Area under the curve with conditions?

I want to do following tasks,

First generate a time series load data between 550-1000 for one day 30 min interval, so is load(48*1) dataset

then set level_1 = 750 and draw a line on the graph,

then find out the area above this level_1 line and area under seprate level (lets say level_2 = 600) line seprately

Answer 1

[Star Strider]

Try this:

t = 1:48;                                                   % Time Vector
load = randi(1000, 1, 48);                                  % Create Data
level_1 = 750;
level_2 = 600;

above_level_1 = load >= level_1;                            % Logical Index Vector
area_1 = trapz(t(above_level_1), load(above_level_1));      % Area Under ‘Level_1’
below_level_2 = load <= level_2;                            % Logical Index Vector
area_2 = trapz(t(below_level_2), load(below_level_2));      % Area Under ‘Level_2’

figure
plot(t, load)
hold on
plot(xlim, [1 1]*level_1)
plot(xlim, [1 1]*level_2)
hold off
grid

[MUKESH KUMAR]

Can we find the min or max area if the Level_2 vary between the range of [600 800], find at which point the area(below the Level_2) is min or max?

with another constraint is that

area_1 - area_2 + K >= 0; % K is constant and lets say K= 800 ( 80% of max load)

[Star Strider]

I do not understand what you are asking.

You can easily calculate the area under ‘Level_2’ simply by re-defining it to be a different value. What do you intend by ‘min or max’?

With respect to:

area_1 - area_2 + K >= 0;

Do you want to calculate ‘K’, or given a specific value for ‘K’, determine if that statement is true?

[MUKESH KUMAR]

I just want to calculate min area (task 2: max area ) if the Level_2 in the range of [600 800] and at which value of Level_2 , area is min and also when area is min, there must be

area_1 - area_2 + 800 >=0 satisfy.

[Star Strider]

I also read your other post: Find area under and above the curve with horizontal line and its min/max values in a given range of line ?

You can probably use fmincon, however I cannot figure out how to set those constraints.

[MUKESH KUMAR]

Yes it it further task of my prev que. but dont know how to set constaints and min area ?

[Star Strider]

It is not obvious to me, either. Since your other Question got several views although no replies, it appears that others also could not solve it.

[MUKESH KUMAR]

How can I find the area above for level_1 for each two continuous time stamp like for example in figure(L1 is line of Level_1), find area seprate for each color code simillary for area below level_2. and after that how to find the sum of area for 1,(1+2), (1+2+3),(1+2+3+4),.....and so on strips.......

[Star Strider]

Try this:

t = linspace(0, 24, 48);                                    % Time Vector
load = 450*sin(2*pi*t/20)+550;                              % Create Data
level_1 = 750;
above_level_1 = load >= level_1;                            % Logical Index Vector

cload = cumtrapz(load(above_level_1));                      % Cumulative Integral Of ‘load’
sload = [0 diff(cload)];                                    % Segmental (30 Min) Integral Of ‘load’

figure
plot(t, load)
hold on
bar(t(above_level_1), sload)
hold off
grid
legend('Load','30-Minute Integral', 'Location','S')

Experiment to get the result you want.

[MUKESH KUMAR]

Can i get the area with these conditons at each continous interval.

The problem is that when above_level_1 having only one continuous data(1) then it can not calculate area but it should calculate for that interval at that point.??

[Star Strider]

I do not understand what you are asking.