130, 180, 230])
      >>> np.einsum(a, [0,1], b, [1])
      array([ 30,  80, 130, 180, 230])
      >>> np.dot(a, b)
      array([ 30,  80, 130, 180, 230])
      >>> np.einsum('...j,j', a, b)
      array([ 30,  80, 130, 180, 230])
  
      Broadcasting and scalar multiplication:
  
      >>> np.einsum('..., ...', 3, c)
      array([[ 0,  3,  6],
             [ 9, 12, 15]])
      >>> np.einsum(',ij', 3, c)
      array([[ 0,  3,  6],
             [ 9, 12, 15]])
      >>> np.einsum(3, [Ellipsis], c, [Ellipsis])
      array([[ 0,  3,  6],
             [ 9, 12, 15]])
      >>> np.multiply(3, c)
      array([[ 0,  3,  6],
             [ 9, 12, 15]])
  
      Vector outer product:
  
      >>> np.einsum('i,j', np.arange(2)+1, b)
      array([[0, 1, 2, 3, 4],
             [0, 2, 4, 6, 8]])
      >>> np.einsum(np.arange(2)+1, [0], b, [1])
      array([[0, 1, 2, 3, 4],
             [0, 2, 4, 6, 8]])
      >>> np.outer(np.arange(2)+1, b)
      array([[0, 1, 2, 3, 4],
             [0, 2, 4, 6, 8]])
  
      Tensor contraction:
  
      >>> a = np.arange(60.).reshape(3,4,5)
      >>> b = np.arange(24.).reshape(4,3,2)
      >>> np.einsum('ijk,jil->kl', a, b)
      array([[ 4400.,  4730.],
             [ 4532.,  4874.],
             [ 4664.,  5018.],
             [ 4796.,  5162.],
             [ 4928.,  5306.]])
      >>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
      array([[ 4400.,  4730.],
             [ 4532.,  4874.],
             [ 4664.,  5018.],
             [ 4796.,  5162.],
             [ 4928.,  5306.]])
      >>> np.tensordot(a,b, axes=([1,0],[0,1]))
      array([[ 4400.,  4730.],
             [ 4532.,  4874.],
             [ 4664.,  5018.],
             [ 4796.,  5162.],
             [ 4928.,  5306.]])
  
      Writeable returned arrays (since version 1.10.0):
  
      >>> a = np.zeros((3, 3))
      >>> np.einsum('ii->i', a)[:] = 1
      >>> a
      array([[ 1.,  0.,  0.],
             [ 0.,  1.,  0.],
             [ 0.,  0.,  1.]])
  
      Example of ellipsis use:
  
      >>> a = np.arange(6).reshape((3,2))
      >>> b = np.arange(12).reshape((4,3))
      >>> np.einsum('ki,jk->ij', a, b)
      array([[10, 28, 46, 64],
             [13, 40, 67, 94]])
      >>> np.einsum('ki,...k->i...', a, b)
      array([[10, 28, 46, 64],
             [13, 40, 67, 94]])
      >>> np.einsum('k...,jk', a, b)
      array([[10, 28, 46, 64],
             [13, 40, 67, 94]])
  
      """)
  
  
  ##############################################################################
  #
  # Documentation for ndarray attributes and methods
  #
  ##############################################################################
  
  
  ##############################################################################
  #
  # ndarray object
  #
  ##############################################################################
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray',
      """
      ndarray(shape, dtype=float, buffer=None, offset=0,
              strides=None, order=None)
  
      An array object represents a multidimensional, homogeneous array
      of fixed-size items.  An associated data-type object describes the
      format of each element in the array (its byte-order, how many bytes it
      occupies in memory, whether it is an integer, a floating point number,
      or something else, etc.)
  
      Arrays should be constructed using `array`, `zeros` or `empty` (refer
      to the See Also section below).  The parameters given here refer to
      a low-level method (`ndarray(...)`) for instantiating an array.
  
      For more information, refer to the `numpy` module and examine the
      methods and attributes of an array.
  
      Parameters
      ----------
      (for the __new__ method; see Notes below)
  
      shape : tuple of ints
          Shape of created array.
      dtype : data-type, optional
          Any object that can be interpreted as a numpy data type.
      buffer : object exposing buffer interface, optional
          Used to fill the array with data.
      offset : int, optional
          Offset of array data in buffer.
      strides : tuple of ints, optional
          Strides of data in memory.
      order : {'C', 'F'}, optional
          Row-major (C-style) or column-major (Fortran-style) order.
  
      Attributes
      ----------
      T : ndarray
          Transpose of the array.
      data : buffer
          The array's elements, in memory.
      dtype : dtype object
          Describes the format of the elements in the array.
      flags : dict
          Dictionary containing information related to memory use, e.g.,
          'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.
      flat : numpy.flatiter object
          Flattened version of the array as an iterator.  The iterator
          allows assignments, e.g., ``x.flat = 3`` (See `ndarray.flat` for
          assignment examples; TODO).
      imag : ndarray
          Imaginary part of the array.
      real : ndarray
          Real part of the array.
      size : int
          Number of elements in the array.
      itemsize : int
          The memory use of each array element in bytes.
      nbytes : int
          The total number of bytes required to store the array data,
          i.e., ``itemsize * size``.
      ndim : int
          The array's number of dimensions.
      shape : tuple of ints
          Shape of the array.
      strides : tuple of ints
          The step-size required to move from one element to the next in
          memory. For example, a contiguous ``(3, 4)`` array of type
          ``int16`` in C-order has strides ``(8, 2)``.  This implies that
          to move from element to element in memory requires jumps of 2 bytes.
          To move from row-to-row, one needs to jump 8 bytes at a time
          (``2 * 4``).
      ctypes : ctypes object
          Class containing properties of the array needed for interaction
          with ctypes.
      base : ndarray
          If the array is a view into another array, that array is its `base`
          (unless that array is also a view).  The `base` array is where the
          array data is actually stored.
  
      See Also
      --------
      array : Construct an array.
      zeros : Create an array, each element of which is zero.
      empty : Create an array, but leave its allocated memory unchanged (i.e.,
              it contains "garbage").
      dtype : Create a data-type.
  
      Notes
      -----
      There are two modes of creating an array using ``__new__``:
  
      1. If `buffer` is None, then only `shape`, `dtype`, and `order`
         are used.
      2. If `buffer` is an object exposing the buffer interface, then
         all keywords are interpreted.
  
      No ``__init__`` method is needed because the array is fully initialized
      after the ``__new__`` method.
  
      Examples
      --------
      These examples illustrate the low-level `ndarray` constructor.  Refer
      to the `See Also` section above for easier ways of constructing an
      ndarray.
  
      First mode, `buffer` is None:
  
      >>> np.ndarray(shape=(2,2), dtype=float, order='F')
      array([[ -1.13698227e+002,   4.25087011e-303],
             [  2.88528414e-306,   3.27025015e-309]])         #random
  
      Second mode:
  
      >>> np.ndarray((2,), buffer=np.array([1,2,3]),
      ...            offset=np.int_().itemsize,
      ...            dtype=int) # offset = 1*itemsize, i.e. skip first element
      array([2, 3])
  
      """)
  
  
  ##############################################################################
  #
  # ndarray attributes
  #
  ##############################################################################
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_interface__',
      """Array protocol: Python side."""))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_finalize__',
      """None."""))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_priority__',
      """Array priority."""))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_struct__',
      """Array protocol: C-struct side."""))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('base',
      """
      Base object if memory is from some other object.
  
      Examples
      --------
      The base of an array that owns its memory is None:
  
      >>> x = np.array([1,2,3,4])
      >>> x.base is None
      True
  
      Slicing creates a view, whose memory is shared with x:
  
      >>> y = x[2:]
      >>> y.base is x
      True
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('ctypes',
      """
      An object to simplify the interaction of the array with the ctypes
      module.
  
      This attribute creates an object that makes it easier to use arrays
      when calling shared libraries with the ctypes module. The returned
      object has, among others, data, shape, and strides attributes (see
      Notes below) which themselves return ctypes objects that can be used
      as arguments to a shared library.
  
      Parameters
      ----------
      None
  
      Returns
      -------
      c : Python object
          Possessing attributes data, shape, strides, etc.
  
      See Also
      --------
      numpy.ctypeslib
  
      Notes
      -----
      Below are the public attributes of this object which were documented
      in "Guide to NumPy" (we have omitted undocumented public attributes,
      as well as documented private attributes):
  
      .. autoattribute:: numpy.core._internal._ctypes.data
  
      .. autoattribute:: numpy.core._internal._ctypes.shape
  
      .. autoattribute:: numpy.core._internal._ctypes.strides
  
      .. automethod:: numpy.core._internal._ctypes.data_as
  
      .. automethod:: numpy.core._internal._ctypes.shape_as
  
      .. automethod:: numpy.core._internal._ctypes.strides_as
  
      If the ctypes module is not available, then the ctypes attribute
      of array objects still returns something useful, but ctypes objects
      are not returned and errors may be raised instead. In particular,
      the object will still have the as parameter attribute which will
      return an integer equal to the data attribute.
  
      Examples
      --------
      >>> import ctypes
      >>> x
      array([[0, 1],
             [2, 3]])
      >>> x.ctypes.data
      30439712
      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long))
      <ctypes.LP_c_long object at 0x01F01300>
      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_long)).contents
      c_long(0)
      >>> x.ctypes.data_as(ctypes.POINTER(ctypes.c_longlong)).contents
      c_longlong(4294967296L)
      >>> x.ctypes.shape
      <numpy.core._internal.c_long_Array_2 object at 0x01FFD580>
      >>> x.ctypes.shape_as(ctypes.c_long)
      <numpy.core._internal.c_long_Array_2 object at 0x01FCE620>
      >>> x.ctypes.strides
      <numpy.core._internal.c_long_Array_2 object at 0x01FCE620>
      >>> x.ctypes.strides_as(ctypes.c_longlong)
      <numpy.core._internal.c_longlong_Array_2 object at 0x01F01300>
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('data',
      """Python buffer object pointing to the start of the array's data."""))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('dtype',
      """
      Data-type of the array's elements.
  
      Parameters
      ----------
      None
  
      Returns
      -------
      d : numpy dtype object
  
      See Also
      --------
      numpy.dtype
  
      Examples
      --------
      >>> x
      array([[0, 1],
             [2, 3]])
      >>> x.dtype
      dtype('int32')
      >>> type(x.dtype)
      <type 'numpy.dtype'>
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('imag',
      """
      The imaginary part of the array.
  
      Examples
      --------
      >>> x = np.sqrt([1+0j, 0+1j])
      >>> x.imag
      array([ 0.        ,  0.70710678])
      >>> x.imag.dtype
      dtype('float64')
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('itemsize',
      """
      Length of one array element in bytes.
  
      Examples
      --------
      >>> x = np.array([1,2,3], dtype=np.float64)
      >>> x.itemsize
      8
      >>> x = np.array([1,2,3], dtype=np.complex128)
      >>> x.itemsize
      16
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('flags',
      """
      Information about the memory layout of the array.
  
      Attributes
      ----------
      C_CONTIGUOUS (C)
          The data is in a single, C-style contiguous segment.
      F_CONTIGUOUS (F)
          The data is in a single, Fortran-style contiguous segment.
      OWNDATA (O)
          The array owns the memory it uses or borrows it from another object.
      WRITEABLE (W)
          The data area can be written to.  Setting this to False locks
          the data, making it read-only.  A view (slice, etc.) inherits WRITEABLE
          from its base array at creation time, but a view of a writeable
          array may be subsequently locked while the base array remains writeable.
          (The opposite is not true, in that a view of a locked array may not
          be made writeable.  However, currently, locking a base object does not
          lock any views that already reference it, so under that circumstance it
          is possible to alter the contents of a locked array via a previously
          created writeable view onto it.)  Attempting to change a non-writeable
          array raises a RuntimeError exception.
      ALIGNED (A)
          The data and all elements are aligned appropriately for the hardware.
      WRITEBACKIFCOPY (X)
          This array is a copy of some other array. The C-API function
          PyArray_ResolveWritebackIfCopy must be called before deallocating
          to the base array will be updated with the contents of this array.
      UPDATEIFCOPY (U)
          (Deprecated, use WRITEBACKIFCOPY) This array is a copy of some other array.
          When this array is
          deallocated, the base array will be updated with the contents of
          this array.
      FNC
          F_CONTIGUOUS and not C_CONTIGUOUS.
      FORC
          F_CONTIGUOUS or C_CONTIGUOUS (one-segment test).
      BEHAVED (B)
          ALIGNED and WRITEABLE.
      CARRAY (CA)
          BEHAVED and C_CONTIGUOUS.
      FARRAY (FA)
          BEHAVED and F_CONTIGUOUS and not C_CONTIGUOUS.
  
      Notes
      -----
      The `flags` object can be accessed dictionary-like (as in ``a.flags['WRITEABLE']``),
      or by using lowercased attribute names (as in ``a.flags.writeable``). Short flag
      names are only supported in dictionary access.
  
      Only the WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED flags can be
      changed by the user, via direct assignment to the attribute or dictionary
      entry, or by calling `ndarray.setflags`.
  
      The array flags cannot be set arbitrarily:
  
      - UPDATEIFCOPY can only be set ``False``.
      - WRITEBACKIFCOPY can only be set ``False``.
      - ALIGNED can only be set ``True`` if the data is truly aligned.
      - WRITEABLE can only be set ``True`` if the array owns its own memory
        or the ultimate owner of the memory exposes a writeable buffer
        interface or is a string.
  
      Arrays can be both C-style and Fortran-style contiguous simultaneously.
      This is clear for 1-dimensional arrays, but can also be true for higher
      dimensional arrays.
  
      Even for contiguous arrays a stride for a given dimension
      ``arr.strides[dim]`` may be *arbitrary* if ``arr.shape[dim] == 1``
      or the array has no elements.
      It does *not* generally hold that ``self.strides[-1] == self.itemsize``
      for C-style contiguous arrays or ``self.strides[0] == self.itemsize`` for
      Fortran-style contiguous arrays is true.
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('flat',
      """
      A 1-D iterator over the array.
  
      This is a `numpy.flatiter` instance, which acts similarly to, but is not
      a subclass of, Python's built-in iterator object.
  
