StridedSlice

Return a strided slice from `input`.

Note, most python users will want to use the Python Tensor.__getitem__ or Variable.__getitem__ rather than this op directly.

The goal of this op is to produce a new tensor with a subset of the elements from the `n` dimensional `input` tensor. The subset is chosen using a sequence of `m` sparse range specifications encoded into the arguments of this function. Note, in some cases `m` could be equal to `n`, but this need not be the case. Each range specification entry can be one of the following:

- An ellipsis (...). Ellipses are used to imply zero or more dimensions of full-dimension selection and are produced using `ellipsis_mask`. For example, `foo[...]` is the identity slice.

- A new axis. This is used to insert a new shape=1 dimension and is produced using `new_axis_mask`. For example, `foo[:, ...]` where `foo` is shape `(3, 4)` produces a `(1, 3, 4)` tensor.

- A range `begin:end:stride`. This is used to specify how much to choose from a given dimension. `stride` can be any integer but 0. `begin` is an integer which represents the index of the first value to select while `end` represents the index of the last value to select. The number of values selected in each dimension is `end - begin` if `stride > 0` and `begin - end` if `stride < 0`. `begin` and `end` can be negative where `-1` is the last element, `-2` is the second to last. `begin_mask` controls whether to replace the explicitly given `begin` with an implicit effective value of `0` if `stride > 0` and `-1` if `stride < 0`. `end_mask` is analogous but produces the number required to create the largest open interval. For example, given a shape `(3,)` tensor `foo[:]`, the effective `begin` and `end` are `0` and `3`. Do not assume this is equivalent to `foo[0:-1]` which has an effective `begin` and `end` of `0` and `2`. Another example is `foo[-2::-1]` which reverses the first dimension of a tensor while dropping the last two (in the original order elements). For example `foo = [1,2,3,4]; foo[-2::-1]` is `[4,3]`.

- A single index. This is used to keep only elements that have a given index. For example (`foo[2, :]` on a shape `(5,6)` tensor produces a shape `(6,)` tensor. This is encoded in `begin` and `end` and `shrink_axis_mask`.

Each conceptual range specification is encoded in the op's argument. This encoding is best understand by considering a non-trivial example. In particular, `foo[1, 2:4, None, ..., :-3:-1, :]` will be encoded as

begin = [1, 2, x, x, 0, x] # x denotes don't care (usually 0)
 end = [2, 4, x, x, -3, x]
 strides = [1, 1, x, x, -1, 1]
 begin_mask = 1<<4 | 1<<5 = 48
 end_mask = 1<<5 = 32
 ellipsis_mask = 1<<3 = 8
 new_axis_mask = 1<<2 = 4
 shrink_axis_mask = 1<<0 = 1
 

1. The first argument in the example slice is turned into `begin = 1` and `end = begin + 1 = 2`. To disambiguate from the original spec `2:4` we also set the appropriate bit in `shrink_axis_mask`.

2. `2:4` is contributes 2, 4, 1 to begin, end, and stride. All masks have zero bits contributed.

3. None is a synonym for tf.newaxis. This means insert a dimension of size 1 dimension in the final shape. Dummy values are contributed to begin, end and stride, while the new_axis_mask bit is set.

4. `...` grab the full ranges from as many dimensions as needed to fully specify a slice for every dimension of the input shape.

5. `:-3:-1` shows the use of negative indices. A negative index `i` associated with a dimension that has shape `s` is converted to a positive index `s + i`. So `-1` becomes `s-1` (i.e. the last element). This conversion is done internally so begin, end and strides receive x, -3, and -1. The appropriate begin_mask bit is set to indicate the start range is the full range (ignoring the x).

6. `:` indicates that the entire contents of the corresponding dimension is selected. This is equivalent to `::` or `0::1`. begin, end, and strides receive 0, 0, and 1, respectively. The appropriate bits in `begin_mask` and `end_mask` are also set.

Requirements: `0 != strides[i] for i in [0, m)` `ellipsis_mask must be a power of two (only one ellipsis)`