tf.linalg.diag

Returns a batched diagonal tensor with given batched diagonal values.

tf.linalg.diag(
    diagonal,
    name='diag',
    k=0,
    num_rows=-1,
    num_cols=-1,
    padding_value=0,
    align='RIGHT_LEFT'
)

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
    padding_value                             ; otherwise

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]
    padding_value                                     ; 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:

# 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.