      See Also
      --------
      flatten : Return a copy of the array collapsed into one dimension.
  
      flatiter
  
      Examples
      --------
      >>> x = np.arange(1, 7).reshape(2, 3)
      >>> x
      array([[1, 2, 3],
             [4, 5, 6]])
      >>> x.flat[3]
      4
      >>> x.T
      array([[1, 4],
             [2, 5],
             [3, 6]])
      >>> x.T.flat[3]
      5
      >>> type(x.flat)
      <type 'numpy.flatiter'>
  
      An assignment example:
  
      >>> x.flat = 3; x
      array([[3, 3, 3],
             [3, 3, 3]])
      >>> x.flat[[1,4]] = 1; x
      array([[3, 1, 3],
             [3, 1, 3]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('nbytes',
      """
      Total bytes consumed by the elements of the array.
  
      Notes
      -----
      Does not include memory consumed by non-element attributes of the
      array object.
  
      Examples
      --------
      >>> x = np.zeros((3,5,2), dtype=np.complex128)
      >>> x.nbytes
      480
      >>> np.prod(x.shape) * x.itemsize
      480
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('ndim',
      """
      Number of array dimensions.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3])
      >>> x.ndim
      1
      >>> y = np.zeros((2, 3, 4))
      >>> y.ndim
      3
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('real',
      """
      The real part of the array.
  
      Examples
      --------
      >>> x = np.sqrt([1+0j, 0+1j])
      >>> x.real
      array([ 1.        ,  0.70710678])
      >>> x.real.dtype
      dtype('float64')
  
      See Also
      --------
      numpy.real : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('shape',
      """
      Tuple of array dimensions.
  
      The shape property is usually used to get the current shape of an array,
      but may also be used to reshape the array in-place by assigning a tuple of
      array dimensions to it.  As with `numpy.reshape`, one of the new shape
      dimensions can be -1, in which case its value is inferred from the size of
      the array and the remaining dimensions. Reshaping an array in-place will
      fail if a copy is required.
  
      Examples
      --------
      >>> x = np.array([1, 2, 3, 4])
      >>> x.shape
      (4,)
      >>> y = np.zeros((2, 3, 4))
      >>> y.shape
      (2, 3, 4)
      >>> y.shape = (3, 8)
      >>> y
      array([[ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.],
             [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]])
      >>> y.shape = (3, 6)
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      ValueError: total size of new array must be unchanged
      >>> np.zeros((4,2))[::2].shape = (-1,)
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      AttributeError: incompatible shape for a non-contiguous array
  
      See Also
      --------
      numpy.reshape : similar function
      ndarray.reshape : similar method
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('size',
      """
      Number of elements in the array.
  
      Equal to ``np.prod(a.shape)``, i.e., the product of the array's
      dimensions.
  
      Notes
      -----
      `a.size` returns a standard arbitrary precision Python integer. This
      may not be the case with other methods of obtaining the same value
      (like the suggested ``np.prod(a.shape)``, which returns an instance
      of ``np.int_``), and may be relevant if the value is used further in
      calculations that may overflow a fixed size integer type.
  
      Examples
      --------
      >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
      >>> x.size
      30
      >>> np.prod(x.shape)
      30
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('strides',
      """
      Tuple of bytes to step in each dimension when traversing an array.
  
      The byte offset of element ``(i[0], i[1], ..., i[n])`` in an array `a`
      is::
  
          offset = sum(np.array(i) * a.strides)
  
      A more detailed explanation of strides can be found in the
      "ndarray.rst" file in the NumPy reference guide.
  
      Notes
      -----
      Imagine an array of 32-bit integers (each 4 bytes)::
  
        x = np.array([[0, 1, 2, 3, 4],
                      [5, 6, 7, 8, 9]], dtype=np.int32)
  
      This array is stored in memory as 40 bytes, one after the other
      (known as a contiguous block of memory).  The strides of an array tell
      us how many bytes we have to skip in memory to move to the next position
      along a certain axis.  For example, we have to skip 4 bytes (1 value) to
      move to the next column, but 20 bytes (5 values) to get to the same
      position in the next row.  As such, the strides for the array `x` will be
      ``(20, 4)``.
  
      See Also
      --------
      numpy.lib.stride_tricks.as_strided
  
      Examples
      --------
      >>> y = np.reshape(np.arange(2*3*4), (2,3,4))
      >>> y
      array([[[ 0,  1,  2,  3],
              [ 4,  5,  6,  7],
              [ 8,  9, 10, 11]],
             [[12, 13, 14, 15],
              [16, 17, 18, 19],
              [20, 21, 22, 23]]])
      >>> y.strides
      (48, 16, 4)
      >>> y[1,1,1]
      17
      >>> offset=sum(y.strides * np.array((1,1,1)))
      >>> offset/y.itemsize
      17
  
      >>> x = np.reshape(np.arange(5*6*7*8), (5,6,7,8)).transpose(2,3,1,0)
      >>> x.strides
      (32, 4, 224, 1344)
      >>> i = np.array([3,5,2,2])
      >>> offset = sum(i * x.strides)
      >>> x[3,5,2,2]
      813
      >>> offset / x.itemsize
      813
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('T',
      """
      Same as self.transpose(), except that self is returned if
      self.ndim < 2.
  
      Examples
      --------
      >>> x = np.array([[1.,2.],[3.,4.]])
      >>> x
      array([[ 1.,  2.],
             [ 3.,  4.]])
      >>> x.T
      array([[ 1.,  3.],
             [ 2.,  4.]])
      >>> x = np.array([1.,2.,3.,4.])
      >>> x
      array([ 1.,  2.,  3.,  4.])
      >>> x.T
      array([ 1.,  2.,  3.,  4.])
  
      """))
  
  
  ##############################################################################
  #
  # ndarray methods
  #
  ##############################################################################
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array__',
      """ a.__array__(|dtype) -> reference if type unchanged, copy otherwise.
  
      Returns either a new reference to self if dtype is not given or a new array
      of provided data type if dtype is different from the current dtype of the
      array.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_prepare__',
      """a.__array_prepare__(obj) -> Object of same type as ndarray object obj.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__array_wrap__',
      """a.__array_wrap__(obj) -> Object of same type as ndarray object a.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__copy__',
      """a.__copy__()
  
      Used if :func:`copy.copy` is called on an array. Returns a copy of the array.
  
      Equivalent to ``a.copy(order='K')``.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__deepcopy__',
      """a.__deepcopy__(memo, /) -> Deep copy of array.
  
      Used if :func:`copy.deepcopy` is called on an array.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__reduce__',
      """a.__reduce__()
  
      For pickling.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('__setstate__',
      """a.__setstate__(state, /)
  
      For unpickling.
  
      The `state` argument must be a sequence that contains the following
      elements:
  
      Parameters
      ----------
      version : int
          optional pickle version. If omitted defaults to 0.
      shape : tuple
      dtype : data-type
      isFortran : bool
      rawdata : string or list
          a binary string with the data (or a list if 'a' is an object array)
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('all',
      """
      a.all(axis=None, out=None, keepdims=False)
  
      Returns True if all elements evaluate to True.
  
      Refer to `numpy.all` for full documentation.
  
      See Also
      --------
      numpy.all : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('any',
      """
      a.any(axis=None, out=None, keepdims=False)
  
      Returns True if any of the elements of `a` evaluate to True.
  
      Refer to `numpy.any` for full documentation.
  
      See Also
      --------
      numpy.any : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('argmax',
      """
      a.argmax(axis=None, out=None)
  
      Return indices of the maximum values along the given axis.
  
      Refer to `numpy.argmax` for full documentation.
  
      See Also
      --------
      numpy.argmax : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('argmin',
      """
      a.argmin(axis=None, out=None)
  
      Return indices of the minimum values along the given axis of `a`.
  
      Refer to `numpy.argmin` for detailed documentation.
  
      See Also
      --------
      numpy.argmin : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('argsort',
      """
      a.argsort(axis=-1, kind='quicksort', order=None)
  
      Returns the indices that would sort this array.
  
      Refer to `numpy.argsort` for full documentation.
  
      See Also
      --------
      numpy.argsort : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('argpartition',
      """
      a.argpartition(kth, axis=-1, kind='introselect', order=None)
  
      Returns the indices that would partition this array.
  
      Refer to `numpy.argpartition` for full documentation.
  
      .. versionadded:: 1.8.0
  
      See Also
      --------
      numpy.argpartition : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('astype',
      """
      a.astype(dtype, order='K', casting='unsafe', subok=True, copy=True)
  
      Copy of the array, cast to a specified type.
  
      Parameters
      ----------
      dtype : str or dtype
          Typecode or data-type to which the array is cast.
      order : {'C', 'F', 'A', 'K'}, optional
          Controls the memory layout order of the result.
          'C' means C order, 'F' means Fortran order, 'A'
          means 'F' order if all the arrays are Fortran contiguous,
          'C' order otherwise, and 'K' means as close to the
          order the array elements appear in memory as possible.
          Default is 'K'.
      casting : {'no', 'equiv', 'safe', 'same_kind', 'unsafe'}, optional
          Controls what kind of data casting may occur. Defaults to 'unsafe'
          for backwards compatibility.
  
            * 'no' means the data types should not be cast at all.
            * 'equiv' means only byte-order changes are allowed.
            * 'safe' means only casts which can preserve values are allowed.
            * 'same_kind' means only safe casts or casts within a kind,
              like float64 to float32, are allowed.
            * 'unsafe' means any data conversions may be done.
      subok : bool, optional
          If True, then sub-classes will be passed-through (default), otherwise
          the returned array will be forced to be a base-class array.
      copy : bool, optional
          By default, astype always returns a newly allocated array. If this
          is set to false, and the `dtype`, `order`, and `subok`
          requirements are satisfied, the input array is returned instead
          of a copy.
  
      Returns
      -------
      arr_t : ndarray
          Unless `copy` is False and the other conditions for returning the input
          array are satisfied (see description for `copy` input parameter), `arr_t`
          is a new array of the same shape as the input array, with dtype, order
          given by `dtype`, `order`.
  
      Notes
      -----
      .. versionchanged:: 1.17.0
         Casting between a simple data type and a structured one is possible only
         for "unsafe" casting.  Casting to multiple fields is allowed, but
         casting from multiple fields is not.
  
      .. versionchanged:: 1.9.0
         Casting from numeric to string types in 'safe' casting mode requires
         that the string dtype length is long enough to store the max
         integer/float value converted.
  
      Raises
      ------
      ComplexWarning
          When casting from complex to float or int. To avoid this,
          one should use ``a.real.astype(t)``.
  
      Examples
      --------
      >>> x = np.array([1, 2, 2.5])
      >>> x
      array([ 1. ,  2. ,  2.5])
  
      >>> x.astype(int)
      array([1, 2, 2])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('byteswap',
      """
      a.byteswap(inplace=False)
  
      Swap the bytes of the array elements
  
      Toggle between low-endian and big-endian data representation by
      returning a byteswapped array, optionally swapped in-place.
  
      Parameters
      ----------
      inplace : bool, optional
          If ``True``, swap bytes in-place, default is ``False``.
  
      Returns
      -------
      out : ndarray
          The byteswapped array. If `inplace` is ``True``, this is
          a view to self.
  
      Examples
      --------
      >>> A = np.array([1, 256, 8755], dtype=np.int16)
      >>> map(hex, A)
      ['0x1', '0x100', '0x2233']
      >>> A.byteswap(inplace=True)
      array([  256,     1, 13090], dtype=int16)
      >>> map(hex, A)
      ['0x100', '0x1', '0x3322']
  
      Arrays of strings are not swapped
  
      >>> A = np.array(['ceg', 'fac'])
      >>> A.byteswap()
      array(['ceg', 'fac'],
            dtype='|S3')
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('choose',
      """
      a.choose(choices, out=None, mode='raise')
  
      Use an index array to construct a new array from a set of choices.
  
      Refer to `numpy.choose` for full documentation.
  
      See Also
      --------
      numpy.choose : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('clip',
      """
      a.clip(min=None, max=None, out=None)
  
      Return an array whose values are limited to ``[min, max]``.
      One of max or min must be given.
  
      Refer to `numpy.clip` for full documentation.
  
      See Also
      --------
      numpy.clip : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('compress',
      """
      a.compress(condition, axis=None, out=None)
  
      Return selected slices of this array along given axis.
  
      Refer to `numpy.compress` for full documentation.
  
      See Also
      --------
      numpy.compress : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('conj',
      """
      a.conj()
  
      Complex-conjugate all elements.
  
      Refer to `numpy.conjugate` for full documentation.
  
      See Also
      --------
      numpy.conjugate : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('conjugate',
      """
      a.conjugate()
  
      Return the complex conjugate, element-wise.
  
      Refer to `numpy.conjugate` for full documentation.
  
      See Also
      --------
      numpy.conjugate : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('copy',
      """
      a.copy(order='C')
  
      Return a copy of the array.
  
      Parameters
      ----------
      order : {'C', 'F', 'A', 'K'}, optional
          Controls the memory layout of the copy. 'C' means C-order,
          'F' means F-order, 'A' means 'F' if `a` is Fortran contiguous,
          'C' otherwise. 'K' means match the layout of `a` as closely
          as possible. (Note that this function and :func:`numpy.copy` are very
          similar, but have different default values for their order=
          arguments.)
  
      See also
      --------
      numpy.copy
      numpy.copyto
  
      Examples
      --------
      >>> x = np.array([[1,2,3],[4,5,6]], order='F')
  
      >>> y = x.copy()
  
      >>> x.fill(0)
  
      >>> x
      array([[0, 0, 0],
             [0, 0, 0]])
  
      >>> y
      array([[1, 2, 3],
             [4, 5, 6]])
  
      >>> y.flags['C_CONTIGUOUS']
      True
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('cumprod',
      """
      a.cumprod(axis=None, dtype=None, out=None)
  
      Return the cumulative product of the elements along the given axis.
  
      Refer to `numpy.cumprod` for full documentation.
  
      See Also
      --------
      numpy.cumprod : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('cumsum',
      """
      a.cumsum(axis=None, dtype=None, out=None)
  
      Return the cumulative sum of the elements along the given axis.
  
      Refer to `numpy.cumsum` for full documentation.
  
      See Also
      --------
      numpy.cumsum : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('diagonal',
      """
      a.diagonal(offset=0, axis1=0, axis2=1)
  
      Return specified diagonals. In NumPy 1.9 the returned array is a
      read-only view instead of a copy as in previous NumPy versions.  In
      a future version the read-only restriction will be removed.
  
