Linear Algebra and the C Language/a049

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as: c00c.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ #define RA R5 #define CA C5 /* ------------------------------------ */ #define FACTOR_E +1.E-2 /* ------------------------------------ */ int main(void) { double txy[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(txy, 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 **Pinv = Pinv_Rn_mR(A, i_mR(CA,RA),FACTOR_E); double **Pinvb = mul_mR(Pinv,b, 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(" Pinv = V invS_T U_T "); pE_mR(Pinv, S12,P4,C10); stop(); clrscrn(); printf(" Pinv = V invS_T U_T "); p_mR(Pinv, S10,P4,C10); printf(" x = Pinv b "); p_mR(Pinvb, S10,P4,C10); printf(" The coefficients a, b, c, d, e, of the curve are: \n\n" " %+.2f*x^2 %+.2f*y^2 %+.2f*x %+.2f*y %+.2f = 0\n\n" ,Pinvb[R1][C1],Pinvb[R2][C1],Pinvb[R3][C1], Pinvb[R4][C1],Pinvb[R5][C1]); stop(); f_mR(xy); f_mR(A); f_mR(b); f_mR(Pinv); f_mR(Pinvb); 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 Pinv = V * invS_T * U_T +1.0000e+00 +1.7254e-09 +3.6743e-12 -6.3020e-10 -1.3827e-11 -2.1077e-10 +1.0000e+00 -2.4611e-12 +3.9388e-11 +2.1562e-12 +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. Pinv = V * invS_T * U_T +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 = Pinv * b +1.0000 +1.0000 +996.0000 +100.0000 -2097.0000 The coefficients a, b, c, d, e, of the curve are : +1.00*x^2 +1.00*y^2 +996.00*x +100.00*y -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)