[SciPy-User] 2D bilinear interpolation from low to high resolution
Andreas Hilboll
lists at hilboll.de
Wed Jul 11 04:25:55 EDT 2012
> Hi,
>
> I've been trying to copy and modify a Scipy Cookbook function that does a
> 2d spline interpolation using the same data limits but with higher
> resolution. In my function I use a bilinear interpolation.
> I've struggled to get this working and now that I have the results are
> horrible and incorrect. Would love some help with this if anyone has some
> experience with this particular subject.
> I assume the lat and lon must be ascending, since it is not in the
> original data, I have moved the data around. I've tried this without
> sorting the lats and the results are the similar: garbled! The data is a
> slice of an array. The slice is centered at lat0 lon0 and is ±10 degrees
> on all 4 sides forming a 20x20 degree window. The initial resolution is
> 1.125 and the new resolution is 0.703125.
>
> The input dictionary and data is posted below.
>
> def Low2HighRes(plist,ivals):
> """N-D interpolation for equally-spaced data"""
> latsort = np.argsort(plist['xlats'])
> lonsort = np.argsort(plist['xlons'])
> ix,jy = np.meshgrid(plist['newx'],plist['newy'])
> coords = scipy.array([ix,jy])
> vals = ivals[latsort,:]
> nvals =
> scipy.ndimage.map_coordinates(vals,coords,order=1,mode='nearest')
> return nvals
>
> The new resolution is 0.703125:
> 'newx': array([-9.84375 , -9.140625, -8.4375 , -7.734375, -7.03125 ,
> -6.328125,
> -5.625 , -4.921875, -4.21875 , -3.515625,
> -2.8125 , -2.109375,
> -1.40625 , -0.703125, -0. , 0.703125,
> 1.40625 , 2.109375,
> 2.8125 , 3.515625, 4.21875 , 4.921875, 5.625
> , 6.328125,
> 7.03125 , 7.734375, 8.4375 , 9.140625,
> 9.84375 ])
>
> 'newy': array([-9.84375 , -9.140625, -8.4375 , -7.734375, -7.03125 ,
> -6.328125,
> -5.625 , -4.921875, -4.21875 , -3.515625,
> -2.8125 , -2.109375,
> -1.40625 , -0.703125, -0. , 0.703125,
> 1.40625 , 2.109375,
> 2.8125 , 3.515625, 4.21875 , 4.921875, 5.625
> , 6.328125,
> 7.03125 , 7.734375, 8.4375 , 9.140625,
> 9.84375 ])
>
> original coordinates of the data to be interpolated are lats and lons with
> a 1.125 resolution:
> 'modx': array([-10.125, -9. , -7.875, -6.75 , -5.625, -4.5 ,
> -3.375,
> -2.25 , -1.125, -0. , 1.125, 2.25 ,
> 3.375, 4.5 ,
> 5.625, 6.75 , 7.875, 9. , 10.125])
> 'mody': array([-10.125, -9. , -7.875, -6.75 , -5.625, -4.5 ,
> -3.375,
> -2.25 , -1.125, -0. , 1.125, 2.25 ,
> 3.375, 4.5 ,
> 5.625, 6.75 , 7.875, 9. , 10.125])
>
> 'lats': array([ 18.50457985, 17.38309053, 16.26160115, 15.14011169,
> 14.01862218, 12.8971326 , 11.77564298,
> 10.65415331,
> 9.53266359, 8.41117384, 7.28968406,
> 6.16819425,
> 5.04670442, 3.92521457, 2.8037247 ,
> 1.68223483,
> 0.56074494, -0.56074494, -1.68223483]),
> 'lons': array([ 229.5 , 230.625, 231.75 , 232.875, 234. , 235.125,
> 236.25 , 237.375, 238.5 , 239.625, 240.75 ,
> 241.875,
> 243. , 244.125, 245.25 , 246.375, 247.5 ,
> 248.625, 249.75 ]),
>
> The data:
>
> array([[ 2.91407923e-03, 3.39587848e-03, 1.21381157e-03,