      Refer to :func:`numpy.diagonal` for full documentation.
  
      See Also
      --------
      numpy.diagonal : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('dot',
      """
      a.dot(b, out=None)
  
      Dot product of two arrays.
  
      Refer to `numpy.dot` for full documentation.
  
      See Also
      --------
      numpy.dot : equivalent function
  
      Examples
      --------
      >>> a = np.eye(2)
      >>> b = np.ones((2, 2)) * 2
      >>> a.dot(b)
      array([[ 2.,  2.],
             [ 2.,  2.]])
  
      This array method can be conveniently chained:
  
      >>> a.dot(b).dot(b)
      array([[ 8.,  8.],
             [ 8.,  8.]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('dump',
      """a.dump(file)
  
      Dump a pickle of the array to the specified file.
      The array can be read back with pickle.load or numpy.load.
  
      Parameters
      ----------
      file : str
          A string naming the dump file.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('dumps',
      """
      a.dumps()
  
      Returns the pickle of the array as a string.
      pickle.loads or numpy.loads will convert the string back to an array.
  
      Parameters
      ----------
      None
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('fill',
      """
      a.fill(value)
  
      Fill the array with a scalar value.
  
      Parameters
      ----------
      value : scalar
          All elements of `a` will be assigned this value.
  
      Examples
      --------
      >>> a = np.array([1, 2])
      >>> a.fill(0)
      >>> a
      array([0, 0])
      >>> a = np.empty(2)
      >>> a.fill(1)
      >>> a
      array([ 1.,  1.])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('flatten',
      """
      a.flatten(order='C')
  
      Return a copy of the array collapsed into one dimension.
  
      Parameters
      ----------
      order : {'C', 'F', 'A', 'K'}, optional
          'C' means to flatten in row-major (C-style) order.
          'F' means to flatten in column-major (Fortran-
          style) order. 'A' means to flatten in column-major
          order if `a` is Fortran *contiguous* in memory,
          row-major order otherwise. 'K' means to flatten
          `a` in the order the elements occur in memory.
          The default is 'C'.
  
      Returns
      -------
      y : ndarray
          A copy of the input array, flattened to one dimension.
  
      See Also
      --------
      ravel : Return a flattened array.
      flat : A 1-D flat iterator over the array.
  
      Examples
      --------
      >>> a = np.array([[1,2], [3,4]])
      >>> a.flatten()
      array([1, 2, 3, 4])
      >>> a.flatten('F')
      array([1, 3, 2, 4])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('getfield',
      """
      a.getfield(dtype, offset=0)
  
      Returns a field of the given array as a certain type.
  
      A field is a view of the array data with a given data-type. The values in
      the view are determined by the given type and the offset into the current
      array in bytes. The offset needs to be such that the view dtype fits in the
      array dtype; for example an array of dtype complex128 has 16-byte elements.
      If taking a view with a 32-bit integer (4 bytes), the offset needs to be
      between 0 and 12 bytes.
  
      Parameters
      ----------
      dtype : str or dtype
          The data type of the view. The dtype size of the view can not be larger
          than that of the array itself.
      offset : int
          Number of bytes to skip before beginning the element view.
  
      Examples
      --------
      >>> x = np.diag([1.+1.j]*2)
      >>> x[1, 1] = 2 + 4.j
      >>> x
      array([[ 1.+1.j,  0.+0.j],
             [ 0.+0.j,  2.+4.j]])
      >>> x.getfield(np.float64)
      array([[ 1.,  0.],
             [ 0.,  2.]])
  
      By choosing an offset of 8 bytes we can select the complex part of the
      array for our view:
  
      >>> x.getfield(np.float64, offset=8)
      array([[ 1.,  0.],
         [ 0.,  4.]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('item',
      """
      a.item(*args)
  
      Copy an element of an array to a standard Python scalar and return it.
  
      Parameters
      ----------
      \\*args : Arguments (variable number and type)
  
          * none: in this case, the method only works for arrays
            with one element (`a.size == 1`), which element is
            copied into a standard Python scalar object and returned.
  
          * int_type: this argument is interpreted as a flat index into
            the array, specifying which element to copy and return.
  
          * tuple of int_types: functions as does a single int_type argument,
            except that the argument is interpreted as an nd-index into the
            array.
  
      Returns
      -------
      z : Standard Python scalar object
          A copy of the specified element of the array as a suitable
          Python scalar
  
      Notes
      -----
      When the data type of `a` is longdouble or clongdouble, item() returns
      a scalar array object because there is no available Python scalar that
      would not lose information. Void arrays return a buffer object for item(),
      unless fields are defined, in which case a tuple is returned.
  
      `item` is very similar to a[args], except, instead of an array scalar,
      a standard Python scalar is returned. This can be useful for speeding up
      access to elements of the array and doing arithmetic on elements of the
      array using Python's optimized math.
  
      Examples
      --------
      >>> x = np.random.randint(9, size=(3, 3))
      >>> x
      array([[3, 1, 7],
             [2, 8, 3],
             [8, 5, 3]])
      >>> x.item(3)
      2
      >>> x.item(7)
      5
      >>> x.item((0, 1))
      1
      >>> x.item((2, 2))
      3
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('itemset',
      """
      a.itemset(*args)
  
      Insert scalar into an array (scalar is cast to array's dtype, if possible)
  
      There must be at least 1 argument, and define the last argument
      as *item*.  Then, ``a.itemset(*args)`` is equivalent to but faster
      than ``a[args] = item``.  The item should be a scalar value and `args`
      must select a single item in the array `a`.
  
      Parameters
      ----------
      \\*args : Arguments
          If one argument: a scalar, only used in case `a` is of size 1.
          If two arguments: the last argument is the value to be set
          and must be a scalar, the first argument specifies a single array
          element location. It is either an int or a tuple.
  
      Notes
      -----
      Compared to indexing syntax, `itemset` provides some speed increase
      for placing a scalar into a particular location in an `ndarray`,
      if you must do this.  However, generally this is discouraged:
      among other problems, it complicates the appearance of the code.
      Also, when using `itemset` (and `item`) inside a loop, be sure
      to assign the methods to a local variable to avoid the attribute
      look-up at each loop iteration.
  
      Examples
      --------
      >>> x = np.random.randint(9, size=(3, 3))
      >>> x
      array([[3, 1, 7],
             [2, 8, 3],
             [8, 5, 3]])
      >>> x.itemset(4, 0)
      >>> x.itemset((2, 2), 9)
      >>> x
      array([[3, 1, 7],
             [2, 0, 3],
             [8, 5, 9]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('max',
      """
      a.max(axis=None, out=None, keepdims=False)
  
      Return the maximum along a given axis.
  
      Refer to `numpy.amax` for full documentation.
  
      See Also
      --------
      numpy.amax : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('mean',
      """
      a.mean(axis=None, dtype=None, out=None, keepdims=False)
  
      Returns the average of the array elements along given axis.
  
      Refer to `numpy.mean` for full documentation.
  
      See Also
      --------
      numpy.mean : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('min',
      """
      a.min(axis=None, out=None, keepdims=False)
  
      Return the minimum along a given axis.
  
      Refer to `numpy.amin` for full documentation.
  
      See Also
      --------
      numpy.amin : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('newbyteorder',
      """
      arr.newbyteorder(new_order='S')
  
      Return the array with the same data viewed with a different byte order.
  
      Equivalent to::
  
          arr.view(arr.dtype.newbytorder(new_order))
  
      Changes are also made in all fields and sub-arrays of the array data
      type.
  
  
  
      Parameters
      ----------
      new_order : string, optional
          Byte order to force; a value from the byte order specifications
          below. `new_order` codes can be any of:
  
          * 'S' - swap dtype from current to opposite endian
          * {'<', 'L'} - little endian
          * {'>', 'B'} - big endian
          * {'=', 'N'} - native order
          * {'|', 'I'} - ignore (no change to byte order)
  
          The default value ('S') results in swapping the current
          byte order. The code does a case-insensitive check on the first
          letter of `new_order` for the alternatives above.  For example,
          any of 'B' or 'b' or 'biggish' are valid to specify big-endian.
  
  
      Returns
      -------
      new_arr : array
          New array object with the dtype reflecting given change to the
          byte order.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('nonzero',
      """
      a.nonzero()
  
      Return the indices of the elements that are non-zero.
  
      Refer to `numpy.nonzero` for full documentation.
  
      See Also
      --------
      numpy.nonzero : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('prod',
      """
      a.prod(axis=None, dtype=None, out=None, keepdims=False)
  
      Return the product of the array elements over the given axis
  
      Refer to `numpy.prod` for full documentation.
  
      See Also
      --------
      numpy.prod : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('ptp',
      """
      a.ptp(axis=None, out=None, keepdims=False)
  
      Peak to peak (maximum - minimum) value along a given axis.
  
      Refer to `numpy.ptp` for full documentation.
  
      See Also
      --------
      numpy.ptp : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('put',
      """
      a.put(indices, values, mode='raise')
  
      Set ``a.flat[n] = values[n]`` for all `n` in indices.
  
      Refer to `numpy.put` for full documentation.
  
      See Also
      --------
      numpy.put : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('ravel',
      """
      a.ravel([order])
  
      Return a flattened array.
  
      Refer to `numpy.ravel` for full documentation.
  
      See Also
      --------
      numpy.ravel : equivalent function
  
      ndarray.flat : a flat iterator on the array.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('repeat',
      """
      a.repeat(repeats, axis=None)
  
      Repeat elements of an array.
  
      Refer to `numpy.repeat` for full documentation.
  
      See Also
      --------
      numpy.repeat : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('reshape',
      """
      a.reshape(shape, order='C')
  
      Returns an array containing the same data with a new shape.
  
      Refer to `numpy.reshape` for full documentation.
  
      See Also
      --------
      numpy.reshape : equivalent function
  
      Notes
      -----
      Unlike the free function `numpy.reshape`, this method on `ndarray` allows
      the elements of the shape parameter to be passed in as separate arguments.
      For example, ``a.reshape(10, 11)`` is equivalent to
      ``a.reshape((10, 11))``.
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('resize',
      """
      a.resize(new_shape, refcheck=True)
  
      Change shape and size of array in-place.
  
      Parameters
      ----------
      new_shape : tuple of ints, or `n` ints
          Shape of resized array.
      refcheck : bool, optional
          If False, reference count will not be checked. Default is True.
  
      Returns
      -------
      None
  
      Raises
      ------
      ValueError
          If `a` does not own its own data or references or views to it exist,
          and the data memory must be changed.
          PyPy only: will always raise if the data memory must be changed, since
          there is no reliable way to determine if references or views to it
          exist.
  
      SystemError
          If the `order` keyword argument is specified. This behaviour is a
          bug in NumPy.
  
      See Also
      --------
      resize : Return a new array with the specified shape.
  
      Notes
      -----
      This reallocates space for the data area if necessary.
  
      Only contiguous arrays (data elements consecutive in memory) can be
      resized.
  
      The purpose of the reference count check is to make sure you
      do not use this array as a buffer for another Python object and then
      reallocate the memory. However, reference counts can increase in
      other ways so if you are sure that you have not shared the memory
      for this array with another Python object, then you may safely set
      `refcheck` to False.
  
      Examples
      --------
      Shrinking an array: array is flattened (in the order that the data are
      stored in memory), resized, and reshaped:
  
      >>> a = np.array([[0, 1], [2, 3]], order='C')
      >>> a.resize((2, 1))
      >>> a
      array([[0],
             [1]])
  
      >>> a = np.array([[0, 1], [2, 3]], order='F')
      >>> a.resize((2, 1))
      >>> a
      array([[0],
             [2]])
  
      Enlarging an array: as above, but missing entries are filled with zeros:
  
      >>> b = np.array([[0, 1], [2, 3]])
      >>> b.resize(2, 3) # new_shape parameter doesn't have to be a tuple
      >>> b
      array([[0, 1, 2],
             [3, 0, 0]])
  
      Referencing an array prevents resizing...
  
      >>> c = a
      >>> a.resize((1, 1))
      Traceback (most recent call last):
      ...
      ValueError: cannot resize an array that has been referenced ...
  
      Unless `refcheck` is False:
  
      >>> a.resize((1, 1), refcheck=False)
      >>> a
      array([[0]])
      >>> c
      array([[0]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('round',
      """
      a.round(decimals=0, out=None)
  
      Return `a` with each element rounded to the given number of decimals.
  
      Refer to `numpy.around` for full documentation.
  
      See Also
      --------
      numpy.around : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('searchsorted',
      """
      a.searchsorted(v, side='left', sorter=None)
  
      Find indices where elements of v should be inserted in a to maintain order.
  
      For full documentation, see `numpy.searchsorted`
  
      See Also
      --------
      numpy.searchsorted : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('setfield',
      """
      a.setfield(val, dtype, offset=0)
  
      Put a value into a specified place in a field defined by a data-type.
  
      Place `val` into `a`'s field defined by `dtype` and beginning `offset`
      bytes into the field.
  
      Parameters
      ----------
      val : object
          Value to be placed in field.
      dtype : dtype object
          Data-type of the field in which to place `val`.
      offset : int, optional
          The number of bytes into the field at which to place `val`.
  
      Returns
      -------
      None
  
      See Also
      --------
      getfield
  
      Examples
      --------
      >>> x = np.eye(3)
      >>> x.getfield(np.float64)
      array([[ 1.,  0.,  0.],
             [ 0.,  1.,  0.],
             [ 0.,  0.,  1.]])
      >>> x.setfield(3, np.int32)
      >>> x.getfield(np.int32)
      array([[3, 3, 3],
             [3, 3, 3],
             [3, 3, 3]])
      >>> x
      array([[  1.00000000e+000,   1.48219694e-323,   1.48219694e-323],
             [  1.48219694e-323,   1.00000000e+000,   1.48219694e-323],
             [  1.48219694e-323,   1.48219694e-323,   1.00000000e+000]])
      >>> x.setfield(np.eye(3), np.int32)
      >>> x
      array([[ 1.,  0.,  0.],
             [ 0.,  1.,  0.],
             [ 0.,  0.,  1.]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('setflags',
      """
      a.setflags(write=None, align=None, uic=None)
  
      Set array flags WRITEABLE, ALIGNED, (WRITEBACKIFCOPY and UPDATEIFCOPY),
      respectively.
  
