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# tf.linalg.diag

Returns a batched diagonal tensor with given batched diagonal values.

Returns a tensor with the contents in `diagonal` as `k[0]`-th to `k[1]`-th diagonals of a matrix, with everything else padded with `padding`. `num_rows` and `num_cols` specify the dimension of the innermost matrix of the output. If both are not specified, the op assumes the innermost matrix is square and infers its size from `k` and the innermost dimension of `diagonal`. If only one of them is specified, the op assumes the unspecified value is the smallest possible based on other criteria.

Let `diagonal` have `r` dimensions `[I, J, ..., L, M, N]`. The output tensor has rank `r+1` with shape `[I, J, ..., L, M, num_rows, num_cols]` when only one diagonal is given (`k` is an integer or `k[0] == k[1]`). Otherwise, it has rank `r` with shape `[I, J, ..., L, num_rows, num_cols]`.

The second innermost dimension of `diagonal` has double meaning. When `k` is scalar or `k[0] == k[1]`, `M` is part of the batch size [I, J, ..., M], and the output tensor is:

``````output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, n-max(d_upper, 0)] ; if n - m == d_upper
``````

Otherwise, `M` is treated as the number of diagonals for the matrix in the same batch (`M = k[1]-k[0]+1`), and the output tensor is:

``````output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, diag_index, index_in_diag] ; if k[0] <= d <= k[1]
``````

where `d = n - m`, `diag_index = k[1] - d`, and `index_in_diag = n - 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))`.

#### For example:

``````# The main diagonal.
diagonal = np.array([[1, 2, 3, 4],            # Input shape: (2, 4)
[5, 6, 7, 8]])
tf.matrix_diag(diagonal) ==> [[[1, 0, 0, 0],  # Output shape: (2, 4, 4)
[0, 2, 0, 0],
[0, 0, 3, 0],
[0, 0, 0, 4]],
[[5, 0, 0, 0],
[0, 6, 0, 0],
[0, 0, 7, 0],
[0, 0, 0, 8]]]

# A superdiagonal (per batch).
diagonal = np.array([[1, 2, 3],  # Input shape: (2, 3)
[4, 5, 6]])
tf.matrix_diag(diagonal, k = 1)
==> [[[0, 1, 0, 0],  # Output shape: (2, 4, 4)
[0, 0, 2, 0],
[0, 0, 0, 3],
[0, 0, 0, 0]],
[[0, 4, 0, 0],
[0, 0, 5, 0],
[0, 0, 0, 6],
[0, 0, 0, 0]]]

# A tridiagonal band (per batch).
diagonals = np.array([[[8, 9, 0],  # Input shape: (2, 2, 3)
[1, 2, 3],
[0, 4, 5]],
[[2, 3, 0],
[6, 7, 9],
[0, 9, 1]]])
tf.matrix_diag(diagonals, k = (-1, 1))
==> [[[1, 8, 0],  # Output shape: (2, 3, 3)
[4, 2, 9],
[0, 5, 3]],
[[6, 2, 0],
[9, 7, 3],
[0, 1, 9]]]

# RIGHT_LEFT alignment.
diagonals = np.array([[[0, 8, 9],  # Input shape: (2, 2, 3)
[1, 2, 3],
[4, 5, 0]],
[[0, 2, 3],
[6, 7, 9],
[9, 1, 0]]])
tf.matrix_diag(diagonals, k = (-1, 1), align="RIGHT_LEFT")
==> [[[1, 8, 0],  # Output shape: (2, 3, 3)
[4, 2, 9],
[0, 5, 3]],
[[6, 2, 0],
[9, 7, 3],
[0, 1, 9]]]

# Rectangular matrix.
diagonal = np.array([1, 2])  # Input shape: (2)
tf.matrix_diag(diagonal, k = -1, num_rows = 3, num_cols = 4)
==> [[0, 0, 0, 0],  # Output shape: (3, 4)
[1, 0, 0, 0],
[0, 2, 0, 0]]

# Rectangular matrix with inferred num_cols and padding_value = 9.
tf.matrix_diag(diagonal, k = -1, num_rows = 3, padding_value = 9)
==> [[9, 9],  # Output shape: (3, 2)
[1, 9],
[9, 2]]
``````

`diagonal` A `Tensor` with `rank k >= 1`.
`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]`.
`num_rows` The number of rows of the output matrix. If it is not provided, the op assumes the output matrix is a square matrix and infers the matrix size from `d_lower`, `d_upper`, and the innermost dimension of `diagonal`.
`num_cols` The number of columns of the output matrix. If it is not provided, the op assumes the output matrix is a square matrix and infers the matrix size from `d_lower`, `d_upper`, and the innermost dimension of `diagonal`.
`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. Has the same type as `diagonal`.

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