How to build up linear functions in MATLAB and plot the?

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M 2022-8-3

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编辑： dpb 2022-8-4

Hi, I am new in MATLAB and I want to build a code for these linear functions and plot them to use it in my research paper.

The general shape of the linear fuctions are attached.

The idea from these functions that if I have values for example from (0 to 0.04999) in x axis and i substitute them in the first linear function, I want the output to be from (0-0.25) ...

in the second linear function the input from (0.05 to 0.24999) so the output that I want to be are (0.3 - 0.55).

in the third linear function the input from (0.25 to 0.6) so the output that I want to be are (0.6 - 1).

I dont intrest in exact value of the slope at this stage, I just want general functions to achieve what i want.

Thanks in advance

回答（3 个）

Star Strider 2022-8-3

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https://ww2.mathworks.cn/matlabcentral/answers/1773295-how-to-build-up-linear-functions-in-matlab-and-plot-the#answer_1020560

在 MATLAB Online 中打开

The lilnes are easy enough to plot —

xm = [0 0.04999; 0.05 0.24999; 0.25 0.6];

ym = [0 0.25; 0.3 0.55; 0.6 1];

for k = 1:size(xm,1)

B(:,k) = [xm(k,:); 1 1].' \ ym(k,:).'; % Slopes & Intercepts

end

figure

hold on

for k = 1:size(xm,1)

plot(xm(k,:), ym(k,:), '-k')

end

hold off

What do you want to do with them after that?

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dpb 2022-8-3

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"... I have many values and I want to substitute them in these functions and see save their outputs.."

Show us why what I gave you to begin with will not let you do precisely that...I showed you precisely that result as the first plot where the vector yh was computed from a whole bunch of x values; the x can be totally arbitrary in number and value (although they ought to be within the range of the defined breakpoints range, obviously).

Illustrate again --

>> yNew=fnY(pi/10)      % save a new single value at some arbitrary point, x
yNew =
    0.6733
>>

or, with a vector of points...

>> xvals=rescale(rand(1,7),0,0.6)       % 7 random points between 0 and 0.6
xvals =
         0    0.6000    0.4549    0.5091    0.2921    0.4800    0.0824
>> yvals=fnY(xvals)                     % and the function values to go with 'em...
yvals =
         0    1.0000    0.8341    0.8961    0.6481    0.8629    0.3405
>> 

and just to show that they satisfy the criteria we'll put 'em on that original figure yet again...

>> plot(xvals,yvals,'or')

which again shows they all are identically on the given line segments as defined...

You've yet to show us why this won't work for you.

Star Strider 2022-8-3

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I do not know what other values you have, so I created some — .

xm = [0 0.04999; 0.05 0.24999; 0.25 0.6];

ym = [0 0.25; 0.3 0.55; 0.6 1];

for k = 1:size(xm,1)

B(:,k) = [xm(k,:); 1 1].' \ ym(k,:).'; % Slopes & Intercepts

end

xq = [0.12 rand(1,9)*0.6]; % Supplied Values For 'x'

for k = 1:numel(xq)

xm_row = @(x) find(xm(:,1) <= x & xm(:,2) >= x); % Function To Determine Segment Membership

yq(k) = [xq(k) 1] * B(:,xm_row(xq(k))); % Call Function & Find 'y'

end

Points = [xq; yq]

Points = 2×10

0.1200 0.1433 0.5412 0.4145 0.2087 0.4961 0.3901 0.5859 0.0221 0.4086 0.3875 0.4166 0.9328 0.7880 0.4983 0.8813 0.7601 0.9839 0.1103 0.7813

figure

hold on

for k = 1:size(xm,1)

plot(xm(k,:), [xm(k,:); 1 1].'*B(:,k), '-', 'DisplayName',sprintf('Segment %d',k))

end

plot(xq,yq,'rs', 'DisplayName','(xq,yq)')

hold off

legend('Location','best')

The points are random, however they all appear to plot correctly.

Star Strider 2022-8-3

I agree, however it’s the way OP framed the problem, so I kept with it.

dpb 2022-8-3

Understand; pointing out for OP's benefit...

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dpb 2022-8-3

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1773295-how-to-build-up-linear-functions-in-matlab-and-plot-the#answer_1020570

在 MATLAB Online 中打开

% the lookup table/interpolant function...
y=[0 0.25 0.30 0.55 0.6 1];
x=[0 0.05-eps(0.05) 0.05 0.25-eps(0.25) 0.25 0.6];
% let's use it...
xh=[0:0.01:0.6];                    % sample points to evaluate
yh=interp1(x,y,xh);                 % functional values
plot(xh,yh,'x')                     % see what it looks like...

results in

plot() by default would draw the line between the breakpoints; hence the markers only here to illustrate...

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dpb 2022-8-3

在 MATLAB Online 中打开

Do what, specifically?

Why can't you pass/use the function I defined? Have you even tried it?

Show us code that you've tried and that doesn't function; don't just complain.

Alternatively, you could do something like

>> bkpt=reshape(x,2,[]).'
bkpt =
         0    0.0500
    0.0500    0.2500
    0.2500    0.6000
>> resp=reshape(y,2,[]).'
resp =
         0    0.2500
    0.3000    0.5500
    0.6000    1.0000
>> b=arrayfun(@(i)polyfit(bkpt(i,:),resp(i,:),1),1:size(bkpt,1),'UniformOutput',0);
>> for i=1:numel(b)
     fnY(i)={@(x)polyval(b{i},x)};
   end
>> whos fnY
  Name      Size            Bytes  Class    Attributes
  fnY       1x3               408  cell               
>> fnY{3}(pi/10)
ans =
    0.6733
>> 

gives a handle array of the three line segments defined above that could be passed as separate array elemnts but it's not clear what advantage this has over simply using the one global function wherever it is needed.

I'll 'fess that I don't have and have never used the fuzzy logic TB so there may be something I'm missing, but we would need to see why that solution doesn't work to figure out what might do instead or to correct whatever is wrong with it (or in your use thereof).

M 2022-8-3

Thank you @dpb

dpb 2022-8-3

编辑：dpb 2022-8-4

在 MATLAB Online 中打开

The lookup table aspects of @doc:interp1 can be extremely handy tool for shortening user code such as here -- using it for reverse lookup is also something not to be overlooked.

The only disadvantage here I can see is that one does, indeed, have to use values within each segment only to draw a continuous line segment that will show the discontinuity without a line segment drawn between sections. But, the other solutions also all have to have some other way to handle it that is at least as much code/logic as would be using the segment breakpoints in a loop similarly as to @Star Strider

xq = [0.12 rand(1,9)*0.6];  % Supplied Values For 'x'
yq=fnY(xq);                 % 'y'
Points = [xq; yq]
figure
hold on
xm=reshape(x,2,[]).';                       % convert to S-S's variable from mine
for k = 1:size(xm,1)
  plot(xm(k,:), fnY(xm(k,:)), '-', 'DisplayName',sprintf('Segment %d',k))
end
plot(xq,yq,'rs', 'DisplayName','(xq,yq)')
hold off
legend('Location','best')

gives

which is same plot with slightly different set of randomized xq,yq points...I was just too lazy to go to the extra trouble so just dumped the points out to simulate the lines.

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M 2022-8-3