      These Boolean-valued flags affect how numpy interprets the memory
      area used by `a` (see Notes below). The ALIGNED flag can only
      be set to True if the data is actually aligned according to the type.
      The WRITEBACKIFCOPY and (deprecated) UPDATEIFCOPY flags can never be set
      to True. The flag WRITEABLE can only be set to True if the array owns its
      own memory, or the ultimate owner of the memory exposes a writeable buffer
      interface, or is a string. (The exception for string is made so that
      unpickling can be done without copying memory.)
  
      Parameters
      ----------
      write : bool, optional
          Describes whether or not `a` can be written to.
      align : bool, optional
          Describes whether or not `a` is aligned properly for its type.
      uic : bool, optional
          Describes whether or not `a` is a copy of another "base" array.
  
      Notes
      -----
      Array flags provide information about how the memory area used
      for the array is to be interpreted. There are 7 Boolean flags
      in use, only four of which can be changed by the user:
      WRITEBACKIFCOPY, UPDATEIFCOPY, WRITEABLE, and ALIGNED.
  
      WRITEABLE (W) the data area can be written to;
  
      ALIGNED (A) the data and strides are aligned appropriately for the hardware
      (as determined by the compiler);
  
      UPDATEIFCOPY (U) (deprecated), replaced by WRITEBACKIFCOPY;
  
      WRITEBACKIFCOPY (X) this array is a copy of some other array (referenced
      by .base). When the C-API function PyArray_ResolveWritebackIfCopy is
      called, the base array will be updated with the contents of this array.
  
      All flags can be accessed using the single (upper case) letter as well
      as the full name.
  
      Examples
      --------
      >>> y
      array([[3, 1, 7],
             [2, 0, 0],
             [8, 5, 9]])
      >>> y.flags
        C_CONTIGUOUS : True
        F_CONTIGUOUS : False
        OWNDATA : True
        WRITEABLE : True
        ALIGNED : True
        WRITEBACKIFCOPY : False
        UPDATEIFCOPY : False
      >>> y.setflags(write=0, align=0)
      >>> y.flags
        C_CONTIGUOUS : True
        F_CONTIGUOUS : False
        OWNDATA : True
        WRITEABLE : False
        ALIGNED : False
        WRITEBACKIFCOPY : False
        UPDATEIFCOPY : False
      >>> y.setflags(uic=1)
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      ValueError: cannot set WRITEBACKIFCOPY flag to True
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('sort',
      """
      a.sort(axis=-1, kind='quicksort', order=None)
  
      Sort an array, in-place.
  
      Parameters
      ----------
      axis : int, optional
          Axis along which to sort. Default is -1, which means sort along the
          last axis.
      kind : {'quicksort', 'mergesort', 'heapsort', 'stable'}, optional
          Sorting algorithm. Default is 'quicksort'.
      order : str or list of str, optional
          When `a` is an array with fields defined, this argument specifies
          which fields to compare first, second, etc.  A single field can
          be specified as a string, and not all fields need be specified,
          but unspecified fields will still be used, in the order in which
          they come up in the dtype, to break ties.
  
      See Also
      --------
      numpy.sort : Return a sorted copy of an array.
      argsort : Indirect sort.
      lexsort : Indirect stable sort on multiple keys.
      searchsorted : Find elements in sorted array.
      partition: Partial sort.
  
      Notes
      -----
      See ``sort`` for notes on the different sorting algorithms.
  
      Examples
      --------
      >>> a = np.array([[1,4], [3,1]])
      >>> a.sort(axis=1)
      >>> a
      array([[1, 4],
             [1, 3]])
      >>> a.sort(axis=0)
      >>> a
      array([[1, 3],
             [1, 4]])
  
      Use the `order` keyword to specify a field to use when sorting a
      structured array:
  
      >>> a = np.array([('a', 2), ('c', 1)], dtype=[('x', 'S1'), ('y', int)])
      >>> a.sort(order='y')
      >>> a
      array([('c', 1), ('a', 2)],
            dtype=[('x', '|S1'), ('y', '<i4')])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('partition',
      """
      a.partition(kth, axis=-1, kind='introselect', order=None)
  
      Rearranges the elements in the array in such a way that the value of the
      element in kth position is in the position it would be in a sorted array.
      All elements smaller than the kth element are moved before this element and
      all equal or greater are moved behind it. The ordering of the elements in
      the two partitions is undefined.
  
      .. versionadded:: 1.8.0
  
      Parameters
      ----------
      kth : int or sequence of ints
          Element index to partition by. The kth element value will be in its
          final sorted position and all smaller elements will be moved before it
          and all equal or greater elements behind it.
          The order of all elements in the partitions is undefined.
          If provided with a sequence of kth it will partition all elements
          indexed by kth of them into their sorted position at once.
      axis : int, optional
          Axis along which to sort. Default is -1, which means sort along the
          last axis.
      kind : {'introselect'}, optional
          Selection algorithm. Default is 'introselect'.
      order : str or list of str, optional
          When `a` is an array with fields defined, this argument specifies
          which fields to compare first, second, etc. A single field can
          be specified as a string, and not all fields need to be specified,
          but unspecified fields will still be used, in the order in which
          they come up in the dtype, to break ties.
  
      See Also
      --------
      numpy.partition : Return a parititioned copy of an array.
      argpartition : Indirect partition.
      sort : Full sort.
  
      Notes
      -----
      See ``np.partition`` for notes on the different algorithms.
  
      Examples
      --------
      >>> a = np.array([3, 4, 2, 1])
      >>> a.partition(3)
      >>> a
      array([2, 1, 3, 4])
  
      >>> a.partition((1, 3))
      array([1, 2, 3, 4])
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('squeeze',
      """
      a.squeeze(axis=None)
  
      Remove single-dimensional entries from the shape of `a`.
  
      Refer to `numpy.squeeze` for full documentation.
  
      See Also
      --------
      numpy.squeeze : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('std',
      """
      a.std(axis=None, dtype=None, out=None, ddof=0, keepdims=False)
  
      Returns the standard deviation of the array elements along given axis.
  
      Refer to `numpy.std` for full documentation.
  
      See Also
      --------
      numpy.std : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('sum',
      """
      a.sum(axis=None, dtype=None, out=None, keepdims=False)
  
      Return the sum of the array elements over the given axis.
  
      Refer to `numpy.sum` for full documentation.
  
      See Also
      --------
      numpy.sum : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('swapaxes',
      """
      a.swapaxes(axis1, axis2)
  
      Return a view of the array with `axis1` and `axis2` interchanged.
  
      Refer to `numpy.swapaxes` for full documentation.
  
      See Also
      --------
      numpy.swapaxes : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('take',
      """
      a.take(indices, axis=None, out=None, mode='raise')
  
      Return an array formed from the elements of `a` at the given indices.
  
      Refer to `numpy.take` for full documentation.
  
      See Also
      --------
      numpy.take : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('tofile',
      """
      a.tofile(fid, sep="", format="%s")
  
      Write array to a file as text or binary (default).
  
      Data is always written in 'C' order, independent of the order of `a`.
      The data produced by this method can be recovered using the function
      fromfile().
  
      Parameters
      ----------
      fid : file or str
          An open file object, or a string containing a filename.
      sep : str
          Separator between array items for text output.
          If "" (empty), a binary file is written, equivalent to
          ``file.write(a.tobytes())``.
      format : str
          Format string for text file output.
          Each entry in the array is formatted to text by first converting
          it to the closest Python type, and then using "format" % item.
  
      Notes
      -----
      This is a convenience function for quick storage of array data.
      Information on endianness and precision is lost, so this method is not a
      good choice for files intended to archive data or transport data between
      machines with different endianness. Some of these problems can be overcome
      by outputting the data as text files, at the expense of speed and file
      size.
  
      When fid is a file object, array contents are directly written to the
      file, bypassing the file object's ``write`` method. As a result, tofile
      cannot be used with files objects supporting compression (e.g., GzipFile)
      or file-like objects that do not support ``fileno()`` (e.g., BytesIO).
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('tolist',
      """
      a.tolist()
  
      Return the array as a (possibly nested) list.
  
      Return a copy of the array data as a (nested) Python list.
      Data items are converted to the nearest compatible Python type.
  
      Parameters
      ----------
      none
  
      Returns
      -------
      y : list
          The possibly nested list of array elements.
  
      Notes
      -----
      The array may be recreated, ``a = np.array(a.tolist())``.
  
      Examples
      --------
      >>> a = np.array([1, 2])
      >>> a.tolist()
      [1, 2]
      >>> a = np.array([[1, 2], [3, 4]])
      >>> list(a)
      [array([1, 2]), array([3, 4])]
      >>> a.tolist()
      [[1, 2], [3, 4]]
  
      """))
  
  
  tobytesdoc = """
      a.{name}(order='C')
  
      Construct Python bytes containing the raw data bytes in the array.
  
      Constructs Python bytes showing a copy of the raw contents of
      data memory. The bytes object can be produced in either 'C' or 'Fortran',
      or 'Any' order (the default is 'C'-order). 'Any' order means C-order
      unless the F_CONTIGUOUS flag in the array is set, in which case it
      means 'Fortran' order.
  
      {deprecated}
  
      Parameters
      ----------
      order : {{'C', 'F', None}}, optional
          Order of the data for multidimensional arrays:
          C, Fortran, or the same as for the original array.
  
      Returns
      -------
      s : bytes
          Python bytes exhibiting a copy of `a`'s raw data.
  
      Examples
      --------
      >>> x = np.array([[0, 1], [2, 3]])
      >>> x.tobytes()
      b'\\x00\\x00\\x00\\x00\\x01\\x00\\x00\\x00\\x02\\x00\\x00\\x00\\x03\\x00\\x00\\x00'
      >>> x.tobytes('C') == x.tobytes()
      True
      >>> x.tobytes('F')
      b'\\x00\\x00\\x00\\x00\\x02\\x00\\x00\\x00\\x01\\x00\\x00\\x00\\x03\\x00\\x00\\x00'
  
      """
  
  add_newdoc('numpy.core.multiarray', 'ndarray',
             ('tostring', tobytesdoc.format(name='tostring',
                                            deprecated=
                                            'This function is a compatibility '
                                            'alias for tobytes. Despite its '
                                            'name it returns bytes not '
                                            'strings.')))
  add_newdoc('numpy.core.multiarray', 'ndarray',
             ('tobytes', tobytesdoc.format(name='tobytes',
                                           deprecated='.. versionadded:: 1.9.0')))
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('trace',
      """
      a.trace(offset=0, axis1=0, axis2=1, dtype=None, out=None)
  
      Return the sum along diagonals of the array.
  
      Refer to `numpy.trace` for full documentation.
  
      See Also
      --------
      numpy.trace : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('transpose',
      """
      a.transpose(*axes)
  
      Returns a view of the array with axes transposed.
  
      For a 1-D array, this has no effect. (To change between column and
      row vectors, first cast the 1-D array into a matrix object.)
      For a 2-D array, this is the usual matrix transpose.
      For an n-D array, if axes are given, their order indicates how the
      axes are permuted (see Examples). If axes are not provided and
      ``a.shape = (i[0], i[1], ... i[n-2], i[n-1])``, then
      ``a.transpose().shape = (i[n-1], i[n-2], ... i[1], i[0])``.
  
      Parameters
      ----------
      axes : None, tuple of ints, or `n` ints
  
       * None or no argument: reverses the order of the axes.
  
       * tuple of ints: `i` in the `j`-th place in the tuple means `a`'s
         `i`-th axis becomes `a.transpose()`'s `j`-th axis.
  
       * `n` ints: same as an n-tuple of the same ints (this form is
         intended simply as a "convenience" alternative to the tuple form)
  
      Returns
      -------
      out : ndarray
          View of `a`, with axes suitably permuted.
  
      See Also
      --------
      ndarray.T : Array property returning the array transposed.
  
      Examples
      --------
      >>> a = np.array([[1, 2], [3, 4]])
      >>> a
      array([[1, 2],
             [3, 4]])
      >>> a.transpose()
      array([[1, 3],
             [2, 4]])
      >>> a.transpose((1, 0))
      array([[1, 3],
             [2, 4]])
      >>> a.transpose(1, 0)
      array([[1, 3],
             [2, 4]])
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('var',
      """
      a.var(axis=None, dtype=None, out=None, ddof=0, keepdims=False)
  
      Returns the variance of the array elements, along given axis.
  
      Refer to `numpy.var` for full documentation.
  
      See Also
      --------
      numpy.var : equivalent function
  
      """))
  
  
  add_newdoc('numpy.core.multiarray', 'ndarray', ('view',
      """
      a.view(dtype=None, type=None)
  
      New view of array with the same data.
  
      Parameters
      ----------
      dtype : data-type or ndarray sub-class, optional
          Data-type descriptor of the returned view, e.g., float32 or int16. The
          default, None, results in the view having the same data-type as `a`.
          This argument can also be specified as an ndarray sub-class, which
          then specifies the type of the returned object (this is equivalent to
          setting the ``type`` parameter).
      type : Python type, optional
          Type of the returned view, e.g., ndarray or matrix.  Again, the
          default None results in type preservation.
  
      Notes
      -----
      ``a.view()`` is used two different ways:
  
      ``a.view(some_dtype)`` or ``a.view(dtype=some_dtype)`` constructs a view
      of the array's memory with a different data-type.  This can cause a
      reinterpretation of the bytes of memory.
  
      ``a.view(ndarray_subclass)`` or ``a.view(type=ndarray_subclass)`` just
      returns an instance of `ndarray_subclass` that looks at the same array
      (same shape, dtype, etc.)  This does not cause a reinterpretation of the
      memory.
  
      For ``a.view(some_dtype)``, if ``some_dtype`` has a different number of
      bytes per entry than the previous dtype (for example, converting a
      regular array to a structured array), then the behavior of the view
      cannot be predicted just from the superficial appearance of ``a`` (shown
      by ``print(a)``). It also depends on exactly how ``a`` is stored in
      memory. Therefore if ``a`` is C-ordered versus fortran-ordered, versus
      defined as a slice or transpose, etc., the view may give different
      results.
  
