Linear Algebra and the C Language/a0c4

__NOTOC__ The coefficients of a circle with the QR Decomposition I use QR_mR(); to calculate the coefficients of a circle. Presentation : Find the coefficients a, b, c, d of the circle, ax**2 + ay**2 + bx + cy + d = 0 which crosses these three points (x[1],y[1]) (x[2],y[2]) (x[3],y[3]) Using the three points we obtain the matrix. (a)x**2 (a)y**2 (b)x (c)y (d) = 0 x[1]**2 y[1]**2 x[1] y[1] 1 0 x[2]**2 y[2]**2 x[2] y[2] 1 0 x[3]**2 y[3]**2 x[3] y[3] 1 0 This system has three lines and four unknowns (a, b, c, d). It is a homogeneous system, so it has an infinite number of solutions. To find a solution, I chose to set a = 1. We therefore have five rows and five unknowns. (a)x**2 (a)y**2 x y 1 0 0 0 0 1 0 1 0 0 0 1 x[1]**2 y[1]**2 x[1] y[1] 1 0 x[2]**2 y[2]**2 x[2] y[2] 1 0 x[3]**2 y[3]**2 x[3] y[3] 1 0 All that remains is to solve the system. c00a.c ..... ..... ax**2 + ay**2 + cx + dy + e = 0 c00b.c c00c.c c00d.c