Issue with finding intersection between randomly generated matrices

I have two matrices randomly generated A and A_new (subset of A). When I use the intersect command, very surprisingly it negates one of the rows, while identifies the other four rows. Below is the screenshot while trying to debug the issue:

However, when I copy A and A_new directly from the workspace into different variables (A1 and A2 respectively) and use the same intersect command, the result comes out perfect:

A1 = [-17.1747990884382	19.2719049157323	99.6315612404934 % note: A is actually 71-by-3, but here I used only 22-by-3
    -10.1200347628603	44.6569202438877	94.7227267967226
    58.6115851834664	-9.53770294596646	92.9138476931620
    47.0203961819196	-18.8814327228311	87.4170841370532
    93.0719877076277	-40.6092086918209	85.2369720823465
    62.7067365154531	-40.8222018404139	82.3859521001850
    28.4948014516781	24.4091032205797	80.3478942902817
    -27.4120788164787	46.4475836126667	80.0165302698221
    52.5520137564189	-86.2238156283654	78.0805162946764
    34.8647540565998	-78.4903445824848	73.9133775177247
    64.6182025041414	-8.02799812625432	71.0037105461384
    -74.2010206861346	27.4023369519983	70.4017187841455
    13.4165633024713	43.2557370559446	70.1735863347631
    79.3294488296403	46.5421363760066	67.5796378292223
    71.7027257281106	-99.6206397947143	66.7042052990168
    8.66568815370449	86.0343589130021	59.3423113221334
    25.6901433887827	-13.4695262062841	58.4318188330688
    -39.5611117917563	47.4462315581845	53.9216963646236
    -8.49830028866433	-46.7213246886748	49.1592271029911
    -74.0052720695440	99.2224561788284	49.0989168204624
    -43.0371001304189	58.8076794390692	46.2077865058290
    78.7271494784465	95.8905249403584	45.4459816955421];

A2 = [93.0719877076277	-40.6092086918209	85.2369720823465
    79.3294488296403	46.5421363760066	67.5796378292223
    8.66568815370449	86.0343589130021	59.3423113221334
    -74.0052720695440	99.2224561788284	49.0989168204624
    78.7271494784465	95.8905249403584	45.4459816955421];

[~,idx2,~] = intersect(A1,A2,'rows');

idx2 =

    20
    16
    22
    14
     5

I wonder why this discrepency? I thought of using rounding option and it works for this random set, however, messes up some other random sets. Any suggestion to fix the issue would be highly appreciated. I am really confused.

Thanks in advance, and sorry for the long question.

[dpb]

We can't duplicate from the above...attach the two arrays as .mat files.

[J AI]

done

Answer 1

[dpb]

The results for intersect are correct ..

>> (A(16,:)-A_new(3,:))
ans =
   1.0e-13 *
         0         0    0.1421
>>

The other data arrays were apparenty constructed by taking fewer significant digits.

Testing floating point for exact equality is always fraught with such issues--if you want matching with eps() of the values or other tolerance and not need exact match to the last bit, use ismembertol

You have to look at the value as stored in memory to make a judgement, you can't just compare the visual representation on the screen.

[J AI]

Thanks a lot - it works now with ismembertol. By the way, I thought workspace stored the actual values and did not have any more decimals places beyond what it shows. However, learned something new about MATLAB today. Thanks once again for your help!

[dpb]

Read the information on display formatting at the format command doc page to see what precision is displayed for various choices of the command window format.

Also be aware that how you generate a floating point value can cause rounding differences owing to whether the result is read in or calculated and things like order of calculations can result in two variables not being identical to the LSB of mantissa and so cause failure to match equality tests.

The default output precision for builtins such as csvwrite are set to use a shorter precision by default so that is another way that one can introduce a discrepancy.