MATLAB: Using interp2 – The grid must be created from grid vectors which are strictly monotonically increasing.

interpolation

I am using MATLAB_R2016b I have data of this format
   Temperature = [310:10:800];
   Pressure = [0.1 0 1.0 10.0 100.0 1000.0];
   Cv = 
[  73.6400   25.3290   73.5920   73.1260   69.4500   61.8600
   72.8060   25.3810   72.7640   72.3450   68.9780   61.7040
   71.9230   25.4380   71.8850   71.5070   68.4230   61.3140
   71.0060   25.4990   70.9710   70.6290   67.8040   60.8160
   70.0680   25.5640   70.0360   69.7270   67.1400   60.2840
   69.1220   25.6340   69.0940   68.8140   66.4460   59.7550
   68.1800   25.7070   68.1540   67.9000   65.7350   59.2500
   27.6640   25.7840   67.2240   66.9940   65.0150   58.7780
   27.3630   25.8640   66.3120   66.1040   64.2950   58.3390
   27.1700   25.9480   65.4220   65.2330   63.5820   57.9340
   27.0440   26.0340   64.5570   64.3850   62.8790   57.5600
   26.9660   26.1230   63.7210   63.5640   62.1900   57.2130
   26.9240   26.2150   62.9130   62.7700   61.5170   56.8890
   26.9110   26.3090   62.1360   62.0050   60.8620   56.5870
   26.9200   26.4050   61.3890   61.2690   60.2250   56.3020
   26.9460   26.5030   33.1250   60.5620   59.6080   56.0320
   26.9870   26.6030   31.8460   59.8850   59.0090   55.7750
   27.0390   26.7050   31.0570   59.2360   58.4290   55.5290
   27.1010   26.8080   30.5000   58.6170   57.8680   55.2920
   27.1700   26.9120   30.0840   58.0280   57.3240   55.0630
   27.2460   27.0170   29.7670   57.4700   56.7980   54.8410
   27.3280   27.1240   29.5260   56.9450   56.2900   54.6250
   27.4140   27.2320   29.3430   56.4560   55.7970   54.4150
   27.5040   27.3410   29.2080   56.0070   55.3210   54.2090
   27.5980   27.4500   29.1110   55.6040   54.8600   54.0080
   27.6940   27.5610   29.0460   55.2610   54.4150   53.8100
   27.7930   27.6720   29.0060   54.9970   53.9840   53.6160
   27.8950   27.7840   28.9870   54.8470   53.5670   53.4260
   27.9980   27.8970   28.9870   51.7540   53.1650   53.2390
   28.1030   28.0110   29.0020   47.2710   52.7760   53.0550
   28.2100   28.1250   29.0290   44.3160   52.4010   52.8750
   28.3180   28.2400   29.0670   42.1390   52.0390   52.6980
   28.4270   28.3550   29.1150   40.4520   51.6910   52.5230
   28.5380   28.4710   29.1710   39.1070   51.3570   52.3520
   28.6500   28.5880   29.2340   38.0170   51.0350   52.1840
   28.7630   28.7060   29.3040   37.1240   50.7260   52.0200
   28.8770   28.8240   29.3780   36.3870   50.4300   51.8580
   28.9920   28.9420   29.4580   35.7750   50.1460   51.7000
   29.1080   29.0610   29.5420   35.2640   49.8730   51.5440
   29.2250   29.1810   29.6290   34.8380   49.6100   51.3930
   29.3420   29.3010   29.7200   34.4810   49.3570   51.2440
   29.4610   29.4220   29.8150   34.1820   49.1120   51.0990
   29.5800   29.5440   29.9120   33.9330   48.8720   50.9570
   29.6990   29.6660   30.0110   33.7250   48.6360   50.8190
   29.8200   29.7880   30.1130   33.5540   48.4000   50.6830
   29.9410   29.9110   30.2170   33.4130   48.1630   50.5520
   30.0630   30.0340   30.3230   33.3000   47.9210   50.4230
   30.1850   30.1580   30.4310   33.2100   47.6720   50.2990
   30.3080   30.2820   30.5400   33.1400   47.4140   50.1770
   30.4310   30.4070   30.6510   33.0890   47.1430   50.0590];
When I try to query a new temperature, pressure, for example 0.2, 341 by doing this
   interp2(Temperature, Pressure, Cv, 0.2, 341)
I get the following error:
    Error using griddedInterpolant
    The grid vectors must be strictly monotonically increasing.
    Error in interp2>makegriddedinterp (line 229)
        F = griddedInterpolant(varargin{:});
    Error in interp2 (line 129)
        F = makegriddedinterp({X, Y}, V, method,extrap);
What am I doing wrong? And how can I get the desired result which I want?

Best Answer

The non-increasing sequence of the pressures is the first problem, and obviously the reason the code failed.
There is also the issue of using linear interpolation with a data sequence that is clearly exponential.
For example, suppose the Pressure axis is actually
Pressure = [0.01 0.1 1 10 100 1000];
Linear interpolation on such an axis will perform poorly. Instead, you are far better off by taking the log10 of Pressure.
So now we have
Pressurelog = log10(Pressure)
It will look like [-2 -1 0 1 2 3].
Linear interpolation will now be more appropriate. This is almost always what you want to do when a variable varies by many orders of magnitude.
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