repDupValWithMean

repDupValWithMean replaces values of y which have non unique elements in vector x with local means

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Syntax

  • ysmo=repDupValWithMean(x,y)example
  • ysmo=repDupValWithMean(x,y,Name,Value)example

Description

example

ysmo =repDupValWithMean(x, y) Case 1: x is already ordered.

example

ysmo =repDupValWithMean(x, y, Name, Value) Case 2: x is non ordered.

Examples

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  • Case 1: x is already ordered.

    • Note that in this case x is ordered therefore the average between consecutive values which are equal or the average of equal values is the same. 

    x=[ones(5,1); 6; 7; 8.2; 8.2; 10];
% y is a vector containing any real number.
y=(1:10)';
ysmo=repDupValWithMean(x,y);
disp(['      x   '   '      y   ' '      ysmo  '])
disp([x y ysmo])
% The first 5 elements of ysmo are equal to mean(y(1:5)) because the
% corresponding elements of x share the same value.
% The elements in position 8 and 9 of ysmo are equal to mean(y([8:9]))
% because the corresponding elements of x share the same value.
% All the other elements of vector ysmo are equal to y.
          x         y         ysmo  
    1.0000    1.0000    3.0000
    1.0000    2.0000    3.0000
    1.0000    3.0000    3.0000
    1.0000    4.0000    3.0000
    1.0000    5.0000    3.0000
    6.0000    6.0000    6.0000
    7.0000    7.0000    7.0000
    8.2000    8.0000    8.5000
    8.2000    9.0000    8.5000
   10.0000   10.0000   10.0000

  • Case 2: x is non ordered.

    • Note that in this case x is not ordered therefore if the function is called with just two arguments it takes the average of the elements of y which correspond to elements of x which are equal 

    x=[8.2; 1.0; 1.0; 6.0; 7.0; 10.0; 1.0; 8.2; 1.0; 1.0];
% y is a vector containing any real number.
y=(11:20)';
ysmo=repDupValWithMean(x,y);
disp(['      x   '   '      y   ' '      ysmo  '])
disp([x y ysmo])
% Elements 1 and 8  share the same value of x therefore
% ysmo(1)=smo(8) = mean(y([1 8])).
% Elements 2, 3, 7, 9 and 10 share the same value of x therefore
% ysmo(2)=ysmo(3)=ysmo(7)=ysmo(9)=ysmo(10)= mean(y([2 3 7 9 10])).
% All the other elements of vector ysmo are equal to y.
          x         y         ysmo  
    8.2000   11.0000   14.5000
    1.0000   12.0000   16.2000
    1.0000   13.0000   16.2000
    6.0000   14.0000   14.0000
    7.0000   15.0000   15.0000
   10.0000   16.0000   16.0000
    1.0000   17.0000   16.2000
    8.2000   18.0000   14.5000
    1.0000   19.0000   16.2000
    1.0000   20.0000   16.2000

    Related Examples

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  • Case 3: x is non ordered and optional argument consec is true.

    • Note that in this case x is not ordered therefore if the function is called with the third argument consec equal to true, this function computes the average of the elements of y which correspond to elements of x which are equal and consecutive. 

    x=[8.2; 1.0; 1.0; 6.0; 7.0; 10.0; 1.0; 1.0; 1.0; 8.2];
% y is a vector containing any real number.
y=(11:20)';
ysmo=repDupValWithMean(x,y,'consec',true);
disp(['      x   '   '      y   ' '      ysmo  '])
disp([x y ysmo])
% Elements 2 and 3 of x are equal and consecutive therefore
% ysmo(2)=ysmo(3) = mean(y([2 3])).
% Elements 7, 8 and 9 of x are equal and consecutive therefore
% ysmo(7)=ysmo(8)=ysmo(9) = mean(y([7 8 9])).
% All the other elements of vector ysmo are equal to y.
          x         y         ysmo  
    8.2000   11.0000   11.0000
    1.0000   12.0000   12.5000
    1.0000   13.0000   12.5000
    6.0000   14.0000   14.0000
    7.0000   15.0000   15.0000
   10.0000   16.0000   16.0000
    1.0000   17.0000   18.0000
    1.0000   18.0000   18.0000
    1.0000   19.0000   18.0000
    8.2000   20.0000   20.0000

  • Simulation study to compare repDupValWithMean with and without loops.

    • Create function 'repDupValWithMeanLoop.m' and write it into a file. 

