Linear Algebra and the C Language/a0jo

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RA R5 #define CA C5 /* ------------------------------------ */ int main(void) { double xy[6] ={ 1, 10, 2, 1, 3, -10 }; double tA[RA*CA]={ /* x**2 y**2 x y e */ +1, +0, +0, +0, +0, +0, +1, +0, +0, +0, +1, +100, +1, +10, +1, +4, +1, +2, +1, +1, +9, +100, +3, -10, +1, }; double tb[RA*C1]={ /* = 0 */ +1, +1, +0, +0, +0, }; double **XY = ca_A_mR(xy,i_mR(R3,C2)); double **A = ca_A_mR(tA,i_mR(RA,CA)); double **b = ca_A_mR(tb,i_mR(RA,C1)); double **Inv = i_mR(CA,RA); double **Invb = i_mR(CA,C1); clrscrn(); printf("\n"); printf(" Find the coefficients a, b, c, d, of a circle \n\n"); printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n"); printf(" that passes through these three XY. \n\n"); printf(" x y"); p_mR(XY,S5,P0,C6); stop(); clrscrn(); printf(" Using the given XY, we obtain this matrix.\n"); printf(" (a = 1. This is my choice)\n\n"); printf(" A :"); p_mR(A,S10,P2,C7); printf(" b :"); p_mR(b,S10,P2,C7); printf(" Inv :"); invgj_mR(A,Inv); pE_mR(Inv,S12,P4,C10); stop(); clrscrn(); printf(" Inv :"); p_mR(Inv,S10,P4,C10); printf(" x = Inv * b "); mul_mR(Inv,b,Invb); p_mR(Invb,S10,P4,C10); printf(" The coefficients a, b, c, d, e, of the curve are : \n\n" " %+.2fx**2 %+.2fy**2 %+.2fx %+.2fy %+.2f = 0\n\n" ,Invb[R1][C1],Invb[R2][C1],Invb[R3][C1], Invb[R4][C1],Invb[R5][C1]); stop(); f_mR(XY); f_mR(A); f_mR(b); f_mR(Inv); f_mR(Invb); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Screen output example: Find the coefficients a, b, c, d, of a circle ax**2 + ay**2 + bx + cy + d = 0 that passes through these three XY. x y +1 +10 +2 +1 +3 -10 Press return to continue. Using the given XY, we obtain this matrix. (a = 1. This is my choice) A : +1.00 +0.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 +100.00 +1.00 +10.00 +1.00 +4.00 +1.00 +2.00 +1.00 +1.00 +9.00 +100.00 +3.00 -10.00 +1.00 b : +1.00 +1.00 +0.00 +0.00 +0.00 Inv : +1.0000e+00 +0.0000e+00 -4.4409e-16 +8.8818e-16 +4.4409e-16 +2.7756e-17 +1.0000e+00 -2.0817e-17 -1.3878e-17 -3.4694e-17 +6.0000e+00 +9.9000e+02 -5.5000e+00 +1.0000e+01 -4.5000e+00 +1.0000e+00 +9.9000e+01 -5.0000e-01 +1.0000e+00 -5.0000e-01 -1.7000e+01 -2.0800e+03 +1.1500e+01 -2.0000e+01 +9.5000e+00 Press return to continue. Inv : +1.0000 +0.0000 -0.0000 +0.0000 +0.0000 +0.0000 +1.0000 -0.0000 -0.0000 -0.0000 +6.0000 +990.0000 -5.5000 +10.0000 -4.5000 +1.0000 +99.0000 -0.5000 +1.0000 -0.5000 -17.0000 -2080.0000 +11.5000 -20.0000 +9.5000 x = Inv * b +1.0000 +1.0000 +996.0000 +100.0000 -2097.0000 The coefficients a, b, c, d, e, of the curve are : +1.00x**2 +1.00y**2 +996.00x +100.00y -2097.00 = 0 Press return to continue. Copy and paste in Octave: function xy = f (x,y) xy = +1.00*x^2 +1.00*y^2 +996.00*x +100.00*y -2097.00; endfunction f (+1,+10) f (+2,+1) f (+3,-10)