Linear Algebra and the C Language/a07t

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00a.c */ /* ------------------------------------ */ #include "v_a.h" #include "dcircle.h" /* ------------------------------------ */ int main(void) { double xy[6] ={ 1, -2, 2, -3, 3, 6 }; double **XY = ca_A_mR(xy,i_mR(R3,C2)); double **A = i_mR(R5,C5); double **b = i_mR(R5,C1); double **Ab = i_Abr_Ac_bc_mR(R5,C5,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); printf("\n"); printf(" Using the given XY, we obtain this matrix.\n"); printf(" (a = 1. This is my choice)\n\n"); printf(" x**2 y**2 x y "); i_A_b_with_XY_mR(XY,A,b); c_A_b_Ab_mR(A,b,Ab); p_mR(Ab,S7,P2,C6); stop(); clrscrn(); printf(" The Gauss Jordan process will reduce this matrix to : \n"); gj_TP_mR(Ab); p_mR(Ab,S7,P2,C6); printf(" The coefficients a, b, c, d, e, of the curve are : \n\n"); p_eq_circle_mR(Ab); stop(); clrscrn(); printf(" x y \n"); p_mR(XY,S5,P0,C6); printf("\n"); printf(" Verify the result : \n\n"); verify_XY_mR(Ab,XY[R1][C1],XY[R1][C2]); verify_XY_mR(Ab,XY[R2][C1],XY[R2][C2]); verify_XY_mR(Ab,XY[R3][C1],XY[R3][C2]); printf("\n\n\n"); stop(); f_mR(XY); f_mR(A); f_mR(b); f_mR(Ab); 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 -2 +2 -3 +3 +6 Using the given XY, we obtain this matrix. (a = 1. This is my choice) x**2 y**2 x y +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 +1.00 +4.00 +1.00 -2.00 +1.00 +0.00 +4.00 +9.00 +2.00 -3.00 +1.00 +0.00 +9.00 +36.00 +3.00 +6.00 +1.00 +0.00 Press return to continue. The Gauss Jordan process will reduce this matrix to : +1.00 +0.00 +0.00 +0.00 +0.00 +1.00 +0.00 +1.00 +0.00 +0.00 +0.00 +1.00 -0.00 -0.00 +1.00 -0.00 -0.00 -10.40 +0.00 +0.00 +0.00 +1.00 +0.00 -2.40 +0.00 +0.00 +0.00 +0.00 +1.00 +0.60 The coefficients a, b, c, d, e, of the curve are : +1.00x**2 +1.00y**2 -10.40x -2.40y +0.60 = 0 Press return to continue. x y +1 -2 +2 -3 +3 +6 Verify the result : With x = +1.0, y = -2.0 p = ax**2 + ay**2 + cx+ dy + e = +0.00000 With x = +2.0, y = -3.0 p = ax**2 + ay**2 + cx+ dy + e = +0.00000 With x = +3.0, y = +6.0 p = ax**2 + ay**2 + cx+ dy + e = -0.00000 Press return to continue. Copy and paste in Octave: function xy = f (x,y) xy = +1.00*x^2 +1.00*y^2 -10.40*x -2.40*y +0.60; endfunction f (+1,-2) f (+2,-3) f (+3,+6)