On Jun 18, 2007, at 1:28 PM, Giovanni A. Cignoni wrote:

The main change to the DTD is addition of 'discrete' as a supported interpolation method for tabular data, yielding a stair- step response from such a function. This came from a suggestion from Geoff Brian of Australia's DSTO.

"Discrete" interpolation is the method also known as "nearest neighbor"? Being x in [a, b], f(x) is f(a) or f(b) depending on x being nearer to a or b. Correct?

Thanks in advance, ciao,
Giovanni Cignoni.

This is a good question, Giovanni. I see that we need to be much more rigorous in our definition of 'discrete' as it applies to these tables.

I had assumed the interpretation would be as follows (I don't think this is 'nearest-neighbor')...

In the case of a one-dimensional function, if the independentVarPts are defined as

     [a, b, c, d]

and an arbitrary griddedTable points are defined as

     [8.5, 9.0, 9.5, 10.0]

the function f(x) would be evaluated as shown below:

f(x)   ^
10.0 - |                        o
       |                        |
       |                        |
 9.5 - |                 o------o
       |                 |
       |                 |
 9.0 - |          o------o
       |          |
       |          |
 8.5 - |   o------o
       |----------------------------------> X
           |      |      |      |
           a      b      c      d

so the independent values state where the function changes value.

Nearest-neighbor would put the transitions exactly between the independent break points.

I'd appreciate any feedback on this topic, especially from Geoff Brian who is apparently making use of this 'extension' to DAVE-ML.

-- Bruce

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