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-"""
-==============
-Array indexing
-==============
-
-Array indexing refers to any use of the square brackets ([]) to index
-array values. There are many options to indexing, which give numpy
-indexing great power, but with power comes some complexity and the
-potential for confusion. This section is just an overview of the
-various options and issues related to indexing. Aside from single
-element indexing, the details on most of these options are to be
-found in related sections.
-
-Assignment vs referencing
-=========================
-
-Most of the following examples show the use of indexing when referencing
-data in an array. The examples work just as well when assigning to an
-array. See the section at the end for specific examples and explanations
-on how assignments work.
-
-Single element indexing
-=======================
-
-Single element indexing for a 1-D array is what one expects. It work
-exactly like that for other standard Python sequences. It is 0-based,
-and accepts negative indices for indexing from the end of the array. ::
-
-    >>> x = np.arange(10)
-    >>> x[2]
-    2
-    >>> x[-2]
-    8
-
-Unlike lists and tuples, numpy arrays support multidimensional indexing
-for multidimensional arrays. That means that it is not necessary to
-separate each dimension's index into its own set of square brackets. ::
-
-    >>> x.shape = (2,5) # now x is 2-dimensional
-    >>> x[1,3]
-    8
-    >>> x[1,-1]
-    9
-
-Note that if one indexes a multidimensional array with fewer indices
-than dimensions, one gets a subdimensional array. For example: ::
-
-    >>> x[0]
-    array([0, 1, 2, 3, 4])
-
-That is, each index specified selects the array corresponding to the rest
-of the dimensions selected. In the above example, choosing 0 means that
-remaining dimension of lenth 5 is being left unspecified, and that what
-is returned is an array of that dimensionality and size. It must be noted
-that the returned array is not a copy of the original, but points to the
-same values in memory as does the original array (a new view of the same
-data in other words, see xxx for details). In this case,
-the 1-D array at the first position (0) is returned. So using a single
-index on the returned array, results in a single element being returned.
-That is: ::
-
-    >>> x[0][2]
-    2
-
-So note that ``x[0,2] = x[0][2]`` though the second case is more inefficient
-a new temporary array is created after the first index that is subsequently
-indexed by 2.
-
-Note to those used to IDL or Fortran memory order as it relates to indexing.
-Numpy uses C-order indexing. That means that the last index usually (see
-xxx for exceptions) represents the most rapidly changing memory location,
-unlike Fortran or IDL, where the first index represents the most rapidly
-changing location in memory. This difference represents a great potential
-for confusion.
-
-Other indexing options
-======================
-
-It is possible to slice and stride arrays to extract arrays of the same
-number of dimensions, but of different sizes than the original. The slicing
-and striding works exactly the same way it does for lists and tuples except
-that they can be applied to multiple dimensions as well. A few
-examples illustrates best: ::
-
- >>> x = np.arange(10)
- >>> x[2:5]
- array([2, 3, 4])
- >>> x[:-7]
- array([0, 1, 2])
- >>> x[1:7:2]
- array([1,3,5])
- >>> y = np.arange(35).reshape(5,7)
- >>> y[1:5:2,::3]
- array([[ 7, 10, 13],
-        [21, 24, 27]])
-
-Note that slices of arrays do not copy the internal array data but
-also produce new views of the original data (see xxx for more
-explanation of this issue).
-
-It is possible to index arrays with other arrays for the purposes of
-selecting lists of values out of arrays into new arrays. There are two
-different ways of accomplishing this. One uses one or more arrays of
-index values (see xxx for details). The other involves giving a boolean
-array of the proper shape to indicate the values to be selected.
-Index arrays are a very powerful tool that allow one to avoid looping
-over individual elements in arrays and thus greatly improve performance
-(see xxx for examples)
-
-It is possible to use special features to effectively increase the
-number of dimensions in an array through indexing so the resulting
-array aquires the shape needed for use in an expression or with a
-specific function. See xxx.
-
-Index arrays
-============
-
-Numpy arrays may be indexed with other arrays (or any other sequence-like
-object that can be converted to an array, such as lists, with the exception
-of tuples; see the end of this document for why this is). The use of index
-arrays ranges from simple, straightforward cases to complex, hard-to-understand
-cases. For all cases of index arrays, what is returned is a copy of the
-original data, not a view as one gets for slices.
-
-Index arrays must be of integer type. Each value in the array indicates which
-value in the array to use in place of the index. To illustrate: ::
-
- >>> x = np.arange(10,1,-1)
- >>> x
- array([10,  9,  8,  7,  6,  5,  4,  3,  2])
- >>> x[np.array([3, 3, 1, 8])]
- array([7, 7, 9, 2])
-
-
-The index array consisting of the values 3, 3, 1 and 8 correspondingly create
-an array of length 4 (same as the index array) where each index is replaced by
-the value the index array has in the array being indexed.
