Find maximum in an interval of a vector

问题:

I want to find the value and the position of the maximum in an interval 1 and the maximum in interval 2 in a vector (as depicted on the example figure). The borders of the interval 1 and 2 are given.

NEW VERSION - CODE MORE REUSEABLE

Uses only one interval as Dennis Jaheruddin suggested and is written as a function.

function test

%% Test data
x=0:0.1:10-0.1;
x_total=0:0.1:20-0.1;

y=-(x-5.8).^2+25;
y_total=[y,y+10];

figure(1);
plot(x_total,y_total); grid on;

interval=[12,18];

[maxValue,maxValuePositon] = findMaxInInterval(x_total,y_total,interval)
[maxValue,maxValuePositon] = findMaxInInterval2(x_total,y_total,interval)
end

%% Algorithm
function [maxValue,maxValuePositon] = findMaxInInterval(x,y,interval)
    index = x>=interval(1) & x <= interval(2); 
    offset = find(index == 1,1,'first') -1;
    [maxValue,indexMax] = max(y(index));
    maxValuePositon = x(indexMax+offset);
end

%% Algorithm - Alternative
function [maxValue,maxValuePositon] = findMaxInInterval2(x,y,interval)
    index = x>=interval(1) & x <= interval(2); 
    y_temp = y(index);
    x_temp = x(index);
    [maxValue,indexMax] = max(y_temp);
    maxValuePositon = x_temp(indexMax);
end

THIS IS THE OLD VERSION

I have a solution but my code seems pretty complicated to me. Has someone solution more straight forward (or simply the right MATLAB-function?). This is my solution so far:

%Generate test function
x=0:0.1:10-0.1;
x_total=0:0.1:20-0.1;

y=-(x-5).^2+25;
y_total=[y,y+10];

figure(1);
plot(x_total,y_total); grid on;

interval1=[2,8];
interval2=[12,18];

%Algorithm
index1 = x_total>=interval1(1) & x_total <= interval1(2); 
index2 = x_total>=interval2(1) & x_total <= interval2(2);

offset1 = find(index1 == 1,1,'first') -1;
offset2 = find(index2 == 1,1,'first') -1;

disp('Maximum 1 and 2:');
[max1,indexMax1] = max(y_total(index1))
[max2,indexMax2] = max(y_total(index2))

disp('Position of Maximum 1 and 2:');
x_total(indexMax1+offset1)
x_total(indexMax2+offset2)

回答1:

If you have the Signal Processing Toolbox you can use findpeaks, which offers you some convenient additional options also. (documentation)

x=0:0.1:10-0.1;
x_total=0:0.1:20-0.1;
y=-(x-5).^2+25;
y_total=[y,y+10];

[y_peaks,idx] = findpeaks(y_total);

x_peaks = x_total(idx);

returning:

x_peaks = 
         5.0000     15.0000

y_peaks = 
         25.0000     35.0000

which is the same result like after your algorithm. Of couse for the signal in your image it would find much more peaks, but you can just choose the ones you like afterwards.

% lower bound of your interval
int_lb = 10;
% upper bound of your interval
int_ub = 20;

% arguments and values of peaks in your specified interval
x_peaks_int = x_peaks( find(x_peaks > int_lb & x_peaks < int_ub) )
y_peaks_int = y_peaks( find(x_peaks > int_lb & x_peaks < int_ub) )

returning:

x_peaks_int = 
         15.0000
y_peaks_int = 
         35.0000

回答2:

As you say: simple use max function to the interval :)

% peak in the first interval
ids1 = find(x_total >= interval1(1), 1) : find(x_total >= interval1(2), 1);
[value1, index1] = max( y_total(ids1) );

% peak in the second interval
ids2 = find(x_total >= interval1(1), 1) : find(x_total >= interval1(2), 1);
[value2, index2] = max( y_total(ids2) );