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from qgis.utils import iface
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layer = iface.activeLayer()
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layer.startEditing()
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compare_field_index = 15
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concat_field_index = 5 
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new_field_index = 10
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feature_dict = {f.id(): f for f in layer.getFeatures()}
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for f in feature_dict.values(): 
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  if f[concat_field_index]: 
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    new_field_text = f[concat_field_index]
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  else:
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    new_field_text = ''
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  # Another for loop to go over features
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  for compare_f in feature_dict.values():
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    if (f != compare_f
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        and f[compare_field_index] == compare_f[compare_field_index]):
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      print '%s matches' % f[compare_field_index]
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      if compare_f[concat_field_index]:
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        new_field_text += compare_f[concat_field_index]
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  print new_field_text
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  f[new_field_index] = new_field_text
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layer.commitChanges()