> 3.29374452e-04, 7.41946205e-05, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 4.87387297e-05,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 3.60107806e-05, 1.17035036e-03, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00],
> [ 2.40930752e-03, 4.95893275e-03, 2.63592694e-03,
> 1.06014498e-03, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 1.30197592e-03, 1.14706755e-02,
> 1.85952216e-04, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00],
> [ 1.04772742e-03, 2.78711016e-03, 3.14659718e-03,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 6.02249238e-05, 4.03569084e-06,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00],
> [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 1.24175097e-06,
> 0.00000000e+00, 0.00000000e+00, 2.44314520e-04,
> 2.39037072e-05, 3.38377140e-05, 3.95187264e-04,
> 0.00000000e+00],
> [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 2.48350193e-06, 7.45050602e-06, 1.17966347e-05,
> 0.00000000e+00, 1.55218879e-06, 1.86262650e-06,
> 2.60457280e-04, 0.00000000e+00, 4.62552271e-05,
> 9.49318637e-04, 9.99299111e-04, 4.70123850e-02,
> 8.09109434e-02],
> [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 0.00000000e+00, 0.00000000e+00, 1.17966347e-05,
> 7.91616258e-05, 1.24175097e-06, 0.00000000e+00,
> 6.20875483e-07, 4.59447874e-05, 5.22777205e-04,
> 0.00000000e+00, 4.52431990e-03, 1.75440796e-02,
> 8.04008991e-02, 1.31909043e-01, 2.24047899e-01,
> 1.60426781e-01],
> [ 0.00000000e+00, 0.00000000e+00, 0.00000000e+00,
> 9.31313252e-07, 1.14861969e-05, 2.39968387e-04,
> 4.34612866e-06, 2.17306433e-06, 1.44353558e-04,
> 1.58664735e-03, 2.86217406e-02, 1.11849174e-01,
> 9.77677181e-02, 1.43859955e-02, 7.32049495e-02,
> 6.55011237e-02, 3.44568849e-01, 4.58411306e-01,
> 2.49592885e-01],
> [ 0.00000000e+00, 1.61427633e-05, 4.99183894e-04,
> 3.17937918e-02, 4.85810265e-02, 1.03917181e-01,
> 1.25399157e-01, 1.80325225e-01, 2.97502756e-01,
> 5.07521629e-01, 7.01690793e-01, 7.83944130e-01,
> 3.59588116e-01, 4.82781321e-01, 2.19913769e+00,
> 1.45968425e+00, 7.70302236e-01, 6.41377449e-01,
> 1.36474028e-01],
> [ 1.13744393e-03, 6.07185205e-03, 2.85994828e-01,
> 1.50236040e-01, 7.42231190e-01, 1.22813118e+00,
> 6.46776557e-01, 5.81912160e-01, 1.87843180e+00,
> 1.92207563e+00, 1.52547717e+00, 1.32381713e+00,
> 3.73675466e-01, 7.55523860e-01, 2.65545297e+00,
> 1.27209759e+00, 1.13974738e+00, 1.16467550e-01,
> 2.09415719e-01],
> [ 1.38720661e-01, 3.32264960e-01, 4.35250461e-01,
> 7.92550027e-01, 1.22075701e+00, 8.08324039e-01,
> 3.90933961e-01, 3.94844234e-01, 4.14039224e-01,
> 1.87421179e+00, 1.89138579e+00, 1.72843981e+00,
> 5.95286727e-01, 1.14342570e+00, 1.61977232e+00,
> 4.52039897e-01, 2.81218112e-01, 1.66340306e-01,
> 9.93605703e-02],
> [ 9.74169195e-01, 9.17763233e-01, 5.85691392e-01,
> 4.46551383e-01, 2.51251876e-01, 1.49007021e-02,
> 2.15577297e-02, 1.01625830e-01, 9.69323218e-02,
> 2.31756687e-01, 8.57786715e-01, 1.20130097e-02,
> 4.75826561e-02, 1.08127639e-01, 9.12918925e-01,
