Discretise into Equal Intervals

I have an array of data, 2 columns and 19 rows of entries, which can be plotted as a loglog curve. However, the x-data I have does not have standard intervals and I need to approximate the curve as a piecewise linear function. Any suggestions as to how to go about this?

[Bruno Pop-Stefanov]

Do you mean that the x-data is not aligned with your (2-by-19) array of data?

[simply90]

The x-data are increasing values from 0.005 - 2.13, taken straight from the first row of entries, but they do not have standard intervals. I'm able to plot the curve, but this curve I then need to discretise into equal intervals and apply a piecewise linear function over that interval.

[Bruno Pop-Stefanov]

So you would like to interpolate the values of the curve at regularly-spaced points?

[dpb]

What, precisely do you mean by "discretize over equal intervals"? If you mean to interpolate to a uniform (and is this uniform on linear or log axis) interval, just apply interp1 finding a new y for the chosen set of x on the log- or linear-spacing. Of course, by your description the fit is linear only in log-log so you'll want to transform first.

After that it should be relatively straightforward to choose breakpoints -- fit segments and move the breakpoint to minimize R-sq or max residual or whatever chosen criterion is.

[simply90]

Yes. Within x I was considering an interval of 0.07 to fit the data, as it isn't an increasing rate I couldn't make the function interp work as the interval was set, rather than a rate. Thanks so much for your help!

[simply90]

It works! Thank you so much Bruno and dpb. I was able to start messing with the interp1 function, I was using the wrong one beforehand with your suggestion dpb, and Bruno your answer clarified it from there.

Thanks for your help!

Answer 1

[Bruno Pop-Stefanov]

You can use several methods to interpolate data points from non-uniformly spaced points. There are listed here for one dimension:

1-D Interpolation

Here is an example using interp1:

vq = interp1(c, v, xq)

where x are the (non-uniformly spaced) input points (the first row in your vector) with values v (the second row in your vector), and xq are the query points (your uniformly spaced points). The function returns the interpolated values at xq in the vector vq.

For uniformly-spaced query points, you can use:

x_begin   = x(1,1);   % your 0.005
x_end     = x(end,1); % your 2.13  
numPoints = numel(x(:,1)); % number of points in your original vector; you can change that
xq = linspace(x_begin, x_end, numPoints);

for numPoints linearly spaced between x_begin and x_end. If you prefer to specify the length of each interval instead of the number of points, you could write:

xq = x_begin : int_length : x_end;

with int_length = 0.07.