Numerical integration using Trapz
显示 更早的评论
Hi all,
I am trying to calculate a double integral over a rectangular grid using trapz.
The grid is defined as:
[x,z] = meshgrid(xp,zp);
xp and zp are the 1d arrays of x and z coordinates of the grid.
I trying to calculate the function values (F) at the grid nodes as:
F(i,j)=trapz(zp,trapz(xp,g.*f,2));
here,
g is a function of x and z i.e. g(x,z) whereas, f values are already calculated values at each node of the grid i.e. not a function of x and z.
Can someone suggest how may I do it, please.
采纳的回答
Star Strider
2021-5-6
That should produce one scalar value as ‘F’, so the subscripts are not necessary.
I would do something like this —
F = trapz(zp,trapz(xp,g.*f));
The result of the first trapz call will be a vector, and of the second will be a scalar. So long as ‘g’ and ‘f’ have compatible dimensions, and they match ‘xp’ and ‘zp’ appropriately, that should work.
6 个评论
Waseem Akhtar
2021-5-6
Star Strider
2021-5-6
My pleasure!
I am not certain what you want to do. If you want to experiment with different combinations of the elements of ’f’, one way would be to create a separate matrix (perhaps ‘fm’) of ones, then substitute specific elements of ‘f’ into it, then do the integrations.
So for example —
F = zeros(size(f)); % Preallocate
for i = 1:size(f,1)
for j = 1:size(f,2)
fm = ones(size(f));
fm(i,j) = f(i,j);
F(i,j)=trapz(zp,trapz(xp,g.*fm));
end
end
Assuming that I understand that this is what you want to do, that is likely the most efficient way I can think of to do it.
Waseem Akhtar
2021-5-6
Star Strider
2021-5-6
As I understand that, my code does exactly what you want. I do not understand the reason for the loops, however, unless it is to do exactly what my code does.
My code multiplies the ‘fm’ matrix by ‘g’, with corresponding values of ‘fm’ first being replaced by selected values of ‘f’. The multiplication is element-wise, so only the element of ‘g’ that is multiplied by the specific value of ‘f’ selected in the loop changes. That result is then reflected in the corresponding element of ‘F’.
This is the best I can do. If it is still not ‘correct’, please provide an example illustrating the necessary calculation to get the desired result.
Waseem Akhtar
2021-5-7
Star Strider
2021-5-7
As always, my pleasure!
更多回答（0 个）
类别
在 帮助中心 和 File Exchange 中查找有关 Numerical Integration and Differentiation 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
Translated by 
