matrix simultaneous equations returning 0s

Code should return FM values as 2x104 matrix with x and y values but it keeps returning 0s as x values. I think it's because instead of returning values for each square set in equation, it's returning the whole sum of both xA and xB over the solution rather than breaking it up.

Ax = 0;
Ay = 0.25;
Bx = 0;
By = 3.25;
Py = 30 + 3.5118*7;

x=0.5:0.5:4; nx=length(x);
y=-1:0.5:5; ny=length(y);
xM=zeros(2,nx*ny);
for i=1:nx
    for j=1:ny
        xM(:,(i-1)*ny+j)=[x(i),y(j)];
        AxM = Ax - xM(1, :);
        AyM = Ay - xM(2, :);
        BxM = Bx - xM(1, :);
        ByM = By - xM(2, :);
        MA = sqrt(AxM.^2 + AyM.^2);
        MB = sqrt(BxM.^2 + ByM.^2);
        xA = AxM./MA;
        xB = BxM./MB;
        yA = AyM./MA;
        yB = ByM./MB;
        A3 = [xA xB; yA yB];
        B3 = [0;Py];
        FM = A3.\B3;
    end
end  

please help, edited to have all values

[Torsten]

We can't test your code because other variables are missing.

[Walter Roberson]

        xM(:,(i-1)*ny+j)=[x(i),y(j)];
        AxM = Ax - xM(1, :);

The first iteration of the loop, xM starts as all zero and has a column written into. It then uses the entire rows including the column just written and all the zeros.

The second iteration, an additional column is written into, and you then use the entire row including all of the remaining zeros and the two columns written into so far. And so on.

Is that your intention, to fill in one more column each time and use the accumulated values?

[Edward Roberts]

my intention is to solve a simultaneous equation where

F1(Ax-Mx)/MA + F2(Bx-Mx)/MB = 0

and

F1(Ay-My)/MA + F2(By-My)/MB = Py

[Walter Roberson]

I cannot tell which variables in that correspond to which variables in your code. In terms of those equations, I cannot tell which variables you are trying to solve for.

[Edward Roberts]

Im sorry i'm not very good at this, F1 and F2 would be the x and y values for a simultaneous equation, there ax-mx is AxM etc.

[Walter Roberson]

In your F1 and so on formula, what variables are being solved for? When I try to match against your code, everything appears to be constant or input or calculated from input.

It would help if you could annotate your F1 etc. formula showing the size of each variable and whether it is known or to be solved for.

[Edward Roberts]

F1 and F2 are being solved for in my attempted equation

[Walter Roberson]

okay, good luck with that.

Answer 1

[Torsten]

Ax = 0;
Ay = 0.25;
Bx = 0;
By = 3.25;
Py = 30 + 3.5118*7;
x=0.5:0.5:4; nx=length(x);
y=-1:0.5:5; ny=length(y);
xM=zeros(2,nx*ny);
FM=zeros(2,nx*ny);
for i=1:nx
    for j=1:ny
        xM(:,(i-1)*ny+j)=[x(i);y(j)];
        AxM = Ax - xM(1, (i-1)*ny+j);
        AyM = Ay - xM(2, (i-1)*ny+j);
        BxM = Bx - xM(1, (i-1)*ny+j);
        ByM = By - xM(2, (i-1)*ny+j);
        MA = sqrt(AxM.^2 + AyM.^2);
        MB = sqrt(BxM.^2 + ByM.^2);
        xA = AxM./MA;
        xB = BxM./MB;
        yA = AyM./MA;
        yB = ByM./MB;
        A3 = [xA xB; yA yB];
        B3 = [0;Py];
        fm = A3\B3;
        FM(1,(i-1)*ny+j) = fm(1);
        FM(2,(i-1)*ny+j) = fm(2);
    end
end  
xM

xM = 2×104

0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.5000 1.5000 1.5000 1.5000 -1.0000 -0.5000 0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 -1.0000 -0.5000 0 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 -1.0000 -0.5000 0 0.5000

FM

FM = 2×104

-24.4947 -16.4000 -10.1709 -10.1709 -16.4000 -24.4947 -33.1139 -41.9356 -50.8543 -59.8268 -68.8321 -77.8586 -86.8999 -29.1249 -22.7427 -18.7542 -18.7542 -22.7428 -29.1249 -36.6716 -44.7980 -53.2394 -61.8670 -70.6125 -79.4370 -88.3169 -35.5253 -30.5126 -27.6677 -27.6677 77.8586 68.8321 59.8268 50.8543 41.9356 33.1139 24.4947 16.4000 10.1709 10.1709 16.4000 24.4947 33.1139 79.4370 70.6125 61.8670 53.2394 44.7980 36.6716 29.1249 22.7427 18.7542 18.7542 22.7428 29.1249 36.6716 82.0002 73.4841 65.1253 56.9932

[Walter Roberson]

This would make more sense than the original code.

I suspect that there might be a non-looping way to perform the desired calculation, but unfortunately the original poster chooses not to help the volunteers understand the equations even when asked repeatedly.

[Edward Roberts]

This worked perfectly, thank you so much. I apologise if my incompetence with MATLAB is frustrating to deal with.

[Walter Roberson]

We help teach MATLAB, so not knowing MATLAB is not inherently a problem. But when we ask for information multiple times and the information is not provided, we might give up.

Answer 2

[Walter Roberson]

FM = A3.\B3;

You overwrite all of FM each iteration. The final result will be what was assigned for the final i j combination.

If that is deliberate then notice that you could omit everything except the assignment to xM inside of the loop and move everything else in the loop to after the loop since you overwrite all of those variables anyway.

[Edward Roberts]

I'm trying to do a simultaneous equation solve with the variables being matrices.