Continuum Analytics: Documentation

# Memory Management

`numba.cuda.``to_device`(obj, stream=0, copy=True, to=None)

  Allocate and transfer a numpy ndarray or structured scalar to the device.

  To copy host->device a numpy array:

      ary = np.arange(10)
      d_ary = cuda.to_device(ary)

  To enqueue the transfer to a stream:

      stream = cuda.stream()
      d_ary = cuda.to_device(ary, stream=stream)

  The resulting `d_ary` is a `DeviceNDArray`.

  To copy device->host:

      hary = d_ary.copy_to_host()

  To copy device->host to an existing array:

      ary = np.empty(shape=d_ary.shape, dtype=d_ary.dtype)
      d_ary.copy_to_host(ary)

  To enqueue the transfer to a stream:

      hary = d_ary.copy_to_host(stream=stream)

`numba.cuda.``device_array`(shape, dtype=np.float, strides=None, order='C', stream=0)

  Allocate an empty device ndarray. Similar to `numpy.empty()`.

`numba.cuda.``device_array_like`(ary, stream=0)

  Call cuda.devicearray() with information from the array.

`numba.cuda.``pinned_array`(shape, dtype=np.float, strides=None, order='C')

  Allocate a np.ndarray with a buffer that is pinned (pagelocked). Similar to np.empty().

`numba.cuda.``mapped_array`(shape, dtype=np.float, strides=None, order='C', stream=0, portable=False, wc=False)

  Allocate a mapped ndarray with a buffer that is pinned and mapped on to the device. Similar to np.empty()

  Parameters:

  - portable – a boolean flag to allow the allocated device memory to be usable in multiple devices.
  - wc – a boolean flag to enable writecombined allocation which is faster to write by the host and to read by the device, but slower to write by the host and slower to write by the device.

`numba.cuda.``pinned`(*args, **kws)

  A context manager for temporary pinning a sequence of host ndarrays.

`numba.cuda.``mapped`(*args, **kws)

  A context manager for temporarily mapping a sequence of host ndarrays.

## Device Objects

class `numba.cuda.cudadrv.devicearray.``DeviceNDArray`(shape, strides, dtype, stream=0, writeback=None, gpu_data=None)

  An on-GPU array type

  `as_cuda_arg`()

    Returns a device memory object that is used as the argument.

  `bind`(stream=0)

    Bind a CUDA stream to this object so that all subsequent operation on this array defaults to the given stream.

  `copy_to_device`(ary, stream=0)

    Copy ary to self.

    If ary is a CUDA memory, perform a device-to-device transfer. Otherwise, perform a a host-to-device transfer.

  `copy_to_host`(ary=None, stream=0)

    Copy `self` to `ary` or create a new Numpy ndarray if `ary` is `None`.

    If a CUDA `stream` is given, then the transfer will be made asynchronously as part as the given stream. Otherwise, the transfer is synchronous: the function returns after the copy is finished.

    Always returns the host array.

    Example:

        import numpy as np
        from numba import cuda

        arr = np.arange(1000)
        d_arr = cuda.to_device(arr)

        my_kernel[100, 100](d_arr)

        result_array = d_arr.copy_to_host()

  `device_ctypes_pointer`

    Returns the ctypes pointer to the GPU data buffer

  `get_ipc_handle`()

    Returns a IpcArrayHandle object that is safe to serialize and transfer to another process to share the local allocation.

    Note: this feature is only available on Linux.

  `getitem`(item, stream=0)

    Do __getitem__(item) with CUDA stream

  `is_c_contiguous`()

    Return true if the array is C-contiguous.

  `is_f_contiguous`()

    Return true if the array is Fortran-contiguous.

  `ravel`(order='C', stream=0)

    Flatten the array without changing its contents, similar to `numpy.ndarray.ravel()`.

  `reshape`(*newshape, **kws)

    Reshape the array without changing its contents, similarly to `numpy.ndarray.reshape()`. Example:

        d_arr = d_arr.reshape(20, 50, order='F')

  `split`(section, stream=0)

    Split the array into equal partition of the section size. If the array cannot be equally divided, the last section will be smaller.

class `numba.cuda.cudadrv.devicearray.``DeviceRecord`(dtype, stream=0, gpu_data=None)

  An on-GPU record type

  `as_cuda_arg`()

    Returns a device memory object that is used as the argument.

  `bind`(stream=0)

    Bind a CUDA stream to this object so that all subsequent operation on this array defaults to the given stream.

  `copy_to_device`(ary, stream=0)

    Copy ary to self.

    If ary is a CUDA memory, perform a device-to-device transfer. Otherwise, perform a a host-to-device transfer.

  `copy_to_host`(ary=None, stream=0)

    Copy `self` to `ary` or create a new Numpy ndarray if `ary` is `None`.

    If a CUDA `stream` is given, then the transfer will be made asynchronously as part as the given stream. Otherwise, the transfer is synchronous: the function returns after the copy is finished.

    Always returns the host array.

