code: def gradient(f, *varargs, axis=None, edge_order=1):
      """Return the gradient of an N-dimensional array.
  
      The gradient is computed using second order accurate central differences
      in the interior points and either first or second order accurate one-sides
      (forward or backwards) differences at the boundaries.
      The returned gradient hence has the same shape as the input array.
  
      Args:
          f (cupy.ndarray): An N-dimensional array containing samples of a scalar
              function.
          varargs (list of scalar or array, optional): Spacing between f values.
              Default unitary spacing for all dimensions. Spacing can be
              specified using:
  
              1. single scalar to specify a sample distance for all dimensions.
              2. N scalars to specify a constant sample distance for each
                 dimension. i.e. `dx`, `dy`, `dz`, ...
              3. N arrays to specify the coordinates of the values along each
                 dimension of F. The length of the array must match the size of
                 the corresponding dimension
              4. Any combination of N scalars/arrays with the meaning of 2. and
                 3.
  
              If `axis` is given, the number of varargs must equal the number of
              axes. Default: 1.
          edge_order ({1, 2}, optional): The gradient is calculated using N-th
              order accurate differences at the boundaries. Default: 1.
          axis (None or int or tuple of ints, optional): The gradient is
              calculated only along the given axis or axes. The default
              (axis = None) is to calculate the gradient for all the axes of the
              input array. axis may be negative, in which case it counts from the
              last to the first axis.
  
      Returns:
          gradient (cupy.ndarray or list of cupy.ndarray): A set of ndarrays
          (or a single ndarray if there is only one dimension) corresponding
          to the derivatives of f with respect to each dimension. Each
          derivative has the same shape as f.
  
      .. seealso:: :func:`numpy.gradient`
      """
      f = cupy.asanyarray(f)
      ndim = f.ndim  # number of dimensions
      axes = internal._normalize_axis_indices(
          axis, ndim, sort_axes=False
      )
  
      len_axes = len(axes)
      n = len(varargs)
      if n == 0:
          # no spacing argument - use 1 in all axes
          dx = [1.0] * len_axes
      elif n == 1 and cupy.ndim(varargs[0]) == 0:
          # single scalar for all axes
          dx = varargs * len_axes
      elif n == len_axes:
          # scalar or 1d array for each axis
          dx = list(varargs)
          for i, distances in enumerate(dx):
              if cupy.ndim(distances) == 0:
                  continue
              elif cupy.ndim(distances) != 1:
                  raise ValueError(
                      "distances must be either scalars or 1d"
                  )
              if len(distances) != f.shape[axes[i]]:
                  raise ValueError(
                      "when 1d, distances must match "
                      "the length of the corresponding dimension"
                  )
              if numpy.issubdtype(distances.dtype, numpy.integer):
                  # Convert numpy integer types to float64 to avoid modular
                  # arithmetic in np.diff(distances).
                  distances = distances.astype(numpy.float64)
              diffx = cupy.diff(distances)
              # if distances are constant reduce to the scalar case
              # since it brings a consistent speedup
              if (diffx == diffx[0]).all():  # synchronize
                  diffx = diffx[0]
              dx[i] = diffx
      else:
          raise TypeError("invalid number of arguments")
  
      if edge_order > 2:
          raise ValueError("'edge_order' greater than 2 not supported")
  
      # use central differences on interior and one-sided differences on the
      # endpoints. This preserves second order-accuracy over the full domain.
  
      outvals = []
  
      # create slice objects --- initially all are [:, :, ..., :]
      slice1 = [slice(None)] * ndim
      slice2 = [slice(None)] * ndim
      slice3 = [slice(None)] * ndim
      slice4 = [slice(None)] * ndim
  
      otype = f.dtype
      if numpy.issubdtype(otype, numpy.inexact):
          pass
      else:
          # All other types convert to floating point.
          # First check if f is a numpy integer type; if so, convert f to float64
          # to avoid modular arithmetic when computing the changes in f.
          if numpy.issubdtype(otype, numpy.integer):
              f = f.astype(numpy.float64)
          otype = numpy.float64
  
      for axis, ax_dx in zip(axes, dx):
          if f.shape[axis] < edge_order + 1:
              raise ValueError(
                  "Shape of array too small to calculate a numerical gradient, "
                  "at least (edge_order + 1) elements are required."
              )
          # result allocation
          out = cupy.empty_like(f, dtype=otype)
  
