# tf.linalg.set_diag

Returns a batched matrix tensor with new batched diagonal values.

Given input and diagonal, this operation returns a tensor with the same shape and values as input, except for the specified diagonals of the innermost matrices. These will be overwritten by the values in diagonal.

input has r+1 dimensions [I, J, ..., L, M, N]. When k is scalar or k[0] == k[1], diagonal has r dimensions [I, J, ..., L, max_diag_len]. Otherwise, it has r+1 dimensions [I, J, ..., L, num_diags, max_diag_len]. num_diags is the number of diagonals, num_diags = k[1] - k[0] + 1. max_diag_len is the longest diagonal in the range [k[0], k[1]], max_diag_len = min(M + min(k[1], 0), N + min(-k[0], 0))

The output is a tensor of rank k+1 with dimensions [I, J, ..., L, M, N]. If k is scalar or k[0] == k[1]:

output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, n-max(k[1], 0)] ; if n - m == k[1]
output[i, j, ..., l, m, n]             ; otherwise

Otherwise,

output[i, j, ..., l, m, n]
= diagonal[i, j, ..., l, k[1]-d, n-max(d, 0)] ; if d_lower <= d <= d_upper
input[i, j, ..., l, m, n]                   ; otherwise

where d = n - m

#### For example:

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

# A superdiagonal (per batch).
tf.matrix_diag(diagonal, k = 1)
==> [[[7, 1, 7, 7],  # Output shape: (2, 3, 4)
[7, 7, 2, 7],
[7, 7, 7, 3]],
[[7, 4, 7, 7],
[7, 7, 5, 7],
[7, 7, 7, 6]]]

# A band of diagonals.
diagonals = np.array([[[1, 2, 3],  # Diagonal shape: (2, 2, 3)
[4, 5, 0]],
[[6, 1, 2],
[3, 4, 0]]])
tf.matrix_diag(diagonals, k = (-1, 0))
==> [[[1, 7, 7, 7],  # Output shape: (2, 3, 4)
[4, 2, 7, 7],
[0, 5, 3, 7]],
[[6, 7, 7, 7],
[3, 1, 7, 7],
[7, 4, 2, 7]]]

input A Tensor with rank k + 1, where k >= 1.
diagonal A Tensor with rank k, when d_lower == d_upper, or k + 1, otherwise. 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].

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