# I can't seem to call an integral function inside of a plot that has any complexity. I need to plot outputs of a range of values for the integral.

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Brian Hanley on 13 May 2022
Answered: Voss on 13 May 2022
I have an integral function that works correctly when I call it once, directly. If I try to call it from a plot, supplying a range of values, it gets an error that doesn't appear sensible. Yes, I see that I pass real parameters into the integral function from outside the object. But as you can see, there is a real linspace parameter passed into the WD_y function inside the plotWD_y function of the weather object. The object isn't the problem. It's specific to how the integral function works.
What I need to do is plot the results of the integral function from a to n (here, 42 to 42+n).
I have made something work from this example. I still cannot get mine to work, with various permutations, including fplot.
I cannot imagine that this can't be done, but it's definitely not straightforward.
The function name in question is highlighted in bold.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Example of a plot that works fine.
% Call to plot function.
Wthr.plotWD_y
% called function in the Wthr object.
function plotWD_y(obj)
y=linspace(0,179,1000)
plot(y,obj.WD_y(y))
set(gca,'YScale','log')
title('Log plot of Weather by year')
xlabel('Year (1980=0)')
ylabel('Weather USD (log scale)')
hold off
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This call to integral function works as expected.
tIntgrlPV = Wthr.P_SPV_L_dkn(1.427,42,221)
disp('P_SumPV_L_dkn(d_MFed,42,221) =')
vpa(tIntgrlPV,25)
%**** Output
P_SumPV_L_dkn(d_MFed,42,221) = 255275036562037.6936237779
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This call to integral function from inside a plot doesn't work
a= 42
b= 279
x=linspace(a,b,100)
plot(x,Wthr.P_SPV_L_dkn(1.427, x, b))
%**** Output
Error using ^
Matrix must be square.
IntgrlPV = int( (obj.WD_y(x)/(d+1)^(x-k)), [k, n])
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% This is function called inside the Wthr object.
function IntgrlPV = P_SPV_L_dkn(obj, d, k, n)
% Integral PV
syms x
IntgrlPV = int( (obj.WD_y(x)/(d+1)^(x-k)), [k, n])
end

Voss on 13 May 2022
You're calling int with two different sets of inputs and asking why one works and one doesn't, right?
The line:
plot(x,Wthr.P_SPV_L_dkn(1.427, x, b))
generates that error because you should have .^ instead of ^ in P_SPV_L_dkn, and if you change that you'll get a different error that tells you you should have ./ instead of /
If you change both of those you'll get a new error because you're calling int with a vector as a limit of integration.
As the accepted answer in the question you linked to mentions, int returns a constant; you cannot make it return a vector by giving it a vector of limits.
tIntgrlPV = P_SPV_L_dkn(1.427,42,221);
vpa(tIntgrlPV,25)
P_SumPV_L_dkn(d_MFed,42,221) =
ans =
1.127833209970976279661255
a= 42;
b= 279;
x=linspace(a,b,100);
P_SPV_L_dkn(1.427, a, b) % scalar a and b --> works ok
ans = try
% same arguments to P_SPV_L_dkn as when used in plot
% in the question -> same error, nothing to do with plot
P_SPV_L_dkn(1.427, x, b)
catch e
disp(e.message);
end % error message you saw:
Matrix must be square.
% now, with .^ and ./
% --> can't integrate w.r.t. a vector
P_SPV_L_dkn_new(1.427, x, b)
Error using sym/int
Unable to integrate with respect to '[42, 1465/33, 1544/33, 541/11, 1702/33, 1781/33, 620/11, 1939/33, 2018/33, 699/11, 2176/33, 205/3, 778/11, 2413/33, 2492/33, 857/11, 2650/33, 2729/33, 936/11,
2887/33, 2966/33, 1015/11, 284/3, 3203/33, 1094/11, 3361/33, 3440/33, 1173/11, 3598/33, 3677/33, 1252/11, 3835/33, 3914/33, 121, 4072/33, 4151/33, 1410/11, 4309/33, 4388/33, 1489/11, 4546/33,
4625/33, 1568/11, 4783/33, 442/3, 1647/11, 5020/33, 5099/33, 1726/11, 5257/33, 5336/33, 1805/11, 5494/33, 5573/33, 1884/11, 521/3, 5810/33, 1963/11, 5968/33, 6047/33, 2042/11, 6205/33, 6284/33,
2121/11, 6442/33, 6521/33, 200, 6679/33, 6758/33, 2279/11, 6916/33, 6995/33, 2358/11, 7153/33, 7232/33, 2437/11, 7390/33, 679/3, 2516/11, 7627/33, 7706/33, 2595/11, 7864/33, 7943/33, 2674/11,
8101/33, 8180/33, 2753/11, 758/3, 8417/33, 2832/11, 8575/33, 8654/33, 2911/11, 8812/33, 8891/33, 2990/11, 9049/33, 9128/33, 279, 279]'. The integration variable must be a symbolic variable.

Error in solution>P_SPV_L_dkn_new (line 32)
IntgrlPV = int( (1./(d+1).^(x-k)), [k, n]);
function IntgrlPV = P_SPV_L_dkn(d, k, n)
% Integral PV
syms x
IntgrlPV = int( (1/(d+1)^(x-k)), [k, n]);
end
function IntgrlPV = P_SPV_L_dkn_new(d, k, n)
% Integral PV
syms x
IntgrlPV = int( (1./(d+1).^(x-k)), [k, n]);
end

R2022a

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