  
      Examples
      --------
      >>> x = np.array([(1, 2)], dtype=[('a', np.int8), ('b', np.int8)])
  
      Viewing array data using a different type and dtype:
  
      >>> y = x.view(dtype=np.int16, type=np.matrix)
      >>> y
      matrix([[513]], dtype=int16)
      >>> print(type(y))
      <class 'numpy.matrixlib.defmatrix.matrix'>
  
      Creating a view on a structured array so it can be used in calculations
  
      >>> x = np.array([(1, 2),(3,4)], dtype=[('a', np.int8), ('b', np.int8)])
      >>> xv = x.view(dtype=np.int8).reshape(-1,2)
      >>> xv
      array([[1, 2],
             [3, 4]], dtype=int8)
      >>> xv.mean(0)
      array([ 2.,  3.])
  
      Making changes to the view changes the underlying array
  
      >>> xv[0,1] = 20
      >>> print(x)
      [(1, 20) (3, 4)]
  
      Using a view to convert an array to a recarray:
  
      >>> z = x.view(np.recarray)
      >>> z.a
      array([1], dtype=int8)
  
      Views share data:
  
      >>> x[0] = (9, 10)
      >>> z[0]
      (9, 10)
  
      Views that change the dtype size (bytes per entry) should normally be
      avoided on arrays defined by slices, transposes, fortran-ordering, etc.:
  
      >>> x = np.array([[1,2,3],[4,5,6]], dtype=np.int16)
      >>> y = x[:, 0:2]
      >>> y
      array([[1, 2],
             [4, 5]], dtype=int16)
      >>> y.view(dtype=[('width', np.int16), ('length', np.int16)])
      Traceback (most recent call last):
        File "<stdin>", line 1, in <module>
      ValueError: new type not compatible with array.
      >>> z = y.copy()
      >>> z.view(dtype=[('width', np.int16), ('length', np.int16)])
      array([[(1, 2)],
             [(4, 5)]], dtype=[('width', '<i2'), ('length', '<i2')])
      """))
  
  
  ##############################################################################
  #
  # umath functions
  #
  ##############################################################################
  
  add_newdoc('numpy.core.umath', 'frompyfunc',
      """
      frompyfunc(func, nin, nout)
  
      Takes an arbitrary Python function and returns a NumPy ufunc.
  
      Can be used, for example, to add broadcasting to a built-in Python
      function (see Examples section).
  
      Parameters
      ----------
      func : Python function object
          An arbitrary Python function.
      nin : int
          The number of input arguments.
      nout : int
          The number of objects returned by `func`.
  
      Returns
      -------
      out : ufunc
          Returns a NumPy universal function (``ufunc``) object.
  
      See Also
      --------
      vectorize : evaluates pyfunc over input arrays using broadcasting rules of numpy
  
      Notes
      -----
      The returned ufunc always returns PyObject arrays.
  
      Examples
      --------
      Use frompyfunc to add broadcasting to the Python function ``oct``:
  
      >>> oct_array = np.frompyfunc(oct, 1, 1)
      >>> oct_array(np.array((10, 30, 100)))
      array([012, 036, 0144], dtype=object)
      >>> np.array((oct(10), oct(30), oct(100))) # for comparison
      array(['012', '036', '0144'],
            dtype='|S4')
  
      """)
  
  add_newdoc('numpy.core.umath', 'geterrobj',
      """
      geterrobj()
  
      Return the current object that defines floating-point error handling.
  
      The error object contains all information that defines the error handling
      behavior in NumPy. `geterrobj` is used internally by the other
      functions that get and set error handling behavior (`geterr`, `seterr`,
      `geterrcall`, `seterrcall`).
  
      Returns
      -------
      errobj : list
          The error object, a list containing three elements:
          [internal numpy buffer size, error mask, error callback function].
  
          The error mask is a single integer that holds the treatment information
          on all four floating point errors. The information for each error type
          is contained in three bits of the integer. If we print it in base 8, we
          can see what treatment is set for "invalid", "under", "over", and
          "divide" (in that order). The printed string can be interpreted with
  
          * 0 : 'ignore'
          * 1 : 'warn'
          * 2 : 'raise'
          * 3 : 'call'
          * 4 : 'print'
          * 5 : 'log'
  
      See Also
      --------
      seterrobj, seterr, geterr, seterrcall, geterrcall
      getbufsize, setbufsize
  
      Notes
      -----
      For complete documentation of the types of floating-point exceptions and
      treatment options, see `seterr`.
  
      Examples
      --------
      >>> np.geterrobj()  # first get the defaults
      [10000, 0, None]
  
      >>> def err_handler(type, flag):
      ...     print("Floating point error (%s), with flag %s" % (type, flag))
      ...
      >>> old_bufsize = np.setbufsize(20000)
      >>> old_err = np.seterr(divide='raise')
      >>> old_handler = np.seterrcall(err_handler)
      >>> np.geterrobj()
      [20000, 2, <function err_handler at 0x91dcaac>]
  
      >>> old_err = np.seterr(all='ignore')
      >>> np.base_repr(np.geterrobj()[1], 8)
      '0'
      >>> old_err = np.seterr(divide='warn', over='log', under='call',
                              invalid='print')
      >>> np.base_repr(np.geterrobj()[1], 8)
      '4351'
  
      """)
  
  add_newdoc('numpy.core.umath', 'seterrobj',
      """
      seterrobj(errobj)
  
      Set the object that defines floating-point error handling.
  
      The error object contains all information that defines the error handling
      behavior in NumPy. `seterrobj` is used internally by the other
      functions that set error handling behavior (`seterr`, `seterrcall`).
  
      Parameters
      ----------
      errobj : list
          The error object, a list containing three elements:
          [internal numpy buffer size, error mask, error callback function].
  
          The error mask is a single integer that holds the treatment information
          on all four floating point errors. The information for each error type
          is contained in three bits of the integer. If we print it in base 8, we
          can see what treatment is set for "invalid", "under", "over", and
          "divide" (in that order). The printed string can be interpreted with
  
          * 0 : 'ignore'
          * 1 : 'warn'
          * 2 : 'raise'
          * 3 : 'call'
          * 4 : 'print'
          * 5 : 'log'
  
      See Also
      --------
      geterrobj, seterr, geterr, seterrcall, geterrcall
      getbufsize, setbufsize
  
      Notes
      -----
      For complete documentation of the types of floating-point exceptions and
      treatment options, see `seterr`.
  
      Examples
      --------
      >>> old_errobj = np.geterrobj()  # first get the defaults
      >>> old_errobj
      [10000, 0, None]
  
      >>> def err_handler(type, flag):
      ...     print("Floating point error (%s), with flag %s" % (type, flag))
      ...
      >>> new_errobj = [20000, 12, err_handler]
      >>> np.seterrobj(new_errobj)
      >>> np.base_repr(12, 8)  # int for divide=4 ('print') and over=1 ('warn')
      '14'
      >>> np.geterr()
      {'over': 'warn', 'divide': 'print', 'invalid': 'ignore', 'under': 'ignore'}
      >>> np.geterrcall() is err_handler
      True
  
      """)
  
  
  ##############################################################################
  #
  # compiled_base functions
  #
  ##############################################################################
  
  add_newdoc('numpy.core.multiarray', 'add_docstring',
      """
      add_docstring(obj, docstring)
  
      Add a docstring to a built-in obj if possible.
      If the obj already has a docstring raise a RuntimeError
      If this routine does not know how to add a docstring to the object
      raise a TypeError
      """)
  
  add_newdoc('numpy.core.umath', '_add_newdoc_ufunc',
      """
      add_ufunc_docstring(ufunc, new_docstring)
  
      Replace the docstring for a ufunc with new_docstring.
      This method will only work if the current docstring for
      the ufunc is NULL. (At the C level, i.e. when ufunc->doc is NULL.)
  
      Parameters
      ----------
      ufunc : numpy.ufunc
          A ufunc whose current doc is NULL.
      new_docstring : string
          The new docstring for the ufunc.
  
      Notes
      -----
      This method allocates memory for new_docstring on
      the heap. Technically this creates a mempory leak, since this
      memory will not be reclaimed until the end of the program
      even if the ufunc itself is removed. However this will only
      be a problem if the user is repeatedly creating ufuncs with
      no documentation, adding documentation via add_newdoc_ufunc,
      and then throwing away the ufunc.
      """)
  
  add_newdoc('numpy.core.multiarray', 'packbits',
      """
      packbits(myarray, axis=None)
  
      Packs the elements of a binary-valued array into bits in a uint8 array.
  
      The result is padded to full bytes by inserting zero bits at the end.
  
      Parameters
      ----------
      myarray : array_like
          An array of integers or booleans whose elements should be packed to
          bits.
      axis : int, optional
          The dimension over which bit-packing is done.
          ``None`` implies packing the flattened array.
  
      Returns
      -------
      packed : ndarray
          Array of type uint8 whose elements represent bits corresponding to the
          logical (0 or nonzero) value of the input elements. The shape of
          `packed` has the same number of dimensions as the input (unless `axis`
          is None, in which case the output is 1-D).
  
      See Also
      --------
      unpackbits: Unpacks elements of a uint8 array into a binary-valued output
                  array.
  
      Examples
      --------
      >>> a = np.array([[[1,0,1],
      ...                [0,1,0]],
      ...               [[1,1,0],
      ...                [0,0,1]]])
      >>> b = np.packbits(a, axis=-1)
      >>> b
      array([[[160],[64]],[[192],[32]]], dtype=uint8)
  
      Note that in binary 160 = 1010 0000, 64 = 0100 0000, 192 = 1100 0000,
      and 32 = 0010 0000.
  
      """)
  
  add_newdoc('numpy.core.multiarray', 'unpackbits',
      """
      unpackbits(myarray, axis=None)
  
      Unpacks elements of a uint8 array into a binary-valued output array.
  
      Each element of `myarray` represents a bit-field that should be unpacked
      into a binary-valued output array. The shape of the output array is either
      1-D (if `axis` is None) or the same shape as the input array with unpacking
      done along the axis specified.
  
      Parameters
      ----------
      myarray : ndarray, uint8 type
         Input array.
      axis : int, optional
          The dimension over which bit-unpacking is done.
          ``None`` implies unpacking the flattened array.
  
      Returns
      -------
      unpacked : ndarray, uint8 type
         The elements are binary-valued (0 or 1).
  
      See Also
      --------
      packbits : Packs the elements of a binary-valued array into bits in a uint8
                 array.
  
      Examples
      --------
      >>> a = np.array([[2], [7], [23]], dtype=np.uint8)
      >>> a
      array([[ 2],
             [ 7],
             [23]], dtype=uint8)
      >>> b = np.unpackbits(a, axis=1)
      >>> b
      array([[0, 0, 0, 0, 0, 0, 1, 0],
             [0, 0, 0, 0, 0, 1, 1, 1],
             [0, 0, 0, 1, 0, 1, 1, 1]], dtype=uint8)
  
      """)
  
  add_newdoc('numpy.core._multiarray_tests', 'format_float_OSprintf_g',
      """
      format_float_OSprintf_g(val, precision)
  
      Print a floating point scalar using the system's printf function,
      equivalent to:
  
          printf("%.*g", precision, val);
  
      for half/float/double, or replacing 'g' by 'Lg' for longdouble. This
      method is designed to help cross-validate the format_float_* methods.
  
      Parameters
      ----------
      val : python float or numpy floating scalar
          Value to format.
  
      precision : non-negative integer, optional
          Precision given to printf.
  
      Returns
      -------
      rep : string
          The string representation of the floating point value
  
      See Also
      --------
      format_float_scientific
      format_float_positional
      """)
  
  
  ##############################################################################
  #
  # Documentation for ufunc attributes and methods
  #
  ##############################################################################
  
  
  ##############################################################################
  #
  # ufunc object
  #
  ##############################################################################
  
  add_newdoc('numpy.core', 'ufunc',
      """
      Functions that operate element by element on whole arrays.
  
      To see the documentation for a specific ufunc, use `info`.  For
      example, ``np.info(np.sin)``.  Because ufuncs are written in C
      (for speed) and linked into Python with NumPy's ufunc facility,
      Python's help() function finds this page whenever help() is called
      on a ufunc.
  
      A detailed explanation of ufuncs can be found in the docs for :ref:`ufuncs`.
  
      Calling ufuncs:
      ===============
  
      op(*x[, out], where=True, **kwargs)
      Apply `op` to the arguments `*x` elementwise, broadcasting the arguments.
  
      The broadcasting rules are:
  
      * Dimensions of length 1 may be prepended to either array.
      * Arrays may be repeated along dimensions of length 1.
  
      Parameters
      ----------
      *x : array_like
          Input arrays.
      out : ndarray, None, or tuple of ndarray and None, optional
          Alternate array object(s) in which to put the result; if provided, it
          must have a shape that the inputs broadcast to. A tuple of arrays
          (possible only as a keyword argument) must have length equal to the
          number of outputs; use `None` for uninitialized outputs to be
          allocated by the ufunc.
      where : array_like, optional
          Values of True indicate to calculate the ufunc at that position, values
          of False indicate to leave the value in the output alone.  Note that if
          an uninitialized return array is created via the default ``out=None``,
          then the elements where the values are False will remain uninitialized.
      **kwargs
          For other keyword-only arguments, see the :ref:`ufunc docs <ufuncs.kwargs>`.
  
      Returns
      -------
      r : ndarray or tuple of ndarray
          `r` will have the shape that the arrays in `x` broadcast to; if `out` is
          provided, it will be returned. If not, `r` will be allocated and
          may contain uninitialized values. If the function has more than one
          output, then the result will be a tuple of arrays.
  
      """)
  
  
  ##############################################################################
  #
  # ufunc attributes
  #
  ##############################################################################
  
  add_newdoc('numpy.core', 'ufunc', ('identity',
      """
      The identity value.
  
      Data attribute containing the identity element for the ufunc, if it has one.
      If it does not, the attribute value is None.
  
      Examples
      --------
      >>> np.add.identity
      0
      >>> np.multiply.identity
      1
      >>> np.power.identity
      1
      >>> print(np.exp.identity)
      None
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('nargs',
      """
      The number of arguments.
  
      Data attribute containing the number of arguments the ufunc takes, including
      optional ones.
  
      Notes
      -----
      Typically this value will be one more than what you might expect because all
      ufuncs take  the optional "out" argument.
  
      Examples
      --------
      >>> np.add.nargs
      3
      >>> np.multiply.nargs
      3
      >>> np.power.nargs
      3
      >>> np.exp.nargs
      2
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('nin',
      """
      The number of inputs.
  
