I have to find absolute values of each element of ksaix1, ksaix2, ksaiy1 and ksaiy2 e.g. abs (ksaix1(1)) etc. I know how to find the absolute but can anyone help me to write a concise code to find the absolute values because each ksai has 31 elements and if I find absolute one by one then then I have to use absolute command 124 times. Kindly help.
clear all; close all; clc;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Simulation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%value of constants
a1=0.1;a2=0.2;omega1=5;omega2=4;G=1;C12=0.01;C21=0.02;dt=0.01; %step size
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
x1(1)=0.5;y1(1)=0.5;x2(1)=1;y2(1)=1;for i=2:1000 x1(i)=x1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*x1(i-1)-omega1*y1(i-1)+G*C12*(x2(i-1)-x1(i-1)))*dt; y1(i)=y1(i-1)+((a1-x1(i-1)^2-y1(i-1)^2)*y1(i-1)+omega1*x1(i-1)+G*C12*(y2(i-1)-y1(i-1)))*dt; x2(i)=x2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*x2(i-1)-omega2*y2(i-1)+G*C21*(x1(i-1)-x2(i-1)))*dt; y2(i)=y2(i-1)+((a2-x2(i-1)^2-y2(i-1)^2)*y2(i-1)+omega2*x2(i-1)+G*C21*(y1(i-1)-y2(i-1)))*dt;end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Observation %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% N_measurements=31; N_basis=31; index=randi([100,999],1,N_measurements); Xdot1=zeros([1,N_measurements]); Ydot1=zeros([1,N_measurements]); Xdot2=zeros([1,N_measurements]); Ydot2=zeros([1,N_measurements]); for ni=1:N_measurements Xdot1(ni)=(x1(index(ni)+1)-x1(index(ni)))/dt; Ydot1(ni)=(y1(index(ni)+1)-y1(index(ni)))/dt; Xdot2(ni)=(x2(index(ni)+1)-x2(index(ni)))/dt; Ydot2(ni)=(y2(index(ni)+1)-y2(index(ni)))/dt; end M=zeros([N_measurements,N_basis]); for i=1:N_measurements for j=1:N_basis if j==1 M(i,j)=1; elseif j==2 M(i,j)=x1(index(i)); elseif j==3 M(i,j)=y1(index(i)); elseif j==4 M(i,j)=x2(index(i)); elseif j==5 M(i,j)=y2(index(i)); elseif j==6 M(i,j)=x1(index(i))^2; elseif j==7 M(i,j)=x2(index(i))^2; elseif j==8 M(i,j)=y1(index(i))^2; elseif j==9 M(i,j)=y2(index(i))^2; elseif j==10 M(i,j)=x1(index(i))*x2(index(i)); elseif j==11 M(i,j)=x1(index(i))*y1(index(i)); elseif j==12 M(i,j)=x1(index(i))*y2(index(i)); elseif j==13 M(i,j)=x2(index(i))*y1(index(i)); elseif j==14 M(i,j)=x2(index(i))*y2(index(i)); elseif j==15 M(i,j)=y1(index(i))*y2(index(i)); elseif j==16 M(i,j)=x1(index(i))^3; elseif j==17 M(i,j)=y1(index(i))^3; elseif