Solving system of equations for different combinations of symbolic variables

Hello,

I have a system of equations like [x1; x2; x3] = [3x3 coefficient matrix]*[y1; y2; y3]

Depending on user inputs 3 of the x or y terms will have numerical values. I would like to solve for the remaining 3 terms symbolically so that I have something like:

x1=3
x3=4
y1=5
I can solve the equations using:
syms x1 x3 y1
A=[x1; x2; x3]
B=[3x3 coefficient matrix]
C=[y1; y2; y3]
D=B*C
equations = [A(1)==D(1), A(2)==D(2), A(3)==D(3)]
answer = solve(equations, [x1, x3, y1])
x1=answer.x1
x3=answer.x3
y1=answer.y1

I know the symbolic variables that I want solve for by checking what user input fileds were left empty:

unknowns=[x1, x3, y1]

The problem is I don't know how to get symbolic unknowns ie.(x1, x3, y1) to be the variable that are solved for in answer = solve(equations, [x1, x3, y1]).

It seems like x1, x3, y1 should be dynamic variables but this is not recommended in matlab. Is there a way to accomplish what I am trying to do? Eventually I will need to expand to 6 equations and perform these calculations potentially hundreds of times for different values.

Thanks

Answer 1

[Star Strider]

I am not certain what result you want.

Try this:

syms x y 
A = sym('x',[3,1]);
C = sym('y',[3,1]);
A(1) = 3;
A(3) = 4;
C(1) = 5;
B = randi(9,3);
S = solve(A == B*C);
v = fieldnames(S);
for k = 1:numel(v)
    Out{k,:} = sprintf('%s = %f', v{k}, getfield(S,v{k}));
end

For one random ‘B’ this produces:

Out =

  3×1 cell array

    {'x2 = -26.500000'}
    {'y2 = -18.166667'}
    {'y3 = 4.833333'  }

Make appropriate changes to get the result you want.

[vaporcone767]

Thank you for the help. How would I accomplish this so that x2, y2, y3 are variables themselves that can be used in further calculations? I will want to perform these calculations in a loop untill x2, y2, y3 are all under some threshold.

[Star Strider]

My pleasure.

I characteristically do not use the eval function for a number of reasons, however that appears to be the only option for what you want to do:

for k = 1:numel(v)
    eval(Out{k})
end

That will assign them appropriately for later use. (I checked to be sure.)

DO NOT use eval other than this restricted context!

[Ana Soph]

Hi, if i have an equation that this variable depend from a data of another equation ??