      Data attribute containing the number of arguments the ufunc treats as input.
  
      Examples
      --------
      >>> np.add.nin
      2
      >>> np.multiply.nin
      2
      >>> np.power.nin
      2
      >>> np.exp.nin
      1
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('nout',
      """
      The number of outputs.
  
      Data attribute containing the number of arguments the ufunc treats as output.
  
      Notes
      -----
      Since all ufuncs can take output arguments, this will always be (at least) 1.
  
      Examples
      --------
      >>> np.add.nout
      1
      >>> np.multiply.nout
      1
      >>> np.power.nout
      1
      >>> np.exp.nout
      1
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('ntypes',
      """
      The number of types.
  
      The number of numerical NumPy types - of which there are 18 total - on which
      the ufunc can operate.
  
      See Also
      --------
      numpy.ufunc.types
  
      Examples
      --------
      >>> np.add.ntypes
      18
      >>> np.multiply.ntypes
      18
      >>> np.power.ntypes
      17
      >>> np.exp.ntypes
      7
      >>> np.remainder.ntypes
      14
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('types',
      """
      Returns a list with types grouped input->output.
  
      Data attribute listing the data-type "Domain-Range" groupings the ufunc can
      deliver. The data-types are given using the character codes.
  
      See Also
      --------
      numpy.ufunc.ntypes
  
      Examples
      --------
      >>> np.add.types
      ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
      'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
      'GG->G', 'OO->O']
  
      >>> np.multiply.types
      ['??->?', 'bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l',
      'LL->L', 'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D',
      'GG->G', 'OO->O']
  
      >>> np.power.types
      ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
      'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G',
      'OO->O']
  
      >>> np.exp.types
      ['f->f', 'd->d', 'g->g', 'F->F', 'D->D', 'G->G', 'O->O']
  
      >>> np.remainder.types
      ['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L',
      'qq->q', 'QQ->Q', 'ff->f', 'dd->d', 'gg->g', 'OO->O']
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('signature',
      """
      Definition of the core elements a generalized ufunc operates on.
  
      The signature determines how the dimensions of each input/output array
      are split into core and loop dimensions:
  
      1. Each dimension in the signature is matched to a dimension of the
         corresponding passed-in array, starting from the end of the shape tuple.
      2. Core dimensions assigned to the same label in the signature must have
         exactly matching sizes, no broadcasting is performed.
      3. The core dimensions are removed from all inputs and the remaining
         dimensions are broadcast together, defining the loop dimensions.
  
      Notes
      -----
      Generalized ufuncs are used internally in many linalg functions, and in
      the testing suite; the examples below are taken from these.
      For ufuncs that operate on scalars, the signature is `None`, which is
      equivalent to '()' for every argument.
  
      Examples
      --------
      >>> np.core.umath_tests.matrix_multiply.signature
      '(m,n),(n,p)->(m,p)'
      >>> np.linalg._umath_linalg.det.signature
      '(m,m)->()'
      >>> np.add.signature is None
      True  # equivalent to '(),()->()'
      """))
  
  ##############################################################################
  #
  # ufunc methods
  #
  ##############################################################################
  
  add_newdoc('numpy.core', 'ufunc', ('reduce',
      """
      reduce(a, axis=0, dtype=None, out=None, keepdims=False, initial)
  
      Reduces `a`'s dimension by one, by applying ufunc along one axis.
  
      Let :math:`a.shape = (N_0, ..., N_i, ..., N_{M-1})`.  Then
      :math:`ufunc.reduce(a, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]` =
      the result of iterating `j` over :math:`range(N_i)`, cumulatively applying
      ufunc to each :math:`a[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]`.
      For a one-dimensional array, reduce produces results equivalent to:
      ::
  
       r = op.identity # op = ufunc
       for i in range(len(A)):
         r = op(r, A[i])
       return r
  
      For example, add.reduce() is equivalent to sum().
  
      Parameters
      ----------
      a : array_like
          The array to act on.
      axis : None or int or tuple of ints, optional
          Axis or axes along which a reduction is performed.
          The default (`axis` = 0) is perform a reduction over the first
          dimension of the input array. `axis` may be negative, in
          which case it counts from the last to the first axis.
  
          .. versionadded:: 1.7.0
  
          If this is `None`, a reduction is performed over all the axes.
          If this is a tuple of ints, a reduction is performed on multiple
          axes, instead of a single axis or all the axes as before.
  
          For operations which are either not commutative or not associative,
          doing a reduction over multiple axes is not well-defined. The
          ufuncs do not currently raise an exception in this case, but will
          likely do so in the future.
      dtype : data-type code, optional
          The type used to represent the intermediate results. Defaults
          to the data-type of the output array if this is provided, or
          the data-type of the input array if no output array is provided.
      out : ndarray, None, or tuple of ndarray and None, optional
          A location into which the result is stored. If not provided or `None`,
          a freshly-allocated array is returned. For consistency with
          :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a
          1-element tuple.
  
          .. versionchanged:: 1.13.0
             Tuples are allowed for keyword argument.
      keepdims : bool, optional
          If this is set to True, the axes which are reduced are left
          in the result as dimensions with size one. With this option,
          the result will broadcast correctly against the original `arr`.
  
          .. versionadded:: 1.7.0
      initial : scalar, optional
          The value with which to start the reduction.
          If the ufunc has no identity or the dtype is object, this defaults
          to None - otherwise it defaults to ufunc.identity.
          If ``None`` is given, the first element of the reduction is used,
          and an error is thrown if the reduction is empty.
  
          .. versionadded:: 1.15.0
  
      Returns
      -------
      r : ndarray
          The reduced array. If `out` was supplied, `r` is a reference to it.
  
      Examples
      --------
      >>> np.multiply.reduce([2,3,5])
      30
  
      A multi-dimensional array example:
  
      >>> X = np.arange(8).reshape((2,2,2))
      >>> X
      array([[[0, 1],
              [2, 3]],
             [[4, 5],
              [6, 7]]])
      >>> np.add.reduce(X, 0)
      array([[ 4,  6],
             [ 8, 10]])
      >>> np.add.reduce(X) # confirm: default axis value is 0
      array([[ 4,  6],
             [ 8, 10]])
      >>> np.add.reduce(X, 1)
      array([[ 2,  4],
             [10, 12]])
      >>> np.add.reduce(X, 2)
      array([[ 1,  5],
             [ 9, 13]])
  
      You can use the ``initial`` keyword argument to initialize the reduction with a
      different value.
  
      >>> np.add.reduce([10], initial=5)
      15
      >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initializer=10)
      array([14., 14.])
  
      Allows reductions of empty arrays where they would normally fail, i.e.
      for ufuncs without an identity.
  
      >>> np.minimum.reduce([], initial=np.inf)
      inf
      >>> np.minimum.reduce([])
      Traceback (most recent call last):
          ...
      ValueError: zero-size array to reduction operation minimum which has no identity
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('accumulate',
      """
      accumulate(array, axis=0, dtype=None, out=None)
  
      Accumulate the result of applying the operator to all elements.
  
      For a one-dimensional array, accumulate produces results equivalent to::
  
        r = np.empty(len(A))
        t = op.identity        # op = the ufunc being applied to A's  elements
        for i in range(len(A)):
            t = op(t, A[i])
            r[i] = t
        return r
  
      For example, add.accumulate() is equivalent to np.cumsum().
  
      For a multi-dimensional array, accumulate is applied along only one
      axis (axis zero by default; see Examples below) so repeated use is
      necessary if one wants to accumulate over multiple axes.
  
      Parameters
      ----------
      array : array_like
          The array to act on.
      axis : int, optional
          The axis along which to apply the accumulation; default is zero.
      dtype : data-type code, optional
          The data-type used to represent the intermediate results. Defaults
          to the data-type of the output array if such is provided, or the
          the data-type of the input array if no output array is provided.
      out : ndarray, None, or tuple of ndarray and None, optional
          A location into which the result is stored. If not provided or `None`,
          a freshly-allocated array is returned. For consistency with
          :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a
          1-element tuple.
  
          .. versionchanged:: 1.13.0
             Tuples are allowed for keyword argument.
  
      Returns
      -------
      r : ndarray
          The accumulated values. If `out` was supplied, `r` is a reference to
          `out`.
  
      Examples
      --------
      1-D array examples:
  
      >>> np.add.accumulate([2, 3, 5])
      array([ 2,  5, 10])
      >>> np.multiply.accumulate([2, 3, 5])
      array([ 2,  6, 30])
  
      2-D array examples:
  
      >>> I = np.eye(2)
      >>> I
      array([[ 1.,  0.],
             [ 0.,  1.]])
  
      Accumulate along axis 0 (rows), down columns:
  
      >>> np.add.accumulate(I, 0)
      array([[ 1.,  0.],
             [ 1.,  1.]])
      >>> np.add.accumulate(I) # no axis specified = axis zero
      array([[ 1.,  0.],
             [ 1.,  1.]])
  
      Accumulate along axis 1 (columns), through rows:
  
      >>> np.add.accumulate(I, 1)
      array([[ 1.,  1.],
             [ 0.,  1.]])
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('reduceat',
      """
      reduceat(a, indices, axis=0, dtype=None, out=None)
  
      Performs a (local) reduce with specified slices over a single axis.
  
      For i in ``range(len(indices))``, `reduceat` computes
      ``ufunc.reduce(a[indices[i]:indices[i+1]])``, which becomes the i-th
      generalized "row" parallel to `axis` in the final result (i.e., in a
      2-D array, for example, if `axis = 0`, it becomes the i-th row, but if
      `axis = 1`, it becomes the i-th column).  There are three exceptions to this:
  
      * when ``i = len(indices) - 1`` (so for the last index),
        ``indices[i+1] = a.shape[axis]``.
      * if ``indices[i] >= indices[i + 1]``, the i-th generalized "row" is
        simply ``a[indices[i]]``.
      * if ``indices[i] >= len(a)`` or ``indices[i] < 0``, an error is raised.
  
      The shape of the output depends on the size of `indices`, and may be
      larger than `a` (this happens if ``len(indices) > a.shape[axis]``).
  
      Parameters
      ----------
      a : array_like
          The array to act on.
      indices : array_like
          Paired indices, comma separated (not colon), specifying slices to
          reduce.
      axis : int, optional
          The axis along which to apply the reduceat.
      dtype : data-type code, optional
          The type used to represent the intermediate results. Defaults
          to the data type of the output array if this is provided, or
          the data type of the input array if no output array is provided.
      out : ndarray, None, or tuple of ndarray and None, optional
          A location into which the result is stored. If not provided or `None`,
          a freshly-allocated array is returned. For consistency with
          :ref:`ufunc.__call__`, if given as a keyword, this may be wrapped in a
          1-element tuple.
  
          .. versionchanged:: 1.13.0
             Tuples are allowed for keyword argument.
  
      Returns
      -------
      r : ndarray
          The reduced values. If `out` was supplied, `r` is a reference to
          `out`.
  
      Notes
      -----
      A descriptive example:
  
      If `a` is 1-D, the function `ufunc.accumulate(a)` is the same as
      ``ufunc.reduceat(a, indices)[::2]`` where `indices` is
      ``range(len(array) - 1)`` with a zero placed
      in every other element:
      ``indices = zeros(2 * len(a) - 1)``, ``indices[1::2] = range(1, len(a))``.
  
      Don't be fooled by this attribute's name: `reduceat(a)` is not
      necessarily smaller than `a`.
  
      Examples
      --------
      To take the running sum of four successive values:
  
      >>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2]
      array([ 6, 10, 14, 18])
  
      A 2-D example:
  
      >>> x = np.linspace(0, 15, 16).reshape(4,4)
      >>> x
      array([[  0.,   1.,   2.,   3.],
             [  4.,   5.,   6.,   7.],
             [  8.,   9.,  10.,  11.],
             [ 12.,  13.,  14.,  15.]])
  
      ::
  
       # reduce such that the result has the following five rows:
       # [row1 + row2 + row3]
       # [row4]
       # [row2]
       # [row3]
       # [row1 + row2 + row3 + row4]
  
      >>> np.add.reduceat(x, [0, 3, 1, 2, 0])
      array([[ 12.,  15.,  18.,  21.],
             [ 12.,  13.,  14.,  15.],
             [  4.,   5.,   6.,   7.],
             [  8.,   9.,  10.,  11.],
             [ 24.,  28.,  32.,  36.]])
  
      ::
  
       # reduce such that result has the following two columns:
       # [col1 * col2 * col3, col4]
  
      >>> np.multiply.reduceat(x, [0, 3], 1)
      array([[    0.,     3.],
             [  120.,     7.],
             [  720.,    11.],
             [ 2184.,    15.]])
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('outer',
      """
      outer(A, B, **kwargs)
  
      Apply the ufunc `op` to all pairs (a, b) with a in `A` and b in `B`.
  
      Let ``M = A.ndim``, ``N = B.ndim``. Then the result, `C`, of
      ``op.outer(A, B)`` is an array of dimension M + N such that:
  
      .. math:: C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] =
         op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])
  
      For `A` and `B` one-dimensional, this is equivalent to::
  
        r = empty(len(A),len(B))
        for i in range(len(A)):
            for j in range(len(B)):
                r[i,j] = op(A[i], B[j]) # op = ufunc in question
  
      Parameters
      ----------
      A : array_like
          First array
      B : array_like
          Second array
      kwargs : any
          Arguments to pass on to the ufunc. Typically `dtype` or `out`.
  
      Returns
      -------
      r : ndarray
          Output array
  
      See Also
      --------
      numpy.outer
  
      Examples
      --------
      >>> np.multiply.outer([1, 2, 3], [4, 5, 6])
      array([[ 4,  5,  6],
             [ 8, 10, 12],
             [12, 15, 18]])
  
      A multi-dimensional example:
  
      >>> A = np.array([[1, 2, 3], [4, 5, 6]])
      >>> A.shape
      (2, 3)
      >>> B = np.array([[1, 2, 3, 4]])
      >>> B.shape
      (1, 4)
      >>> C = np.multiply.outer(A, B)
      >>> C.shape; C
      (2, 3, 1, 4)
      array([[[[ 1,  2,  3,  4]],
              [[ 2,  4,  6,  8]],
              [[ 3,  6,  9, 12]]],
             [[[ 4,  8, 12, 16]],
              [[ 5, 10, 15, 20]],
              [[ 6, 12, 18, 24]]]])
  
      """))
  
  add_newdoc('numpy.core', 'ufunc', ('at',
      """
      at(a, indices, b=None)
  
      Performs unbuffered in place operation on operand 'a' for elements
      specified by 'indices'. For addition ufunc, this method is equivalent to
      ``a[indices] += b``, except that results are accumulated for elements that
      are indexed more than once. For example, ``a[[0,0]] += 1`` will only
      increment the first element once because of buffering, whereas
      ``add.at(a, [0,0], 1)`` will increment the first element twice.
  
