tf.linalg.diag_part

TensorFlow 1 version View source on GitHub

Returns the batched diagonal part of a batched tensor.

Aliases: tf.compat.v1.linalg.diag_part, tf.compat.v1.matrix_diag_part, tf.compat.v2.linalg.diag_part

tf.linalg.diag_part(
    input,
    name='diag_part',
    k=0,
    padding_value=0
)

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] ; when 0 <= n-y < M and 0 <= n-x < N,
    0                             ; otherwise.

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] ; when 0 <= n-y < M and 0 <= n-x < N,
    0                             ; otherwise.

where d = k[1] - m, y = max(-d, 0), and x = max(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.matrix_diag_part(input) ==> [[1, 6, 7],  # Output shape: (2, 3)
                                [5, 2, 7]]

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

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

# Padding = 9
tf.matrix_diag_part(input, k = (1, 3), padding = 9)
  ==> [[[4, 9, 9],  # Output shape: (2, 3, 3)
        [3, 8, 9],
        [2, 7, 6]],
       [[2, 9, 9],
        [3, 4, 9],
        [4, 3, 8]]]

Args:

  • 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.

Returns:

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