The function definition element

The function definition element
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The function element connects breakpoint sets (for gridded tables), independent variables, and data tables to their respective output variable.

    function* : name
        description? :
        provenance? :
            author : name, org, [email]
                address?
                    (address character data)
            functionCreationDate :
            extraDocRef* : docID
            modificationRef* : modID
        EITHER 
        {
          independentVarPts+ : varID, [name, units, sign, extrapolate, interpolate]
              (input values as character data)
          dependentVarPts : varID, [name, units, sign]
              (output values as character data)
        } 
        OR 
        {
          independentVarRef+ : varID, [min, max, extrapolate, interpolate]
          dependentVarRef : varID
          functionDefn : [name]
              CHOICE OF
              {
                CHOICE OF
                {
                  griddedTableRef : gtID
                OR
                  griddedTableDef : [name]
                    breakpointRefs
                        bpRef+ : bpID
                    confidenceBound? : value
                    dataTable
                        (gridded data table as character data)
                }
              }
              OR
              {
                CHOICE OF
                {
                  ungriddedTableRef : utID
                OR
                  ungriddedTableDef : [name]
                    confidenceBound? : value
                        dataPoint+
                        (coordinate/value sets as character data)
                }
              }
        }

function attributes:

name: A UNICODE name for the function.

function sub-elements:

description

The optional description element allows the author to describe the data contained within this function.

provenance

The optional provenance element allows the author to describe the source and history of the data within this function.

independentVarPts

If the author chooses, [he|she] can express a linearly-interpolated functions by specifying the independent (breakpoint) values sets as one or more independentVarPts which are comma-separated, monotonically increasing floating-point coordinate values corresponding to the dependentVarPts given next. In the case of multiple dimensions, more than one independentVarPts must be specified, one for each dimension. The mandatory varID attribute is used to connect each independentVarPts with an input variable.

An optional 'interpolate' attribute specifies the preference for using linear, quadratic, or cubic relaxed splines for calculating dependent values when the independent arguments are in between specified values. When not specified, the expectation would be a linear spline interpolation between points. The performance of interpolation of various orders is left up to the processing application. More information on relaxed spline interpolation may be found in [wiki01].

dependentVarPts

This element goes along with the previous element to specify a function table. Only one dependentVarPts may be specified. If the function is multidimensional, the convention is the last breakpoint dimension changes most rapidly in this comma-separated list of floating-point output values. The mandatory varID attribute is used to connect this table's output to an output variable.

independentVarRef

One or more of these elements refer to separately-defined variableDefs. For multidimensional tables, the order of specification is important and must match the order in which breakpoints are specified or the order of coordinates in ungridded table coordinate/value sets.

dependentVarRef

One dependentVarRef must be specified to connect the output of this function to a particular variableDef.

functionDefn

This element identifies either a separately-specified data table definition or specifies a private table, either gridded or ungridded.

griddedTableRef

If not defining a simple function table, the author may use this element to point to a separately-specified griddedTableDef element.

griddedTable

As an alternative to reutilization of a previously defined table, this element may be used to define a private output gridded table. See the writeup on griddedTableDef for more information. [Deprecated: use of this element is discouraged and will not be supported in future DAVE-ML versions. Use a griddedTableDef instead.]

ungriddedTableRef

If not using a simple function table, the author may use this element to point to separately-specified ungriddedTableDef element.

ungriddedTable

As an alternative to reuse of a previously defined table, this element may be used to define a private output ungridded table. See the writeup on ungriddedTableDef for more information. [Deprecated: use of this element is discouraged and will not be supported in future DAVE-ML versions. Use an griddedTableDef instead.]

Example 11. An example of a function which refers to a previously defined griddedTableDef

      <!-- ============================== -->
      <!-- Lower left body flap functions -->
      <!-- ============================== -->

  <function name="CLBFLL0">
    <description>
      Lower left body flap lookup function for lift, polynomial constant term.
    </description>
    <independentVarRef varID="DBFLL"  min="0.0" max="60." extrapolate="neither"/> 
    <independentVarRef varID="XMACH" min="0.3" max="4.0" extrapolate="neither"/>
    <dependentVarRef varID="CLBFLL0"/> 
    <functionDefn name="CLBFL0_fn">
      <griddedTableRef gtID="CLBFL0_table"/> 
    </functionDefn>
  </function>

	The independent variables must be given in the order of least-rapidly-changing to most-rapidly-changing values in the function table. The processing application needs to pay attention to the `extrapolate` attribute, which details how to treat a variable whose value exceeds the stated limits on input.
	The dependent variable (XML name `CLBFLL0`) is the output variable for this function. `CLBFLL0` must have been declared previously with a `variableDef` element.
	This is a reference to the previously declared `griddedTableDef`.