      .. versionadded:: 1.8.0
  
      Parameters
      ----------
      a : array_like
          The array to perform in place operation on.
      indices : array_like or tuple
          Array like index object or slice object for indexing into first
          operand. If first operand has multiple dimensions, indices can be a
          tuple of array like index objects or slice objects.
      b : array_like
          Second operand for ufuncs requiring two operands. Operand must be
          broadcastable over first operand after indexing or slicing.
  
      Examples
      --------
      Set items 0 and 1 to their negative values:
  
      >>> a = np.array([1, 2, 3, 4])
      >>> np.negative.at(a, [0, 1])
      >>> print(a)
      array([-1, -2, 3, 4])
  
      Increment items 0 and 1, and increment item 2 twice:
  
      >>> a = np.array([1, 2, 3, 4])
      >>> np.add.at(a, [0, 1, 2, 2], 1)
      >>> print(a)
      array([2, 3, 5, 4])
  
      Add items 0 and 1 in first array to second array,
      and store results in first array:
  
      >>> a = np.array([1, 2, 3, 4])
      >>> b = np.array([1, 2])
      >>> np.add.at(a, [0, 1], b)
      >>> print(a)
      array([2, 4, 3, 4])
  
      """))
  
  ##############################################################################
  #
  # Documentation for dtype attributes and methods
  #
  ##############################################################################
  
  ##############################################################################
  #
  # dtype object
  #
  ##############################################################################
  
  add_newdoc('numpy.core.multiarray', 'dtype',
      """
      dtype(obj, align=False, copy=False)
  
      Create a data type object.
  
      A numpy array is homogeneous, and contains elements described by a
      dtype object. A dtype object can be constructed from different
      combinations of fundamental numeric types.
  
      Parameters
      ----------
      obj
          Object to be converted to a data type object.
      align : bool, optional
          Add padding to the fields to match what a C compiler would output
          for a similar C-struct. Can be ``True`` only if `obj` is a dictionary
          or a comma-separated string. If a struct dtype is being created,
          this also sets a sticky alignment flag ``isalignedstruct``.
      copy : bool, optional
          Make a new copy of the data-type object. If ``False``, the result
          may just be a reference to a built-in data-type object.
  
      See also
      --------
      result_type
  
      Examples
      --------
      Using array-scalar type:
  
      >>> np.dtype(np.int16)
      dtype('int16')
  
      Structured type, one field name 'f1', containing int16:
  
      >>> np.dtype([('f1', np.int16)])
      dtype([('f1', '<i2')])
  
      Structured type, one field named 'f1', in itself containing a structured
      type with one field:
  
      >>> np.dtype([('f1', [('f1', np.int16)])])
      dtype([('f1', [('f1', '<i2')])])
  
      Structured type, two fields: the first field contains an unsigned int, the
      second an int32:
  
      >>> np.dtype([('f1', np.uint), ('f2', np.int32)])
      dtype([('f1', '<u4'), ('f2', '<i4')])
  
      Using array-protocol type strings:
  
      >>> np.dtype([('a','f8'),('b','S10')])
      dtype([('a', '<f8'), ('b', '|S10')])
  
      Using comma-separated field formats.  The shape is (2,3):
  
      >>> np.dtype("i4, (2,3)f8")
      dtype([('f0', '<i4'), ('f1', '<f8', (2, 3))])
  
      Using tuples.  ``int`` is a fixed type, 3 the field's shape.  ``void``
      is a flexible type, here of size 10:
  
      >>> np.dtype([('hello',(int,3)),('world',np.void,10)])
      dtype([('hello', '<i4', 3), ('world', '|V10')])
  
      Subdivide ``int16`` into 2 ``int8``'s, called x and y.  0 and 1 are
      the offsets in bytes:
  
      >>> np.dtype((np.int16, {'x':(np.int8,0), 'y':(np.int8,1)}))
      dtype(('<i2', [('x', '|i1'), ('y', '|i1')]))
  
      Using dictionaries.  Two fields named 'gender' and 'age':
  
      >>> np.dtype({'names':['gender','age'], 'formats':['S1',np.uint8]})
      dtype([('gender', '|S1'), ('age', '|u1')])
  
      Offsets in bytes, here 0 and 25:
  
      >>> np.dtype({'surname':('S25',0),'age':(np.uint8,25)})
      dtype([('surname', '|S25'), ('age', '|u1')])
  
      """)
  
  ##############################################################################
  #
  # dtype attributes
  #
  ##############################################################################
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('alignment',
      """
      The required alignment (bytes) of this data-type according to the compiler.
  
      More information is available in the C-API section of the manual.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('byteorder',
      """
      A character indicating the byte-order of this data-type object.
  
      One of:
  
      ===  ==============
      '='  native
      '<'  little-endian
      '>'  big-endian
      '|'  not applicable
      ===  ==============
  
      All built-in data-type objects have byteorder either '=' or '|'.
  
      Examples
      --------
  
      >>> dt = np.dtype('i2')
      >>> dt.byteorder
      '='
      >>> # endian is not relevant for 8 bit numbers
      >>> np.dtype('i1').byteorder
      '|'
      >>> # or ASCII strings
      >>> np.dtype('S2').byteorder
      '|'
      >>> # Even if specific code is given, and it is native
      >>> # '=' is the byteorder
      >>> import sys
      >>> sys_is_le = sys.byteorder == 'little'
      >>> native_code = sys_is_le and '<' or '>'
      >>> swapped_code = sys_is_le and '>' or '<'
      >>> dt = np.dtype(native_code + 'i2')
      >>> dt.byteorder
      '='
      >>> # Swapped code shows up as itself
      >>> dt = np.dtype(swapped_code + 'i2')
      >>> dt.byteorder == swapped_code
      True
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('char',
      """A unique character code for each of the 21 different built-in types."""))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('descr',
      """
      `__array_interface__` description of the data-type.
  
      The format is that required by the 'descr' key in the
      `__array_interface__` attribute.
  
      Warning: This attribute exists specifically for `__array_interface__`,
      and is not a datatype description compatible with `np.dtype`.
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('fields',
      """
      Dictionary of named fields defined for this data type, or ``None``.
  
      The dictionary is indexed by keys that are the names of the fields.
      Each entry in the dictionary is a tuple fully describing the field::
  
        (dtype, offset[, title])
  
      Offset is limited to C int, which is signed and usually 32 bits.
      If present, the optional title can be any object (if it is a string
      or unicode then it will also be a key in the fields dictionary,
      otherwise it's meta-data). Notice also that the first two elements
      of the tuple can be passed directly as arguments to the ``ndarray.getfield``
      and ``ndarray.setfield`` methods.
  
      See Also
      --------
      ndarray.getfield, ndarray.setfield
  
      Examples
      --------
      >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
      >>> print(dt.fields)
      {'grades': (dtype(('float64',(2,))), 16), 'name': (dtype('|S16'), 0)}
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('flags',
      """
      Bit-flags describing how this data type is to be interpreted.
  
      Bit-masks are in `numpy.core.multiarray` as the constants
      `ITEM_HASOBJECT`, `LIST_PICKLE`, `ITEM_IS_POINTER`, `NEEDS_INIT`,
      `NEEDS_PYAPI`, `USE_GETITEM`, `USE_SETITEM`. A full explanation
      of these flags is in C-API documentation; they are largely useful
      for user-defined data-types.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('hasobject',
      """
      Boolean indicating whether this dtype contains any reference-counted
      objects in any fields or sub-dtypes.
  
      Recall that what is actually in the ndarray memory representing
      the Python object is the memory address of that object (a pointer).
      Special handling may be required, and this attribute is useful for
      distinguishing data types that may contain arbitrary Python objects
      and data-types that won't.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('isbuiltin',
      """
      Integer indicating how this dtype relates to the built-in dtypes.
  
      Read-only.
  
      =  ========================================================================
      0  if this is a structured array type, with fields
      1  if this is a dtype compiled into numpy (such as ints, floats etc)
      2  if the dtype is for a user-defined numpy type
         A user-defined type uses the numpy C-API machinery to extend
         numpy to handle a new array type. See
         :ref:`user.user-defined-data-types` in the NumPy manual.
      =  ========================================================================
  
      Examples
      --------
      >>> dt = np.dtype('i2')
      >>> dt.isbuiltin
      1
      >>> dt = np.dtype('f8')
      >>> dt.isbuiltin
      1
      >>> dt = np.dtype([('field1', 'f8')])
      >>> dt.isbuiltin
      0
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('isnative',
      """
      Boolean indicating whether the byte order of this dtype is native
      to the platform.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('isalignedstruct',
      """
      Boolean indicating whether the dtype is a struct which maintains
      field alignment. This flag is sticky, so when combining multiple
      structs together, it is preserved and produces new dtypes which
      are also aligned.
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('itemsize',
      """
      The element size of this data-type object.
  
      For 18 of the 21 types this number is fixed by the data-type.
      For the flexible data-types, this number can be anything.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('kind',
      """
      A character code (one of 'biufcmMOSUV') identifying the general kind of data.
  
      =  ======================
      b  boolean
      i  signed integer
      u  unsigned integer
      f  floating-point
      c  complex floating-point
      m  timedelta
      M  datetime
      O  object
      S  (byte-)string
      U  Unicode
      V  void
      =  ======================
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('name',
      """
      A bit-width name for this data-type.
  
      Un-sized flexible data-type objects do not have this attribute.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('names',
      """
      Ordered list of field names, or ``None`` if there are no fields.
  
      The names are ordered according to increasing byte offset. This can be
      used, for example, to walk through all of the named fields in offset order.
  
      Examples
      --------
      >>> dt = np.dtype([('name', np.str_, 16), ('grades', np.float64, (2,))])
      >>> dt.names
      ('name', 'grades')
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('num',
      """
      A unique number for each of the 21 different built-in types.
  
      These are roughly ordered from least-to-most precision.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('shape',
      """
      Shape tuple of the sub-array if this data type describes a sub-array,
      and ``()`` otherwise.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('ndim',
      """
      Number of dimensions of the sub-array if this data type describes a
      sub-array, and ``0`` otherwise.
  
      .. versionadded:: 1.13.0
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('str',
      """The array-protocol typestring of this data-type object."""))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('subdtype',
      """
      Tuple ``(item_dtype, shape)`` if this `dtype` describes a sub-array, and
      None otherwise.
  
      The *shape* is the fixed shape of the sub-array described by this
      data type, and *item_dtype* the data type of the array.
  
      If a field whose dtype object has this attribute is retrieved,
      then the extra dimensions implied by *shape* are tacked on to
      the end of the retrieved array.
  
      """))
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('type',
      """The type object used to instantiate a scalar of this data-type."""))
  
  ##############################################################################
  #
  # dtype methods
  #
  ##############################################################################
  
  add_newdoc('numpy.core.multiarray', 'dtype', ('newbyteorder',
      """
      newbyteorder(new_order='S')
  
      Return a new dtype with a different byte order.
  
      Changes are also made in all fields and sub-arrays of the data type.
  
      Parameters
      ----------
      new_order : string, optional
          Byte order to force; a value from the byte order specifications
          below.  The default value ('S') results in swapping the current
          byte order.  `new_order` codes can be any of:
  
          * 'S' - swap dtype from current to opposite endian
          * {'<', 'L'} - little endian
          * {'>', 'B'} - big endian
          * {'=', 'N'} - native order
          * {'|', 'I'} - ignore (no change to byte order)
  
          The code does a case-insensitive check on the first letter of
          `new_order` for these alternatives.  For example, any of '>'
          or 'B' or 'b' or 'brian' are valid to specify big-endian.
  
      Returns
      -------
      new_dtype : dtype
          New dtype object with the given change to the byte order.
  
      Notes
      -----
      Changes are also made in all fields and sub-arrays of the data type.
  
      Examples
      --------
      >>> import sys
      >>> sys_is_le = sys.byteorder == 'little'
      >>> native_code = sys_is_le and '<' or '>'
      >>> swapped_code = sys_is_le and '>' or '<'
      >>> native_dt = np.dtype(native_code+'i2')
      >>> swapped_dt = np.dtype(swapped_code+'i2')
      >>> native_dt.newbyteorder('S') == swapped_dt
      True
      >>> native_dt.newbyteorder() == swapped_dt
      True
      >>> native_dt == swapped_dt.newbyteorder('S')
      True
      >>> native_dt == swapped_dt.newbyteorder('=')
      True
      >>> native_dt == swapped_dt.newbyteorder('N')
      True
      >>> native_dt == native_dt.newbyteorder('|')
      True
      >>> np.dtype('<i2') == native_dt.newbyteorder('<')
      True
      >>> np.dtype('<i2') == native_dt.newbyteorder('L')
      True
      >>> np.dtype('>i2') == native_dt.newbyteorder('>')
      True
      >>> np.dtype('>i2') == native_dt.newbyteorder('B')
      True
  
      """))
  
  
  ##############################################################################
  #
  # Datetime-related Methods
  #
  ##############################################################################
  
  add_newdoc('numpy.core.multiarray', 'busdaycalendar',
      """
      busdaycalendar(weekmask='1111100', holidays=None)
  
      A business day calendar object that efficiently stores information
      defining valid days for the busday family of functions.
  
      The default valid days are Monday through Friday ("business days").
      A busdaycalendar object can be specified with any set of weekly
      valid days, plus an optional "holiday" dates that always will be invalid.
  
      Once a busdaycalendar object is created, the weekmask and holidays
      cannot be modified.
  
