the matrix addition should come 0 but it is not happening

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

[Avni Agrawal]

Hi, can you share the constant values used for the above mentioned code?

Answer 1

[Aquatris]

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'

[Pranshu]

then how to get rid of this thing?

[Aquatris]

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

Answer 2

[SACHIN KHANDELWAL]

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

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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

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matA+matB

ans = 2x2

1.0e-04 * 0.0450 -0.0890 0.1345 0

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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.

[Pranshu]

your matrix values are different ,but my values are exactly same as you can see in fig, this B matrix is bh1*Cb