Matlab is giving conflicting results, please help.

Using the code below for a cross product, the cross products should be equal but Matlab is saying they aren't.

v = [ 1, 2, 3 ];
r1 = [ 0.3, -0.4, 0.5 ];
r2 = r1 + v;
r1Xf = cross(r1,v)
r2Xf = cross(r2,v)
isequal(r1Xf,r2Xf)

==================

in the command window:

>> isequal(r1Xf,r2Xf)

ans =

logical

0

====================

However, in a little trial I did I am still getting conflicting results:

>> r1Xf

r1Xf =

-2.2000 -0.4000 1.0000

>> r2Xf

r2Xf =

-2.2000 -0.4000 1.0000

>> x=[-2.2, -0.4, 1.0]

x =

-2.2000 -0.4000 1.0000

>> x==r2Xf

ans =

1×3 logical array

0 0 1

>> x==r1Xf

ans =

1×3 logical array

1 0 1

=================

I don't understand why the arrays are all [-2.2, -0.4, 1.0], but Matlab still says they aren't equal?

Answer 1

[Stephen23]

"...but Matlab still says they aren't equal?"

Because they aren't equal.

This is very easy to check (you already used one method, here is another):

>> r1Xf - r2Xf
ans =
  -8.8818e-016  4.4409e-016  0
>> x - r1Xf
ans =
  0  -1.1102e-016  0
>> x - r2Xf
ans =
  -8.8818e-016  3.3307e-016  0

"... the cross products should be equal "

Nope, I don't see any reason to expect them to be equal. Operations on floating point numbers collect floating point error. You need to learn about the limits of floating point arithmetic.

"I don't understand why the arrays are all [-2.2, -0.4, 1.0]..."

Because the operations collect different floating point error for different input values. What you see printed in the command window is the closest representation to 5 or 16 significant digits, depending on your current format setting. To see the "real" value download James Tursa's FEX submission:

https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

Use James Tursa's num2strexact and you will see that none of those values really have the exact value -2.2 or -0.4. All you are looking at is a representation of those floating point numbers displayed in the command window, to the precision defined by your format setting. Just because you see -2.2 or -0.4 displayed tells you nothing about the "real" floating point number's value.

Note that you can change how the value is displayed by changing the format.

You need to learn about the limits of floating point numbers. Start by reading these:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

[AE_Engnr]

Thanks for your answer. This makes sense now.