Efficient table lookup

I have a simple question, but related answers in this forum are confusing to me and seem overly complex. Thermodynamic properties of gases such as enthalpy h and entropy s are often given in tables grouped by pressure, then sorted by temperature. For example, a table might look like this:

P (kPa)  T (K)  h (J)    s (J/K)
 100      200   -50.0    -0.202
 100      210   -55.3    -0.198
 100      220   -60.2    -0.188
 200      200   -100.1   -0.717
 200      210   -95.2    -0.683
 200      220   -92.4    -0.659

I have imported a much larger version of the table above and I have defined a vector for each column. The vectors are called P, T, h, and s. What's the simplest, most computationally-efficient method of linearly interpolating h and s for a given P and T?

Answer 1

[Sean de Wolski]

One of these:

doc interp1
doc interp2

Are h,s dependent on both P,T? If so, interp2(), else if each is dependent only on one, interp1()

[Chad Greene]

Yes, it would be interp2, but I do not understand how to use meshgrid. It's especially unintuitive because my table is much larger than the one I gave in the example above--I would like to return entropy, enthalpy, density, Cp, Cv, etc as a function. How do I manage meshgrid and interp2 with such a large table?

[Walter Roberson]

Use ndgrid() if you have more than 2 variables being spanned.

Also consider using bsxfun()

[Jan]

interp1() is surprisingly slow. Some replacements found in the FEX are more than 100 times faster. I did not find a submission, which solves the problem directly for two variables. But I expect a modified version will beat Matlab's interpolation methods easily.

[Sean de Wolski]

in you above case you would define a grid as:

[xx yy] = meshgrid([100 200],[200 210 220]);

This would be the grid corresponding to your data. You would need to reshape h, s so that they are 2x3 (or 3x2)matrices with each point being the corresponding point from P,T. Then you need to make a new grid you wish to interpolate to, for example:

[xxi yyi] = meshgrid(100:10:200,200:1:220);

And then interp2 with the above, twice, once for h and once for s.

hi = interp2(the_other_stuff, h)

si = interp2(the_other_stuff,s)

Vi will

[Chad Greene]

Ah, reshaping was the ticket. I followed the wage example in the interp2 help file, and in doing so avoided the need for any meshing.

Answer 2

[Honglei Chen]

On top of Sean's answer. In case your grid is not uniform (although it seems that they are based on your description), you can use griddedInterpolant and TriScatteredInterp

doc griddedInterpolant
doc TriScatteredInterp

[Chad Greene]

Hmm... I don't have griddedInterpolant. Regarding TriScatteredInterp, I've found that it's awfully slow considering the algebraic calculation of a simple linear 2D interpolation could be done by hand. I am not volunteering to actually do these calculations by hand, but the slowness of TriScatteredInterp makes me think it's doing a lot more work than it needs to do.

[Sean de Wolski]

Your data appears to be on regular grid and thus you are correct. The triangulated interpolatants are overkill.