Problem with find or floating point issue

Lets say we have this problem,

a=-1:0.01:1;

b=-0.9:0.01:1.1;

find(a==b)

ans = 1×0 empty double row vector

Mathematically, -0.9 should lie in sequence a. I figured it out that it is something floating point issue but is it not weired that find command for this simple problem can not work? Is there some solution to work this out?

[Stephen23]

"... is it not weired that find command for this simple problem can not work?"

Operations on floating point numbers do not follow the same rules as the mathematics you learned in high-school.

"Is there some solution to work this out?"

The job of the programmer to understand the data that they are manipulating and how to manipulate it, so the solution is to learn about how floating point numbers behave and write your code accordingly. Most likely any finite number representation, even ones that are based on symbolic representation, will necessarily diverge from "high-school mathematics" at some point, so no matter what "solution" someone comes up with there will always be edge-cases where its behavior does not match your "high-school mathematics".

[Walter Roberson]

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

[Peng Li]

Nice resource ?

Answer 1

[Peng Li]

There is always some tricky things with floating precision. Usually it solves thing if you make the comparison by determining if the difference is smaller than a small enough value eps.

Try

find(abs(a-b) < eps)

Answer 2

[Walter Roberson]

a=-1:0.01:1;
b=-0.9:0.01:1.1;

That creates two vectors, the second one of which is algebraically 0.1 larger than the first at any given point. Because 0.01 cannot be exactly represented in binary floating point, and those errors accumulate when you use the colon operator, there will be places where the difference is not exactly the same as in other places:

>> num2str(unique(b.'-a.'), '%-.100g')

ans =

  4×56 char array

    '0.0999999999999998667732370449812151491641998291015625  '
    '0.09999999999999997779553950749686919152736663818359375 '
    '0.100000000000000033306690738754696212708950042724609375'
    '0.100000000000000088817841970012523233890533447265625   '

Now, remember that a==b between two vectors of the same size compares each element to each corresponding element, so a(1) would be compared to b(1), a(2) to b(2) and so on. But we know that each b is approximately 0.1 larger than the corresponding a, so there will not be even a single match between corresponding elements.

Perhaps you want

    >> num2str(a(ismember(a,b)).','%-.100g')

