Incorrect results from intersect when entering imaginary numbers

Question

Thomas Tang 2021-10-23

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https://ww2.mathworks.cn/matlabcentral/answers/1569888-incorrect-results-from-intersect-when-entering-imaginary-numbers

评论： Dave B 2021-10-26

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!

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Dave B 2021-10-23

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

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Answer 1

Stephen23 2021-10-23

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https://ww2.mathworks.cn/matlabcentral/answers/1569888-incorrect-results-from-intersect-when-entering-imaginary-numbers#answer_814593

A = readmatrix('data1.txt')
A = 465×2
4000    1.5000
6000    1.5000
8000    1.5000
0000    1.5000
2000    1.5000
4000    1.5000
8000    1.5000
0000    1.5000
4000    2.0000
6000    2.0000
B = readmatrix('data2.txt')
B = 408×2
2000    1.5000
4000    1.5000
6000    1.5000
8000    1.5000
0000    1.5000
2000    1.5000
4000    1.5000
6000    1.5000
8000    1.5000
2000    2.0000
C = intersect(A,B,'rows')
C = 388×2
2000    1.5000
2000    2.0000
2000    2.5000
2000    3.0000
2000    3.5000
2000    4.0000
2000    4.5000
2000    5.0000
2000    5.5000
2000    6.0000

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Answer 2

Thomas Tang 2021-10-26

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https://ww2.mathworks.cn/matlabcentral/answers/1569888-incorrect-results-from-intersect-when-entering-imaginary-numbers#answer_816533

A.mat
B.mat

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))

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Thomas Tang 2021-10-26

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 2021-10-26

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

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