MATLAB: Imprecise Basic operations

faq6.1floating point

Hi everyone,

I am using Matlab 2009a. When I try to calculate

0.9 – 0.8 – 0.1

then the result is

-2.775557561562891 e-017

Close to zero, but not zero. Is it not possible to get a precise solution for a floating point operation? This minor imprecision has large implications for my programs.

Is there a way to get precise calculations? Why does matlab get this (quite easy task) wrong?

Thanks for your help!

Best Answer

See: http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F

Welcome to the world of floating point computing.

A computer can't exactly represent most floating point numbers.

Example: Try calculating 3*(1/3) by hand, with writing out 1/3 to as many decimal places as you please. You will get .9999..., which is CLOSE to 1, but is not equal to 1 (which the true answer should be).

Related Solutions

MATLAB: Rounding using ‘fix’… possibly a bug

To see what is going on you can examine the exact floating point values. Note that none of your original numbers except 0.5 can be represented in IEEE double format exactly:

>> num2strexact(.7)
ans =
0.6999999999999999555910790149937383830547332763671875
>> num2strexact(.5)
ans =
0.5
>> num2strexact(.4)
ans =
0.40000000000000002220446049250313080847263336181640625
>> num2strexact(.3)
ans =
0.299999999999999988897769753748434595763683319091796875
>> num2strexact(.1)
ans =
0.1000000000000000055511151231257827021181583404541015625
>> num2strexact(.7/.1)
ans =
6.99999999999999911182158029987476766109466552734375
>> num2strexact(.5/.1)
ans =
5
>> num2strexact(.4/.1)
ans =
4
>> num2strexact(.3/.1)
ans =
2.999999999999999555910790149937383830547332763671875

You can find num2strexact here:

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

MATLAB: Split imprecise checkerboard pattern

Hi Nassim,

I tried finding the checkerboard lines and I could easily do it using edge+hough.

i1=imread('chess.png');
imedge = edge(i1,'Canny',[], 2);
[H,T,R] = hough(imedge,'Theta',[-90:-87 -3:3 87:89]);
P  = houghpeaks(H,20);
lines = houghlines(imedge,T,R,P);
figure;
imshow(imedge);
hold on;
for k=1:length(lines)
xy=[lines(k).point1,lines(k).point2];
if abs(lines(k).theta)==90 
    plot([xy(2) xy(4)],[0 size(i,1)],'r');
else
    plot([0 size(i,2)],[xy(1) xy(3)],'r');
end
end

You basically have to play with the number of 'houghpeaks' to be detected as some lines are detected multiple times. By further processing, you can remove the multiple lines.

Hope this helps.

Best Answer

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MATLAB: Rounding using ‘fix’… possibly a bug

MATLAB: Split imprecise checkerboard pattern

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