The number of inputs to a RateMap is the same as the number of inputs to its encapsulated Mapping. The number of outputs from a RateMap is always one. This one output equals the rate of change of a specified output of the encapsulated Mapping with respect to a specified input of the encapsulated Mapping (the input and output to use are specified when the RateMap is created).
A RateMap which has not been inverted does not define an inverse transformation. If a RateMap has been inverted then it will define an inverse transformation but not a forward transformation.
AST A Library for Handling World Coordinate Systems in Astronomy