-
-Negative values are permitted and work as they do with single indices or slices: ::
-
- >>> x[np.array([3,3,-3,8])]
- array([7, 7, 4, 2])
-
-It is an error to have index values out of bounds: ::
-
- >>> x[np.array([3, 3, 20, 8])]
- <type 'exceptions.IndexError'>: index 20 out of bounds 0<=index<9
-
-Generally speaking, what is returned when index arrays are used is an array with
-the same shape as the index array, but with the type and values of the array being
-indexed. As an example, we can use a multidimensional index array instead: ::
-
- >>> x[np.array([[1,1],[2,3]])]
- array([[9, 9],
-        [8, 7]])
-
-Indexing Multi-dimensional arrays
-=================================
-
-Things become more complex when multidimensional arrays are indexed, particularly
-with multidimensional index arrays. These tend to be more unusal uses, but they
-are permitted, and they are useful for some problems. We'll  start with the
-simplest multidimensional case (using the array y from the previous examples): ::
-
- >>> y[np.array([0,2,4]), np.array([0,1,2])]
- array([ 0, 15, 30])
-
-In this case, if the index arrays have a matching shape, and there is an index
-array for each dimension of the array being indexed, the resultant array has the
-same shape as the index arrays, and the values correspond to the index set for each
-position in the index arrays. In this example, the first index value is 0 for both
-index arrays, and thus the first value of the resultant array is y[0,0]. The next
-value is y[2,1], and the last is y[4,2].
-
-If the index arrays do not have the same shape, there is an attempt to broadcast
-them to the same shape. Broadcasting won't be discussed here but is discussed in
-detail in xxx. If they cannot be broadcast to the same shape, an exception is
-raised: ::
-
- >>> y[np.array([0,2,4]), np.array([0,1])]
- <type 'exceptions.ValueError'>: shape mismatch: objects cannot be broadcast to a single shape
-
-The broadcasting mechanism permits index arrays to be combined with scalars for
-other indices. The effect is that the scalar value is used for all the corresponding
-values of the index arrays: ::
-
- >>> y[np.array([0,2,4]), 1]
- array([ 1, 15, 29])
-
-Jumping to the next level of complexity, it is possible to only partially index an array
-with index arrays. It takes a bit of thought to understand what happens in such cases.
-For example if we just use one index array with y: ::
-
- >>> y[np.array([0,2,4])]
- array([[ 0,  1,  2,  3,  4,  5,  6],
-        [14, 15, 16, 17, 18, 19, 20],
-        [28, 29, 30, 31, 32, 33, 34]])
-
-What results is the construction of a new array where each value of the index array
-selects one row from the array being indexed and the resultant array has the resulting
-shape (size of row, number index elements).
-
-An example of where this may be useful is for a color lookup table where we want to map
-the values of an image into RGB triples for display. The lookup table could have a shape
-(nlookup, 3). Indexing such an array with an image with shape (ny, nx) with dtype=np.uint8
-(or any integer type so long as values are with the bounds of the lookup table) will
-result in an array of shape (ny, nx, 3) where a triple of RGB values is associated with
-each pixel location.
-
-In general, the shape of the resulant array will be the concatenation of the shape of
-the index array (or the shape that all the index arrays were broadcast to) with the
-shape of any unused dimensions (those not indexed) in the array being indexed.
-
-Boolean or "mask" index arrays
-==============================
-
-Boolean arrays used as indices are treated in a different manner entirely than index
-arrays. Boolean arrays must be of the same shape as the array being indexed, or
-broadcastable to the same shape. In the most straightforward case, the boolean array
-has the same shape: ::
-
- >>> b = y>20
- >>> y[b]
- array([21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34])
-
-The result is a 1-D array containing all the elements in the indexed array corresponding
-to all the true elements in the boolean array. As with index arrays, what is returned
-is a copy of the data, not a view as one gets with slices.
-
-With broadcasting, multidimesional arrays may be the result. For example: ::
-
- >>> b[:,5] # use a 1-D boolean that broadcasts with y
- array([False, False, False,  True,  True], dtype=bool)
- >>> y[b[:,5]]
- array([[21, 22, 23, 24, 25, 26, 27],
-        [28, 29, 30, 31, 32, 33, 34]])
-
-Here the 4th and 5th rows are selected from the indexed array and combined to make a
-2-D array.