ans =

  98×56 char array

    '-0.90000000000000002220446049250313080847263336181640625'
    '-0.89000000000000001332267629550187848508358001708984375'
    '-0.88000000000000000444089209850062616169452667236328125'
    '-0.86999999999999999555910790149937383830547332763671875'
    '-0.85999999999999998667732370449812151491641998291015625'
    '-0.84999999999999997779553950749686919152736663818359375'
    '-0.8200000000000000621724893790087662637233734130859375 '
    '-0.810000000000000053290705182007513940334320068359375  '
    '-0.8000000000000000444089209850062616169452667236328125 '
    '-0.79000000000000003552713678800500929355621337890625   '
    '-0.7800000000000000266453525910037569701671600341796875 '
    '-0.770000000000000017763568394002504646778106689453125  '
    '-0.7600000000000000088817841970012523233890533447265625 '
    '-0.75                                                   '
    '-0.7399999999999999911182158029987476766109466552734375 '
    '-0.729999999999999982236431605997495353221893310546875  '
    '-0.7199999999999999733546474089962430298328399658203125 '
    '-0.70999999999999996447286321199499070644378662109375   '
    '-0.6999999999999999555910790149937383830547332763671875 '
    '-0.64000000000000001332267629550187848508358001708984375'
    '-0.63000000000000000444089209850062616169452667236328125'
    '-0.61999999999999999555910790149937383830547332763671875'
    '-0.5800000000000000710542735760100185871124267578125    '
    '-0.5700000000000000621724893790087662637233734130859375 '
    '-0.560000000000000053290705182007513940334320068359375  '
    '-0.5500000000000000444089209850062616169452667236328125 '
    '-0.54000000000000003552713678800500929355621337890625   '
    '-0.5300000000000000266453525910037569701671600341796875 '
    '-0.520000000000000017763568394002504646778106689453125  '
    '-0.5100000000000000088817841970012523233890533447265625 '
    '-0.5                                                    '
    '-0.4899999999999999911182158029987476766109466552734375 '
    '-0.42000000000000003996802888650563545525074005126953125'
    '-0.41000000000000003108624468950438313186168670654296875'
    '-0.40000000000000002220446049250313080847263336181640625'
    '-0.39000000000000001332267629550187848508358001708984375'
    '-0.38000000000000000444089209850062616169452667236328125'
    '-0.36999999999999999555910790149937383830547332763671875'
    '-0.35999999999999998667732370449812151491641998291015625'
    '-0.34999999999999997779553950749686919152736663818359375'
    '-0.33999999999999996891375531049561686813831329345703125'
    '-0.32999999999999996003197111349436454474925994873046875'
    '-0.29000000000000003552713678800500929355621337890625   '
    '-0.2800000000000000266453525910037569701671600341796875 '
    '-0.270000000000000017763568394002504646778106689453125  '
    '-0.2600000000000000088817841970012523233890533447265625 '
    '-0.25                                                   '
    '-0.2399999999999999911182158029987476766109466552734375 '
    '-0.229999999999999982236431605997495353221893310546875  '
    '-0.2199999999999999733546474089962430298328399658203125 '
    '-0.20999999999999996447286321199499070644378662109375   '
    '-0.1999999999999999555910790149937383830547332763671875 '
    '-0.16000000000000003108624468950438313186168670654296875'
    '-0.15000000000000002220446049250313080847263336181640625'
    '-0.14000000000000001332267629550187848508358001708984375'
    '-0.13000000000000000444089209850062616169452667236328125'
    '-0.11999999999999999555910790149937383830547332763671875'
    '-0.10999999999999998667732370449812151491641998291015625'
    '-0.09999999999999997779553950749686919152736663818359375'
    '-0.08999999999999996891375531049561686813831329345703125'
    '-0.07999999999999996003197111349436454474925994873046875'
    '-0.06999999999999995115018691649311222136020660400390625'
    '-0.04000000000000003552713678800500929355621337890625   '
    '-0.0300000000000000266453525910037569701671600341796875 '
    '-0.020000000000000017763568394002504646778106689453125  '
    '-0.0100000000000000088817841970012523233890533447265625 '
    '0                                                       '
    '0.0100000000000000088817841970012523233890533447265625  '
    '0.020000000000000017763568394002504646778106689453125   '
    '0.0300000000000000266453525910037569701671600341796875  '
    '0.04000000000000003552713678800500929355621337890625    '
    '0.05999999999999994226840271949185989797115325927734375 '
    '0.06999999999999995115018691649311222136020660400390625 '
    '0.07999999999999996003197111349436454474925994873046875 '
    '0.08999999999999996891375531049561686813831329345703125 '
    '0.15000000000000002220446049250313080847263336181640625 '
    '0.16000000000000003108624468950438313186168670654296875 '
    '0.270000000000000017763568394002504646778106689453125   '
    '0.2800000000000000266453525910037569701671600341796875  '
    '0.29000000000000003552713678800500929355621337890625    '
    '0.40000000000000002220446049250313080847263336181640625 '
    '0.41000000000000003108624468950438313186168670654296875 '
    '0.42000000000000003996802888650563545525074005126953125 '
    '0.5300000000000000266453525910037569701671600341796875  '
    '0.54000000000000003552713678800500929355621337890625    '
    '0.5500000000000000444089209850062616169452667236328125  '
    '0.560000000000000053290705182007513940334320068359375   '
    '0.5700000000000000621724893790087662637233734130859375  '
    '0.5800000000000000710542735760100185871124267578125     '
    '0.75                                                    '
    '0.7600000000000000088817841970012523233890533447265625  '
    '0.770000000000000017763568394002504646778106689453125   '
    '0.7800000000000000266453525910037569701671600341796875  '
    '0.79000000000000003552713678800500929355621337890625    '
    '0.8000000000000000444089209850062616169452667236328125  '
    '0.810000000000000053290705182007513940334320068359375   '
    '0.8200000000000000621724893790087662637233734130859375  '
    '1                                                       '

As for values that do not match, see for example,

    >> [d,idx] = min(abs(b-0.5))
d =
      1.11022302462516e-16
idx =
   141
>> fprintf('%.99g\n', b(idx))
0.50000000000000011102230246251565404236316680908203125