| Re: Interpolation routines [message #92657 is a reply to message #92656] |
Tue, 02 February 2016 13:31   |
laura.hike
Messages: 87
Registered: September 2013
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Member |
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On Tuesday, February 2, 2016 at 12:17:06 PM UTC-8, wlandsman wrote:
> I don't believe this is true anymore. INTERPOL() used to be biggest problem but since IDL 7.0, it is a professional level interpolation routine (and certainly more powerful than QUADTERP).
>
> I do agree that you best bet is to probably remove the NAN values (using WHERE and FINITE() ). I would use INTERPOL() without the /NAN keyword.
>
> g = where(finite(y))
> result = interpol( y[g], x[g], xinterp, /spline)
Thanks for the comment, wlandsman. I tried the "finite" method and got the same result as when I left the NaNs in and included the /NaN keyword. The interpolation works correctly (except when there are fewer than 4 valid points left, so I would have to write a trap for this in any case), but it continues beyond the end of the input range, becoming extrapolation instead of interpolation. This is completely invalid, so I specifically want to prevent it. I show an example below in order to be clear. Yes, this is a vertical profile in pressure coordinates, for anyone who cares:
Input abscissa Pin:
0.187500 0.362500 0.675000 1.26250 2.02500 2.98750 4.47500 6.75000 8.40000 8.98750 9.62500 10.2875 11.0000 11.7750 12.6000 13.4875 14.4500 15.4750 16.5750 17.7625 19.0250 20.3875 21.8625 23.4375 25.1250 26.9375 28.8875 30.9750 33.2125 35.6125 38.1875 40.9750 43.9750 46.3375 48.0000 49.7250 51.5125 53.3625 55.2875 57.2875 59.3500 61.4875 63.7000 66.0000 68.3875 70.8625 73.4250 76.0750 78.8250 81.6875 84.6500 87.7125 90.9000 94.2000 97.6125 101.150 104.825 108.637 112.587 116.688 120.938 125.337 129.900 134.638 139.538 144.625 149.913 155.388 161.062 166.938 173.025 179.350 185.913 192.700 199.737 207.038 214.663 222.625 230.888 239.513 248.513 257.913 267.725 277.925 288.575 299.688 311.237 323.100 335.288 347.938 361.050 374.463 388.188 402.400 417.025 432.087 447.612 463.550 479.925 496.812 514.300 532.287 550.725 569.738 589.312 609.463 630.287 651.825 NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
Output abscissa Pout:
0.100000 0.300000 0.400000 0.500000 0.700000 1.00000 2.00000 3.00000 4.00000 5.00000 7.00000 10.0000 20.0000 30.0000 40.0000 50.0000 70.0000 100.000 150.000 200.000 250.000 300.000 350.000 400.000 450.000 500.000 550.000 600.000 650.000 700.000 725.000 750.000 775.000 800.000 825.000 850.000 875.000 900.000 925.000 950.000 975.000 1000.00
Values obviously occur in Pout that are beyond the range of Pin.
Ordinate in SWin:
0.000156151 0.000173488 0.000207377 0.000210915 0.000169155 0.000110047 7.45450e-05 5.23441e-05 3.99181e-05 3.90353e-05
3.75340e-05 3.97617e-05 3.25255e-05 3.04963e-05 3.44416e-05 2.90153e-05 2.68362e-05 3.02042e-05 2.54594e-05 2.58893e-05
2.62765e-05 2.39674e-05 2.39971e-05 2.40214e-05 2.37010e-05 2.34202e-05 2.16869e-05 2.26950e-05 1.99376e-05 2.16858e-05
1.91526e-05 1.85088e-05 1.88882e-05 1.80156e-05 1.72226e-05 1.67287e-05 1.73794e-05 1.56135e-05 1.48229e-05 1.44584e-05
1.51021e-05 1.45813e-05 1.19285e-05 1.34967e-05 1.10665e-05 1.15942e-05 1.21990e-05 1.08427e-05 9.58437e-06 1.00086e-05
8.94639e-06 9.36905e-06 8.25729e-06 8.73890e-06 7.72265e-06 7.45533e-06 6.50589e-06 6.92547e-06 6.66663e-06 6.42854e-06
6.20490e-06 5.99692e-06 5.77185e-06 5.05578e-06 4.90454e-06 4.69174e-06 4.99278e-06 4.37616e-06 3.80173e-06 3.67547e-06
3.93453e-06 3.40434e-06 3.28958e-06 3.18232e-06 3.06034e-06 2.62840e-06 2.80613e-06 2.71086e-06 2.02691e-06 2.48816e-06
1.59571e-06 2.53445e-06 2.43971e-06 3.04975e-06 4.47653e-06 4.95492e-06 6.00842e-06 7.14583e-06 7.06873e-06 7.76889e-06
7.85854e-06 8.32823e-06 8.90338e-06 9.45487e-06 9.72611e-06 9.55187e-06 9.46401e-06 8.91291e-06 9.40596e-06 8.94922e-06
9.59435e-06 9.93338e-06 9.91535e-06 1.02259e-05 1.02142e-05 1.00091e-05 8.75643e-06 8.13227e-06 NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
NaN NaN NaN NaN NaN NaN NaN NaN
Ordinate out:
0.000147821 0.000166955 0.000177699 0.000189441 0.000209155 0.000217363 0.000170853 0.000109465 8.07843e-05 6.65560e-05
4.99181e-05 3.92060e-05 2.45898e-05 2.22732e-05 1.85323e-05 1.68197e-05 1.12288e-05 7.54906e-06 4.98966e-06 3.04681e-06
1.66306e-06 4.97638e-06 7.80974e-06 9.37925e-06 9.38277e-06 9.00669e-06 9.91276e-06 1.01958e-05 8.16361e-06 4.44220e-06
-3.16524e-06 -1.78092e-05 -4.18935e-05 -7.78224e-05 -0.000128000 -0.000194829 -0.000280715 -0.000388062 -0.000519273 -0.000676752
-0.000862904 -0.00108013
Values are returned for every Pout, whether it's off the end of Pin or not. If you plot these, they form an arc in the negative going to magnitudes higher than any of the input values. Is there any way to get rid of these short of searching for the max and min values of Pin and excluding Pouts outside this range? How does interpol come up with values out there anyway, given that inputs on either side of the output should be required for the spline function? Adding all these searches and exclusions would make using this function impractical, given that I have to apply it thousands of times. Note that Pin varies over time while Pout is fixed.
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