Create a triangular function
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Hello.
I want to create a function in MatLab, which represents the image below.
Now, I can easily create a linear function for one of the lines and set the remaining to some constant, but I fail to do it for the combined two.
I was thinking about making a piecewise function or perhaps an inequality with the following restrictions:
I simply can't get it to work for both. If you have an idea, I'd love to hear it.
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Johannes Hougaard
2020-4-22
Hi Mikkel
I'm not quite sure whether I have understood how much of a mathematical function you would prefer for the graph to be.
But if it should just be a practical solution to the problem in a parametrical, piecewise way. I think this function (attached as m-file). Feel free to use it without any credits, copyright or whatever - and change everything you care to change :D
% Example data roughly taken from your question
x = 0:2500;
cutoff = 1250;
maxwidth = 1250;
minwidth = 100;
And here is the function in clear text (same as attached)
function y = triangularplot(x,maxwidth,minwidth,cutoff)
% TRIANGULARPLOT
% Creates a triangular plot in response to MATLAB Central question 519827
%
% I/O
% y = triangularplot(x,maxwidth,minwidth,cutoff);
%
% INPUT
% x = the x-data to use for the calculation
% maxwidth = the width at x = 0
% minwidth = the minimum width of the channel
% cutoff = the x value at which the width reaches the minimum
%
% 2020-04-2020 Johannes Hougaard <xjhh@novonordisk.com>
% Preallocation of y
y = nan(size(x));
% Calculating the slope for the linear section of the graph
slope = (minwidth-maxwidth)/cutoff;
% Calculating the y-values for x <= cutoff
y(x <= cutoff) = maxwidth + x(x <= cutoff).*slope;
% Setting the y-values aboce cutoff as the minimum width
y(x > cutoff) = minwidth;
% Plotting the result
figure;
plot(x,y,'k-');
set(gca,'NextPlot','add');
plot(x,-y,'k-');
set(gca,'NextPlot','replace');
ylabel('Width (km)');
5 个评论
Mikkel Christensen
2020-4-22
Thank you so much for this - that is quite cool.
I might have formulated my question poorly, but I think it is much simplere.
So, I need a function for the width of a glacier. I would like that function to represent the image above.
Basically a mathematical function 
and similary for the other side of the triangle 
I need it as one function if that make sense.
Should it be a peicewise function with the intervals ?
Would that work?
Johannes Hougaard
2020-4-22
Ah - it relates to the value of 'y' not of 'x' - I misread that but I can't see how you would make conditions on the output rather than on your input.
e.g. what is 
is that 
or is that 
?
is that or is that ?Based on the description you give I have a hard time seeing how you would ever reach the 'constant' part of the image shown.
Mikkel Christensen
2020-4-22
Johannes Hougaard
2020-4-22
But that is exactly what you get from the above function if you run it as.
y = triangularplot(0:2500,1250,100,1200);
I just still don't get which value you want at e.g. 
or 
or if you want the function I sent you to be simpler (just the input a) that would be fairly easy keeping most of the code and just changing the first few lines and hard-coding some stuff - but I'm still not quite sure what the math should be.
function y = triangularplot(x,a)
% TRIANGULARPLOT
% Creates a triangular plot in response to MATLAB Central question 519827
%
% I/O
% y = triangularplot(x,maxwidth,minwidth,cutoff);
%
% INPUT
% x = the x-data to use for the calculation
% a = the constant 'slope' of the initial part
%
% 2020-04-2020 Johannes Hougaard <xjhh@novonordisk.com>
% Preallocation of y
maxwidth = 1250;
minwidth = 100;
y = nan(size(x));
cutoff = (maxwidth - minwidth)/a;
% Calculating the y-values for x <= cutoff
y(x <= cutoff) = maxwidth - a .* x(x <= cutoff);
% Setting the y-values aboce cutoff as the minimum width
y(x > cutoff) = minwidth;
% Plotting the result
figure;
plot(x,y,'k-');
set(gca,'NextPlot','add');
plot(x,-y,'k-');
set(gca,'NextPlot','replace');
ylabel('Width (km)');
could also be that you're simply looking for the built-in function 'sign' which could be multiplied to your a.
Mikkel Christensen
2020-4-22
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