Mathematical interpolation

[etingwall]

Hi,

 

Let's say I've got a table of air properties in a MySQL database. For simplicity let's say it looks like:

 

Temperature | Density

100 | 1.03

150 | 0.99

200 | 0.94

300 | 0.87

400 | 0.82

 

Notice that the temperature data is not necessarily in equal increments.

 

I grab the data and create arrays with it.

 

Now I have a surface temperature $TSurface that will be in between these values....say $TSurface = 212

 

I want to interpolate the density data so that I can get the density at 212 degrees.

 

How would I grab the two temperatures above and below 212 and then the corresponding densities?

[corbin]

You will need to find some kind of regression calculator.

 

 

It's obviously not linear regression, but besides that, I have no idea.

[etingwall]

Thanks for the response...it's moving me in the right direction.

 

Maybe I included too much detail with the original question. The math involved is simple. For a novice like me, the hard part is figuring how to pull specific numbers out of the array.

 

If I have a value of 212, how can I grab 200 and 250 out of the array, along with the corresponding densities?

[.josh]

depends on what your array format is. 

 

Are you using a multi-dim array like this?

 

$data[0] = array('temp' => 100, 'dens' => 1.03);

$data[1] = array('temp' => 150, 'dens' => 0.99);

etc...

 

or are you doing a single key=>val temp=>dens array like this?

 

$data = array(100 => 1.03, 150 => 0.99, etc...);

 

Or are you doing some other array format?

[Daniel0]

You will need to find some kind of regression calculator.

 

 

It's obviously not linear regression, but besides that, I have no idea.

 

It's a fourth degree polynomial...

 

[tex]f(x) = -8 \cdot 10^{-11} \cdot x^4 + 8 \cdot 10^8 \cdot x^3 - .000027x^2 + .0028x + .948[/tex]

 

Approximately...

[.josh]

 

f(x) = -8*10^-11 * x⁴ + 8*10⁸ * x³ - .000027*x² + .0028x + .948

 

Hey I'm not sure if you knew or not, but we have a nifty latex button for this sort of thing.  Yep. Some admin recently installed it because he thought it would be useful. 

[Daniel0]

 

f(x) = -8*10^-11 * x⁴ + 8*10⁸ * x³ - .000027*x² + .0028x + .948

 

Hey I'm not sure if you knew or not, but we have a nifty latex button for this sort of thing.  Yep. Some admin recently installed it because he thought it would be useful. 

 

Thought of that after I posted and edited it shortly after

[etingwall]

Thanks for the input. This is what I ended up with. Using the high and low keys and high and low temperatures allows me to interpolate several different arrays for Diffusivity, Conductivity, etc.

 

$TInteriorAverage = ($TInteriorSurface + $TColdSpace)/2;
foreach($TemperatureArray as $key=>$value){
if($value-$TInteriorAverage>=0){
	$TInteriorHigh=$value;
	$InteriorHighKey=$key;
	$TInteriorLow=$LastValue;
	$InteriorLowKey=$LastKey;
	break;
	}
else{
	$LastValue=$value;
	$LastKey=$key;
}
}