Speed comparison between polyfit and A\y

I have a program where I am fitting a straight line to a set of data repeatedly over a million times. I wanted to get the most efficient possible code for doing this and thought polyfit would be the way to go. Surprisingly I found that polyfit is about 60 times slower than a simple A\y type estimation. I used the code below to test this out. Why is polyfit so slow ?

X = 0:50;
Y = X + 0.3 + randn(size(X));
N = 1000;

tic
for count = 1:N
   temp = polyfit(X,Y,1);
 end
 tm = toc;
 disp(sprintf('Polyfit too %g ms per call',tm/N/1e3));

tic
for count = 1:N
   temp = [ones(length(X),1) ,reshape(X,length(X),1)] \ reshape(Y,length(Y),1);
end
tm = toc;
disp(sprintf('A\\y too %g ms per call',tm/N/1e3));

The output is

Polyfit took 614.351 micro seconds per call
A\y took 10.2792 micro seconds per call

Karthik

[Sean de Wolski]

If you:

>>edit polyfit

You'll see that it's a big fancy wrapper for A\b.

Answer 1

[per isakson]

Study the performance of the code with the function, profile. Thus

    profile on
    code under test
    profile viewer

Note especially that this line is dark red

     0.97    1000   72 elseif warnIfLargeConditionNumber(R)

[Karthik]

Thanks! That makes sense!

Karthik