Incorrect results from intersect when entering imaginary numbers

The attached file, data1.txt, contains the X-Y coordinates of the points in Set A.

The other file, data2.txt, contains the X-Y coordinates of the points in Set B.

My objective is to find the intersection of the two sets.

I used intersect() in MATLAB in three ways but got different answers.

First way, combining the X array and the Y array in the same set as table(X, Y) and then input the two tables to intersect();

Second way, combining the X array, Y array in the same set as X+1i.*Y and then input the two imaginary number arrays to intersect();

Third way, combining the X array, Y array in the same set as X+100.*Y and then input the two real number arrays to intersect().

I found the answers from the first two ways were wrong!

[Dave B]

Can you expand on what you mean by the first two ways were wrong? From what I can tell all three methods produce the same result (other than how the values are sorted)...

load('data1.txt')
load('data2.txt')

% I think these are the three ways you used intersect:
t1=table(data1(:,1),data1(:,2));
t2=table(data2(:,1),data2(:,2));
res1=intersect(t1,t2);
res2=intersect(data1(:,1)+data1(:,2)*1i,data2(:,1)+data2(:,2)*1i);
res3=intersect(data1(:,1)+data1(:,2)*100,data2(:,1)+data2(:,2)*100);

% Here's an alternative that doesn't use intersect:
res_alt=data2(ismember(data2,data1(ismember(data1,data2,'rows'),:),'rows'),:);

% Are the the same number of elements?
height(res1)==height(res2)

ans = logical
   1

height(res1)==height(res3)

ans = logical
   1

height(res1)==height(res_alt)

ans = logical
   1

% Decompose the complex back into real components and sort rows to compare with res1:
isequal(sortrows(table2array(res1)), sortrows([real(res2) imag(res2)]))

ans = logical
   1

% Decompose the *100 out of res3
res3_y=(floor(res3/50)*50)/100;
res3_x=res3-res3_y*100;
a=sortrows(table2array(res1))-sortrows([res3_x res3_y]);

% some floating point error is to be expected, right?
max(abs(sort(res1.Var1)-sort(res3_x)))

ans = 9.1038e-14

max(abs(sort(res1.Var2)-sort(res3_y)))

ans = 0

% check res1 against res_alt
isequal(sortrows(table2array(res1)), sortrows(res_alt))

ans = logical
   1

Answer 1

[Stephen23]

A = readmatrix('data1.txt')

A = 465×2

0.4000 1.5000 0.6000 1.5000 0.8000 1.5000 1.0000 1.5000 1.2000 1.5000 1.4000 1.5000 1.8000 1.5000 2.0000 1.5000 0.4000 2.0000 0.6000 2.0000

B = readmatrix('data2.txt')

B = 408×2

0.2000 1.5000 0.4000 1.5000 0.6000 1.5000 0.8000 1.5000 1.0000 1.5000 1.2000 1.5000 1.4000 1.5000 1.6000 1.5000 1.8000 1.5000 0.2000 2.0000

C = intersect(A,B,'rows')

C = 388×2

0.2000 1.5000 0.2000 2.0000 0.2000 2.5000 0.2000 3.0000 0.2000 3.5000 0.2000 4.0000 0.2000 4.5000 0.2000 5.0000 0.2000 5.5000 0.2000 6.0000

Answer 2

[Thomas Tang]

In my application, the actual situation is like running the following scripts in R2021a.

clear

load('A.mat','overturn_Pi_p','overturn_Pi_a');

A = table(overturn_Pi_p, overturn_Pi_a);

load('B.mat','overturn_Pi_p','overturn_Pi_a');

B = table(overturn_Pi_p, overturn_Pi_a);

%First way gives the wrong answer 232

height(intersect(A, B))

%Second way gives the wrong answer 232

A_comb1 = A.overturn_Pi_p + 1i.*A.overturn_Pi_a;

B_comb1 = B.overturn_Pi_p + 1i.*B.overturn_Pi_a;

length(intersect(A_comb1, B_comb1))

%Third way gives the correct answer 388

A_comb2 = A.overturn_Pi_p + 100.*A.overturn_Pi_a;

B_comb2 = B.overturn_Pi_p + 100.*B.overturn_Pi_a;

length(intersect(A_comb2, B_comb2))

[Dave B]

My guess is you're seeing different results because of floating point error. I already see a small difference between the values in B.mat and the values in data1.txt. When you multiply by 100 the change in precision produces a different result. intersect does not accept a tolerance, it just uses strict equality.

You can find a nice answer here:

https://www.mathworks.com/matlabcentral/answers/564920-problem-with-intersect-function

load('B.mat','overturn_Pi_p','overturn_Pi_a');
B = table(overturn_Pi_p, overturn_Pi_a);
B_txt=readtable('data1.txt');
histogram(B_txt.Var1-B.overturn_Pi_p)

[Thomas Tang]

Thank you, Dave! You are absolutely right.

Now I can get identical answer from the three approaches after modifying the codes as below to get rid of the floating point error.

The array overturn_Pi_p was generated elsewhere by assigning 0.2:0.2:8 to it with certain filtering criterion and then saved it to *.mat. This process causes floating point error!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

load('A.mat','overturn_Pi_p','overturn_Pi_a');

overturn_Pi_p=round(overturn_Pi_p.*10)./10;

overturn_Pi_a=round(overturn_Pi_a.*10)./10;

A = table(overturn_Pi_p, overturn_Pi_a);

load('B.mat','overturn_Pi_p','overturn_Pi_a');

overturn_Pi_p=round(overturn_Pi_p.*10)./10;

overturn_Pi_a=round(overturn_Pi_a.*10)./10;

B = table(overturn_Pi_p, overturn_Pi_a);

......

[Dave B]

I wish all of the set operations had a tolerance option!