j==18 M(i,j)=x2(index(i))^3; elseif j==19 M(i,j)=y2(index(i))^3; elseif j==20 M(i,j)=x1(index(i))^2*x2(index(i)); elseif j==21 M(i,j)=x1(index(i))^2*y1(index(i)); elseif j==22 M(i,j)=x1(index(i))^2*y2(index(i)); elseif j==23 M(i,j)=x2(index(i))^2*x1(index(i)); elseif j==24 M(i,j)=x2(index(i))^2*y1(index(i)); elseif j==25 M(i,j)=x2(index(i))^2*y2(index(i)); elseif j==26 M(i,j)=y1(index(i))^2*x1(index(i)); elseif j==27 M(i,j)=y1(index(i))^2*x2(index(i)); elseif j==28 M(i,j)=y1(index(i))^2*y2(index(i)); elseif j==29 M(i,j)=y2(index(i))^2*x1(index(i)); elseif j==30 M(i,j)=y2(index(i))^2*x2(index(i)); else j==31 M(i,j)=y2(index(i))^2*y1(index(i)); end end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RIP %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Norms=zeros([1,N_basis]); for j=1:N_basis Norms(j)=norm(M(:,j)); end for i=1:N_measurements for j=1:N_basis M(i,j)=M(i,j)/Norms(j); end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
lambda=0.001; Xdot1=Xdot1'; cd 'E:\MATLAB\bin\cvx\cvx' cvx_setup cvx_begin variable ksaix1(31); minimize(norm(M*ksaix1-Xdot1)+ lambda*norm(ksaix1,1)); cvx_end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Ydot1=Ydot1'; cvx_setup cvx_begin variable ksaiy1(31); minimize(norm(M*ksaiy1-Ydot1)+ lambda*norm(ksaiy1,1)); cvx_end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Xdot2=Xdot2'; cvx_setup cvx_begin variable ksaix2(31); minimize(norm(M*ksaix2-Xdot2)+ lambda*norm(ksaix2,1)); cvx_end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Ydot2=Ydot2'; cvx_setup cvx_begin variable ksaiy2(31); minimize(norm(M*ksaiy2-Ydot2)+ lambda*norm(ksaiy2,1)); cvx_end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % RIP % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% for j=1:N_basis ksaix1(j)=ksaix1(j)/Norms(j); ksaiy1(j)=ksaiy1(j)/Norms(j); ksaix2(j)=ksaix2(j)/Norms(j); ksaiy2(j)=ksaiy2(j)/Norms(j); end ksaix1 ksaiy1 ksaix2 ksaiy2 figure hold on plot(x1,'r') plot(x2,'g')%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Reconstructed Signal %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%x1_rec(1)= x1(1);x2_rec(1)= x2(1);y1_rec(2)= y1(1);y2_rec(2)= y2(1);a1=ksaix1(1);a2=ksaix1(2);a3=ksaix1(3);a4=ksaix1(4);a5=ksaix1(5);a6=ksaix1(6);a7=ksaix1(7);a8=ksaix1(8);a9=ksaix1(9);a10=ksaix1(10);a11=ksaix1(11);a12=ksaix1(12);a13=ksaix1(13);a14=ksaix1(14);a15=ksaix1(15);a16=ksaix1(16);a17=ksaix1(17);a18=ksaix1(18);a19=ksaix1(19);a20=ksaix1(20);a21=ksaix1(21);a22=ksaix1(22);a23=ksaix1(23);a24=ksaix1(24);a25=ksaix1(25);a26=ksaix1(26);a27=ksaix1(27);a28=ksaix1(28);a29=ksaix1(29);a30=ksaix1(30);a31=ksaix1(31);% a32=ksaix1(32);
