### AST_RATE

Calculate the rate of change of a Mapping output

#### Description:

This routine evaluates the rate of change of a specified output of the supplied Mapping with respect to a specified input, at a specified input position.

The result is estimated by interpolating the function using a fourth order polynomial in the neighbourhood of the specified position. The size of the neighbourhood used is chosen to minimise the RMS residual per unit length between the interpolating polynomial and the supplied Mapping function. This method produces good accuracy but can involve evaluating the Mapping 100 or more times.

#### Invocation

RESULT = AST_RATE( THIS, AT, AX1, AX2, STATUS )

#### Arguments

##### THIS = INTEGER (Given)
Pointer to the Mapping to be applied.
##### AT( $\ast$ ) = DOUBLE PRECISION (Given)
An array holding the axis values at the position at which the rate of change is to be evaluated. The number of elements in this array should equal the number of inputs to the Mapping.
##### AX1 = INTEGER (Given)
The index of the Mapping output for which the rate of change is to be found (output numbering starts at 1 for the first output).
##### AX2 = INTEGER (Given)
The index of the Mapping input which is to be varied in order to find the rate of change (input numbering starts at 1 for the first input).
##### STATUS = INTEGER (Given and Returned)
The global status.

#### Returned Value

##### AST_RATE = DOUBLE PRECISION
The rate of change of Mapping output AX1 with respect to input AX2, evaluated at AT, or AST__BAD if the value cannot be calculated.

#### Notes:

• A value of AST__BAD will be returned if this function is invoked with the global error status set, or if it should fail for any reason.