Thread Subject:

Fitting to match pre-specified means

Dear All,

This probably has as much to do with maths and the like as with Matlab. But I'm not so great in either department, so figured I might be able to get some help from someone…

% Suppose I have the following 'bands' and 'vals':
bands = [0 50 75 90 95 100 110 125 200];
vals = [20 120 110 60 40 20 10 5];
meanperband = vals ./ (bands(2:end) - bands(1:end-1));

% I can then break this aggregate data down into individual 'integer bands' like this:
[~, ints] = histc((0:bands(end)-1), bands);
res = [ints.', meanperband(ints).'];

% I can then get back to my starting values like this:
accumarray(res(:, 1), res(:, 2))

The question is, Is there anything I can do to give my breakdown a more realistic "shape"--even if I just end up connecting points with straight lines. (Sorry, I can't think of a better way of putting it). Basically, I'm assuming that, within each band, every integer band has the same value. But I don't really want to. My starting 'vals' will suggest a kind of shape which I'm not capturing. Does this make any sense?

> The question is, Is there anything I can do to give my breakdown a more
> realistic "shape"--even if I just end up connecting points with straight
> lines. (Sorry, I can't think of a better way of putting it). Basically,
> I'm assuming that, within each band, every integer band has the same
> value. But I don't really want to. My starting 'vals' will suggest a
> kind of shape which I'm not capturing. Does this make any sense?

I can't say that I completely understand this, but is this the kind of thing
you want?

xx = linspace(50,200);
plot(bands(2:end),vals,'b-',xx,pchip(bands(2:end),vals,xx),'r-')

-- Tom