Problem with the evaluation of the product of triple integral

Question

DIMITRIS GEORGIADIS 2021-11-4

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https://ww2.mathworks.cn/matlabcentral/answers/1578945-problem-with-the-evaluation-of-the-product-of-triple-integral

评论： DIMITRIS GEORGIADIS 2021-11-4

采纳的回答： Yongjian Feng

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Consider a set of positive values

,

and

.

How can I compute q passing the integrand function as a function handle ? With the followind code an error occurs...

% Inputs:
t       = 15;
sigma   = 0.25;
y       = [1.0 1.2]';
h  = @(x1,x2,x3)       x1.*(t - x2).^x3;
g  = @(x1,x2,x3)       exp(-0.5.*((y - h(x1,x2,x3))./sigma).^2 );  
q  = prod(integral3(@(x1,x2,x3) g(x1,x2,x3), 0, 1, 0, t, 0.3, 1));

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Answer 1

Yongjian Feng 2021-11-4

1
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https://ww2.mathworks.cn/matlabcentral/answers/1578945-problem-with-the-evaluation-of-the-product-of-triple-integral#answer_823625

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y is an array. You can't use it directly in integral3. Do the product yourself as a for loop.

t       = 15;
sigma   = 0.25;
y       = [1.0 1.2]';
accu = 1;
for i = 1:length(y)
    h  = @(x1,x2,x3)       x1.*(t - x2).^x3;
    g  = @(x1,x2,x3)       exp(-0.5.*((y(i) - h(x1,x2,x3))./sigma).^2 );  
    q  = integral3(@(x1,x2,x3) g(x1,x2,x3), 0, 1, 0, t, 0.3, 1);
    accu = accu * q;
end
accu

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Yongjian Feng 2021-11-4

在 MATLAB Online 中打开

Use arrayfun

y = [1.0 1.2];
result = prod(arrayfun(@(x) int3(x), y));
function q = int3(y)
    t       = 15;
    sigma   = 0.25;
    h  = @(x1,x2,x3)       x1.*(t - x2).^x3;
    g  = @(x1,x2,x3)       exp(-0.5.*((y - h(x1,x2,x3))./sigma).^2 );  
    q  = integral3(@(x1,x2,x3) g(x1,x2,x3), 0, 1, 0, t, 0.3, 1);
end