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I was wondering if give a number of 2D points, how do calculate where to draw a point on a screen in a logarithmic y scale?

I tried to just take the logarithm of all the y-values of points and than plot them 'normally' (plot point [x, log(y)] => on height: height*log(y)/log(max)). But this approach causes problems for y-values under 1. So this makes me wonder if my method in general is the right approach. A tweak i could maybe use would be to use log(y/min) instead of log(y).

Any advice on improvement or better approaches are welcome!

Samuel
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  • What do you want to do with y-values under 1? You can just take the absolute value, so your y-axis will look like: 1000, 100, 10, 1, 0, 1, 10, 100, 1000 etc. – Hidde May 13 '12 at 13:39

4 Answers4

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By assuming y values are positive, use your own approach with a small bias, like: height*log(y-min+1)/log(max-min+1) to prevent from very big negative values.

Saeed Amiri
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  • By shift bias on "-min" value you removed the graph constant. In some tasks this is not acceptable, may be shifting all dynamic range on "1" is more successful variant. You save all graph data and receive good logarithmic transforming. – 23W May 20 '15 at 05:45
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If you plot y/ymin logarithmically, you'll scale the smallest value to 1, guaranteeing that all the logarithmic values are non-negative.

Adam Liss
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  • This is more interesting version, because this is normalization, not shifting bias. Thank you. – 23W May 20 '15 at 05:37
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Check out the R implementation of plot which may provide you with some clues. If you use plot(x,y,log='y') then y axis is plotted on log scale.

About points<1, you will face same problem with -ve numbers, right? So basically you need to normalize data such that all points are within visible range on the screen. Use the following transformation:

ny = number_of_pixels*(log(y) - min(log(Y)))/(max(log(Y))-min(log(Y)))

ElKamina
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  • Suppose this simple scenario: min(Y) could be near to zero, assume 0.0000001 and max again could be small, like 10 (assume all things are in base 10), your approach for this state results something near to `number_of_pixels` for all points. (may be exactly, by considering rounding to integers). – Saeed Amiri May 15 '12 at 21:11
  • @SaeedAmiri Since y in log scale, you have to normalize log values. You need to roughly subtract log(min(y)) from every log(y) and plot it. – ElKamina May 15 '12 at 21:44
  • Not necessary to subtract log(min(Y)), you can subtract min value, as seems by OPs problem (negative values), he had some values less than `1` so min is smaller than `1` so this subtracting doesn't make a lot of changes (e.g see my answer). anyway I think this small rounding is better than possibly loosing so many other information. – Saeed Amiri May 15 '12 at 23:39
  • @SaeedAmiri My suggestion was merely to look at R implementation which is one of the best IMHO. – ElKamina May 16 '12 at 03:06
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from what i understand, you seem to be trying to plot log(y) but keeping the y axis as it was for y? that doesn't really make sense.

the way you are plotting is fine: you plot a point at (x, log(y)).

but what you need to change is the limits of the y axis. if it originally went from ymin to ymax, it now needs to go from log(ymin) to log(ymax).

if you change the y axis limits that way then the points will fit in just fine.

andrew cooke
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