How to calculate Area under a curve (negatif side)

I have a dataset and I made it curve. I want to calculate the area (like result_2) of ​​the curve but I get a result like the picture on the result_1. Is there anyone who can help with this issue?

f = [-0.390930468901234	-0.346778353936444	-0.304499753808231	-0.264063453713497	-0.225438238849140	-0.188592894412060	-0.153496205599158	-0.120116957607333	-0.0884239356334846	-0.0583859248745134	-0.0299717105273190	-0.00315007778880116	0.0221101881441402	0.0458403020746052	0.0680714788056940	0.0888349331405067	0.108161879882144	0.126083533833705	0.142631109798290	0.157835822579000	0.171728886978934	0.184341517801193	0.195704929848877	0.205850337925086	0.214808956832921	0.222612001375480	0.229290686355865	0.234876226577176	0.239399836842512	0.242892731954974	0.245386126717662	0.246911235933676	0.247499274406116	0.247181456938083	0.245988998332677	0.243953113392996	0.241105016922143	0.237475923723217	0.233097048599318	0.227999606353545	0.222214811789001	0.215773879708783	0.208708024915994	0.201048462213732	0.192826406405098	0.184073072293192	0.174819674681114	0.165097428371965	0.154937548168844	0.144371248874851	0.133429745293087	0.122144252226652	0.110545984478646	0.0986661568521688	0.0865359841503211	0.0741866811762028	0.0616494627329141	0.0489555436235550	0.0361361386512258	0.0232224626190266	0.0102457303300567	-0.00276284341258221	-0.0157720438057912	-0.0287506560464691	-0.0416674653315173	-0.0544912568578337	-0.0671908158223202	-0.0797349274218757	-0.0920923768533994	-0.104231949313792	-0.116122429999953	-0.127732604108783	-0.139031256837181	-0.149987173382047	-0.160569138940281	-0.170745938708783	-0.180486357884452	-0.189759181664190	-0.198533195244895	-0.206777183823467	-0.214459932596806	-0.221550226761814	-0.228016851515387	-0.233828592054427	-0.238954233575834	-0.243362561276507	-0.247022360353347	-0.249902416003253	-0.251971513423126	-0.253198437809864	-0.253551974360368	-0.253000908271538	-0.251514024740273	-0.249060108963473	-0.245607946138040	-0.241126321460871	-0.235584020128867	-0.228949827338928	-0.221192528287954	-0.212280908172844]
t = linspace(0,100,100);

sinus_f = sin(f)
plot(t,sinus_f)

min_f = find(islocalmin(sinus_f));
max_f = find(islocalmax(sinus_f));
axis tight
P1_1 = gca; % gca creates a cartesian axes object
P1_1.XAxisLocation = 'origin'
hold on
basevalue_A1 = 1;
xline(t(min_f),'--b')
yline(sinus_f(min_f),'--r')
xline(t(max_f),'--b')
yline(sinus_f(max_f),'--r')
area_A1 = area(t(max_f:min_f),sinus_f(max_f:min_f),'FaceColor','g') % the area by points

Answer 1

[Star Strider]

I went with the patch function because I’m more familiar with it.

Try ths —

f = [-0.390930468901234	-0.346778353936444	-0.304499753808231	-0.264063453713497	-0.225438238849140	-0.188592894412060	-0.153496205599158	-0.120116957607333	-0.0884239356334846	-0.0583859248745134	-0.0299717105273190	-0.00315007778880116	0.0221101881441402	0.0458403020746052	0.0680714788056940	0.0888349331405067	0.108161879882144	0.126083533833705	0.142631109798290	0.157835822579000	0.171728886978934	0.184341517801193	0.195704929848877	0.205850337925086	0.214808956832921	0.222612001375480	0.229290686355865	0.234876226577176	0.239399836842512	0.242892731954974	0.245386126717662	0.246911235933676	0.247499274406116	0.247181456938083	0.245988998332677	0.243953113392996	0.241105016922143	0.237475923723217	0.233097048599318	0.227999606353545	0.222214811789001	0.215773879708783	0.208708024915994	0.201048462213732	0.192826406405098	0.184073072293192	0.174819674681114	0.165097428371965	0.154937548168844	0.144371248874851	0.133429745293087	0.122144252226652	0.110545984478646	0.0986661568521688	0.0865359841503211	0.0741866811762028	0.0616494627329141	0.0489555436235550	0.0361361386512258	0.0232224626190266	0.0102457303300567	-0.00276284341258221	-0.0157720438057912	-0.0287506560464691	-0.0416674653315173	-0.0544912568578337	-0.0671908158223202	-0.0797349274218757	-0.0920923768533994	-0.104231949313792	-0.116122429999953	-0.127732604108783	-0.139031256837181	-0.149987173382047	-0.160569138940281	-0.170745938708783	-0.180486357884452	-0.189759181664190	-0.198533195244895	-0.206777183823467	-0.214459932596806	-0.221550226761814	-0.228016851515387	-0.233828592054427	-0.238954233575834	-0.243362561276507	-0.247022360353347	-0.249902416003253	-0.251971513423126	-0.253198437809864	-0.253551974360368	-0.253000908271538	-0.251514024740273	-0.249060108963473	-0.245607946138040	-0.241126321460871	-0.235584020128867	-0.228949827338928	-0.221192528287954	-0.212280908172844]

