Histogram for pairs of values
in [Matlab]
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From: Walter Roberson on 21 Jul 2010 16:46 Jim O'Doherty wrote: > Thanks for the point in the right direction Bruno. Does my data need to > be sorted? My X, Y arrays are electron positions so they are not in any > increasing/decreasing order. I seem to be getting an error saying it > requires monotonically decreasing arrays The specified edges would have to be sorted, but it should not be necessary to sort the data to be binned. You can do a 2D sort using sortrows() if you need to. In your problem statement, you asked how to determine how often each pair of X, Y occurred, which suggests that your X and Y are quantized values. In the above note, you indicate that the X and Y are electron positions, which I would not normally think of as quantized, at least not when using those variable names (as the names are not suggestive of shell numbers or similar.) Are your X and Y indeed quantized, or do you perhaps wish to quantize them? If so, are the quanta regularly spaced? If so, then if you subtract off the minimum values and divide by the quantum spacing and floor() the results, and add 1, the results would be bin numbers that should then be relatively easy to count (perhaps using accumarray)
From: Jim O'Doherty on 21 Jul 2010 17:16 Hi, thanks for your replies. The X,Y daya is indeed quantised, and the values will always be integers, its simply a location in space coming from a detector face that I need to reconstruct. I've pasted a sample of my million points below. They won't be regularly spaced, or at least they shouldn't be. Basically I want to build up an image, so I wanted to know how often each pair of values occurs (i.e. bin by location) so I can somehow image it. X Y 449 2741 2968 3511 2650 1990 1552 1122 1481 2698 3524 622 2649 1588 1204 1918 1972 2129 986 2140 1625 991 1120 1032 2395 2097 1935 3334 459 531 1907 1978 1341 1302 .. . .. . .. . .. . .. . Jim Walter Roberson <roberson(a)hushmail.com> wrote in message <i27mj3$cpc$1(a)canopus.cc.umanitoba.ca>... > Jim O'Doherty wrote: > > Thanks for the point in the right direction Bruno. Does my data need to > > be sorted? My X, Y arrays are electron positions so they are not in any > > increasing/decreasing order. I seem to be getting an error saying it > > requires monotonically decreasing arrays > > The specified edges would have to be sorted, but it should not be necessary to > sort the data to be binned. > > You can do a 2D sort using sortrows() if you need to. > > > In your problem statement, you asked how to determine how often each pair of > X, Y occurred, which suggests that your X and Y are quantized values. In the > above note, you indicate that the X and Y are electron positions, which I > would not normally think of as quantized, at least not when using those > variable names (as the names are not suggestive of shell numbers or similar.) > Are your X and Y indeed quantized, or do you perhaps wish to quantize them? > If so, are the quanta regularly spaced? If so, then if you subtract off the > minimum values and divide by the quantum spacing and floor() the results, and > add 1, the results would be bin numbers that should then be relatively easy to > count (perhaps using accumarray)
From: Walter Roberson on 21 Jul 2010 17:32 Jim O'Doherty wrote: > Hi, thanks for your replies. The X,Y daya is indeed quantised, and the > values will always be integers, its simply a location in space coming > from a detector face that I need to reconstruct. I've pasted a sample of > my million points below. They won't be regularly spaced, or at least > they shouldn't be. Basically I want to build up an image, so I wanted to > know how often each pair of values occurs (i.e. bin by location) so I > can somehow image it. > > X Y > 449 2741 > 2968 3511 > 2650 1990 > 1552 1122 Ah, then supplying edges of 1:max(X) and 1:max(Y) should do the trick for the N-dimensional histogram routine. Possibly John D'Errico's "consolidator" FEX contribution would also be useful. Looking back through some of my prior postings, I found an alternative approach using accumarray. This assumes that the minimum X and Y are 1: maxx = max(x); maxy = max(y); xycounted = reshape( accumarray( sub2ind([maxx, maxy], x, y), 1 ), maxx, maxy); You could then surf() or pcolor() or densityplot() that array.
From: Jim O'Doherty on 21 Jul 2010 18:45 Ok, I see where you're going.... I ran the snippet of code for 1000 elements in X and Y and RESHAPE threw up an error saying that the number of elements must not change. Also when I ran it with only 4 elements in X and Y, I got xycounted to be a 2968 x 3511 array! Something amiss somewhere...... I'll check out the consolidator though, cheers Walter Roberson <roberson(a)hus hmail.com> wrote in message <i27p8n$gp0$1(a)canopus.cc.umanitoba.ca>... > Jim O'Doherty wrote: > > Hi, thanks for your replies. The X,Y daya is indeed quantised, and the > > values will always be integers, its simply a location in space coming > > from a detector face that I need to reconstruct. I've pasted a sample of > > my million points below. They won't be regularly spaced, or at least > > they shouldn't be. Basically I want to build up an image, so I wanted to > > know how often each pair of values occurs (i.e. bin by location) so I > > can somehow image it. > > > > X Y > > 449 2741 > > 2968 3511 > > 2650 1990 > > 1552 1122 > > Ah, then supplying edges of 1:max(X) and 1:max(Y) should do the trick for the > N-dimensional histogram routine. > > Possibly John D'Errico's "consolidator" FEX contribution would also be useful. > > > Looking back through some of my prior postings, I found an alternative > approach using accumarray. > > This assumes that the minimum X and Y are 1: > > maxx = max(x); > maxy = max(y); > > xycounted = reshape( accumarray( sub2ind([maxx, maxy], x, y), 1 ), maxx, maxy); > > > You could then surf() or pcolor() or densityplot() that array.
From: Walter Roberson on 21 Jul 2010 19:38
Jim O'Doherty wrote: > Ok, I see where you're going.... > I ran the snippet of code for 1000 elements in X and Y and RESHAPE threw > up an error saying that the number of elements must not change. Also > when I ran it with only 4 elements in X and Y, I got xycounted to be a > 2968 x 3511 array! Something amiss somewhere...... > I'll check out the consolidator though, cheers >> This assumes that the minimum X and Y are 1: >> >> maxx = max(x); >> maxy = max(y); >> >> xycounted = reshape( accumarray( sub2ind([maxx, maxy], x, y), 1 ), >> maxx, maxy); Ah, you might need to add .' after the sub2ind() call; the first parameter must be a column vector. Hmmm, looks like xycounted = accumarray( horzcat(x(:),y(:)), 1); would perhaps work just as well. You should expect a fairly large output array -- one for each possible (x,y) pair. If that isn't what you want, then you need to define more clearly how you want the data to be imaged. You may also wish to use scatter() to image the data. |