matrix logical indexing

I have a matrix A with dimensions nxm. I want to extract all values x that are between two values a and b, that is: (a<x<b). How can I do it in one step?

I know i can do it in two steps: A1 = A(A>a); A2 = A1(A1<b);

how do I combine the two logical statements?

Answer 1

[Fangjun Jiang]

A1=A(A>a & A<b)

[HRmatlab]

thank you!

Answer 2

[Teja Muppirala]

In the case of checking bounds by combining two logical statements, I think the following expression will generally be significantly faster:

B = A(abs(A-(a+b)/2) < (b-a)/2);

The only thing is, you need to make sure that the datatypes and magnitudes of numbers you are working with can be used in this expression. For example, if you are working with integers, you might get overflow/underflow in some situations, etc. For regular double precision numbers you should probably be ok.

[Jan]

A = rand(1000); a = 0.2, b = 0.6;

tic; z = A(A>a & A<b); toc % 0.0577

tic; z = A(abs(A-(a+b)/2) < (b-a)/2); toc % 0.0443

But why is it faster? With N=numel(A): It uses N*9 bytes as temporary memory, performs N*2 arithemtical operations and compares N values. Fangjun's method needs N*3 bytes as temporary memory and compares N*2 values without arithmetic operations.

[Fangjun Jiang]

Interesting but hard to believe. I made an example to dis-prove that. Do you have a count-example?

%%

A=rand(1000);

a=0.2;

b=0.8;

t1=0;

t2=0;

for k=1:100

tic;

A1=A(A>a & A<b);

t1=t1+toc;

tic;

A2=A(abs(A-(a+b)/2) < (b-a)/2);

t2=t2+toc;

end

fprintf('t1=%f\n',t1);

fprintf('t2=%f\n',t2);

t1=4.654067

t2=5.639990

[Fangjun Jiang]

If I just change the size of A, A=rand(100), the result is opposite. So, we need insights.

t1=0.039258

t2=0.036136

[Teja Muppirala]

It is probably version dependent. I use R2011b and I find that if I run your code for A = rand(1000), I get:

t1=3.190328

t2=2.453046

For A = rand(100), I get:

t1=0.040473

t2=0.030582

I couldn't tell you the reason why, but I do know that a lot of the elementary math functions have been getting much faster lately.

[Jan]

@Teja: The math functions are limited by the processor speed, if the data match into the processor cache. For large data the memory access should be the limiting factor. Therefore I'd expect your function to be much slower for RAND(1000).

@Fangjun: I get these timings on 2009a running in a single core environment: t1=6.282469, t2=5.247344.