Question

Possible Duplicate:
System of linear equations in C++?

I have the following 2 systems of equations:

For a,b,c,d:

0 = a * r1_x + b * r1_x * r1_y + c * r1_y + d
1 = a * r2_x + b * r2_x * r2_y + c * r2_y + d
0 = a * r3_x + b * r3_x * r3_y + c * r3_y + d
1 = a * r4_x + b * r4_x * r4_y + c * r4_y + d

For e,f,g,h:

0 = e * r1_x + f * r1_x * r1_y + g * r1_y + h
0 = e * r2_x + f * r2_x * r2_y + g * r2_y + h
1 = e * r3_x + f * r3_x * r3_y + g * r3_y + h
1 = e * r4_x + f * r4_x * r4_y + g * r4_y + h

I know the values of r1_x, r1_y, r2_x, r2_y, r3_x, r3_y, r4_x, r4_y,
and need to solve for a,b,c,d in the first one, and ,e,f,g, h in the second.

I know how I would solve these with pencil and paper, but I’m really unsure how to program it. How could I solve the above equations in C or C++ (or psuedocode).

Thanks

Answer 1

You can map it to a matrix system, A x = b, where A is the coefficient matrix, b is the solution vector, and x are the unknowns. You can either implement Gaussian elimination, or use a well known library. If you use LAPACK, the routine you want it dgesv.