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NL_libs.m
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NL_libs.m
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clear all; close all; clc;
load A1.mat
A1=abs(A1.');
% waterfall(abs(A1(300:600,100:161)'))
% break
%
st=100;
fin=161;
X=A1(:,st:end);
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=1.45; %mu
nu=0;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
nl_Psi=[u(:,1)];
figure(11)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 10])
title('svals nl beta1')
figure(12)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 10])
title('cumsum svals beta1')
clear NL X u s v
%%
load A2.mat
A2=abs(A2.');
st=100;
fin=161;
X=A2(:,st:end);
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=1.4; %mu
nu=0;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
nl_Psi=[nl_Psi u(:,1)];
figure(21)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 10])
title('svals nl beta2 ')
figure(22)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 10])
title('cumsum svals beta2')
clear NL X u s v
%%
load A3.mat
A3=abs(A3.');
st=100;
fin=161;
X=A3(:,st:end);
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=0.66; %mu
nu=-0.1;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
nl_Psi=[nl_Psi u(:,1:6)];
figure(31)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 10])
title('svals nl beta3 ')
figure(32)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 10])
title('cumsum svals beta3')
% break
clear NL X u s v
%%
load A4.mat
A4=abs(A4.');
st=100;
fin=161;
X=A4(:,st:end);
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=1; %mu
nu=-0.6;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
%%%%%% 11 modes are neough though
nl_Psi=[nl_Psi u(:,1:14)];
figure(41)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 20])
title('svals nl beta4 ')
figure(42)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 20])
ylim([0.98 1])
title('cumsum svals beta4')
clear NL X u s v
%%
load A5.mat
A5=abs(A5.');
st=100;
fin=161;
X=A5(:,st:end);
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=0.6; %mu
nu=-0.1;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
nl_Psi=[nl_Psi u(:,1)];
figure(51)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 10])
title('svals nl beta5 ')
figure(52)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 10])
title('cumsum svals beta5')
clear NL X u s v
%%
load A6.mat
A6=abs(A6.');
st=100;
fin=161;
X=A6(:,st:end);
% [VX,SX,WX]=svd(X,0);
% figure(61)
% plot(diag(SX)/sum(diag(SX)), 'ko')
% figure(62)
% plot(cumsum(diag(SX)/sum(diag(SX))), 'ko')
%compute the nonlinear part
n=1024;
NL=zeros(n,fin-st+1);
beta=0.5; %mu
nu=-0.1;
sigma=-0.1; %eps
for j=1:fin-st+1
NL(:,j)=(i+beta)*(abs(X(:,j))).^2.*X(:,j)+...
(i*nu+sigma)*(abs(X(:,j))).^4.*X(:,j);
end
[u,s,v]=svd(abs(NL),0);
nl_Psi=[nl_Psi u(:,1)];
figure(61)
plot(diag(s)/sum(diag(s)), 'ko')
xlim([0 10])
title('svals nl beta6 ')
figure(62)
plot(cumsum(diag(s)/sum(diag(s))), 'ko')
xlim([0 10])
title('cumsum svals beta6')
clear NL X u s v
save NL nl_Psi