Thread Subject:

2nd max is max of vec minus max(vec)

2nd maximum is the max of the group when you remove the max from group.
lets say your vector is vec,
2nd maximum = max(vec(vec<max(vec)));

"Dhruv Chhabra" wrote in message <jsl4g0$3tv$1@newscl01ah.mathworks.com>...

--------------------------------------------------------------

I am confident you will find

>> doc sort

absolutely fascinating.

Dear Dhruv Chhabra,

> 2nd maximum is the max of the group when you remove the max from group.
> 2nd maximum = max(vec(vec<max(vec)));

This is not efficient. Faster:

  [max1, index1] = max(vec);
  vec(index1) = -inf;
  [max2, index2] = max(vec);
  
Please note that the results differ, if the maximum value is not unique.
For a [1e6x1] random vector, this requires the half time.

Kind regards, Jan

"Jan Simon" wrote in message <jsnmhb$755$1@newscl01ah.mathworks.com>...
> Dear Dhruv Chhabra,
>
> > 2nd maximum is the max of the group when you remove the max from group.
> > 2nd maximum = max(vec(vec<max(vec)));
>
> This is not efficient. Faster:
>
> [max1, index1] = max(vec);
> vec(index1) = -inf;
> [max2, index2] = max(vec);
>
> Please note that the results differ, if the maximum value is not unique.
> For a [1e6x1] random vector, this requires the half time.


I haven't tried it, but this is probably even more efficient:

http://www.mathworks.com/matlabcentral/fileexchange/23576-minmax-selection

"Matt J" wrote in message <jsnoav$cvb$1@newscl01ah.mathworks.com>...
>
> I haven't tried it, but this is probably even more efficient:
>
> http://www.mathworks.com/matlabcentral/fileexchange/23576-minmax-selection

As I understand, OP want the strict-next max value, this FEX won't do (sort() also don't do either, but unique() would do). Jan's suggestion is good.

Bruno

"Jan Simon" wrote in message <jsnmhb$755$1@newscl01ah.mathworks.com>...
> Dear Dhruv Chhabra,
>
> > 2nd maximum is the max of the group when you remove the max from group.
> > 2nd maximum = max(vec(vec<max(vec)));
>
> This is not efficient. Faster:
>
> [max1, index1] = max(vec);
> vec(index1) = -inf;

vec(index) = []; % is about 10% faster

> [max2, index2] = max(vec);
>
> Please note that the results differ, if the maximum value is not unique.
> For a [1e6x1] random vector, this requires the half time.

Hope this helps.

Greg

"Greg Heath" <heath@alumni.brown.edu> wrote in message <jspeha$bmv$1@newscl01ah.mathworks.com>...

> >
> > [max1, index1] = max(vec);
> > vec(index1) = -inf;
>
> vec(index) = []; % is about 10% faster

It depends on the MATLAB you run.

On the more recent MATLAB, the first version vec(index1) = -inf does the filling inplace, and avoid moving memory around.

In the second way (deleting) MATLAB must create a new array and move the memory which is much costly.

For example in 2012a:

vec = ceil(100*rand(1,1e6));
[max1, index] = max(vec);

tic
vec(index) = -inf;
toc % Elapsed time is 0.000017 seconds.

tic
vec(index) = []; % is about 1000 times slower
toc % Elapsed time is 0.019579 seconds.

% Bruno

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jsov2b$l0v$1@newscl01ah.mathworks.com>...
> "Matt J" wrote in message <jsnoav$cvb$1@newscl01ah.mathworks.com>...
> >
> > I haven't tried it, but this is probably even more efficient:
> >
> > http://www.mathworks.com/matlabcentral/fileexchange/23576-minmax-selection
>
> As I understand, OP want the strict-next max value, this FEX won't do (sort() also don't do either, but unique() would do). Jan's suggestion is good.
>

Yes, but Jan's suggestion has the same problem when non-unique maxs are present.

"Matt J" wrote in message <jspkpv$2gv$1@newscl01ah.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jsov2b$l0v$1@newscl01ah.mathworks.com>...
>
> Yes, but Jan's suggestion has the same problem when non-unique maxs are present.

Oh yeah, Jan's solution should be changed to

vec(vec==max1) = -inf;

as OP's request.

Bruno

"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <jspf7t$dpb$1@newscl01ah.mathworks.com>...
> "Greg Heath" <heath@alumni.brown.edu> wrote in message <jspeha$bmv$1@newscl01ah.mathworks.com>...
>
> > >
> > > [max1, index1] = max(vec);
> > > vec(index1) = -inf;
> >
> > vec(index) = []; % is about 10% faster
>
> It depends on the MATLAB you run.
>
> On the more recent MATLAB, the first version vec(index1) = -inf does the filling inplace, and avoid moving memory around.
>
> In the second way (deleting) MATLAB must create a new array and move the memory which is much costly.
>
> For example in 2012a:
>
> vec = ceil(100*rand(1,1e6));
> [max1, index] = max(vec);
>
> tic
> vec(index) = -inf;
> toc % Elapsed time is 0.000017 seconds.
>
> tic
> vec(index) = []; % is about 1000 times slower
> toc % Elapsed time is 0.019579 seconds.

It also depends on how you time the process. Below I get a consistent (5 runs each)
factor of two

> ver

MATLAB Version 7.13.0.564 (R2011b)
Operating System: Microsoft Windows 7 Version 6.1 (Build 7601: Service Pack 1)
Java VM Version: Java 1.6.0_17-b04 with Sun Microsystems Inc. Java HotSpot(TM)
Client VM mixed mode

> clear all, clc
vec0 = rand(1,1e3);
tic
   for k =1:1e3
                  vec = vec0;
       [max1, index1] = max(vec);
            %vec(index1) = - inf;
                vec(index1) = [];
      [max2, index2] = max(vec);
   end
toc % 0.033 sec for -inf vs 0.064 sec for []

Hope this helps.

Greg