Problem with find or floating point issue

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Sher Ali Cheema
Sher Ali Cheema 2020-4-13
评论： Peng Li 2020-4-14
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?
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回答（2 个）

Peng Li
Peng Li 2020-4-13
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)
Walter Roberson
Walter Roberson 2020-4-14
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

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