How to do the summation of two graphs?

Dear Colleagues,

I have two different graphs with different Y values and x values. it is hard to predict an equation with minimum error for this graph. Is there anyway to plot the sum of following two graphs?

Graph 1=[ 
        414.00          1.00
        400.00          1.00
        384.00          1.00
        381.00          1.00
        367.00          1.00
        348.00          1.00
        321.00          1.19
        308.00          1.39
        299.00          1.61
        279.00          1.78
        275.00          2.00
        264.00          2.59
        272.00          3.39
        259.00          3.59
        262.00          4.00
        274.00          4.59
        286.00          5.63
        305.00          6.00
        341.00          6.19
        366.00          6.39
        395.00          7.00
        408.00          7.19
        408.00          7.41
        394.00          7.61
        408.00          7.81
        408.00          8.00
        412.00          8.19]

Graph 2=[688.00          1.00
        690.00          1.00
        672.00          1.00
        644.00          1.00
        638.00          1.00
        660.00          1.01
        626.00          1.22
        602.00          1.40
        602.00          1.59
        604.00          1.80
        582.00          2.00
        560.00          2.22
        574.00          2.40
        563.00          2.60
        557.00          2.79
        565.00          3.00
        593.00          3.22
        602.00          3.40
        598.00          3.59
        606.00          3.79
        592.00          4.00
        607.00          4.22
        593.00          4.40
        603.00          4.59
        589.00          4.79
        602.00          5.00
        581.00          5.22
        591.00          5.40
        577.00          5.59
        585.00          5.80
        572.00          6.00
        567.00          6.22
        559.00          6.40
        560.00          6.59
        572.00          6.80
        592.00          7.00
        635.00          7.22
        675.00          7.40
        702.00          7.59
        709.00          7.80
        726.00          8.00
        728.00          8.22
        725.00          8.41
        751.00          8.60
        775.00          8.80
        785.00          9.00
        780.00          9.22
        794.00          9.41]

1st column is Y axis and second column is x axis.

Thanks in advance.

[Nadeera Gunartna]

values are attached as text doc

Answer 1

[Star Strider]

I don’t understand what you mean by ‘sum’. The two matrices have different numbers of elements, so you can shorten the longer one, or you can interpolate one to the x-values of the other one with interp1 (without extrapolating), but you cannot do any calculations with them as they currently exist.

What equation are you trying to fit to them?

[Nadeera Gunartna]

Thank you for the answer, I was trying the "polyfit" command , to plot the sum of two graphs. but is it hard to predict a polynomial for this graph with minimum error.

[Star Strider]

My pleasure.

I am not quite certain what you want to do, but if you want to fit both curves to one polynomial, this is one option:

Graph_1 = [ 414.00 1.00 400.00 1.00 384.00 1.00 381.00 1.00 367.00 1.00 348.00 1.00 321.00 1.19 308.00 1.39 299.00 1.61 279.00 1.78 275.00 2.00 264.00 2.59 272.00 3.39 259.00 3.59 262.00 4.00 274.00 4.59 286.00 5.63 305.00 6.00 341.00 6.19 366.00 6.39 395.00 7.00 408.00 7.19 408.00 7.41 394.00 7.61 408.00 7.81 408.00 8.00 412.00 8.19];
Mtx_1 = reshape(Graph_1, 2, [])';
Graph_2 = [688.00 1.00 690.00 1.00 672.00 1.00 644.00 1.00 638.00 1.00 660.00 1.01 626.00 1.22 602.00 1.40 602.00 1.59 604.00 1.80 582.00 2.00 560.00 2.22 574.00 2.40 563.00 2.60 557.00 2.79 565.00 3.00 593.00 3.22 602.00 3.40 598.00 3.59 606.00 3.79 592.00 4.00 607.00 4.22 593.00 4.40 603.00 4.59 589.00 4.79 602.00 5.00 581.00 5.22 591.00 5.40 577.00 5.59 585.00 5.80 572.00 6.00 567.00 6.22 559.00 6.40 560.00 6.59 572.00 6.80 592.00 7.00 635.00 7.22 675.00 7.40 702.00 7.59 709.00 7.80 726.00 8.00 728.00 8.22 725.00 8.41 751.00 8.60 775.00 8.80 785.00 9.00 780.00 9.22 794.00 9.41];
Mtx_2 = reshape(Graph_2, 2, [])';