%b=y1
b1=ksaiy1(1);b2=ksaiy1(2);b3=ksaiy1(3);b4=ksaiy1(4);b5=ksaiy1(5);b6=ksaiy1(6);b7=ksaiy1(7);b8=ksaiy1(8);b9=ksaiy1(9);b10=ksaiy1(10);b11=ksaiy1(11);b12=ksaiy1(12);b13=ksaiy1(13);b14=ksaiy1(14);b15=ksaiy1(15);b16=ksaiy1(16);b17=ksaiy1(17);b18=ksaiy1(18);b19=ksaiy1(19);b20=ksaiy1(20);b21=ksaiy1(21);b22=ksaiy1(22);b23=ksaiy1(23);b24=ksaiy1(24);b25=ksaiy1(25);b26=ksaiy1(26);b27=ksaiy1(27);b28=ksaiy1(28);b29=ksaiy1(29);b30=ksaiy1(30);b31=ksaiy1(31);%c=x2
c1=ksaix2(1);c2=ksaix2(2);c3=ksaix2(3);c4=ksaix2(4);c5=ksaix2(5);c6=ksaix2(6);c7=ksaix2(7);c8=ksaix2(8);c9=ksaix2(9);c10=ksaix2(10);c11=ksaix2(11);c12=ksaix2(12);c13=ksaix2(13);c14=ksaix2(14);c15=ksaix2(15);c16=ksaix2(16);c17=ksaix2(17);c18=ksaix2(18);c19=ksaix2(19);c20=ksaix2(20);c21=ksaix2(21);c22=ksaix2(22);c23=ksaix2(23);c24=ksaix2(24);c25=ksaix2(25);c26=ksaix2(26);c27=ksaix2(27);c28=ksaix2(28);c29=ksaix2(29);c30=ksaix2(30);c31=ksaix2(31); %d=y2
d1=ksaiy2(1);d2=ksaiy2(2);d3=ksaiy2(3);d4=ksaiy2(4);d5=ksaiy2(5);d6=ksaiy2(6);d7=ksaiy2(7);d8=ksaiy2(8);d9=ksaiy2(9);d10=ksaiy2(10);d11=ksaiy2(11);d12=ksaiy2(12);d13=ksaiy2(13);d14=ksaiy2(14);d15=ksaiy2(15);d16=ksaiy2(16);d17=ksaiy2(17);d18=ksaiy2(18);d19=ksaiy2(19);d20=ksaiy2(20);d21=ksaiy2(21);d22=ksaiy2(22);d23=ksaiy2(23);d24=ksaiy2(24);d25=ksaiy2(25);d26=ksaiy2(26);d27=ksaiy2(27);d28=ksaiy2(28);d29=ksaiy2(29);d30=ksaiy2(30);d31=ksaiy2(31);for i=2:32y1_rec(i)= b1+b2*x1_rec(i-1)+b3*y1_rec(i-1)+b4*x2_rec(i-1)+b5*y2_rec(i-1)+b6*x1_rec(i-1)^2+b7*x2_rec(i-1)^2+b8*y1_rec(i-1)^2+b9*y2_rec(i-1)^2+b10*x1_rec(i-1)*x2_rec(i-1)+b11*x1_rec(i-1)*y1_rec(i-1)+b12*x1_rec(i-1)*y2_rec(i-1)+b13*x2_rec(i-1)*y1_rec(i-1)+b14*x2_rec(i-1)*y2_rec(i-1)+b15*y1_rec(i-1)*y2_rec(i-1)+b16*x1_rec(i-1)^3+b17*y1_rec(i-1)^3+b18*x2_rec(i-1)^3+b19*y2_rec(i-1)^3+b20*x1_rec(i-1)^2*x2_rec(i-1)+b21*x1_rec(i-1)^2*y1_rec(i-1)+b22*x1_rec(i-1)^2*y2_rec(i-1)+b23*x2_rec(i-1)^2*x1_rec(i-1)+b24*x2_rec(i-1)^2*y1_rec(i-1)+b25*x2_rec(i-1)^2*y2_rec(i-1)+b26*y1_rec(i-1)^2*x1_rec(i-1)+b27*y1_rec(i-1)^2*x2_rec(i-1)+b28*y1_rec(i-1)^2*y2_rec(i-1)+b29*y2_rec(i-1)^2*x1_rec(i-1)+b30*y2_rec(i-1)^2*x2_rec(i-1)+b31*y2_