    Example:

        import numpy as np
        from numba import cuda

        arr = np.arange(1000)
        d_arr = cuda.to_device(arr)

        my_kernel[100, 100](d_arr)

        result_array = d_arr.copy_to_host()

  `device_ctypes_pointer`

    Returns the ctypes pointer to the GPU data buffer

  `get_ipc_handle`()

    Returns a IpcArrayHandle object that is safe to serialize and transfer to another process to share the local allocation.

    Note: this feature is only available on Linux.

  `split`(section, stream=0)

    Split the array into equal partition of the section size. If the array cannot be equally divided, the last section will be smaller.

class `numba.cuda.cudadrv.devicearray.``MappedNDArray`(shape, strides, dtype, stream=0, writeback=None, gpu_data=None)

  A host array that uses CUDA mapped memory.

  `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.])

  `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
  `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
  `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
  `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
  `argpartition`(kth, axis=-1, kind='introselect', order=None)

    Returns the indices that would partition this array.

    Refer to numpy.argpartition for full documentation.

    New in version 1.8.0.

    See also

    `numpy.argpartition()`
      equivalent function
  `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
  `as_cuda_arg`()

    Returns a device memory object that is used as the argument.

  `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 – 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.
    Return type: | ndarray

    Notes

    Starting in NumPy 1.9, astype method now returns an error if the string dtype to cast to is not long enough in ‘safe’ casting mode to hold the max value of integer/float array that is being casted. Previously the casting was allowed even if the result was truncated.

    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])

  `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

  `bind`(stream=0)

    Bind a CUDA stream to this object so that all subsequent operation on this array defaults to the given stream.

  `byteswap`(inplace)

    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 – The byteswapped array. If inplace is `True`, this is a view to self.
    Return type: | ndarray

    Examples

        >>> A = np.array([1, 256, 8755], dtype=np.int16)
        >>> map(hex, A)
        ['0x1', '0x100', '0x2233']
        >>> A.byteswap(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')

  `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
  `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
  `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
  `conj`()

    Complex-conjugate all elements.

    Refer to numpy.conjugate for full documentation.

    See also

    `numpy.conjugate()`
      equivalent function
  `conjugate`()

    Return the complex conjugate, element-wise.

    Refer to numpy.conjugate for full documentation.

    See also

    `numpy.conjugate()`
      equivalent function
  `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

  `copy_to_device`(ary, stream=0)

    Copy ary to self.

    If ary is a CUDA memory, perform a device-to-device transfer. Otherwise, perform a a host-to-device transfer.

  `copy_to_host`(ary=None, stream=0)

    Copy `self` to `ary` or create a new Numpy ndarray if `ary` is `None`.

    If a CUDA `stream` is given, then the transfer will be made asynchronously as part as the given stream. Otherwise, the transfer is synchronous: the function returns after the copy is finished.

    Always returns the host array.

    Example:

        import numpy as np
        from numba import cuda

        arr = np.arange(1000)
        d_arr = cuda.to_device(arr)

        my_kernel[100, 100](d_arr)

        result_array = d_arr.copy_to_host()

  `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 – Possessing attributes data, shape, strides, etc.
    Return type: | Python object

    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):

    - data: A pointer to the memory area of the array as a Python integer. This memory area may contain data that is not aligned, or not in correct byte-order. The memory area may not even be writeable. The array flags and data-type of this array should be respected when passing this attribute to arbitrary C-code to avoid trouble that can include Python crashing. User Beware! The value of this attribute is exactly the same as self._array_interface_[‘data’][0].
    - shape (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the C-integer corresponding to dtype(‘p’) on this platform. This base-type could be c_int, c_long, or c_longlong depending on the platform. The c_intp type is defined accordingly in numpy.ctypeslib. The ctypes array contains the shape of the underlying array.
    - strides (c_intp*self.ndim): A ctypes array of length self.ndim where the basetype is the same as for the shape attribute. This ctypes array contains the strides information from the underlying array. This strides information is important for showing how many bytes must be jumped to get to the next element in the array.
    - data_as(obj): Return the data pointer cast to a particular c-types object. For example, calling self._as_parameter_ is equivalent to self.data_as(ctypes.c_void_p). Perhaps you want to use the data as a pointer to a ctypes array of floating-point data: self.data_as(ctypes.POINTER(ctypes.c_double)).
    - shape_as(obj): Return the shape tuple as an array of some other c-types type. For example: self.shape_as(ctypes.c_short).
    - strides_as(obj): Return the strides tuple as an array of some other c-types type. For example: self.strides_as(ctypes.c_longlong).

    Be careful using the ctypes attribute - especially on temporary arrays or arrays constructed on the fly. For example, calling `(a+b).ctypes.data_as(ctypes.c_void_p)` returns a pointer to memory that is invalid because the array created as (a+b) is deallocated before the next Python statement. You can avoid this problem using either `c=a+b` or `ct=(a+b).ctypes`. In the latter case, ct will hold a reference to the array until ct is deleted or re-assigned.

