MatrixDiagV3

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

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

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
 }

# 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([[[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))
   ==> [[[1, 8, 0],  # Output shape: (2, 3, 3)
         [4, 2, 9],
         [0, 5, 3]],
        [[6, 2, 0],
         [9, 7, 3],
         [0, 1, 9]]]
 
 # LEFT_RIGHT alignment.
 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), align="LEFT_RIGHT")
   ==> [[[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]]