rec(i-1)^2*y1_rec(i-1);y2_rec(i)= d1+d2*x1_rec(i-1)+d3*y1_rec(i-1)+d4*x2_rec(i-1)+d5*y2_rec(i-1)+d6*x1_rec(i-1)^2+d7*x2_rec(i-1)^2+d8*y1_rec(i-1)^2+d9*y2_rec(i-1)^2+d10*x1_rec(i-1)*x2_rec(i-1)+d11*x1_rec(i-1)*y1_rec(i-1)+d12*x1_rec(i-1)*y2_rec(i-1)+d13*x2_rec(i-1)*y1_rec(i-1)+d14*x2_rec(i-1)*y2_rec(i-1)+d15*y1_rec(i-1)*y2_rec(i-1)+d16*x1_rec(i-1)^3+d17*y1_rec(i-1)^3+d18*x2_rec(i-1)^3+d19*y2_rec(i-1)^3+d20*x1_rec(i-1)^2*x2_rec(i-1)+d21*x1_rec(i-1)^2*y1_rec(i-1)+d22*x1_rec(i-1)^2*y2_rec(i-1)+d23*x2_rec(i-1)^2*x1_rec(i-1)+d24*x2_rec(i-1)^2*y1_rec(i-1)+d25*x2_rec(i-1)^2*y2_rec(i-1)+d26*y1_rec(i-1)^2*x1_rec(i-1)+d27*y1_rec(i-1)^2*x2_rec(i-1)+d28*y1_rec(i-1)^2*y2_rec(i-1)+d29*y2_rec(i-1)^2*x1_rec(i-1)+d30*y2_rec(i-1)^2*x2_rec(i-1)+d31*y2_rec(i-1)^2*y1_rec(i-1);x1_rec(i)= a1+a2*x1_rec(i-1)+a3*y1_rec(i-1)+a4*x2_rec(i-1)+a5*y2_rec(i-1)+a6*x1_rec(i-1)^2+a7*x2_rec(i-1)^2+a8*y1_rec(i-1)^2+a9*y2_rec(i-1)^2+a10*x1_rec(i-1)*x2_rec(i-1)+a11*x1_rec(i-1)*y1_rec(i-1)+a12*x1_rec(i-1)*y2_rec(i-1)+a13*x2_rec(i-1)*y1_rec(i-1)+a14*x2_rec(i-1)*y2_rec(i-1)+a15*y1_rec(i-1)*y2_rec(i-1)+a16*x1_rec(i-1)^3+a17*y1_rec(i-1)^3+a18*x2_rec(i-1)^3+a19*y2_rec(i-1)^3+a20*x1_rec(i-1)^2*x2_rec(i-1)+a21*x1_rec(i-1)^2*y1_rec(i-1)+a22*x1_rec(i-1)^2*y2_rec(i-1)+a23*x2_rec(i-1)^2*x1_rec(i-1)+a24*x2_rec(i-1)^2*y1_rec(i-1)+a25*x2_rec(i-1)^2*y2_rec(i-1)+a26*y1_rec(i-1)^2*x1_rec(i-1)+a27*y1_rec(i-1)^2*x2_rec(i-1)+a28*y1_rec(i-1)^2*y2_rec(i-1)+a29*y2_rec(i-1)^2*x1_rec(i-1)+a30*y2_rec(i-1)^2*x2_rec(i-1)+a31*y2_rec(i-1)^2*y1_rec(i-1);x2_rec(i)= c1+c2*x1_rec(i-1)+c3*y1_rec(i-1)+c4*x2_rec(i-1)+c5*y2_rec(i-1)+c6*x1_rec(i-1)^2+c7*x2_rec(i-1)^2+c8*y1_rec(i-1)^2+c9*y2_rec(i-1)^2+c10*x1_rec(i-1)*x2_rec(i-1)+c11*x1_rec(i-1)*y1_rec(i-1)+c12*x1_rec(i-1)*y2_rec(i-1)+c13*x2_rec(i-1)*y1_rec(i-1)+c14*x2_rec(i-1)*y2_rec(i-1)+c15*y1_rec(i-1)*y2_rec(i-1)+c16*x1_rec(i-1)^3+c17*y1_rec(i-1)^3+c18*x2_rec(i-1)^3+c19*y2_rec(i-1)^3+c20*x1_rec(i-1)^2*x2_rec(i-1)+c21*x1_rec(i-1)^2*y1_rec(i-1)+c22*x1_rec(i-1)^2*y2_rec(i-1)+c23*x2_rec(i-1)^2*x1_rec(i-1)+c24*x2_rec(i-1)^2*y1_rec(i-1)+c25*x2_rec(i-1)^2*y2_rec(i-1)+c26*y1_rec(i-1)^2*x1_rec(i-1)+c27*y1_rec(i-1)^2*x2_rec(i-1)+c28*y1_rec(i-1)^2*y2_rec(i-1)+c29*y2_rec(i-1)^2*x1_rec(i-1)+c30*y2_rec(i-1)^2*x2_rec(i-1)+c31*y2_rec(i-1)^2*y1_rec(i-1);end figure hold on plot(x1_rec,'Y') plot(x2_rec,'b')
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