6.2.5. The ungridded table definition element

6.2.5. The ungridded table definition element
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The ungriddedTableDef element defines a set of non-orthogonal data points, along with their independent values (coordinates), corresponding with the dependent value of an arbitrary function.

A 'non-orthogonal' data set, as opposed to a gridded or 'orthogonal' data set, means that the independent values are not laid out in an orthogonal grid. This form must be used if the dependent coordinates in any table dimension cannot be expressed by a single monotonically-increasing vector.

See the excerpts below for two instances of ungridded data.

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.

    ungriddedTableDef* : [utID, name, units]
        description? :
            (description character data)
        provenanceRef? : provID  OR
        provenance? :
            author : name, org, [email]
                address? :
                    (address character data)
            creationDate :
                (date in YYYY-MM-DD format, character data)
            documentRef* : docID
            modificationRef* : modID
        uncertainty? : effect
            (normalPDF : numSigmas | uniformPDF )
        dataPoint+ :

ungriddedTableDef attributes:

utID: A mandatory XML-legal name that is unique within the file
name: An optional UNICODE name for the table (may be the same string as utID).
units: Optional units-of-measure for the table's output signal.

ungriddedTableDef sub-elements:

description: The optional description element allows the author to describe the data contained within this ungriddedTable.
provenance: The optional provenance element allows the author to describe the source and history of the data within this ungriddedTable. Alternatively, a <provenanceRef> reference can be made to a previously defined provenance.
uncertainty: This optional element, if present, describes the uncertainty of this parameter. See the section on Statistics below for more information about this element.
dataPoint: One or more sets of coordinate and output numeric values of the function at various locations within it's input space. This element includes one coordinate for each function input variable. Parsing this information into a usable interpolative function is up to the implementor. By convention, the coordinates are listed in the same order that they appear in the using function.

Example 9. An excerpt showing an ungriddedTableDef element, encoding the data depicted in here.

This two-dimensional function table is an example provided by Dr. Peter Grant of the University of Toronto. Such a table definition would be used in a subsequent function to describe how an output variable would be defined based on two independent input variables. The function table doesn't indicate which input and output variables are represented; this information is supplied by the function element later so that a single function table can be reused by multiple functions.


 <ungriddedTableDef name="CLBASIC as function of flap angle and angle of 
        attack" utID="CLBAlfaFlap_Table" units="">
   <description>
     CL basic as a function of flap angle and angle of attack. Note the alpha 
     used in this table is with respect to the wing design plane (in degrees). 
     Flap is in degrees as well.
   </description>

   <provenance>
     <author name="Peter Grant" org="UTIAS"/>  
     <creationDate date="2006-11-01"/>
     <documentRef refID="PRG1" />
   </provenance>

   <!--For ungridded tables you provide a list of dataPoints--> 
        <dataPoint> 1.0 -5.00  -0.44 <!-- flap, alfawdp, CLB--></dataPoint>	
        <dataPoint> 1.0  10.00  0.95 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 1.0  12.00  1.12 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 1.0  14.00  1.26 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 1.0  15.00  1.32 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 1.0  17.00  1.41 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0 -5.00  -0.55 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  0.00  -0.03 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  5.00   0.50 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  10.00  1.02 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  12.00  1.23 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  14.00  1.44 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  16.00  1.63 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  17.00  1.70 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 5.0  18.00  1.75 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint modID='A'> 10.0 -5.00 -0.40 <!-- flap, alfawdp, CLB--></dataPoint>	
        <dataPoint> 10.0 14.00  1.57 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 10.0 15.00  1.66 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 10.0 16.00  1.75 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 10.0 17.00  1.80 <!-- flap, alfawdp, CLB--></dataPoint>
        <dataPoint> 10.0 18.00  1.84 <!-- flap, alfawdp, CLB--></dataPoint>
        
</ungriddedTableDef>

	Example courtesy of Dr. Peter Grant, U. Toronto
	Comments are a good idea for human readers
	For a two-dimensional table such as this one, data points give two columns of independent breakpoint values and third column of function value at those breakpoints.
	The `modID` attribute implies this point was edited during modification 'A' of this model, as described in the file header information.

Figure 2. The two-dimensional lift function given in Example 9, “ An excerpt showing an ungriddedTableDef element, encoding the data depicted in here. ”

Example 10. An excerpt from a sample aero model giving an example of a three-dimensional ungriddedTableDef element, encoding the data shown in Figure 3, “The three-dimensional function given in the previous example”.

In this example, the dependent coordinates all vary in each dimension.

