very similar dataset and yet 'TRAPZ' function gives very different answers

Dear All,

I am kind of struggling to figure out why two sets of data - quantitatively very similar - gives very different answers when numerically integrated uisng 'TRAPZ' funciton; data is attached in the .xls document.

Any insights in this regard are highly appreciated!

Thanks in advance!

Regards,

KD

Answer 1

[John D'Errico]

"Very" different? "VERY"? Lets be serious.

xy1 = [1.43155281315397	0.00255865851191916
1.35675838019809	0.0145131910703132
1.27925136527898	0.063166446949049
1.19895069245412	0.210990679450789
1.1157710244529	0.540955972655767
1.02962188546981	1.06472307447546
0.940406331363923	1.60888586350091
0.848018802346465	1.86658100394464
0.752341384965735	1.66264882670706
0.653236684654374	1.13700864870653
0.550532598338051	0.596885427112396
0.443984551996628	0.240497869152622
0.333159864072945	0.0743572051584443
0.216939570864193	0.0176351499842711
0.0888515203255917	0.00320643723615615];
a1 = trapz(flip(xy1(:,1)),flip(xy1(:,2)))

a1 = 0.8602

xy2 = [1.3574514696438	0.00230062694421278
1.29605548980418	0.0132435702443471
1.23099970732201	0.0584912051989921
1.16214843460327	0.198236594379449
1.08935954807805	0.51564908418259
1.01248347607602	1.02957271312853
0.931361701492302	1.57808683823824
0.84582439298594	1.85693323865362
0.75568634779567	1.67746620095548
0.660739348290927	1.16327656092461
0.560735966899023	0.619215364238612
0.455349613170889	0.252967924578314
0.344052551344047	0.0792989196684651
0.22559115331588	0.0190697822153908
0.0930728988402219	0.00351835370743469];
a2 = trapz(flip(xy2(:,1)),flip(xy2(:,2)))

a2 = 0.8048

The difference is roughly 6.5%

100*(a1 - a2)/a1

ans = 6.4501

plot(xy1(:,1),xy1(:,2),'r-',xy2(:,1),xy2(:,2),'b-')

So around 6.5% difference in area. Why should that surprise you? This has nothing to do with the use of trapz. The two have a different area, and trapz tells you that.