Matrix is close to singular or badly scaled. Results may be inaccurate.

Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.986089e-23.

for k=1:40
    a(k,1)=1;
    a(k,2)=sin(W0*t(k));
    a(k,3)=cos(W0*t(k));
    a(k,4)=sin(3*W0*t(k));
    a(k,5)=cos(3*W0*t(k));
    a(k,6)=t(k);
    a(k,7)=(t(k).^2); 
    b1(k,1)=V(k,1);
    b2(k,1)=I(k,1);
end

a2=a';
a3=inv(a2*a);%warning come from this line itried a2\a but its not working and different here
a4=a3*a2;
Xv=a4*b1;
Xi=a4*b2;
thetav=atan(Xv(3,1)/Xv(2,1));
tv=rad2deg(thetav);
thetai=atan(Xi(3,1)/Xi(2,1));
ti=rad2deg(thetai);
z=((Xv(2)+(i*Xv(3)))/((Xi(2)+(i*Xi(3)))));
thetaz=atan(Xv(3,1)/Xv(2,1))-atan(Xi(3,1)/Xi(2,1));
tz=rad2deg(thetaz);
Z=abs(z);

[Rik]

What are you attempting to do?

[Walter Roberson]

We will need your W0 and t values to test with.

Note that a2\a is entirely different than inv(a2*a) . a2\a is closer to inv(a2)*a

[arian hoseini]

t=[0;0.0000;0.0001;0.0001;0.0001;0.0002;0.0003;0.0003;0.0004;0.0004;0.0004;0.0005;0.0006;0.0006;0.0006;0.0007;
    0.0008;0.0008;0.0008;0.0009;0.0010;0.0010;0.0010;0.0011;0.0012;0.0012;0.0013;0.0013;0.0014;0.0014;0.0014
    ;0.0015;0.0015;0.0016;0.0017;0.0017;0.0018;0.0018;0.0019;0.0019]
W0=2*60*pi;

Answer 1

[Walter Roberson]

You have enough duplicate t values that when you calculate "a" the rank does not reach 7; rank of a2*a does not reach 7, so your 7 x 7 matrix is singular.

format long g

t=[0;0.0000;0.0001;0.0001;0.0001;0.0002;0.0003;0.0003;0.0004;0.0004;0.0004;0.0005;0.0006;0.0006;0.0006;0.0007;
    0.0008;0.0008;0.0008;0.0009;0.0010;0.0010;0.0010;0.0011;0.0012;0.0012;0.0013;0.0013;0.0014;0.0014;0.0014
    ;0.0015;0.0015;0.0016;0.0017;0.0017;0.0018;0.0018;0.0019;0.0019];
W0=2*60*sym(pi);

t = sym(t);
a = zeros(40, 7, 'sym');

for k=1:40
    a(k,1)=1;
    a(k,2)=sin(W0*t(k));
    a(k,3)=cos(W0*t(k));
    a(k,4)=sin(3*W0*t(k));
    a(k,5)=cos(3*W0*t(k));
    a(k,6)=t(k);
    a(k,7)=(t(k).^2); 
end
a2=a';

temp = a2*a;
vpa(temp,4)

ans = 

size(temp)

ans = 1×2

7 7

rank(temp)

ans = 
     6

ans = 
     6

size(a)

ans = 1×2

40 7

rank(a)

ans = 
     6

vpa(a, 4)

ans = 

a3 = inv(double(temp))

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 2.416580e-23.

a3 = 7×7

1.0e+00 * 67777253140.7658 -25603921793.069 -68225493381.5305 832812928.230255 448180506.302481 8712787650753.09 -4.57448194877832e+15 -25603921793.069 9760155248.57385 25770549709.5447 -316501185.988968 -166602910.913942 -3322436200988.51 1.72985152712877e+15 -68225493381.5305 25770549709.5447 68676781393.5081 -838262957.332607 -451227960.544581 -8769453942155.95 4.60468026606908e+15 832812928.230255 -316501185.988968 -838262957.332607 10274885.178035 5449251.51887214 107725990691.348 -56246480173259.8 448180506.302481 -166602910.913942 -451227960.544581 5449251.51887214 3047137.72603941 56657738350.4292 -30194231027123.4 8712787650753.09 -3322436200988.51 -8769453942155.95 107725990691.348 56657738350.4292 1.13100046719802e+15 -5.88676856525905e+17 -4.57448194877832e+15 1.72985152712877e+15 4.60468026606908e+15 -56246480173259.8 -30194231027123.4 -5.88676856525905e+17 3.08780937003526e+20