I need some help to solve non-linear equation with three unknowns and three knowns with having 170 different values for one known.

Xw, Yw, Zw (170 * 1 matrices) are known with 170 different values.

Xe, Ye, Ze are the unknowns.

Tx, Ty, Tz, Rx, Ry, Rz, and neta are some of other knowns.

I want to find the values for Xe, Ye, and Ze.

Answer 1

[Torsten]

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
M = repmat(M,170,1);
b = [];
for i = 1:170
  b = [b;Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
end
sol = M\b;
Xe = sol(1)
Ye = sol(2)
Ze = sol(3)

[Prabhath Manuranga]

Thanks Mr. Torsten.

This give only one value for each Xe, Ye, and Ze. But i need to get all values that comes for each Xe, Ye, and Ze value. if Xw, Yw and Zw is having 170 values for each, when solving the equations for each Xw, Yw and Zw should gives its respective Xe, Ye and Ze value (170 different values for each). How to get that?

[Torsten]

You wrote you want to determine three unknowns for all your 170 data points, i.e. a solution for Xe, Ye and Ze that solves the system optimal for all data points in some kind of average sense.

If you want to have three solutions for each of the 170 data points, just use

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
Minv = inv(M);
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = Minv*b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end

[Prabhath Manuranga]

Thanks Mr. Torsten.

[Walter Roberson]

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = M\b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end

[Torsten]

:-)

M = [eta+1,Rz,-Ry;-Rz,eta+1,Rx;Ry,-Rx,eta+1];
dM = decomposition(M);
Xe = zeros(170,1);
Ye = zeros(170,1);
Ze = zeros(170,1);
for i = 1:170
    b = [Xw(i)-Tx;Yw(i)-Ty;Zw(i)-Tz];
    sol = dM\b;
    Xe(i) = sol(1);
    Ye(i) = sol(2);
    Ze(i) = sol(3);
end