Can't integrate function using Matlab

Question

David Harra 2023-2-9

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1909240-can-t-integrate-function-using-matlab

评论： David Harra 2023-2-9

I am trying to do a basic integration of a formula for 4 different values. After doing a bit of reading, apparently I need to create a function handle but I am not getting any success. I have put my attempt below. I might be missing more though.

L=0:100;
L_bar=25;
sigma_d =[0.25, 0.5, 0.75, 1.0]; 
mu = log(L_bar) - 0.5*(sigma_d).^2;
L_tilda = exp(mu);
% eta_r = P.*exp(-r./L);
%  I want to integrate eta from zero to infinity where P has changing
%  variables to give 4 different plots.
r = 0:100;
% I was just testing below to see if a loop would run before attempting to
% plot anything
P = zeros(1,length(L));
fun = @(r) P.*exp(-r./L);
for ii=1:numel(sigma_d)
P= 1./(L.*sqrt(2*pi)*sigma_d(ii)).*exp(-log(L/L_tilda(ii)).^2/(2*sigma_d(ii)^2)) ; 
eta_r = integral(fun,0,inf);
end 

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Answer 1

Torsten 2023-2-9

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在 MATLAB Online 中打开

L_bar=25;

sigma_d =[0.25, 0.5, 0.75, 1.0];

mu = log(L_bar) - 0.5*(sigma_d).^2;

L_tilda = exp(mu);

r = 0:100;

for ii=1:numel(sigma_d)

P= @(L)1./(L.*sqrt(2*pi)*sigma_d(ii)).*exp(-log(L/L_tilda(ii)).^2/(2*sigma_d(ii)^2));

fun = @(L,r) P(L).*exp(-r./L);

eta_r(ii,:)=integral(@(L)fun(L,r),0,Inf,'ArrayValued',true);

end

plot(r,eta_r)

grid on

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Dyuman Joshi 2023-2-9

在 MATLAB Online 中打开

You will have to apply that individually -

L=0:100;

L_bar=25;

sigma_d =[0.25, 0.5, 0.75, 1.0];

mu = log(L_bar) - 0.5*(sigma_d).^2;

L_tilda = exp(mu);

r = 0:100;

LineTypes={'-' '--' ':' '-.'};

for ii=1:numel(sigma_d)

P= @(L)1./(L.*sqrt(2*pi)*sigma_d(ii)).*exp(-log(L/L_tilda(ii)).^2/(2*sigma_d(ii)^2));

fun = @(L) P(L).*exp(-r./L);

eta_r(ii,:)=integral(@(L)fun(L),0,Inf,'ArrayValued',true);

plot(r,eta_r(ii,:),'LineStyle', LineTypes{ii}, 'LineWidth', 1.5)

hold on

end

xlabel('r (\mu m)')

xticks([0 20 40 60 80 100])

ylabel('\eta(r)');

ylim([0 1])

title('Spatial Correlation Function LBAR=25')

set(gca, 'FontSize',10);

legend('\sigma_d =0.25', '\sigma_d= 0.5', '\sigma_d =0.75', '\sigma_d = 1')

David Harra 2023-2-9

Perfect. Thank you so much

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Answer 2

Dyuman Joshi 2023-2-9

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链接

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https://ww2.mathworks.cn/matlabcentral/answers/1909240-can-t-integrate-function-using-matlab#answer_1167280

在 MATLAB Online 中打开

You will have to explicitly change the function handle to change its definition

P=pi;
fun = @(x) P*x;
P=3;
%fun(3) is not equal to 3*3=9
fun(3)
ans = 9.4248
L=0:100;
L_bar=25;
sigma_d =[0.25, 0.5, 0.75, 1.0]; 
mu = log(L_bar) - 0.5*(sigma_d).^2;
L_tilda = exp(mu);
% eta_r = P.*exp(-r./L);
%  I want to integrate eta from zero to infinity where P has changing
%  variables to give 4 different plots.
r = 0:100;
% I was just testing below to see if a loop would run before attempting to
% plot anything
for ii=1:numel(sigma_d)
P= 1./(L.*sqrt(2*pi)*sigma_d(ii)).*exp(-log(L/L_tilda(ii)).^2/(2*sigma_d(ii)^2));
fun = @(x) P.*exp(-x./L);
eta_r=integral(fun,0,Inf,'ArrayValued',true)
end
Warning: Inf or NaN value encountered.
eta_r = 1×101
       NaN    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0000    0.0001    0.0006    0.0030    0.0109    0.0307    0.0718    0.1437    0.2535    0.4022    0.5842    0.7870    0.9943    1.1886    1.3546    1.4810    1.5614    1.5946    1.5834    1.5336    1.4531    1.3500    1.2326
Warning: Inf or NaN value encountered.
eta_r = 1×101
       NaN    0.0000    0.0000    0.0003    0.0023    0.0097    0.0269    0.0572    0.1019    0.1598    0.2281    0.3028    0.3800    0.4560    0.5276    0.5924    0.6491    0.6965    0.7345    0.7630    0.7827    0.7940    0.7979    0.7951    0.7867    0.7733    0.7560    0.7354    0.7122    0.6871
Warning: Inf or NaN value encountered.
eta_r = 1×101
       NaN    0.0002    0.0060    0.0263    0.0626    0.1109    0.1656    0.2219    0.2764    0.3268    0.3717    0.4106    0.4433    0.4701    0.4914    0.5076    0.5192    0.5268    0.5309    0.5319    0.5303    0.5265    0.5209    0.5137    0.5053    0.4958    0.4855    0.4746    0.4632    0.4514
Warning: Inf or NaN value encountered.
eta_r = 1×101
       NaN    0.0099    0.0513    0.1074    0.1642    0.2156    0.2596    0.2959    0.3252    0.3482    0.3658    0.3789    0.3882    0.3942    0.3977    0.3989    0.3984    0.3963    0.3931    0.3889    0.3839    0.3783    0.3722    0.3658    0.3590    0.3521    0.3450    0.3378    0.3305    0.3233