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]
    input[i, j, ..., l, m, n]              ; otherwise

Otherwise,

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

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: