Is it possible to rewrite these equation set to matrix form?

I am dealing with some equation set to calculate coefficients b. The equation set is as below. The x y z are the inputs. b is output.

syms x [4 1]
syms y [4 1]
syms z [4 1]
b = zeros(4,1);
b(1) = y3*z2 - y2*z3 + y2*z4 - y4*z2 - y3*z4 + y4*z3;
b(2) = y1*z3 - y3*z1 - y1*z4 + y4*z1 + y3*z4 - y4*z3;
b(3) = y2*z1 - y1*z2 + y1*z4 - y4*z1 - y2*z4 + y4*z2;
b(4) = y1*z2 - y2*z1 - y1*z3 + y3*z1 + y2*z3 - y3*z2;

The equation set would be calculation many times. It takes long time. I want to speed it up. I would like to rewrite this equation set into matrix multiplication, like b = A*[x,y,z] . So I could calculate the vector b in one time , not 4 times. Is it possible? I think this may need some math mind, I have not figure it out. Please help me.

I also try to use subs function. But it is very slow.

Answer 1

[Ameer Hamza]

These variables are nonlinearly related, so not sure how do you want to write in matrix form. Also, it is unlikely that it will cause a significant improvement in speed. You are using a symbolic toolbox that is inherently slow as compared to finite-precision floating-point maths. If you know the values of x, y, and z and want to find values of b, then I suggest you use regular MATLAB operators. For example

syms x [4 1]
syms y [4 1]
syms z [4 1]
b = sym(zeros(4,1));
b(1) = y3*z2 - y2*z3 + y2*z4 - y4*z2 - y3*z4 + y4*z3;
b(2) = y1*z3 - y3*z1 - y1*z4 + y4*z1 + y3*z4 - y4*z3;
b(3) = y2*z1 - y1*z2 + y1*z4 - y4*z1 - y2*z4 + y4*z2;
b(4) = y1*z2 - y2*z1 - y1*z3 + y3*z1 + y2*z3 - y3*z2;

b_fun = matlabFunction(b, 'Vars', {[x1 x2 x3 x4], [y1 y2 y3 y4], [z1 z2 z3 z4]});

x_vec = rand(1,4);
y_vec = rand(1,4);
z_vec = rand(1,4);
b_val = b_fun(x_vec, y_vec, z_vec)