1 - 1 = -0 on Matlab why? How to fix that?

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Steven Shaaya 2021-11-30

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评论： Steven Shaaya 2021-11-30

I am working with a matrix that has two columns.

I writing a code to do columns 1 minus columns 2. And the matlab display the result which is all fine.

However, some rows have the same values; for example;

x = [1 2 3; 2 2 5; 3 2 6]

y = [ 4 2 6; 1 2 7; 5 2 3]

w=x(:,2)-y(:,2)

% now on this case I get

w =

0

% however, the code that I am working with has one row1 column 1 that has value of 1.0700 and row1 column 2 has value 1.0700

now this give an output of -0.0000

I was wondering if there is a solution for this issue.

Now, I am doing some operation to column 2 and my guess is that there is some rounding issue.

I do look at both columns before I do the subtraction between columns 1 & 2 and I see that both values are 1.0700 so where does this rounding proplem is coming from.

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Stephen23 2021-11-30

在 MATLAB Online 中打开

"However, some rows have the same values"

In fact they don't have the same values.

"however, the code that I am working with has one row1 column 1 that has value of 1.0700 and row1 column 2 has value 1.0700 now this give an output of -0.0000"

Because the values are not the same. This is easy to demonstrate:

format short
X = [pi+1,1.07]
X = 1×2
    4.1416    1.0700
Y = [pi,1.07+eps(2)]
Y = 1×2
    3.1416    1.0700
X-Y
ans = 1×2
    1.0000   -0.0000
X(2)-Y(2)
ans = -4.4409e-16

"I was wondering if there is a solution for this issue."

What is the issue?

You subtract two different values and so MATLAB correctly gives you the non-zero difference (as the closest representable binary floating point number). That is the expected behavior.

"I do look at both columns before I do the subtraction between columns 1 & 2 and I see that both values are 1.0700 so where does this rounding proplem is coming from"

It comes from the values of the numbers. Simply "looking" at two numbers displayed to five signficant figures will not tell you if they differ after the twelfth significant figure. You will need to either display them to a much higher precision or (better) look at their exact hexadecimal representation to see if they are exactly the same.

Most likely your algorithm is not robust for binary floating point numbers: assuming exact equivalence of binary floating point numbers in your algorithm is most likely a bug.

Steven Shaaya 2021-11-30

Can I make the matlab round the values of culmun 2 to four decimal places, so that the value of column 2 will be exactly 1.0700 and I don't have to worry about 10^-16 rounding issue anymore? So I can round the values before using "If statement".

I know how to round values in matlab when using fprintf function

but I am not sure how to do that for a value; for example, say

X = 0.90000000001 % how to round this value to four decimal places without using fprintf

Thank you all

Steven Shaaya 2021-11-30