How do I round to the nearest arbitrary, enumerated value in MATLAB?

If I have values:

v = [0.1 2.2 1.6 7.3 10];

and I want all my values to be rounded to the nearest value in this list:

roundTargets = [0 2.7 8 11.1];

then I would want to make a function that would convert each value in v to the nearest value in roundTargets.

So this function would return me:

vRounded = [0 2.7 2.7 8 11.1];

Any clever ways to do this?

[Yes, I know how to do this. When I get questions from users that make good posts here, I like to put them out for the world to find.]

[Doug Hull]

What I love about this is there are three perfectly good answers, all doing this in a slightly different way. Each of them has the possibility to be the best solution under different constraints (memory, time, ease of development, etc...)

[che_guevara]

Would you mind providing those 3 solutions? :)

[Walter Roberson]

The three solutions are shown below -- interp1, histc, bsxfun

Note: Doug Hull moved on to a different career so he will not be back to respond.

Answer 1

[Matt Fig]

One approach:

roundTargets = [0 2.7 8 11.1];
v = [0.1 2.2 1.6 7.3 10];
vRounded = interp1(roundTargets,roundTargets,v,'nearest')

[Doug Hull]

Exactly! Now, can you think of key words to put into this solution so other people can find it? That is the real art here, no?

[Matt Fig]

I will add some tags, as I think that helps the search most.

[Walter Roberson]

To account for values outside the span of roundTargets, you would need

vRounded = interp1(roundTargets,roundTargets,v,'nearest','extrap')

Answer 2

[Teja Muppirala]

I believe HISTC is the fastest and most memory efficient way to solve this problem for large cases.

v = 10*rand(1,1000000);
roundTargets = [0 sort(10*rand(1,10000)) 10];

%%%histc
tic
  [~,Index1] = histc(v,[-Inf interp1(1:numel(roundTargets),roundTargets,0.5 + (1:numel(roundTargets)-1)) Inf]);
  vRounded1 = roundTargets(Index1);
timehistc = toc

%%%interp1
tic
  vRounded2 = interp1(roundTargets,roundTargets,v,'nearest');
timeinterp1 = toc

isequal(vRounded1,vRounded2)

%%%bsxfun will run out of memory
tic
  [~,idx] = min(bsxfun(@(x,y)abs(x-y),v,roundTargets.')); %index of closest
  vRounded = roundTargets(idx); %extract values
timebsxfun = toc

[Teja Muppirala]

You need roundTargets to be sorted though

Answer 3

[Sean de Wolski]

[~,idx] = min(bsxfun(@(x,y)abs(x-y),v,roundTargets.')); %index of closest
vRounded = roundTargets(idx); %extract values

Keywords?

minimum, absolute, difference, element by element, comparison, index

[Matt Fig]

You are too fast! I was about to post this with the warning that it could take a ton of memory for large problems because of the intermediate array.