The gridded table definition element

The gridded table definition element
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The griddedTableDef element defines a multi-dimensional table of values corresponding with the value of an arbitrary function at the intersection of a set of specified independent inputs. The coordinates along each dimension are defined in separate breakpointDef elements that are referenced within this element by bpRefs, one for each dimension.

The data contained within the data table definition are a comma-separated set of floating-point values. This list of values represents a multidimensional array whose size is inferred from the length of each breakpoint vector. For example, a two-dimensional table that is a function of an eight-element Mach breakpoint set and a ten-element angle-of-attack breakpoint set is expected to contain 80 comma-separated values.

By convention, the breakpointRefs are listed in order such that the last breakpoint set varies most rapidly in the associated data table listing.

An optional uncertainty element may be provided that represents the statistical variation in the values presented. See the section on Statistics below for more information about this element.

    griddedTableDef* : [gtID, name, units]
        description? :
            (description character data)
        provenance? :
            author : name, org, [xns, email]
                address? :
                    (address character data)
            functionCreationDate :
                (date in YYYY-MM-DD format, character data)
            documentRef* : docID
            modificationRef* : modID
        breakpointRefs :
	  bpRef+ : bpID
	uncertainty? : effect
            (normalPDF : numSigmas | uniformPDF : symmetry )
	dataTable
	  (character data)

griddedTableDef attributes:

gtID: An XML-legal name that is unique within the file.
name: A UNICODE name for the table (may be same as gtID).
units: The units-of-measure for the table's output signal. See the section on Conventions below.

griddedTableDef sub-elements:

description: The optional description element allows the author to describe the data contained within this griddedTable.
provenance: The optional provenance element allows the author to describe the source and history of the data within this griddedTable.
breakpointRefs: The mandatory breakpointRefs element contains separate bpRef elements, each pointing to a separately-defined breakpointDef. Thus, the independent coordinates associated with this function table are defined elsewhere and only a reference is given here. The order of appearance of the bpRefs is important; see the text above.
uncertainty: This optional element, if present, describes the uncertainty of this parameter. See the section on Statistics below for more information about this element.
dataTable: The numeric values of the function at the function vertices specified by the breakpoint sets are contained within this element, in a single comma-separated list. Parsing this list and storing it in the appropriate array representation is up to the implementor. By convention, the last breakpoint value increases most rapidly.

Exampleï¿½7.ï¿½An example of a griddedTableDef element

	<!-- ==================================== -->	
	<!-- Lower Body Flap Tables (definitions) -->
	<!-- ==================================== -->

  <griddedTableDef name="CLBFL0" gtID="CLBFL0_table">	
    <description>	
	Lower body flap contribution to lift coefficient,
	polynomial constant term
    </description>
    <provenance>	
      <author name="Bruce Jackson" org="NASA Langley Research Center" xns="@bjax"/>
      <functionCreationDate date="2003-01-31"/>
      <documentRef docID="REF01"/>
    </provenance>
    <breakpointRefs> 
      <bpRef bpID="DBFL_PTS"/>
      <bpRef bpID="XMACH1_PTS"/>
    </breakpointRefs>
    <dataTable> <!-- last breakpoint changes most rapidly --> 
<!--	CLBFL0	POINTS	-->
<!-- DBFL =        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 ,
<!-- DBFL =       15.0	--> 
-0.86429E-02 ,-0.10256E-01 ,-0.11189E-01 ,-0.12121E-01 ,-0.13520E-01 ,
-0.86299E-02 ,-0.53679E-02 , 0.76757E-02 , 0.11300E-01 , 0.62992E-02 ,
 0.51902E-02 , 0.38813E-02 , 0.37366E-02 ,
<!-- DBFL =       30.0	-->
 0.22251E-01 , 0.26405E-01 , 0.28805E-01 , 0.31206E-01 , 0.34806E-01 ,
 0.31321E-01 , 0.28996E-01 , 0.19698E-01 , 0.18808E-01 , 0.12755E-01 ,
 0.10804E-01 , 0.98493E-02 , 0.83719E-02 ,
<!-- DBFL =       45.0	-->
 0.29416E-01 , 0.34907E-01 , 0.38080E-01 , 0.41254E-01 , 0.46014E-01 ,
 0.42215E-01 , 0.39681E-01 , 0.29547E-01 , 0.28211E-01 , 0.19132E-01 ,
 0.16206E-01 , 0.14774E-01 , 0.12558E-01 ,
<!-- DBFL =       60.0	-->
 0.63779E-01 , 0.75685E-01 , 0.82566E-01 , 0.89446E-01 , 0.99767E-01 ,
 0.85587E-01 , 0.76127E-01 , 0.38301E-01 , 0.36569E-01 , 0.24800E-01 ,
 0.21007E-01 , 0.19151E-01 , 0.16278E-01
    </dataTable>
  </griddedTableDef>

	Comments are a good idea for human readers
	`name` is used for documentation purposes; `gtID` is intended for automatic wiring (autocode) tools.
	Descriptions are a good idea whenever possible - Here we explain the contents of the function represented by the data points.
	`provenance` is the story of the origin of the data.
	These `bpRef`s are in the same order as the table is wrapped (see text above) and must be reflected in the referencing function in the same order. In this example, the referencing function must list the `independentVarRefs` such that the signal that represents delta body flap (`DBFL`) must precede the reference to the signal that represents Mach number (`XMACH`).
	The points listed within the `dataTable` element are given as if the last `bpRef` varies most rapidly. See the discussion above.
	Embedded comments are a good idea.

This non-linear function table is used by a subsequent function in example 9 to specify an output value based on two inputs values - body flap deflection and Mach number. This table is defined outside of a function element because this particular function table is used by two functions - one for the left lower body flap and one for the right lower body flap; thus, their actual independent (input) variable values might be different at.

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