the matrix addition should come 0 but it is not happening

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Pranshu
Pranshu 2024-6-28
评论： Aquatris 2024-6-28
i am adding a matrix in for loop
Dtb=zeros(3,3);
Dtrb=Dtb;
Drrb=Dtb;
Dts=zeros(2,2);
for N=1:nlayer
h1=-h/2+(N-1)*th;
h2=h1+th;
ah1=h2-h1;
bh1=(h2^2-h1^2)/2;
ch1=(h2^3-h1^3)/3;
% -----------
if(N <= nlayer/2 || N == 1)
theta=(1+(-1)^N)*pi/4;
else
theta = -1*(-1+(-1)^N)*pi/4;
end
% --------------
theta = rad2deg( theta );
t1=(cosd(theta))^4;
t2=(sind(theta))^4;
t3=(sind(theta)*cosd(theta))^2;
t4=sind(theta)*(cosd(theta))^3;
t5=cosd(theta)*(sind(theta))^3;
%**********************************************************
c111=c11*t1 + 2*(c12+2*c66)*t3 + c22*t2;
c121=(c11 + c22 - 4*c66)*t3 + c12*(t1+t2);
c221=c11*t2 + 2*(c12+2*c66)*t3 + c22*t1;
c161=(c11-c12-2*c66)*t4 + (c12-c22+2*c66)*t5;
c261=(c11-c12-2*c66)*t5 + (c12-c22+2*c66)*t4;
c661=(c11+c22-2*c12-2*c66)*t3 + c66*(t1+t2);
c441=c44*(cos(theta))^2 + c55*(sin(theta))^2;
c451=(c55-c44)*cos(theta)*sin(theta);
c551=c55*(cos(theta))^2 + c44*(sin(theta))^2;
Cb=[c111 c121 c161; c121 c221 c261; c161 c261 c661];
Cs=[c551 c451;c451 c441];
Dtrb = Dtrb + bh1*Cb;
end
but the resulting Dtrb atrix is not coming 0,
as you can see from fig: matrix for iteration 10 is bh1*Cb matrix which is added to Dtrb matrix and in figure both are same but opp in sign so if we add it should come 0 but as you can see in fig the result is not 0 but it is something * e-11 coming

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回答（2 个）

Aquatris
Aquatris 2024-6-28
编辑：Aquatris 2024-6-28
Ran in:
Given the difference is 1e-12, it is probably floating point issue. Floating points list significant bit is generally unreliable.
x = 1/3; % should be 0.3333333...
sprintf('%0.55f',x) % not really
ans = '0.3333333333333333148296162562473909929394721984863281250'
y = 1e10;
z = x + y - y; % lets add a large number to x and then substract the same number
sprintf('%0.55f',z) % should be the same as x but not really due to floating point precision
ans = '0.3333339691162109375000000000000000000000000000000000000'
  2 个评论
Aquatris
Aquatris 2024-6-28
You cannot get rid of it. It is a limitation of representing real numbers in a fixed space. Welcome to the world of computer arithmetic :D

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SACHIN KHANDELWAL
SACHIN KHANDELWAL 2024-6-28
Ran in:
Hi @Pranshu,
It would be difficult to debug the issue without sufficient code files. I suspect that the problem is due to precision limitations of floating point representation. The MATLAB values appear to be the same, but when you add them, discrepancies might occur.
Following code might be helpful to understand the above issue :
a1 = -3.45671;
a2 = 1.34576;
b1 = -4.23678;
b2 = 0;
matA = [a1,a2;b1,b2]
matA = 2x2
-3.4567 1.3458 -4.2368 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
a1 = 3.4567145;
a2 = -1.3457689;
b1 = 4.23679345;
b2 = 0;
matB = [a1,a2;b1,b2]
matB = 2x2
3.4567 -1.3458 4.2368 0
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
matA+matB
ans = 2x2
1.0e-04 * 0.0450 -0.0890 0.1345 0
<mw-icon class=""></mw-icon>
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The issue arises due to the precision limitations of floating-point representation in MATLAB. Even though "matA" and "matB" appear to be the same up to four decimal places, they are not exactly equal due to the additional precision in "matB".
Additionally, you may want to use 'format' function in MATLAB. Kindly, refer the following MathWorks documentation for more information :
https://www.mathworks.com/help/matlab/ref/format.html
Hope this is helpful!
Thanks.
  1 个评论
Pranshu
Pranshu 2024-6-28
your matrix values are different ,but my values are exactly same as you can see in fig, this B matrix is bh1*Cb

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