      .. versionadded:: 1.7.0
  
      Parameters
      ----------
      weekmask : str or array_like of bool, optional
          A seven-element array indicating which of Monday through Sunday are
          valid days. May be specified as a length-seven list or array, like
          [1,1,1,1,1,0,0]; a length-seven string, like '1111100'; or a string
          like "Mon Tue Wed Thu Fri", made up of 3-character abbreviations for
          weekdays, optionally separated by white space. Valid abbreviations
          are: Mon Tue Wed Thu Fri Sat Sun
      holidays : array_like of datetime64[D], optional
          An array of dates to consider as invalid dates, no matter which
          weekday they fall upon.  Holiday dates may be specified in any
          order, and NaT (not-a-time) dates are ignored.  This list is
          saved in a normalized form that is suited for fast calculations
          of valid days.
  
      Returns
      -------
      out : busdaycalendar
          A business day calendar object containing the specified
          weekmask and holidays values.
  
      See Also
      --------
      is_busday : Returns a boolean array indicating valid days.
      busday_offset : Applies an offset counted in valid days.
      busday_count : Counts how many valid days are in a half-open date range.
  
      Attributes
      ----------
      Note: once a busdaycalendar object is created, you cannot modify the
      weekmask or holidays.  The attributes return copies of internal data.
      weekmask : (copy) seven-element array of bool
      holidays : (copy) sorted array of datetime64[D]
  
      Examples
      --------
      >>> # Some important days in July
      ... bdd = np.busdaycalendar(
      ...             holidays=['2011-07-01', '2011-07-04', '2011-07-17'])
      >>> # Default is Monday to Friday weekdays
      ... bdd.weekmask
      array([ True,  True,  True,  True,  True, False, False], dtype='bool')
      >>> # Any holidays already on the weekend are removed
      ... bdd.holidays
      array(['2011-07-01', '2011-07-04'], dtype='datetime64[D]')
      """)
  
  add_newdoc('numpy.core.multiarray', 'busdaycalendar', ('weekmask',
      """A copy of the seven-element boolean mask indicating valid days."""))
  
  add_newdoc('numpy.core.multiarray', 'busdaycalendar', ('holidays',
      """A copy of the holiday array indicating additional invalid days."""))
  
  add_newdoc('numpy.core.multiarray', 'normalize_axis_index',
      """
      normalize_axis_index(axis, ndim, msg_prefix=None)
  
      Normalizes an axis index, `axis`, such that is a valid positive index into
      the shape of array with `ndim` dimensions. Raises an AxisError with an
      appropriate message if this is not possible.
  
      Used internally by all axis-checking logic.
  
      .. versionadded:: 1.13.0
  
      Parameters
      ----------
      axis : int
          The un-normalized index of the axis. Can be negative
      ndim : int
          The number of dimensions of the array that `axis` should be normalized
          against
      msg_prefix : str
          A prefix to put before the message, typically the name of the argument
  
      Returns
      -------
      normalized_axis : int
          The normalized axis index, such that `0 <= normalized_axis < ndim`
  
      Raises
      ------
      AxisError
          If the axis index is invalid, when `-ndim <= axis < ndim` is false.
  
      Examples
      --------
      >>> normalize_axis_index(0, ndim=3)
      0
      >>> normalize_axis_index(1, ndim=3)
      1
      >>> normalize_axis_index(-1, ndim=3)
      2
  
      >>> normalize_axis_index(3, ndim=3)
      Traceback (most recent call last):
      ...
      AxisError: axis 3 is out of bounds for array of dimension 3
      >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg')
      Traceback (most recent call last):
      ...
      AxisError: axes_arg: axis -4 is out of bounds for array of dimension 3
      """)
  
  add_newdoc('numpy.core.multiarray', 'datetime_data',
      """
      datetime_data(dtype, /)
  
      Get information about the step size of a date or time type.
  
      The returned tuple can be passed as the second argument of `numpy.datetime64` and
      `numpy.timedelta64`.
  
      Parameters
      ----------
      dtype : dtype
          The dtype object, which must be a `datetime64` or `timedelta64` type.
  
      Returns
      -------
      unit : str
          The :ref:`datetime unit <arrays.dtypes.dateunits>` on which this dtype
          is based.
      count : int
          The number of base units in a step.
  
      Examples
      --------
      >>> dt_25s = np.dtype('timedelta64[25s]')
      >>> np.datetime_data(dt_25s)
      ('s', 25)
      >>> np.array(10, dt_25s).astype('timedelta64[s]')
      array(250, dtype='timedelta64[s]')
  
      The result can be used to construct a datetime that uses the same units
      as a timedelta
  
      >>> np.datetime64('2010', np.datetime_data(dt_25s))
      numpy.datetime64('2010-01-01T00:00:00', '25s')
      """)
  
  
  ##############################################################################
  #
  # Documentation for `generic` attributes and methods
  #
  ##############################################################################
  
  add_newdoc('numpy.core.numerictypes', 'generic',
      """
      Base class for numpy scalar types.
  
      Class from which most (all?) numpy scalar types are derived.  For
      consistency, exposes the same API as `ndarray`, despite many
      consequent attributes being either "get-only," or completely irrelevant.
      This is the class from which it is strongly suggested users should derive
      custom scalar types.
  
      """)
  
  # Attributes
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('T',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class so as to
      provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('base',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class so as to
      a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('data',
      """Pointer to start of data."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('dtype',
      """Get array data-descriptor."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('flags',
      """The integer value of flags."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('flat',
      """A 1-D view of the scalar."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('imag',
      """The imaginary part of the scalar."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('itemsize',
      """The length of one element in bytes."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('nbytes',
      """The length of the scalar in bytes."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('ndim',
      """The number of array dimensions."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('real',
      """The real part of the scalar."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('shape',
      """Tuple of array dimensions."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('size',
      """The number of elements in the gentype."""))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('strides',
      """Tuple of bytes steps in each dimension."""))
  
  # Methods
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('all',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('any',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('argmax',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('argmin',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('argsort',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('astype',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('byteswap',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class so as to
      provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('choose',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('clip',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('compress',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('conjugate',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('copy',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('cumprod',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('cumsum',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('diagonal',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('dump',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('dumps',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('fill',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('flatten',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('getfield',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('item',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('itemset',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('max',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('mean',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('min',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('newbyteorder',
      """
      newbyteorder(new_order='S')
  
      Return a new `dtype` with a different byte order.
  
      Changes are also made in all fields and sub-arrays of the data type.
  
      The `new_order` code can be any from the following:
  
      * 'S' - swap dtype from current to opposite endian
      * {'<', 'L'} - little endian
      * {'>', 'B'} - big endian
      * {'=', 'N'} - native order
      * {'|', 'I'} - ignore (no change to byte order)
  
      Parameters
      ----------
      new_order : str, optional
          Byte order to force; a value from the byte order specifications
          above.  The default value ('S') results in swapping the current
          byte order. The code does a case-insensitive check on the first
          letter of `new_order` for the alternatives above.  For example,
          any of 'B' or 'b' or 'biggish' are valid to specify big-endian.
  
  
      Returns
      -------
      new_dtype : dtype
          New `dtype` object with the given change to the byte order.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('nonzero',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('prod',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('ptp',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('put',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('ravel',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('repeat',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('reshape',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('resize',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('round',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('searchsorted',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('setfield',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('setflags',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class so as to
      provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('sort',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('squeeze',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('std',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('sum',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('swapaxes',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('take',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('tofile',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('tolist',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('tostring',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('trace',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('transpose',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('var',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  add_newdoc('numpy.core.numerictypes', 'generic', ('view',
      """
      Not implemented (virtual attribute)
  
      Class generic exists solely to derive numpy scalars from, and possesses,
      albeit unimplemented, all the attributes of the ndarray class
      so as to provide a uniform API.
  
      See Also
      --------
      The corresponding attribute of the derived class of interest.
  
      """))
  
  
  ##############################################################################
  #
  # Documentation for scalar type abstract base classes in type hierarchy
  #
  ##############################################################################
  
  
  add_newdoc('numpy.core.numerictypes', 'number',
      """
      Abstract base class of all numeric scalar types.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'integer',
      """
      Abstract base class of all integer scalar types.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'signedinteger',
      """
      Abstract base class of all signed integer scalar types.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'unsignedinteger',
      """
      Abstract base class of all unsigned integer scalar types.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'inexact',
      """
      Abstract base class of all numeric scalar types with a (potentially)
      inexact representation of the values in its range, such as
      floating-point numbers.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'floating',
      """
      Abstract base class of all floating-point scalar types.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'complexfloating',
      """
      Abstract base class of all complex number scalar types that are made up of
      floating-point numbers.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'flexible',
      """
      Abstract base class of all scalar types without predefined length.
      The actual size of these types depends on the specific `np.dtype`
      instantiation.
      
      """)
  
  add_newdoc('numpy.core.numerictypes', 'character',
      """
      Abstract base class of all character string scalar types.
      
      """)
  
  
  ##############################################################################
  #
  # Documentation for concrete scalar classes
  #
  ##############################################################################
  
  def numeric_type_aliases(aliases):
      def type_aliases_gen():
          for alias, doc in aliases:
              try:
                  alias_type = getattr(_numerictypes, alias)
              except AttributeError:
                  # The set of aliases that actually exist varies between platforms
                  pass
              else:
                  yield (alias_type, alias, doc)
      return list(type_aliases_gen())
  
  
  possible_aliases = numeric_type_aliases([
      ('int8', '8-bit signed integer (-128 to 127)'),
      ('int16', '16-bit signed integer (-32768 to 32767)'),
      ('int32', '32-bit signed integer (-2147483648 to 2147483647)'),
      ('int64', '64-bit signed integer (-9223372036854775808 to 9223372036854775807)'),
      ('intp', 'Signed integer large enough to fit pointer, compatible with C ``intptr_t``'),
      ('uint8', '8-bit unsigned integer (0 to 255)'),
      ('uint16', '16-bit unsigned integer (0 to 65535)'),
      ('uint32', '32-bit unsigned integer (0 to 4294967295)'),
      ('uint64', '64-bit unsigned integer (0 to 18446744073709551615)'),
      ('uintp', 'Unsigned integer large enough to fit pointer, compatible with C ``uintptr_t``'),
      ('float16', '16-bit-precision floating-point number type: sign bit, 5 bits exponent, 10 bits mantissa'),
      ('float32', '32-bit-precision floating-point number type: sign bit, 8 bits exponent, 23 bits mantissa'),
      ('float64', '64-bit precision floating-point number type: sign bit, 11 bits exponent, 52 bits mantissa'),
      ('float96', '96-bit extended-precision floating-point number type'),
      ('float128', '128-bit extended-precision floating-point number type'),
      ('complex64', 'Complex number type composed of 2 32-bit-precision floating-point numbers'),
      ('complex128', 'Complex number type composed of 2 64-bit-precision floating-point numbers'),
      ('complex192', 'Complex number type composed of 2 96-bit extended-precision floating-point numbers'),
      ('complex256', 'Complex number type composed of 2 128-bit extended-precision floating-point numbers'),
      ])
  
  
  def add_newdoc_for_scalar_type(obj, fixed_aliases, doc):
      o = getattr(_numerictypes, obj)
  
      character_code = dtype(o).char
      canonical_name_doc = "" if obj == o.__name__ else "Canonical name: ``np.{}``.\n    ".format(obj)
      alias_doc = ''.join("Alias: ``np.{}``.\n    ".format(alias) for alias in fixed_aliases)
      alias_doc += ''.join("Alias *on this platform*: ``np.{}``: {}.\n    ".format(alias, doc)
                           for (alias_type, alias, doc) in possible_aliases if alias_type is o)
  
      docstring = """
      {doc}
      Character code: ``'{character_code}'``.
      {canonical_name_doc}{alias_doc}
      """.format(doc=doc.strip(), character_code=character_code,
                 canonical_name_doc=canonical_name_doc, alias_doc=alias_doc)
  
      add_newdoc('numpy.core.numerictypes', obj, docstring)
  
  
  add_newdoc_for_scalar_type('bool_', ['bool8'],
      """
      Boolean type (True or False), stored as a byte.
      """)
  
  add_newdoc_for_scalar_type('byte', [],
      """
      Signed integer type, compatible with C ``char``.
      """)
  
  add_newdoc_for_scalar_type('short', [],
      """
      Signed integer type, compatible with C ``short``.
      """)
  
  add_newdoc_for_scalar_type('intc', [],
      """
      Signed integer type, compatible with C ``int``.
      """)
  
  add_newdoc_for_scalar_type('int_', [],
      """
      Signed integer type, compatible with Python `int` anc C ``long``.
      """)
  
  add_newdoc_for_scalar_type('longlong', [],
      """
      Signed integer type, compatible with C ``long long``.
      """)
  
  add_newdoc_for_scalar_type('ubyte', [],
      """
      Unsigned integer type, compatible with C ``unsigned char``.
      """)
  
  add_newdoc_for_scalar_type('ushort', [],
      """
      Unsigned integer type, compatible with C ``unsigned short``.
      """)
  
  add_newdoc_for_scalar_type('uintc', [],
      """
      Unsigned integer type, compatible with C ``unsigned int``.
      """)
  
  add_newdoc_for_scalar_type('uint', [],
      """
      Unsigned integer type, compatible with C ``unsigned long``.
      """)
  
  add_newdoc_for_scalar_type('ulonglong', [],
      """
      Signed integer type, compatible with C ``unsigned long long``.
      """)
  
  add_newdoc_for_scalar_type('half', [],
      """
      Half-precision floating-point number type.
      """)
  
  add_newdoc_for_scalar_type('single', [],
      """
      Single-precision floating-point number type, compatible with C ``float``.
      """)
  
  add_newdoc_for_scalar_type('double', ['float_'],
      """
      Double-precision floating-point number type, compatible with Python `float`
      and C ``double``.
      """)
  
  add_newdoc_for_scalar_type('longdouble', ['longfloat'],
      """
      Extended-precision floating-point number type, compatible with C
      ``long double`` but not necessarily with IEEE 754 quadruple-precision.
      """)
  
  add_newdoc_for_scalar_type('csingle', ['singlecomplex'],
      """
      Complex number type composed of two single-precision floating-point
      numbers.
      """)
  
  add_newdoc_for_scalar_type('cdouble', ['cfloat', 'complex_'],
      """
      Complex number type composed of two double-precision floating-point
      numbers, compatible with Python `complex`.
      """)
  
  add_newdoc_for_scalar_type('clongdouble', ['clongfloat', 'longcomplex'],
      """
      Complex number type composed of two extended-precision floating-point
      numbers.
      """)
  
  add_newdoc_for_scalar_type('object_', [],
      """
      Any Python object.
      """)
  