f = 1×100

-0.3909 -0.3468 -0.3045 -0.2641 -0.2254 -0.1886 -0.1535 -0.1201 -0.0884 -0.0584 -0.0300 -0.0032 0.0221 0.0458 0.0681 0.0888 0.1082 0.1261 0.1426 0.1578 0.1717 0.1843 0.1957 0.2059 0.2148 0.2226 0.2293 0.2349 0.2394 0.2429

t = linspace(0,100,100);

sinus_f = sin(f)

sinus_f = 1×100

-0.3810 -0.3399 -0.2998 -0.2610 -0.2235 -0.1875 -0.1529 -0.1198 -0.0883 -0.0584 -0.0300 -0.0032 0.0221 0.0458 0.0680 0.0887 0.1080 0.1257 0.1421 0.1572 0.1709 0.1833 0.1945 0.2044 0.2132 0.2208 0.2273 0.2327 0.2371 0.2405

plot(t,sinus_f)

min_f = find(islocalmin(sinus_f));
max_f = find(islocalmax(sinus_f));
axis tight
P1_1 = gca; % gca creates a cartesian axes object
P1_1.XAxisLocation = 'origin'

P1_1 = 
  Axes with properties:

             XLim: [0 100]
             YLim: [-0.3810 0.2450]
           XScale: 'linear'
           YScale: 'linear'
    GridLineStyle: '-'
         Position: [0.1300 0.1100 0.7750 0.8150]
            Units: 'normalized'

  Show all properties

hold on
basevalue_A1 = 1;
xline(t(min_f),'--b')
yline(sinus_f(min_f),'--r')
xline(t(max_f),'--b')
yline(sinus_f(max_f),'--r')
Lv = t<=t(min_f) & t>=t(max_f);
AUC = trapz(t(Lv), sinus_f(Lv));
text(40, -0.1, sprintf('AUC = %.6f', AUC))
area_A1 = patch([t(Lv) flip(t(Lv))], [ones(size(t(Lv)))*sinus_f(min_f) flip(sinus_f(Lv))], 'g', 'FaceAlpha',0.25);

% area_A1 = area(t(max_f:min_f),sinus_f(max_f:min_f),'FaceColor','g') % the area by points

EDIT — (24 Jan 2022 at 18:18)

Added ‘AUC’ calculation and text display.

.

[Ceren Memis]

Hello, thank you so much with your help. I think your solution is correct, but I want to ask a question, shouldn't the AUC value be positive to be sure? Because I think we should use absolute in the area calculation. So I made an edit like this;

AUC = trapz(t(Lv), abs(sinus_f(Lv)));

[Star Strider]

As always, my pleasure!

The trapz function calculates with respect to the x-axis, so everything above is positive and everything below is negative.

To get the complete area as positive requires a bit of deception with respect to trapz —