-
-Combining index arrays with slices
-==================================
-
-Index arrays may be combined with slices. For example: ::
-
- >>> y[np.array([0,2,4]),1:3]
- array([[ 1,  2],
-        [15, 16],
-        [29, 30]])
-
-In effect, the slice is converted to an index array np.array([[1,2]]) (shape (1,2)) that is
-broadcast with the index array to produce a resultant array of shape (3,2).
-
-Likewise, slicing can be combined with broadcasted boolean indices: ::
-
- >>> y[b[:,5],1:3]
- array([[22, 23],
-        [29, 30]])
-
-Structural indexing tools
-=========================
-
-To facilitate easy matching of array shapes with expressions and in
-assignments, the np.newaxis object can be used within array indices
-to add new dimensions with a size of 1. For example: ::
-
- >>> y.shape
- (5, 7)
- >>> y[:,np.newaxis,:].shape
- (5, 1, 7)
-
-Note that there are no new elements in the array, just that the
-dimensionality is increased. This can be handy to combine two
-arrays in a way that otherwise would require explicitly reshaping
-operations. For example: ::
-
- >>> x = np.arange(5)
- >>> x[:,np.newaxis] + x[np.newaxis,:]
- array([[0, 1, 2, 3, 4],
-        [1, 2, 3, 4, 5],
-        [2, 3, 4, 5, 6],
-        [3, 4, 5, 6, 7],
-        [4, 5, 6, 7, 8]])
-
-The ellipsis syntax maybe used to indicate selecting in full any
-remaining unspecified dimensions. For example: ::
-
- >>> z = np.arange(81).reshape(3,3,3,3)
- >>> z[1,...,2]
- array([[29, 32, 35],
-        [38, 41, 44],
-        [47, 50, 53]])
-
-This is equivalent to: ::
-
- >>> z[1,:,:,2]
-
-Assigning values to indexed arrays
-==================================
-
-As mentioned, one can select a subset of an array to assign to using
-a single index, slices, and index and mask arrays. The value being
-assigned to the indexed array must be shape consistent (the same shape
-or broadcastable to the shape the index produces). For example, it is
-permitted to assign a constant to a slice: ::
-
- >>> x[2:7] = 1
-
-or an array of the right size: ::
-
- >>> x[2:7] = np.arange(5)
-
-Note that assignments may result in changes if assigning
-higher types to lower types (like floats to ints) or even
-exceptions (assigning complex to floats or ints): ::
-
- >>> x[1] = 1.2
- >>> x[1]
- 1
- >>> x[1] = 1.2j
- <type 'exceptions.TypeError'>: can't convert complex to long; use long(abs(z))
-
-
-Unlike some of the references (such as array and mask indices)
-assignments are always made to the original data in the array
-(indeed, nothing else would make sense!). Note though, that some
-actions may not work as one may naively expect. This particular
-example is often surprising to people: ::
-
- >>> x[np.array([1, 1, 3, 1]) += 1
-
-Where people expect that the 1st location will be incremented by 3.
-In fact, it will only be incremented by 1. The reason is because
-a new array is extracted from the original (as a temporary) containing
-the values at 1, 1, 3, 1, then the value 1 is added to the temporary,
-and then the temporary is assigned back to the original array. Thus
-the value of the array at x[1]+1 is assigned to x[1] three times,
-rather than being incremented 3 times.
-
-Dealing with variable numbers of indices within programs
-========================================================
-
-The index syntax is very powerful but limiting when dealing with
-a variable number of indices. For example, if you want to write
-a function that can handle arguments with various numbers of
-dimensions without having to write special case code for each
-number of possible dimensions, how can that be done? If one
-supplies to the index a tuple, the tuple will be interpreted
-as a list of indices. For example (using the previous definition
-for the array z): ::
-
- >>> indices = (1,1,1,1)
- >>> z[indices]
- 40
-
-So one can use code to construct tuples of any number of indices
-and then use these within an index.
-
-Slices can be specified within programs by using the slice() function
-in Python. For example: ::
-
- >>> indices = (1,1,1,slice(0,2)) # same as [1,1,1,0:2]
- array([39, 40])
-
-Likewise, ellipsis can be specified by code by using the Ellipsis object: ::
-
- >>> indices = (1, Ellipsis, 1) # same as [1,...,1]
- >>> z[indices]
- array([[28, 31, 34],
-        [37, 40, 43],
-        [46, 49, 52]])
-
-For this reason it is possible to use the output from the np.where()
-function directly as an index since it always returns a tuple of index arrays.
-
-Because the special treatment of tuples, they are not automatically converted
-to an array as a list would be. As an example: ::
-
- >>> z[[1,1,1,1]]
- ... # produces a large array
- >>> z[(1,1,1,1)]
- 40 # returns a single value
-
-"""