solving complex matrix with symbolic variables

hello, I am trying to solve a complex matrix with symbols, but it returns''Empty sym: 0-by-1''. I would like to know why this happened and how could I solve this problem. Thank you.

[ZENONG]

Hi, I updated my code, and it retured values, but I believe there still are some errors, maybe the ''theta'' and ''abs'' variables?

Answer 1

[Vishnu]

Hi Zenong,

From the code, it seems that you are trying to solve the complex matrix equations using symbolic variables.However, the issue is that the variables used for 'VI' and 'Vscl' are not symbolic variables, and this is causing the error "Empty sym: 0-by-1".

To solve this issue, the you need to define symbolic variables 'p1', 'q1', 'p2', 'q2', 'p3', 'q3', 'p4' and 'q4' using 'syms' function.

syms a b c d e f g h k p1 p2 p3 p4 q1 q2 q3 q4

Here is the modified code:

syms a b c d e f g h k real          %defining symbolic variables

z1=-30j;
z2=0.08+0.40j;
z3=-35j;
z4=0.10+0.50j;
z5=0.10+0.50j;
z6=-25j;
z7=0.30j;

p1=a;
p2=0.55;
p3=0.30;
p4=0.50;

q1=1j*b;
q2=0.15j;
q3=0.201j;
q4=1j*c;

e1=1.05;
e2=d;
e3=e;
e4=f;

f1=0j;
f2=1j*g;
f3=1j*h;
f4=1j*k;

y11=1/z1+1/z2+1/z5;
y12=(-1)*1/z2;
y13=(-1)*1/z5;
y14=0;

y21=y12;
y22=1/z2+1/z4+1/z3;
y23=(-1)*1/z4;
y24=0;

y31=y13;
y32=y23;
y33=1/z6+1/z7+1/z5+1/z4;
y34=0;

y41=y14;
y42=y24;
y43=y34;
y44=1/z7;

Y=[y11,y12,y13,y14;
   y21,y22,y23,y24;
   y31,y32,y33,y34;
   y41,y42,y43,y44];

conjY=conj(Y);                      %conjugate Y
V=[e1+f1;e2+f2;e3+f3;e4+f4];
format shortG

conjY=round(conjY,2,'significant')  %conjugate Y
Vscl=diag(V)                        %scalar matrix V
conjV=conj(V)                       %conjugate V

%Defining symbolic variables
syms a b c d e f g h k p1 p2 p3 p4 q1 q2 q3 q4

[a,b,c,d,e,f,g,h,k] = solve([p1+q1;p2+q2;p3+q3;p4+q4]==Vscl*conjY*conjV,[a,b,c,d,e,f,g,h,k]); 

Answer 2

[MANIK]

Hi @ZENONG,

As per my understanding, you're trying to solve a complex matrix equation in MATLAB

Well, I was going through your code, it is all correct. But, here you're trying to solve a problem, which contains 4 equations and 9 variables which is not possible. That's why you're getting an error here.

Answer 3

[Torsten]

syms a b c d e f g h k real
z1=-30j;
z2=0.08+0.40j;
z3=-35j;
z4=0.10+0.50j;
z5=0.10+0.50j;
z6=-25j;
z7=0.30j;

p1=a;
p2=-0.55;
p3=-0.30;
p4=0.50;

q1=1j*b;
q2=-0.15j;
q3=-0.20j;
q4=1j*c;

e1=1.05;
e2=d;
e3=e;
e4=f;

f1=0j;
f2=1j*g;
f3=1j*h;
f4=1j*k;

y11=1/z1+1/z2+1/z5;
y12=(-1)*1/z2;
y13=(-1)*1/z5;
y14=0;

y21=y12;
y22=1/z2+1/z4+1/z3;
y23=(-1)*1/z4;
y24=0;

y31=y13;
y32=y23;
y33=1/z6+1/z7+1/z5+1/z4;
y34=(-1)*1/z7;

y41=y14;
y42=y24;
y43=y34;
y44=1/z7;

theta=f^2+k^2;
abs=1.1^2;
Y=[y11,y12,y13,y14;
   y21,y22,y23,y24;
   y31,y32,y33,y34;
   y41,y42,y43,y44];
conjY=conj(Y);
V=[e1+f1;e2+f2;e3+f3;e4+f4];
format shortG

conjY=round(conjY,2,'significant');
Vscl=diag(V);
conjV=conj(V);
VIt=Vscl*conjY*conjV;

P=simplify([real([p1;p2;p3;p4]);imag([q1;q2;q3;q4]);theta])

P = 

Q=simplify([real(VIt);imag(VIt);abs])

Q = 

sol=vpasolve(P==Q)

sol = struct with fields:
    a: [4×1 sym]
    b: [4×1 sym]
    c: [4×1 sym]
    d: [4×1 sym]
    e: [4×1 sym]
    f: [4×1 sym]
    g: [4×1 sym]
    h: [4×1 sym]
    k: [4×1 sym]

sol.a

ans = 

sol.b

ans = 

sol.c

ans = 

sol.d

ans = 

sol.e

ans = 

sol.f

ans = 

sol.g

ans = 

sol.h

ans = 

sol.k

ans = 

error = arrayfun(@(i)subs(P-Q,[a b c d e f g h k],[sol.a(i) sol.b(i) sol.c(i) sol.d(i) sol.e(i) sol.f(i) sol.g(i) sol.h(i) sol.k(i)]),1:4,'UniformOutput',0)

error = 1×4 cell array
    {9×1 sym}    {9×1 sym}    {9×1 sym}    {9×1 sym}

error{1}

ans = 

error{2}

ans = 

error{3}

ans = 

error{4}

ans =