     <!--===================================-->  
     <!--  Three-D Table Definition Example -->
     <!--===================================-->

     <ungriddedTableDef name="yawMomentCoefficientTable1" units="" utID="yawMomentCoefficientTable1">
                <!--  alpha,     beta,       delta -->  	
       <dataPoint> -1.8330592 -5.3490387 -4.7258599 -0.00350641</dataPoint>
       <dataPoint> -1.9302179 -4.9698462 0.2798654  -0.0120538</dataPoint>
       <dataPoint> -2.1213095 -5.0383145 5.2146443  -0.0207089</dataPoint>
       <dataPoint> 0.2522004  -4.9587161 -5.2312860 -0.000882368</dataPoint>
       <dataPoint> 0.3368831  -5.0797159 -0.3370540 -0.0111846</dataPoint>
       <dataPoint> 0.2987289  -4.9691198 5.2868938  -0.0208758</dataPoint>
       <dataPoint> 1.8858257  -5.2077654 -4.7313074 -0.00219842</dataPoint>
       <dataPoint> 1.8031083  -4.7072954 0.0541231  -0.0111726</dataPoint>
       <dataPoint> 1.7773659  -5.0317988 5.1507477  -0.0208074</dataPoint>
       <dataPoint> 3.8104785  -5.2982162 -4.7152852 -0.00225906</dataPoint>
       <dataPoint> 4.2631596  -5.1695257 -0.1343410 -0.0116563</dataPoint>
       <dataPoint> 4.0470946  -5.2541017 5.0686926  -0.0215506</dataPoint>
       <dataPoint> -1.8882611 0.2422452  -5.1959304 0.0113462</dataPoint>
       <dataPoint> -2.1796091 0.0542085  0.2454711  -0.000253915</dataPoint>
       <dataPoint> -2.2699103 -0.3146657 4.8638859  -0.00875431</dataPoint>
       <dataPoint> 0.0148579  0.1095599  -4.9639500 0.0105144</dataPoint>
       <dataPoint> -0.1214591 -0.0047960 0.2788827  -0.000487753</dataPoint>
       <dataPoint> 0.0610233  0.2029588  5.0831767  -0.00816086</dataPoint>
       <dataPoint> 1.7593356  -0.0149007 -5.0494446 0.0106762</dataPoint>
       <dataPoint> 1.9717048  -0.0870861 0.0763833  -0.000332616</dataPoint>
       <dataPoint> 2.0228263  -0.2962294 5.1777078  -0.0093807</dataPoint>
       <dataPoint> 4.0567507  -0.2948622 -5.1002243 0.010196</dataPoint>
       <dataPoint> 3.6534822  0.2163747  0.1369900  0.000312733</dataPoint>
       <dataPoint> 3.6848003  0.0884533  4.8214805  -0.00809437</dataPoint>
       <dataPoint> -2.3347682 5.2288720  -4.7193014 0.02453</dataPoint>
       <dataPoint> -2.3060350 4.9652745  0.2324610  0.0133447</dataPoint>
       <dataPoint> -1.8675176 5.0754646  5.1169942  0.00556052</dataPoint>
       <dataPoint> 0.0004379  5.1220145  -5.2734993 0.0250468</dataPoint>
       <dataPoint> -0.1977035 4.7462188  0.0664495  0.0124083</dataPoint>
       <dataPoint> -0.1467742 5.0470092  5.1806131  0.00475277</dataPoint>
       <dataPoint> 1.6599338  4.9352809  -5.1210532 0.0242646</dataPoint>
       <dataPoint> 2.2719825  4.8865093  0.0315210  0.0125658</dataPoint>
       <dataPoint> 2.0406858  5.3253471  5.2880688  0.00491779</dataPoint>
       <dataPoint> 4.0179983  5.0826426  -4.9597629 0.0243518</dataPoint>
       <dataPoint> 4.2863811  4.8806558  -0.2877697 0.0128886</dataPoint>
       <dataPoint> 3.9289361  5.2246849  4.9758705  0.00471241</dataPoint>
       <dataPoint> -2.2809763 9.9844584  -4.8800790 0.0386951</dataPoint>
       <dataPoint> -2.0733070 9.9204337  0.0241722  0.027546</dataPoint>
       <dataPoint> -1.7624546 9.9153493  5.1985794  0.0188357</dataPoint>
       <dataPoint> 0.2279962  9.8962508  -4.7811258 0.0375762</dataPoint>
       <dataPoint> -0.2800363 10.3004593 0.1413907  0.028144</dataPoint>
       <dataPoint> 0.0828562  9.9008011  5.2962722  0.0179398</dataPoint>
       <dataPoint> 1.8262230  10.0939436 -4.6710211 0.037712</dataPoint>
       <dataPoint> 1.7762123  10.1556398 -0.1307093 0.0278079</dataPoint>
       <dataPoint> 2.2258599  9.8009720  4.6721747  0.018244</dataPoint>
       <dataPoint> 3.7892651  9.8017197  -4.8026383 0.0368199</dataPoint>
       <dataPoint> 4.0150716  9.6815531  -0.0630955 0.0252014</dataPoint>
       <dataPoint> 4.1677953  9.8754433  5.1776223  0.0164312</dataPoint>
     </ungriddedTableDef>

	Example courtesy of Mr. Geoff Brian, DSTO
	Columns are labelled with an XML comment for human readers; association of each input (alpha and beta) and the single output (delta) with the function inputs and output happens in the context of the referring function definition(s) which gives independent variables and the dependent (output) variable.

Figure 3. The three-dimensional function given in the previous example

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