Help with interpolating - INTERP2

Hi, I have a table with density values dependent on pressure and temperature, rho(p,T), and I want to be able to interpolate between them. I've tried using interp2, but I keep getting errors. This is an example (lot of numbers, but the code is easy):

p = [8*10^6 8*10^6 8*10^6 8*10^6 8*10^6 8*10^6 8*10^6 8*10^6 8*10^6;
  10*10^6 10*10^6 10*10^6 10*10^6 10*10^6 10*10^6 10*10^6 10*10^6 10*10^6];
T = [280.000 300.000 305.000 310.000 315.000 320.000 325.000 330.000 350.000;
  280.000 300.000 305.000 310.0000 315.000 320.000 325.000 330.000 350.000];
rho = [922.92 753.17 656.77 327.71 261.29 231.91 212.90 198.87 164.16;
  938.22 801.62 751.67 685.77 586.02 448.28 358.04 310.25 228.80];

density = interp2(p, T, rho, 8*10^6, 280.00)

I keep getting the error: "X and Y must be matrices produced by MESHGRID. Use TriScatteredInterp instead of INTERP2 for scattered data." But if I try using TriScatteredInterp I get the error "Input data point locations have invalid dimension." I'm not able to understand what the problem really is. Can someone help me?

[the cyclist]

Just as a side comment, I believe it is more accurate (and faster) to use the notation 8e6 rather than 8*10^6, which involves calculation.

Answer 1

[the cyclist]

Does this give what you expect?

density = interp2(p', T', rho', 8*10^6, 280.00)

Notice that I just transposed your inputs.

Or you could try TriScatteredInterp(), as suggested. In your case, the proper syntax is

F = TriScatteredInterp(p(:),T(:),rho(:));
density = F(8e6,280)

All in all, I think I would perform this calculation as:

p = [8e6 1e7];
T = [280 300 305 310 315 320 325 330 350];

[pp,TT] = meshgrid(p,T);

rho = [922.92 753.17 656.77 327.71 261.29 231.91 212.90 198.87 164.16;
  938.22 801.62 751.67 685.77 586.02 448.28 358.04 310.25 228.80]';

density = interp2(pp,TT,rho,8e6,280.00)

Answer 2

[Sean de Wolski]

From:

doc interp2

X and Y must be monotonic

I was confused for a minute too. Use TriScatteredInterp.