code: def fiedler(a):
      """Returns a symmetric Fiedler matrix
  
      Given an sequence of numbers ``a``, Fiedler matrices have the structure
      ``F[i, j] = np.abs(a[i] - a[j])``, and hence zero diagonals and nonnegative
      entries. A Fiedler matrix has a dominant positive eigenvalue and other
      eigenvalues are negative. Although not valid generally, for certain inputs,
      the inverse and the determinant can be derived explicitly.
  
      Args:
          a (cupy.ndarray): coefficient array
  
      Returns:
          cupy.ndarray: the symmetric Fiedler matrix
  
      .. seealso:: :func:`cupyx.scipy.linalg.circulant`
      .. seealso:: :func:`cupyx.scipy.linalg.toeplitz`
      .. seealso:: :func:`scipy.linalg.fiedler`
      """
      if a.ndim != 1:
          raise ValueError("Input `a` must be a 1D array.")
      if a.size == 0:
          return cupy.zeros(0)
      if a.size == 1:
          return cupy.zeros((1, 1))
      a = a[:, None] - a
      return cupy.abs(a, out=a)
  
imports: import math
  import warnings
  import cupy
  from cupy import _core
  from cupyx.scipy.linalg import _uarray
label_desc: Use image node_id 16 for calling a global function with example usage: fiedler(a) and returns: cupy, cupy, cupy