Clear Filters
Clear Filters

How to find Area Under the Curve of a Smoothing Spline Curve Fitted Model from Discrete Data Points ?

9 views (last 30 days)
For example: I have 12 y values for different 12 x values and by using MATLAB inbuild app of Curve Fitting I got very good result. But now I want to read these coefficients in an equation (which I don't have) and want to know the area under the curve ?
M = [0.3 0.55 0.6 0.7 0.8 1.2 1.4 2.0 2.5 3.0 3.5 4.0];
Cd = [0.0010640542,0.0010009253,0.00097260155,0.0013098622,...
0.0019386101,0.027396185,0.033348465,0.041169242,0.040609591,...
0.040801537,0.041328469,0.042925609];
Got these as outputs after using the Curve Fitting App (Smoothing Spline):
Smoothing spline:
f(x) = piecewise polynomial computed from p
Smoothing parameter:
p = 0.99999298
Goodness of fit:
SSE: 6.345e-09
R-square: 1
Adjusted R-square: 1
RMSE: 0.0001337
Got the coefficients as:
fittedmodel1.p.coefs
ans =
-0.0017 0 -0.0002 0.0011
0.2595 -0.0013 -0.0005 0.0010
-0.2389 0.0376 0.0013 0.0010
0.9024 -0.0340 0.0017 0.0013
-0.3322 0.2367 0.0219 0.0020
0.2633 -0.1620 0.0518 0.0274
-0.0088 -0.0040 0.0186 0.0334
0.0184 -0.0199 0.0042 0.0412
-0.0063 0.0077 -0.0019 0.0406
0.0037 -0.0018 0.0011 0.0408
-0.0024 0.0037 0.0020 0.0413

Answers (1)

darova
darova on 5 Sep 2021
Use code instead of application
x = [0.3 0.55 0.6 0.7 0.8 1.2 1.4 2.0 2.5 3.0 3.5 4.0];
y = [0.0010640542,0.0010009253,0.00097260155,0.0013098622,...
0.0019386101,0.027396185,0.033348465,0.041169242,0.040609591,...
0.040801537,0.041328469,0.042925609];
x1 = linspace(x(1),x(end)); % new x mesh
y1 = spline(x,y,x1); % inrpolation with splin
plot(x,y,'.r')
line(x1,y1)
trapz(x1,y1) % trapezoid summation
ans = 0.1174

Categories

Find more on Interpolation in Help Center and File Exchange

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!