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# tf.linalg.diag_part

Returns the batched diagonal part of a batched tensor.

Returns a tensor with the `k[0]`-th to `k[1]`-th diagonals of the batched `input`.

Assume `input` has `r` dimensions `[I, J, ..., L, M, N]`. Let `max_diag_len` be the maximum length among all diagonals to be extracted, `max_diag_len = min(M + min(k[1], 0), N + min(-k[0], 0))` Let `num_diags` be the number of diagonals to extract, `num_diags = k[1] - k[0] + 1`.

If `num_diags == 1`, the output tensor is of rank `r - 1` with shape `[I, J, ..., L, max_diag_len]` and values:

``````diagonal[i, j, ..., l, n]
= input[i, j, ..., l, n+y, n+x] ; if 0 <= n+y < M and 0 <= n+x < N,
``````

where `y = max(-k[1], 0)`, `x = max(k[1], 0)`.

Otherwise, the output tensor has rank `r` with dimensions `[I, J, ..., L, num_diags, max_diag_len]` with values:

``````diagonal[i, j, ..., l, m, n]
= input[i, j, ..., l, n+y, n+x] ; if 0 <= n+y < M and 0 <= n+x < N,
``````

where `d = k[1] - m`, `y = max(-d, 0) - offset`, and `x = max(d, 0) - offset`.

`offset` is zero except when the alignment of the diagonal is to the right.

``````offset = max_diag_len - diag_len(d) ; if (`align` in {RIGHT_LEFT, RIGHT_RIGHT}
and `d >= 0`) or
(`align` in {LEFT_RIGHT, RIGHT_RIGHT}
and `d <= 0`)
0                          ; otherwise
``````

where `diag_len(d) = min(cols - max(d, 0), rows + min(d, 0))`.

The input must be at least a matrix.

#### For example:

``````input = np.array([[[1, 2, 3, 4],  # Input shape: (2, 3, 4)
[5, 6, 7, 8],
[9, 8, 7, 6]],
[[5, 4, 3, 2],
[1, 2, 3, 4],
[5, 6, 7, 8]]])

# A main diagonal from each batch.
tf.linalg.diag_part(input) ==> [[1, 6, 7],  # Output shape: (2, 3)
[5, 2, 7]]

# A superdiagonal from each batch.
tf.linalg.diag_part(input, k = 1)
==> [[2, 7, 6],  # Output shape: (2, 3)
[4, 3, 8]]

# A band from each batch.
tf.linalg.diag_part(input, k = (-1, 2))
==> [[[3, 8, 0],  # Output shape: (2, 4, 3)
[2, 7, 6],
[1, 6, 7],
[0, 5, 8]],
[[3, 4, 0],
[4, 3, 8],
[5, 2, 7],
[0, 1, 6]]]

# RIGHT_LEFT alignment.
tf.linalg.diag_part(input, k = (-1, 2), align="RIGHT_LEFT")
==> [[[0, 3, 8],  # Output shape: (2, 4, 3)
[2, 7, 6],
[1, 6, 7],
[5, 8, 0]],
[[0, 3, 4],
[4, 3, 8],
[5, 2, 7],
[1, 6, 0]]]

# max_diag_len can be shorter than the main diagonal.
tf.linalg.diag_part(input, k = (-2, -1))
==> [[[5, 8],
[0, 9]],
[[1, 6],
[0, 5]]]

# padding_value = 9
tf.linalg.diag_part(input, k = (1, 3), padding_value = 9)
==> [[[4, 9, 9],  # Output shape: (2, 3, 3)
[3, 8, 9],
[2, 7, 6]],
[[2, 9, 9],
[3, 4, 9],
[4, 3, 8]]]

``````

`input` A `Tensor` with `rank k >= 2`.
`name` A name for the operation (optional).
`k` Diagonal offset(s). Positive value means superdiagonal, 0 refers to the main diagonal, and negative value means subdiagonals. `k` can be a single integer (for a single diagonal) or a pair of integers specifying the low and high ends of a matrix band. `k[0]` must not be larger than `k[1]`.
`padding_value` The value to fill the area outside the specified diagonal band with. Default is 0.
`align` Some diagonals are shorter than `max_diag_len` and need to be padded. `align` is a string specifying how superdiagonals and subdiagonals should be aligned, respectively. There are four possible alignments: "RIGHT_LEFT" (default), "LEFT_RIGHT", "LEFT_LEFT", and "RIGHT_RIGHT". "RIGHT_LEFT" aligns superdiagonals to the right (left-pads the row) and subdiagonals to the left (right-pads the row). It is the packing format LAPACK uses. cuSPARSE uses "LEFT_RIGHT", which is the opposite alignment.

A Tensor containing diagonals of `input`. Has the same type as `input`.

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