Solving for all missing terms at once with "solve" doesn't work

Hello,

I am trying to write a function to automate solving the following problem:

• Given 3D unit vectors N, O, and A with at least 3 knowns (the rest could be symbols)
• Given N is orthogonal to both O and A
• Find the missing vector components

The equations that relate N, O, and A to each other are:

• cross(O, A) == N
• norm(N) == 1
• norm(O) == 1
• norm(A) == 1

Simple example done manually:

syms nx ny nz oz

A = [-0.9100; -0.4146; 0];
O = [0.3362; -0.7379; oz];
N = [nx; ny; nz]

% Solve for z component in the O vector
solve(norm(O) == 1, oz)
% oz: (5^(1/2)*6849463^(1/2))/10000

% Solve for all three components in N vector
solve(cross(O, A) == N, nx, ny, nz)
% nx: (2073*oz)/5000
% ny: -(91*oz)/100
% nz: -10135969/12500000

OK, so clearly that works. Next I would like to write a function to do this:

function S = noa(N, O, A)
  S = solve([
    cross(O, A) == N,
    norm(N) == 1,
    norm(O) == 1,
    norm(A) == 1
  ]);
end

When I execute it using the values for N, O and I in example above, I get no solutions

noa(N, O, A)
% nx: [0x1 sym]
% ny: [0x1 sym]
% nz: [0x1 sym]
% oz: [0x1 sym]

I would also like to generate C code:

ccode(noa(N, O, A))

...but it's complaining about an incorrect number of inputs/outputs even though I provided the correct number

Incorrect number or types of inputs or outputs for function 'ccode'.

Does anyone know what might be wrong here?

Thank you!

Answer 1

[Nathan Hardenberg]

The reason, your solve does not work in the function is most likely that there are more equations than variables. This is no problem under normal conditions, but your equations are not correct. The equations are only a good numerical approximation:

format long
norm([-0.9100; -0.4146; 0])

ans = 
   0.999996579994152

That's why they can't be solved.

Just write you function like your example. The solution is then most likely correct enough.

function S = noa(N, O, A)
    S = solve([cross(O, A) == N, norm(O) == 1])
end

Regarding you C-Code generation:

I think the output type is the incorrect one! S ia a struct. Code generation most likely does not support this data type (but I'm no expert on this). You can try to get all solutions and return them as a matrix. This could work.

[Valeriy]

Had a chance to review your response in detail - thanks for taking the time!

I found that several other issues I had using Matlab were rooted in being loosy-goosey with numeric precision. When I equate terms to other terms that were also calculated by Matlab all the equations have solutions.