Suppose that K observations of an N-dimensional random vector fare given as fi.J
ID: 3604240 • Letter: S
Question
Suppose that K observations of an N-dimensional random vector fare given as fi.J.f Show that the largest (principal) eigenvector of the correlation matrix of fis equal to the solution of the following optimization problem Hint: Use Lagrange multipliers technique. You may choose to refer to any document available (on the web, etc.) for PCA derivation. But actually it's very straight forward: You apply the Lagrange multipliers technique with the constraint that v is unity, and show that it is equivalent to an eigenvalue problem.Explanation / Answer
V
clc; clear all;
pwf= [3865.6, 2991.1, 1770.8];
qo=[988.2, 2167.2, 3180.4];
syms p c n
n=linspace(0.5,1,10)
for (i=0.5:1)
eq1=qo==(c((p^2)-(pwf.^2)).^n(i));
[p,c]=vpasolve(eq1,[p,c],[0,inf]);
end