f = [-0.390930468901234	-0.346778353936444	-0.304499753808231	-0.264063453713497	-0.225438238849140	-0.188592894412060	-0.153496205599158	-0.120116957607333	-0.0884239356334846	-0.0583859248745134	-0.0299717105273190	-0.00315007778880116	0.0221101881441402	0.0458403020746052	0.0680714788056940	0.0888349331405067	0.108161879882144	0.126083533833705	0.142631109798290	0.157835822579000	0.171728886978934	0.184341517801193	0.195704929848877	0.205850337925086	0.214808956832921	0.222612001375480	0.229290686355865	0.234876226577176	0.239399836842512	0.242892731954974	0.245386126717662	0.246911235933676	0.247499274406116	0.247181456938083	0.245988998332677	0.243953113392996	0.241105016922143	0.237475923723217	0.233097048599318	0.227999606353545	0.222214811789001	0.215773879708783	0.208708024915994	0.201048462213732	0.192826406405098	0.184073072293192	0.174819674681114	0.165097428371965	0.154937548168844	0.144371248874851	0.133429745293087	0.122144252226652	0.110545984478646	0.0986661568521688	0.0865359841503211	0.0741866811762028	0.0616494627329141	0.0489555436235550	0.0361361386512258	0.0232224626190266	0.0102457303300567	-0.00276284341258221	-0.0157720438057912	-0.0287506560464691	-0.0416674653315173	-0.0544912568578337	-0.0671908158223202	-0.0797349274218757	-0.0920923768533994	-0.104231949313792	-0.116122429999953	-0.127732604108783	-0.139031256837181	-0.149987173382047	-0.160569138940281	-0.170745938708783	-0.180486357884452	-0.189759181664190	-0.198533195244895	-0.206777183823467	-0.214459932596806	-0.221550226761814	-0.228016851515387	-0.233828592054427	-0.238954233575834	-0.243362561276507	-0.247022360353347	-0.249902416003253	-0.251971513423126	-0.253198437809864	-0.253551974360368	-0.253000908271538	-0.251514024740273	-0.249060108963473	-0.245607946138040	-0.241126321460871	-0.235584020128867	-0.228949827338928	-0.221192528287954	-0.212280908172844]

f = 1×100

-0.3909 -0.3468 -0.3045 -0.2641 -0.2254 -0.1886 -0.1535 -0.1201 -0.0884 -0.0584 -0.0300 -0.0032 0.0221 0.0458 0.0681 0.0888 0.1082 0.1261 0.1426 0.1578 0.1717 0.1843 0.1957 0.2059 0.2148 0.2226 0.2293 0.2349 0.2394 0.2429

t = linspace(0,100,100);

sinus_f = sin(f)

sinus_f = 1×100

-0.3810 -0.3399 -0.2998 -0.2610 -0.2235 -0.1875 -0.1529 -0.1198 -0.0883 -0.0584 -0.0300 -0.0032 0.0221 0.0458 0.0680 0.0887 0.1080 0.1257 0.1421 0.1572 0.1709 0.1833 0.1945 0.2044 0.2132 0.2208 0.2273 0.2327 0.2371 0.2405

plot(t,sinus_f)

min_f = find(islocalmin(sinus_f));
max_f = find(islocalmax(sinus_f));
axis tight
P1_1 = gca; % gca creates a cartesian axes object
P1_1.XAxisLocation = 'origin'

P1_1 = 
  Axes with properties:

             XLim: [0 100]
             YLim: [-0.3810 0.2450]
           XScale: 'linear'
           YScale: 'linear'
    GridLineStyle: '-'
         Position: [0.1300 0.1100 0.7750 0.8150]
            Units: 'normalized'

  Show all properties

hold on
basevalue_A1 = 1;
xline(t(min_f),'--b')
yline(sinus_f(min_f),'--r')
xline(t(max_f),'--b')
yline(sinus_f(max_f),'--r')
Lv = t<=t(min_f) & t>=t(max_f);
Lv2 = Lv & sinus_f>0;
Lv3 = Lv & sinus_f<=0;
AUC = trapz(t(Lv2), sinus_f(Lv2)) - trapz(t(Lv3), sinus_f(Lv3));
Details = [trapz(t(Lv2), sinus_f(Lv2)), trapz(t(Lv3), sinus_f(Lv3))]        % Information Only, Not Used In Calculations

Details = 1×2

4.4799 -4.6480

text(40, -0.1, sprintf('AUC = %.6f', AUC))
area_A1 = patch([t(Lv) flip(t(Lv))], [ones(size(t(Lv)))*sinus_f(min_f) flip(sinus_f(Lv))], 'g', 'FaceAlpha',0.25);

% area_A1 = area(t(max_f:min_f),sinus_f(max_f:min_f),'FaceColor','g') % the area by points

The original ‘AUC’ calculation was mathematically correct, however not the desired result. Now, it is as desired!

.

[Ceren Memis]

Now I got exactly the result I wanted. Thank you so much.

[Star Strider]

As always, my pleasure!