interpolation

I have a grid of ocean depth data by location, and am trying to interpolate depth values for a selection of GPS points. We've been using RSAGA::pick.from.points, which works fine for small data sets. require(RSAGA) depthdata <- cbind.data.frame(x=c(74.136, 74.135, 74.134, 74.133, 74.132, 74.131, 74.130, 74.129, 74.128, 74.127), y=rep(40, times=10), depth=c(-0.6, -0.6, -0.9, -0.9, -0.9, -0.9, -0.9, -0.9, -0.6, -0.6)) mylocs <- rbind(c(-74.1325, 40), c(-74.1305, 40)) colnames(mylocs) <- c("x", "y") results <- pick.from.points(data=mylocs, src=depthdata, pick=c("depth"), method="nearest.neighbour

I noticed that the result of scipy.ndimage.zoom depends on the size of the original image. In the following code sample a checkerboard image is generated and then zoomed with ndimage.zoom. If one checkerboard tile is just 2x2 pixels, the zoom factor seems to be too large and the resulting image gets cropped. In contrast, if the tile has dimensions 10x10, the result looks good. from __future__ import division import numpy as np from scipy import ndimage, misc import wx y,x = 2,2 # change tile size here imgdata = np.zeros((y,x),dtype='uint8') imgdata[y/2:,x/2:] = 255 imgdata[:y/2,:x/2] = 255

The following call: rbf = Rbf(points[0], points[1], values,epsilon=2) results in an error: LinAlgError: singular matrix with the following values: In [3]: points Out[3]: (array([71, 50, 48, 84, 71, 74, 89, 76, 70, 77, 74, 79, 83, 71, 72, 78, 73, 84, 75, 65, 73, 82, 48, 86, 74, 86, 66, 74, 68, 74, 81, 74, 88, 66, 57, 50, 72, 86, 72, 92, 81, 67, 82, 78, 69, 70, 73, 71, 76, 72, 74, 75]), array([32, 34, 4, 35, 1, 7, 47, 16, 37, 14, 65, 18, 32, 4, 3, 27, 25, 34, 18, 25, 6, 25, 34, 41, 16, 35, 44, 2, 32, 2, 37, 60, 45, 32, 33, 42, 54, 31, 18, 38, 24, 18, 45, 48, 9, 63, 56, 45, 9, 59, 5, 12])) In [4]

I want to interpolate a polynomial with the Lagrange method, but this code doesn't work: def interpolate(x_values, y_values): def _basis(j): p = [(x - x_values[m])/(x_values[j] - x_values[m]) for m in xrange(k + 1) if m != j] return reduce(operator.mul, p) assert len(x_values) != 0 and (len(x_values) == len(y_values)), 'x and y cannot be empty and must have the same length' k = len(x_values) return sum(_basis(j) for j in xrange(k)) I followed Wikipedia , but when I run it I receive an IndexError at line 3! Thanks Check the indices, Wikipedia says "k+1 data points", but you're setting k = len(x

First, a bit of background: I am using spherical harmonics as an example of a function on the surface of a sphere like the front spheres in this image: I produced one of these spheres, coloured according to the value of the harmonic function at points on its surface. I do this first for a very large number of points, so my function is very accurate. I've called this my fine sphere. Now that I have my fine sphere, I take a relatively small number of points on the sphere. These are the points I wish to interpolate from, the training data, and I call them interp points. Here are my interp points,