xmax1 = max(Mtx_1(:,2));                                        % Find Maximum ‘x’ Of Shorter Matrix
Rows2 = (Mtx_2(:,2) <= xmax1);                                  % Limit Longer Matrix To That Value
Mtx_C = [Mtx_1; Mtx_2(Rows2,:)];                                % Create New ‘Concatenated’ Matrix
xv = linspace(min(Mtx_C(:,2)), max(Mtx_C(:,2)));                % X-Vector For Plot

b = polyfit(Mtx_C(:,2), Mtx_C(:,1), 5);                         % Fit Data
pv = polyval(b, xv);                                            % Evaluate Polynomial Fit

figure(1)
plot(Mtx_1(:,2), Mtx_1(:,1))
hold on
plot(Mtx_2(:,2), Mtx_2(:,1))
plot(xv, pv, '-g', 'LineWidth',2)
hold off
grid

The code first identifies the maximum x-value of the shorter data sequence, finds the values of the longer data sequence that are less than or equal to that value, concatenates those two matrices into ‘Mtx_C’, does the regression, and then plots the polynomial regression as the wide green line.

I chose a 5th-degree polynomial fit. Experiment with that to get the sort of plot you want, however going higher than a 7th-degree polynomial is likely not going to provide a significantly better fit, and could cause instability in the fitted line.

I do not recommend that you extrapolate the line beyond the limits I have used here, and I do not recommend that you fit it to data that do not have common x-range values.

[Nadeera Gunartna]

Thank you very much. I appreciate it.

[Star Strider]

My pleasure.

If my Answer solved your problem, please Accept it.

Answer 2

[John BG]

you have 2 signals

y1=[ 414.00 1.00 400.00 1.00 384.00 1.00 381.00 1.00 367.00 1.00 348.00 1.00 321.00 1.19 308.00 1.39 299.00 1.61 279.00 1.78 275.00 2.00 264.00 2.59 272.00 3.39 259.00 3.59 262.00 4.00 274.00 4.59 286.00 5.63 305.00 6.00 341.00 6.19 366.00 6.39 395.00 7.00 408.00 7.19 408.00 7.41 394.00 7.61 408.00 7.81 408.00 8.00 412.00 8.19]

y2=[688.00 1.00 690.00 1.00 672.00 1.00 644.00 1.00 638.00 1.00 660.00 1.01 626.00 1.22 602.00 1.40 602.00 1.59 604.00 1.80 582.00 2.00 560.00 2.22 574.00 2.40 563.00 2.60 557.00 2.79 565.00 3.00 593.00 3.22 602.00 3.40 598.00 3.59 606.00 3.79 592.00 4.00 607.00 4.22 593.00 4.40 603.00 4.59 589.00 4.79 602.00 5.00 581.00 5.22 591.00 5.40 577.00 5.59 585.00 5.80 572.00 6.00 567.00 6.22 559.00 6.40 560.00 6.59 572.00 6.80 592.00 7.00 635.00 7.22 675.00 7.40 702.00 7.59 709.00 7.80 726.00 8.00 728.00 8.22 725.00 8.41 751.00 8.60 775.00 8.80 785.00 9.00 780.00 9.22 794.00 9.41]

Ly1=length(y1)
Ly2=length(y2)
Ly1 =
         54.00
Ly2 =
         96.00

You may want to interpolate the shorter signal. The other way round is also possible, but rather than killing samples, you may choose to add them, just for the sake of, if only potentially, not losing information.

ny1 and ny2 are respective reference vectors:

ny1=[1:1:Ly1]
ny2=[1:1:Ly2]

stretch ny1 to reach ny2:

ny1_stretch=linspace(1,Ly2,Ly1)

and interpolate (linear)

y1_interp=interp1(ny1_stretch,y1,ny2)

or interpolate (cubic)

y1_interpc=interp1(ny1_stretch,y1,ny2,'spline')

Now you can combine y1_interp or y1_interpc with y2 in any vector operation or on same plot

 plot(ny2,y1_interp,'Color','r','LineWidth',1.5);
 hold on;plot(ny2,y2,'Color','b','LineWidth',1.5);
 hold on;plot(ny2,y1_interpc,'Color','g','LineWidth',1.5);grid on

.

If you find this answer of any help solving your question,

please click on the thumbs-up vote link,

thanks in advance

John

[e-mail]

[Nadeera Gunartna]

Thank you for the answer, but my question was I need to plot the summation of that two graphs (lets say 1+2=3) like that. anyway thank you for your friendly advice.