### AST_RATEMAP

Create a RateMap

#### Description:

This function creates a new RateMap and optionally initialises its attributes.

A RateMap is a Mapping which represents a single element of the Jacobian matrix of another Mapping. The Mapping for which the Jacobian is required is specified when the new RateMap is created, and is referred to as the " encapsulated Mapping" below.

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.

#### Invocation

RESULT = AST_RATEMAP( MAP, AX1, AX2, OPTIONS, STATUS )

#### Arguments

##### MAP = INTEGER (Given)
Pointer to the encapsulated Mapping.
##### AX1 = INTEGER (Given)
Index of the output from the encapsulated Mapping for which the rate of change is required. This corresponds to the delta quantity forming the numerator of the required element of the Jacobian matrix. The first axis has index 1.
##### AX2 = INTEGER (Given)
Index of the input to the encapsulated Mapping which is to be varied. This corresponds to the delta quantity forming the denominator of the required element of the Jacobian matrix. The first axis has index 1.
##### OPTIONS = CHARACTER $\ast$ ( $\ast$ ) (Given)
A character string containing an optional comma-separated list of attribute assignments to be used for initialising the new RateMap. The syntax used is identical to that for the AST_SET routine.
##### STATUS = INTEGER (Given and Returned)
The global status.

#### Returned Value

##### AST_RATEMAP = INTEGER
A pointer to the new RateMap.

#### Notes:

• The forward transformation of the encapsulated Mapping must be defined.

• Note that the component Mappings supplied are not copied by AST_RATEMAP (the new RateMap simply retains a reference to them). They may continue to be used for other purposes, but should not be deleted. If a RateMap containing a copy of its component Mappings is required, then a copy of the RateMap should be made using AST_COPY.

• A null Object pointer (AST__NULL) will be returned if this function is invoked with STATUS set to an error value, or if it should fail for any reason.