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

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Prabhath Manuranga
Prabhath Manuranga 2024-2-21
评论： Torsten 2024-2-23
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.

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回答（1 个）

Torsten
Torsten 2024-2-21
编辑：Torsten 2024-2-21
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)
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Walter Roberson
Walter Roberson 2024-2-23
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
Torsten 2024-2-23
:-)
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

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