Linear Algebra and the C Language/a0jn

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00b.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RA R5 #define CA C5 /* ------------------------------------ */ int main(void) { double xy[6] ={ 1, -1, 2, -9, 3, -8 }; double tA[RA*CA]={ /* x**2 y**2 x y e */ +1, +0, +0, +0, +0, +0, +1, +0, +0, +0, +1, +1, +1, -1, +1, +4, +81, +2, -9, +1, +9, +64, +3, -8, +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 -1 +2 -9 +3 -8 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 +1.00 +1.00 -1.00 +1.00 +4.00 +81.00 +2.00 -9.00 +1.00 +9.00 +64.00 +3.00 -8.00 +1.00 b : +1.00 +1.00 +0.00 +0.00 +0.00 Inv : +1.0000e+00 +4.9960e-16 -6.9389e-18 +1.7347e-17 +2.4286e-17 -6.9389e-18 +1.0000e+00 +3.4266e-19 -1.7240e-18 +2.2701e-18 -4.7778e+00 +6.2222e+00 -1.1111e-01 -7.7778e-01 +8.8889e-01 -2.2222e-01 +1.0778e+01 +1.1111e-01 -2.2222e-01 +1.1111e-01 +3.5556e+00 +3.5556e+00 +1.2222e+00 +5.5556e-01 -7.7778e-01 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 -4.7778 +6.2222 -0.1111 -0.7778 +0.8889 -0.2222 +10.7778 +0.1111 -0.2222 +0.1111 +3.5556 +3.5556 +1.2222 +0.5556 -0.7778 x = Inv * b +1.0000 +1.0000 +1.4444 +10.5556 +7.1111 The coefficients a, b, c, d, e, of the curve are : +1.00x**2 +1.00y**2 +1.44x +10.56y +7.11 = 0 Press return to continue. Copy and paste in Octave: function xy = f (x,y) xy = +0.999999988*x^2 +1.000000219*y^2 +1.444445879*x +10.555557922*y +7.111111809; endfunction f (+1,-1) f (+2,-9) f (+3,-8)