sum calculation in matlab

Hi, I have problem starting calculation of this sum

SUM(ZnSn-aSnSn+bSnTn)=0
Sum(ZnTn-aSnTn+bTnTn)=0

So I have S1 S2 S3 Z1 Z2 Z3 T1 T2 T3

I need to calculate a and b. I kinda can do it on paper by the point is to see how matlab calculate it. It should go like

Z1S1-aS1S1+bS1T1 + Z2S2-aS2S2+bS2T2 + Z3S3-aS3S3+b32T3=0
Z1T1-aS1T1+bT1T1 + Z1T1-aS1T1+bT1T1 +Z1T1-aS1T1+bT1T1 =0

How should I start it, I m super new at matlab. Should I use sum , and set a and b as vector of 0 ? Any help much appreciated

Answer 1

[Star Strider]

Note that ‘32T3’ is not a valid MATLAB variable name (they cannot begin with numbers). I changed it to ‘S2T3’, and used the Symbolic Math Toolbox:

syms a b Z1S1 S1S1 S1T1 Z2S2 S2S2 S2T2 Z3S3 S3S3 S2T3 Z1T1 T1T1 
Eqns = [Z1S1-a*S1S1+b*S1T1 + Z2S2-a*S2S2+b*S2T2 + Z3S3-a*S3S3+b*S2T3 == ...
        Z1T1-a*S1T1+b*T1T1 + Z1T1-a*S1T1+b*T1T1 +Z1T1-a*S1T1+b*T1T1];

[a,b] = solve(Eqns, [a b])

to produce:

a =
(S1T1*Z1T1 + S2T2*Z1T1 + S2T3*Z1T1 - T1T1*Z1S1 - T1T1*Z2S2 - T1T1*Z3S3)/(S1T1*S2T2 + S1T1*S2T3 - S1S1*T1T1 - S2S2*T1T1 - S3S3*T1T1 + S1T1^2)

b =
(S1S1*Z1T1 - S1T1*Z1S1 + S2S2*Z1T1 - S1T1*Z2S2 + S3S3*Z1T1 - S1T1*Z3S3)/(S1T1*S2T2 + S1T1*S2T3 - S1S1*T1T1 - S2S2*T1T1 - S3S3*T1T1 + S1T1^2)

I have no idea if these will produce usable results, since I do not know what any of the variables are (scalars, matrices, ...).

[MariapL]

Is there any way to not include 'syms'? I have tried to intall it couple of time but still got an error. Thanks:)

[Star Strider]

You do not need to use the Symbolic Math Toolbox. I used it to solve for ‘a’ and ‘b’, so all you need to do is to use the equations I provided, with your numeric variables, to find the parameter values.

Answer 2

[Torsten]

If you define Z, S, T as numerical arrays, you can determine a and b as

A = [-sum(S.*S) sum(S.*T);-sum(S.*T) sum(T.*T)];
rhs = [-sum(Z.*S);-sum(Z.*T)];
x = A\rhs;
a = x(1);
b = x(2);
a 
b

Best wishes

Torsten.