%test pass3()



global_defs;





example = 1;

switch example

	case (1)

		perp = [1;0;0];

		a0= get_unit_vec(randn(3,1));

		b0= get_unit_vec(randn(3,1));

		c0= get_unit_vec(randn()*a0 +randn()*b0);

		e0= get_unit_vec(randn(3,1));



		a1= get_unit_vec(randn(3,1));

		b1= get_unit_vec(cross(a1,randn(3,1)));

		c1= get_unit_vec(cross(b1,randn(3,1)));

		e2= get_unit_vec(randn(3,1));

		

		if(-(cross(a0,b0)'*cross(b0,c0))*(b0'*c0)<0)

				a0=-a0;

		endif

	otherwise

		error("example number is out of range");

end

vecs_in=[e0,c0,b0,a0;e2,c1,b1,a1];

[vecs_out, U1, U0] = pass3(vecs_in, perp);

c0f=vecs_out(1:3,1); e0f=vecs_out(1:3,2); b0f=vecs_out(1:3,3); a0f=vecs_out(1:3,4);

c1f=vecs_out(4:6,1); e2f=vecs_out(4:6,2); b1f=vecs_out(4:6,3); a1f=vecs_out(4:6,4);



% e0  c0  b0  a0       c0f  e0f  b0f   a0f    [U0]

% |   |   |   |   -->  |    |    |     |

% |   c1  b1  a1       c1f  |    b1f   a1f    [U1]

% |                         |

% e2                        e2f               [1]



error_pass3 = norm(dr101(e2,e0)*dr011(c1,c0)*dr011(b1,b0)*dr011(a1,a0) -dr011(c1f,c0f)*dr101(e2f,e0f)*dr011(b1f,b0f)*dr011(a1f,a0f)*kron(kron(eye(2),U1),U0) )