    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>

  `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
  `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
  `data`

    Python buffer object pointing to the start of the array’s data.

  `device_ctypes_pointer`

    Returns the ctypes pointer to the GPU data buffer

  `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 `numpy.diagonal()` for full documentation.

    See also

    `numpy.diagonal()`
      equivalent function
  `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.]])

  `dtype`

    Data-type of the array’s elements.

    Parameters: | None –
    Returns: | d
    Return type: | numpy dtype object

    See also

    `numpy.dtype`

    Examples

        >>> x
        array([[0, 1],
               [2, 3]])
        >>> x.dtype
        dtype('int32')
        >>> type(x.dtype)
        <type 'numpy.dtype'>

  `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.

  `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 –

  `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.])

  `flags`

    Information about the memory layout of the array.

    `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.

    `UPDATEIFCOPY`(U)

      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 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`.
    - 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.

  `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]])

  `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 – A copy of the input array, flattened to one dimension.
    Return type: | ndarray

    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])

  `get_ipc_handle`()

    Returns a IpcArrayHandle object that is safe to serialize and transfer to another process to share the local allocation.

    Note: this feature is only available on Linux.

  `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.]])

  `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')

  `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 – A copy of the specified element of the array as a suitable Python scalar
    Return type: | Standard Python scalar object

    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

  `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]])

  `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

  `max`(axis=None, out=None)

    Return the maximum along a given axis.

    Refer to numpy.amax for full documentation.

    See also

    `numpy.amax()`
      equivalent function
  `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
  `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
  `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

  `ndim`

    Number of array dimensions.

    Examples

        >>> x = np.array([1, 2, 3])
        >>> x.ndim
        1
        >>> y = np.zeros((2, 3, 4))
        >>> y.ndim
        3

  `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 – New array object with the dtype reflecting given change to the byte order.
    Return type: | array

  `nonzero`()

    Return the indices of the elements that are non-zero.

    Refer to numpy.nonzero for full documentation.

    See also

    `numpy.nonzero()`
      equivalent function
  `partition`(kth, axis=-1, kind='introselect', order=None)

    Rearranges the elements in the array in such a way that 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.

    New in version 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 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 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(a, 3)
        >>> a
        array([2, 1, 3, 4])

        >>> a.partition((1, 3))
        array([1, 2, 3, 4])

  `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
  `ptp`(axis=None, out=None)

    Peak to peak (maximum - minimum) value along a given axis.

    Refer to numpy.ptp for full documentation.

    See also

    `numpy.ptp()`
      equivalent function
  `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
  `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.
  `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
  `repeat`(repeats, axis=None)

    Repeat elements of an array.

    Refer to numpy.repeat for full documentation.

    See also

    `numpy.repeat()`
      equivalent function
  `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
  `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: |
    Return type: | 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.
    - `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]])

  `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
  `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
  `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: |
    Return type: | 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.]])

  `setflags`(write=None, align=None, uic=None)

    Set array flags WRITEABLE, ALIGNED, 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 UPDATEIFCOPY flag 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 6 Boolean flags in use, only three of which can be changed by the user: 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) this array is a copy of some other array (referenced by .base). When this array is deallocated, the base array will be updated with the contents of this array.

    All flags can be accessed using their first (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
          UPDATEIFCOPY : False
        >>> y.setflags(write=0, align=0)
        >>> y.flags
          C_CONTIGUOUS : True
          F_CONTIGUOUS : False
          OWNDATA : True
          WRITEABLE : False
          ALIGNED : False
          UPDATEIFCOPY : False
        >>> y.setflags(uic=1)
        Traceback (most recent call last):
          File "<stdin>", line 1, in <module>
        ValueError: cannot set UPDATEIFCOPY flag to True

  `shape`

    Tuple of array dimensions.

    Notes

    May be used to “reshape” the array, as long as this would not require a change in the total number of elements

    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

  `size`

    Number of elements in the array.

    Equivalent to `np.prod(a.shape)`, i.e., the product of the array’s dimensions.

    Examples

        >>> x = np.zeros((3, 5, 2), dtype=np.complex128)
        >>> x.size
        30
        >>> np.prod(x.shape)
        30

  `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'}, 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')])

  `split`(section, stream=0)

    Split the array into equal partition of the section size. If the array cannot be equally divided, the last section will be smaller.

  `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
  `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
  `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

  `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
  `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
  `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
  `tobytes`(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.

    New in version 1.9.0.

    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 – Python bytes exhibiting a copy of a‘s raw data.
    Return type: | bytes

    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'

  `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.

  `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 – The possibly nested list of array elements.
    Return type: | list

    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]]

  `tostring`(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.

    This function is a compatibility alias for tobytes. Despite its name it returns bytes not strings.

    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 – Python bytes exhibiting a copy of a‘s raw data.
    Return type: | bytes

    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'

  `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
  `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 – View of a, with axes suitably permuted.
    Return type: | ndarray

    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]])

  `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
  `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')])