code: def convNd(input, kernel, pad, stride=1, groups=1, n=None):
      """Execute a batch of a stack of N-dimensional convolutions.
  
      Parameters
      ----------
      input : numpy array
      kernel : numpy array
      pad : {0, 'valid', 'same', 'full'}, int or tuple of int
      stride : int or tuple of int
      groups: int
      n : int
  
      Returns
      -------
      numpy array
      """
      if groups > 1:
          input = input.reshape(
              input.shape[0], groups, -1, *input.shape[2:]
          )
          kernel = kernel.reshape(groups, -1, *kernel.shape[1:])
          return np.concatenate(
              [
                  convNd(
                      input[:, g], kernel[g], pad, stride, groups=1, n=n
                  )
                  for g in range(groups)
              ],
              axis=1,
          )
  
      if n is None:
          n = input.ndim - 2
      if pad not in ["valid", "same", "full"]:
          pad = as_tuple(pad, n, int)
          input = np.pad(
              input, [(p, p) for p in (0, 0) + pad], mode="constant"
          )
          pad = "valid"
  
      output = np.zeros(
          (input.shape[0], kernel.shape[0])
          + tuple(
              i + k - 1
              for i, k in zip(input.shape[2:], kernel.shape[2:])
          )
      )
  
      if n == 1:
          for i in range(kernel.shape[2]):
              f = kernel[:, :, i : i + 1]
              c = (input[:, np.newaxis] * f).sum(axis=2)
              output[:, :, i : i + input.shape[2]] += c
      elif n == 2:
          for i in range(kernel.shape[2]):
              for j in range(kernel.shape[3]):
                  f = kernel[:, :, i : i + 1, j : j + 1]
                  c = (input[:, np.newaxis] * f).sum(axis=2)
                  output[
                      :,
                      :,
                      i : i + input.shape[2],
                      j : j + input.shape[3],
                  ] += c
      elif n == 3:
          for i in range(kernel.shape[2]):
              for j in range(kernel.shape[3]):
                  for k in range(kernel.shape[4]):
                      f = kernel[:, :, i : i + 1, j : j + 1, k : k + 1]
                      c = (input[:, np.newaxis] * f).sum(axis=2)
                      output[
                          :,
                          :,
                          i : i + input.shape[2],
                          j : j + input.shape[3],
                          k : k + input.shape[4],
                      ] += c
      else:
          raise NotImplementedError(
              "convNd() only supports n in (1, 2, 3)"
          )
  
      if pad == "valid":
          trim = tuple(k - 1 for k in kernel.shape[2:])
          slices = [slice(None), slice(None)]
          slices += [slice(t, -t or None) for t in trim]
          output = output[slices]
      elif pad == "same":
          shift = tuple((k - 1) // 2 for k in kernel.shape[2:])
          slices = [slice(None), slice(None)]
          slices += [
              slice(s, s + i) for s, i in zip(shift, input.shape[2:])
          ]
          output = output[slices]
  
      stride = as_tuple(stride, n, int)
      if any(s > 1 for s in stride):
          slices = [slice(None), slice(None)]
          slices += [slice(None, None, s) for s in stride]
          output = output[slices]
  
      return output
  
imports: import numpy
  import pytest
  import importlib
  import theano
  from theano import tensor
  import lasagne
  from lasagne.utils import floatX, as_tuple
label_desc: Use image node_id 1 for calling a global function with example usage: convNd(input, kernel, pad, stride, groups, n) and returns: output, np