          # spacing for the current axis
          uniform_spacing = cupy.ndim(ax_dx) == 0
  
          # Numerical differentiation: 2nd order interior
          slice1[axis] = slice(1, -1)
          slice2[axis] = slice(None, -2)
          slice3[axis] = slice(1, -1)
          slice4[axis] = slice(2, None)
  
          if uniform_spacing:
              out[tuple(slice1)] = (
                  f[tuple(slice4)] - f[tuple(slice2)]
              ) / (2.0 * ax_dx)
          else:
              dx1 = ax_dx[0:-1]
              dx2 = ax_dx[1:]
              dx_sum = dx1 + dx2
              a = -(dx2) / (dx1 * dx_sum)
              b = (dx2 - dx1) / (dx1 * dx2)
              c = dx1 / (dx2 * dx_sum)
              # fix the shape for broadcasting
              shape = [1] * ndim
              shape[axis] = -1
              a.shape = b.shape = c.shape = tuple(shape)
              # 1D equivalent -- out[1:-1] = a * f[:-2] + b * f[1:-1] + c * f[2:]
              out[tuple(slice1)] = (
                  a * f[tuple(slice2)]
                  + b * f[tuple(slice3)]
                  + c * f[tuple(slice4)]
              )
  
          # Numerical differentiation: 1st order edges
          if edge_order == 1:
              slice1[axis] = 0
              slice2[axis] = 1
              slice3[axis] = 0
              dx_0 = ax_dx if uniform_spacing else ax_dx[0]
              # 1D equivalent -- out[0] = (f[1] - f[0]) / (x[1] - x[0])
              out[tuple(slice1)] = (
                  f[tuple(slice2)] - f[tuple(slice3)]
              ) / dx_0
  
              slice1[axis] = -1
              slice2[axis] = -1
              slice3[axis] = -2
              dx_n = ax_dx if uniform_spacing else ax_dx[-1]
              # 1D equivalent -- out[-1] = (f[-1] - f[-2]) / (x[-1] - x[-2])
              out[tuple(slice1)] = (
                  f[tuple(slice2)] - f[tuple(slice3)]
              ) / dx_n
  
          # Numerical differentiation: 2nd order edges
          else:
              slice1[axis] = 0
              slice2[axis] = 0
              slice3[axis] = 1
              slice4[axis] = 2
              if uniform_spacing:
                  a = -1.5 / ax_dx
                  b = 2.0 / ax_dx
                  c = -0.5 / ax_dx
              else:
                  dx1 = ax_dx[0]
                  dx2 = ax_dx[1]
                  dx_sum = dx1 + dx2
                  a = -(2.0 * dx1 + dx2) / (dx1 * (dx_sum))
                  b = dx_sum / (dx1 * dx2)
                  c = -dx1 / (dx2 * (dx_sum))
              # 1D equivalent -- out[0] = a * f[0] + b * f[1] + c * f[2]
              out[tuple(slice1)] = (
                  a * f[tuple(slice2)]
                  + b * f[tuple(slice3)]
                  + c * f[tuple(slice4)]
              )
  
              slice1[axis] = -1
              slice2[axis] = -3
              slice3[axis] = -2
              slice4[axis] = -1
              if uniform_spacing:
                  a = 0.5 / ax_dx
                  b = -2.0 / ax_dx
                  c = 1.5 / ax_dx
              else:
                  dx1 = ax_dx[-2]
                  dx2 = ax_dx[-1]
                  dx_sum = dx1 + dx2
                  a = (dx2) / (dx1 * (dx_sum))
                  b = -dx_sum / (dx1 * dx2)
                  c = (2.0 * dx2 + dx1) / (dx2 * (dx_sum))
              # 1D equivalent -- out[-1] = a * f[-3] + b * f[-2] + c * f[-1]
              out[tuple(slice1)] = (
                  a * f[tuple(slice2)]
                  + b * f[tuple(slice3)]
                  + c * f[tuple(slice4)]
              )
          outvals.append(out)
  
          # reset the slice object in this dimension to ":"
          slice1[axis] = slice(None)
          slice2[axis] = slice(None)
          slice3[axis] = slice(None)
          slice4[axis] = slice(None)
  
      if len_axes == 1:
          return outvals[0]
      else:
          return outvals
  
imports: import warnings
  import numpy
  import cupy
  from cupy._core import _routines_math
  from cupy._core import _fusion_thread_local
  from cupy._core import internal
label_desc: Use image node_id 11 for calling a global function with example usage: gradient(f) and returns: outvals, outvals