# Re: In search of elegant indices searching

Dear Tim,

I am a bit tired today and the task is a little involved,
so I try to let others work for me I want to evaluate some mathematical function , which has
arguments ‘x’,‘y’,‘z’ etc. (think of something like

(x,y,z) -> 5zy+x*y**2)

)
at different values for these variables x,y,z.
Actually, I’ve got data, and I am trying to get back that function, or
an
approximation to it, from these data, so it’s actually a (multivariate)
interpolation problem. To do that efficiently, I need to hold
several variable values fixed at some point in time while varying
others.

So, in my example, if I have a Hash like

my_hash={‘x’,[1,1,3,1,5,6],‘w’,[1,2,3,1,4,5],‘y’,[1,1,1,4,4,6]} ,

then these are coordinates where the unknown function is evaluated at.

If, now, the nice and wonderful method I search for, gives me

res={{‘x’=>1,‘w’=>1}=>[0,3],{‘x’=>3,‘w’=>3}=>,{‘x’=>5,‘w’=>4}=>,{‘x’=>6,
‘w’=>5}=>},

I know that at the 0-th and 3-th measurement point, ‘x’ and ‘w’ didn’t
vary,
so, any
change in the function values is due to the change of ‘y’ from 1 to 4.

Do you have any elegant ideas for that ?

Thank you,

Best regards,

Axel

my_hash={‘x’,[1,1,3,1,5,6],‘w’,[1,2,3,1,4,5],‘y’,[1,1,1,4,4,6]} ,

res={{‘x’=>1,‘w’=>1}=>[0,3],{‘x’=>3,‘w’=>3}=>,{‘x’=>5,‘w’=>4}=>,{‘x’=>6,
‘w’=>5}=>},

I know that at the 0-th and 3-th measurement point, ‘x’ and ‘w’ didn’t vary,
so, any change in the function values is due to the change of ‘y’ from 1 to 4.

I still don’t get it:

{‘x’=>1,‘w’=>1}=>[0,3]
means the 0th and 3rd point are both ‘1’

{‘x’=>3,‘w’=>3}=>
means the 2nd point is 3 in both

{‘x’=>5,‘w’=>4}=>
now it gets weird, this means the 4th position of x is 5 and of w is
4… Why only that result? Seems a little arbitrary, why doesn’t the
result contain:
{‘x’=>1,‘w’=>2}=>
?

And how come `y` is left out of the results alltogether?