Equivalent of A&(~B) without using ~

I am looking for a way to generate the same output as A&(~B) w/o using the ~ operator. The problem is both A and B are very large sparse matrices with only a few non-zero elements (trues). Evaluating ~B will produce a temporary matrix that cannot fit in memory. What's the best way to circumvent this?

[David Goodmanson]

Hi YL,

does

a-(a&b)

get it done?

Answer 1

[Yi-xiao Liu]

Hat tip to @David Goodmanson and @Stephen23. I found 4 solutions:

A=rand(5)<0.6;B=rand(5)>0.2;
ref=A&(~B);

Method1=A;
Method1(B)=false;

Method2=A-(A&B);

Method3=(A-B)>0;

Method4=xor(A,A&B);

all((Method1==ref)&(Method2==ref)&(Method3==ref)&(Method4==ref),"all")

ans = logical
   1

rng("shuffle")

t1=nan(10,1);t2=nan(10,1);t3=nan(10,1);t4=nan(10,1);
for ii=1:10
    idx=ceil(1e6*rand(2e6,2));
    idx=unique(idx,"rows");
    i=idx(:,1);j=idx(:,2);
    A=sparse(i(1:1e6),j(1:1e6),true(1e6,1),1e6,1e6);
    B=sparse(i((1e6+1):end),j((1e6+1):end),true(numel(i)-1e6,1),1e6,1e6);
    
    tic
    Method1=A;
    Method1(B)=false;
    t1(ii)=toc;
    
    tic
    Method2=A-(A&B);
    t2(ii)=toc;
    
    tic
    Method3=(A-B)>0;
    t3(ii)=toc;
    
    tic
    Method4=xor(A,A&B);
    t4(ii)=toc;
end
t1=mean(t1);t2=mean(t2);t3=mean(t3);t4=mean(t4);

bar([t1,t2,t3,t4])

Personally I like the 4th one the most. It's fast, it's short, and it does not invoke type conversion in case you are short on Bytes.

[Paul]

Note that Method2 returns a double, not logical.

A=rand(5)<0.6;B=rand(5)>0.2;
ref=A&(~B);
Method1=A;
Method1(B)=false;
Method2=A-(A&B);
Method3=(A-B)>0;
Method4=xor(A,A&B);
whos Method*

  Name         Size            Bytes  Class      Attributes

  Method1      5x5                25  logical              
  Method2      5x5               200  double               
  Method3      5x5                25  logical              
  Method4      5x5                25  logical              

[Yi-xiao Liu]

@Paul

You are correct. However Method2 is a double with only 2 possible values (0 and 1) so this shouldn't matter.

A B A&B A-(A&B)

1 1 1 0

1 0 0 1

0 1 0 0

0 0 0 0

And you can always add logical(Method2)

[Paul]

I thought there was a concern about memory consumption, so thought it worthwile to point out that Method2 requires 8x more memory, in addtion to the need to cast to logical if used later on as logical.

[Yi-xiao Liu]

@Paul You are absolutely right. This is in fact (one of) the reason I prefer method 4 (see last line of my answer).

On conversion back to logical, my experience is that MATLAB will do the conversion for you if you try to use double as logical. there is no need to do it explicitly.