Re: table_model constraints

Jon -
I think I understand what you wrote.

It appears that this method will not produce the same
results if you exchange the axes: ie, if I switch
x and y, then the first splines are built in y.
I think it is important to point this out.

Let's consider a concrete example, namely, the one
in the LRM draft. I see data points for
x=-10,-9,-8,-7 and y=-10,-9,-8,-7,-6,-5,-4,-3

Note that there is only one data point with y=-3,
so if we built splines in y first, then that "spline"
would be constant.

I think your method would call for building 4 splines
for the Xi values -10,-9,-8,-7. These would be four
separate functions of y.

Now, if I wanted to compute the value of the table model
at x=8.2, y=7.6, I would compute the values of the four
Xi splines at y=7.6, and use these four data points to
compute a spline function of x, and then I would
evaluate this final spline function at x=8.2

Do I have this right?

In the case of this example, the actual function is
f(x,y) = (x-y)/5. The Xi splines would be straight lines,
and the function would be accurately reproduced by the
table model.

On the other hand, if I interchanged x and y, then
there are two splines, y=-3 and y=-4, that would be
constant because there is only one data point for each.
If I now try to evaluate the table_model for the point
x=-8, y=-3.5, I would get the value -1 instead of -0.9

> No Cartesian grid is required nor are derivatives
> although if you wanted there are methods to calculate them.

I see that the Cartesian grid is not required. However,
it looks like you want to minimize the number of discrete
X values. Ie, if I had noise in my X measurement, such
that the 3 data points in the example at -10 were
actually -10.1, -10, and -9.9, then I would have 3 splines
in the place of one, and they would all be constant in y,
instead of linear.

Also, though derivatives are (you say) not required for
the method, they will in general be required by the
analog solver.

-Geoffrey
Received on Wed Aug 11 10:25:09 2004