> 1.77337572e-01, 2.07490385e-01, 8.76067802e-02,
> 7.50075638e-01],
> [ 7.03467131e-01, 5.82458824e-02, 9.40253865e-03,
> 5.74371964e-03, 2.25005276e-03, 5.12843195e-04,
> 3.22482735e-03, 6.15287630e-04, 0.00000000e+00,
> 0.00000000e+00, 3.08016338e-03, 7.09070871e-03,
> 1.34970576e-01, 2.69089937e-01, 5.28816462e-01,
> 7.75388122e-01, 9.10060704e-02, 3.86802018e-01,
> 5.62999070e-01],
> [ 1.45083088e-02, 1.42366753e-03, 2.19852012e-03,
> 8.08690325e-04, 2.21124804e-03, 1.78905274e-03,
> 1.85610738e-03, 2.66821240e-03, 1.23740488e-03,
> 7.45671510e-04, 1.78346480e-03, 6.83180336e-03,
> 2.30602473e-02, 6.35242537e-02, 5.68188019e-02,
> 7.31670763e-03, 6.97802007e-03, 1.26199163e-02,
> 2.35131755e-02],
> [ 6.02249238e-05, 2.92432378e-04, 1.13030383e-03,
> 5.85175178e-04, 1.46557658e-03, 1.88808236e-03,
> 3.10065225e-03, 3.55264964e-03, 4.15862398e-03,
> 7.17980415e-03, 4.59075347e-03, 2.15481054e-02,
> 4.47589159e-03, 6.03925623e-03, 9.55558382e-03,
> 1.08743245e-02, 4.59385756e-03, 6.76350715e-03,
> 1.05188731e-02],
> [ 1.71982509e-04, 7.66781232e-05, 2.50212825e-03,
> 4.58050938e-03, 3.75257153e-03, 3.77368135e-03,
> 3.04756756e-03, 4.28559305e-03, 1.21471193e-02,
> 1.85669716e-02, 2.26231515e-02, 2.37028543e-02,
> 7.72741623e-03, 1.21803358e-02, 7.17204344e-03,
> 1.18307828e-03, 9.51678026e-03, 8.88597034e-03,
> 1.38688069e-02],
> [ 7.85935298e-03, 1.02338903e-02, 2.00772509e-02,
> 1.29666738e-02, 8.32718238e-03, 7.63056008e-03,
> 6.14076946e-03, 9.90855228e-03, 1.00889169e-02,
> 1.48749352e-02, 1.88460555e-02, 8.26913025e-03,
> 9.51088127e-03, 7.60696689e-03, 1.25758338e-03,
> 4.51376487e-04, 1.18463056e-03, 2.09514447e-03,
> 2.51206243e-03],
> [ 2.33238097e-02, 2.73073465e-02, 3.22693810e-02,
> 1.88162532e-02, 5.83653990e-03, 3.47224623e-03,
> 1.80892076e-03, 9.19796061e-03, 8.73230398e-03,
> 1.45570468e-02, 1.55864581e-02, 1.42422626e-02,
> 1.35748219e-02, 1.19139794e-02, 3.64764361e-03,
> 5.92625700e-04, 2.55024619e-03, 1.44043122e-03,
> 1.51959271e-03],
> [ 4.65045050e-02, 4.04065773e-02, 2.90905014e-02,
> 1.47327557e-02, 6.68620877e-03, 5.12005016e-03,
> 4.09746822e-03, 5.41186146e-03, 1.08640799e-02,
> 1.43946875e-02, 1.87681355e-02, 2.52960213e-02,
> 1.79439243e-02, 1.72994547e-02, 7.33191893e-03,
> 4.66867350e-03, 1.00023043e-03, 9.08961752e-04,
> 2.14481447e-03],
> [ 7.23621100e-02, 4.10851948e-02, 8.70250165e-03,
> 5.37367724e-03, 2.11873767e-03, 3.15994583e-03,
> 2.98547978e-03, 5.60216000e-03, 5.73099125e-03,
> 9.40564275e-03, 1.04456097e-02, 1.35018695e-02,
> 2.56229118e-02, 2.75842566e-02, 2.80958600e-02,
> 3.02949995e-02, 4.40449081e-03, 1.03189505e-03,
> 1.60216924e-03]], dtype=float32)
>
> Appreciate any help with getting this function to work.
> /M
For lat/lon data, I suggest taking a look at the new classes for spherical
coordinates which got introduced in SciPy 0.11:
scipy.interpolate.LSQSphereBivariateSpline, SmoothSphereBivariateSpline,
and RectSphereBivariateSpline.
A.
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