    % At the end this file will be deleted.
name='repDupValWithMeanLoop.m';
filetmpID=fopen([pwd filesep name],'w');
% % The implementation of this function using loops is given below.
%     function  ysmoC=repDupValWithMeanLoop(x,y)
%     n=length(x);
%     ysmoC=y;
%     j0=1;
%     salta=0;
%     for j=1:n-1
%         if salta==0
%             sm=ysmoC(j);
%         end
%         if x(j+1) <=x(j)
%             sm=sm+ysmoC(j+1);
%             salta=1;
%             if j==n-1
%                 sm=sm/(j-j0+2);
%                 ysmoC(j0:j+1)=sm;
%             end
%         else
%             salta=0;
%             sm=sm/(j-j0+1);
%             ysmoC(j0:j)=sm;
%             j0=j+1;
%         end
%     end
%     end
%
% In principle one should take the above function and save it in a file
% In order to speed up thing we put it inside variable outstring and write
% the content of outstring into a file.
outstring=sprintf(['function  ysmoC=repDupValWithMeanLoop(x,y) \r' ...
'n=length(x); \r' ...
' ysmoC=y; \r' ...
'j0=1;     \r' ...
'salta=0;      \r' ...
'for j=1:n-1     \r' ...
'    if salta==0  \r' ...
'        sm=ysmoC(j); \r' ...
'    end               \r ' ...
'    if x(j+1) <=x(j)   \r' ...
'       sm=sm+ysmoC(j+1);   \r' ...
'        salta=1;          \r ' ...
'        if j==n-1          \r' ...
'            sm=sm/(j-j0+2); \r' ...
'            ysmoC(j0:j+1)=sm; \r' ...
'        end                    \r' ...
'    else                       \r' ...
'        salta=0;               \r' ...
'        sm=sm/(j-j0+1);       \r ' ...
'        ysmoC(j0:j)=sm;       \r ' ...
'        j0=j+1;               \r ' ...
'    end                        \r' ...
'end                            \r' ...
'end']);
fprintf(filetmpID,'%s',outstring);
fclose(filetmpID);
% Simulation study to compare the two implementations.
nsimul=10000;
n=10000;
imax=20;
totimeOpt2=0;
totimeOpt3=0;
for j=1:nsimul
x=randi(imax,n,1);
y=randn(n,1);
x=sort(x);
tic
ysmo2=repDupValWithMean(x,y);
totimeOpt2=toc+totimeOpt2;
tic
ysmo3=repDupValWithMeanLoop(x,y);
totimeOpt3=toc+totimeOpt3;
% Check that the two implementations produce the same results.
if max(abs(ysmo2-ysmo3))>1e-9
error('The two implementations do not produCe equal results')
end
end
disp('Comparison of times based on 10000 replicates')
disp('Implementation without loops')
disp(totimeOpt2)
disp('Implementation using loops')
disp(totimeOpt3)
% Remove temporary file repDupValWithMeanLoop.m
delete repDupValWithMeanLoop.m
    Comparison of times based on 10000 replicates
Implementation without loops
    3.2437

Implementation using loops
    0.4803

  • Case 4: x is already ordered and weights are supplied.

    • Note that in this case x is ordered therefore the average between consecutive values which are equal or the average of equal values is the same. 

    x=[ones(5,1); 6; 7; 8.2; 8.2; 10];
% y is a vector containing any real number.
y=(1:10)';
w=(21:30)';
ysmo=repDupValWithMean(x,y,'w',w);
disp(['      x   '   '      y   ' '     w' '      ysmo  '])
disp([x y w ysmo])
% The first 5 elements of ysmo are equal to sum(y(1:5).*w(1:5))/sum(w(1:5))
% because the corresponding elements of x share the same value.
% The elements in position 8 and 9 of ysmo are equal to
% sum(y(8:9).*w(8:9))/sum(w(8:9)) because the corresponding elements of x
% share the same value.
% All the other elements of vector ysmo are equal to y.

    Input Arguments

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    x — vector with values to analyze. Vector.

    A vector with n elements that may contain duplicated values.

    It can be either a row or a column vector.

    Data Types: single| double

    y — Vector on which the computations have to be made. Vector.

    It can be either a row or a column vector.

    Data Types: single| double

    Name-Value Pair Arguments

    Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

    Example: false , 'w',1:n

    consec —how to compute the local means.boolean.

    If consec is true the unique entries in vector x are defined as those values which are equal and consecutive.

    The default value of consec is false, therefore the unique entries in vector x are defined as those values which are equal and consecutive. When x is already sorted in order to speed up calculations it is efficient to call the procedure with the third argument consec set to true, because in this case it avoids calling the MATLAB routine issorted to check whether input vector x is sorted.

    Example: false

    Data Types: Boolean

    w —weights for the observations.vector.

    Row or column vector of length n containing the weights associated to each observations. If w is not specified we assum $w=1$ for $i=1, 2, \ldots, n$.

    Example: 'w',1:n

    Data Types: double

    Output Arguments

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    ysmo —Smoothed vector y with local means for non unique x values. Vector

    ysmo is a vector with the same dimension of y containing in correspondence of the values of y which have non unique entries in vector x, the arithmetic means of y for the corresponding elements. The unique entries in vector x can be defined as the values which are equal and consecutive or simply equal but non necessarily consecutive (depending on optional input argument consec).

    More About

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    Additional Details

    This function does not use loops and is based just on built in MATLAB functions: diff, cumsum and accumarray. See also function accumulator from John D'Errico in the file exchange.

    References

    See Also

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