This example ties the input variables DBFLL and XMACH into output variable CLBFLLO through a function called CLBFLO_fn, which is represented by the linear interpolation of the gridded table defined by the CLBFL0_table griddedTableDef (see example 7 above).

Example 12. A function that has an internal table

      <!-- ================ -->
      <!-- Rudder functions -->
      <!-- ================ -->

<!-- The rudder functions are only used once, so their table
     definitions are internal to the function definition.
--> 

  <function name="CLRUD0">
    <description>
        Rudder contribution to lift coefficient,
        polynomial multiplier for constant term.
    </description>
    <provenance> 
      <author name="Bruce Jackson" org="NASA Langley Research Center" email="[email protected]"/>
      <functionCreationDate date="2003-01-31"/>
      <documentRef docID="REF01"/>
    </provenance>
    <independentVarRef varID="abs_rud"  min="0.0" max="15." extrapolate="neither"/>
    <independentVarRef varID="XMACH" min="0.3" max="4.0" extrapolate="neither"/>
    <dependentVarRef varID="CLRUD0"/>

    <functionDefn name="CLRUD0_fn">
      <griddedTableDef name="CLRUD0_table"> 
        <breakpointRefs>
          <bpRef bpID="DRUD_PTS"/>
          <bpRef bpID="XMACH1_PTS"/>
        </breakpointRefs>
        <dataTable> <!-- last breakpoint changes most rapidly -->
<!--	CLRUD0  POINTS  -->
<!-- RUD =    0.0    -->
 0.00000E+00 , 0.00000E+00 , 0.00000E+00 , 0.00000E+00 , 0.00000E+00 ,
 0.00000E+00 , 0.00000E+00 , 0.00000E+00 , 0.00000E+00 , 0.00000E+00 ,
 0.00000E+00 , 0.00000E+00 , 0.00000E+00 ,
<!-- RUD =   15.0    -->
-0.13646E-01 , 0.26486E-01 , 0.16977E-01 ,-0.16891E-01 , 0.10682E-01 ,
 0.75071E-02 , 0.53891E-02 ,-0.30802E-02 ,-0.59013E-02 ,-0.95733E-02 ,
 0.00000E+00 , 0.00000E+00 , 0.00000E+00 ,
<!-- RUD =   30.0    -->
-0.12709E-02 , 0.52971E-01 , 0.33953E-01 ,-0.33782E-01 , 0.21364E-01 ,
 0.15014E-01 , 0.10778E-01 ,-0.61604E-02 ,-0.11803E-01 ,-0.19147E-01 ,
 0.00000E+00 , 0.00000E+00 , 0.00000E+00 
        </dataTable>
      </griddedTable>
    </functionDefn>
  </function>

	This comment helps humans understand the reason for an embedded table.
	The `provenance` element is required by the AIAA standard.
	This example has an embedded gridded table.

In this example, the function CLRUD0 returns, in the variable CLRUD0, the value of function CLRUD0_fn represented by gridded table CLRUD0_table. The inputs to the function are abs_rud and XMACH which are used to normalize breakpoint sets DRUD_PTS and XMACH1_PTS respectively. The input variables are limited between 0.0 to 15.0 and 0.3 to 4.0, respectively.

Example 13. A simple one-dimensional function

<function name="CL">
  <independentVarPts varID="alpdeg"> 
   -4.0, 0., 4.0, 8.0, 12.0, 16.0
  </independentVarPts>
  <dependentVarPts varID="cl"> 
    0.0, 0.2, 0.4, 0.8, 1.0, 1.2
  </dependentVarPts>
</function>

	Breakpoints in angle-of-attack are listed here.
	Values of `cl` are given, corresponding to the angle-of-attack breakpoints given previously.

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