How can I set x-variable cutoffs using a script to include or exclude points

Hi there! I'm somewhat new to using MATLAB and wanted to know what commands would help me create a script like this:

I have a set of 5 data points that look like this:

x = [40 ; 43 ; 50; 52; 60]

y = [12 ; 15 ; 20; 21; 26]

I want to create a script that I can apply to any set of data such that if the difference between consecutive x-values is less than 3, only keep the data point that has a larger y-value. On the other hand, if the consecutive x-values are greater than or equal to 3, keep both points as part of the data set. I tried using a for loop and an if statement to create a script that looks like this but am unsure what should go after the difference function to keep both data points included. Likewise, how should I format the code after the else statement to account for the scenario in which the consecutive x-value difference is less than 3 and should only keep the data point with the higher y-value?

for ii = x

if diff(x)>=3

......

else

.......

end

Thanks

Answer 1

[Rub Ron]

x = [40 ; 42; 43 ; 50; 52; 60; 70; 71 ; 73; 80];
y = [12 ; 3; 5 ; 20; 21; 26; 3; 10; 1; 15];
xy = [x y];
v = [0; diff(x)<3]';

idSt=strfind([0,v==1],[0,1])-1;
idEn=strfind([v==1,0],[1,0]);

for k=1:numel(idSt)
    temp = xy(idSt(k):idEn(k),:);
    [~,idMax] = max(temp(:,2));
    xy(idSt(k):idEn(k),:)=repmat(temp(idMax,:),size(temp,1),1);
end

x = xy(:,1);
y = xy(:,2);

Input:

xy =

    40    12
    42     3
    43     5
    50    20
    52    21
    60    26
    70     3
    71    10
    73     1
    80    15

output;

xy =

    40    12
    40    12
    40    12
    52    21
    52    21
    60    26
    71    10
    71    10
    71    10
    80    15

[Isa Samad]

Thanks for the help! Is there any way to modify the code such that the output could look like this? It seems as though certain data points were repeated in the output you had listed above so would it be possible to not have those same data points repeated like this?

xy =
    40    12
    43    5
    52    21
    60    26
    71    10
    80    15

[Rub Ron]

I think you should specify what you want to do when there is 3 or more consecutives points with delta minor than 3.

For intance here:

    40    12
    42     3
    43     5
    

and here:

    70     3
    71    10
    73     1

[Isa Samad]

In those cases, where delta x is less than 3, the highest y-value should be kept. So in the two instances you mentioned, (42, 3) should be removed since it does not satisfy delta x>=3 with respect to (40,12). Since we exclude (42,3), (43, 5) should be kept given it satisifies delta x>=3 when compared to (40,12). For the bottom data set, only (71,10) should be kept since it has the higher y-value compared to (70,3). (73,1) should be excluded since it does not satisfy the requirement of delta x >=3 when compared to (71,10).

[Rub Ron]

then, the procedure is different. Thy this.

x = [40 ; 42; 43 ; 50; 52; 60; 70; 71 ; 73; 80];
y = [12 ; 3; 5 ; 20; 21; 26; 3; 10; 1; 15];
xy = [x y];

watchVar = 1;
while watchVar
    for k= 2:size(xy,1)
        if xy(k,1)-xy(k-1,1)<3
            [~,idMax] = max(xy(k-1:k,2));
            xy(k+1-idMax,:)=[];             
            break;            
        end
    end
    
    watchVar = ~(k==size(xy,1));
end

x = xy(:,1);
y = xy(:,2);

input:

xy =

    40    12
    42     3
    43     5
    50    20
    52    21
    60    26
    70     3
    71    10
    73     1
    80    15
    
   

output:

xy =

    40    12
    43     5
    52    21
    60    26
    71    10
    80    15