Linear Algebra and the C Language/a0ju

__NOTOC__ Install and compile this file in your working directory. /* ------------------------------------ */ /* Save as : c00a.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ /* ------------------------------------ */ #define RA R3 #define CA C3 #define CXY C2 /* ------------------------------------ */ int main(void) { double tA[RA*CA]={ /* x**2 x**1 x**0 */ +1, +1, +1, +4, +2, +1, +9, +3, +1, }; double tb[RA*C1]={ /* y */ 6, 3, 5 }; double xy[RA*CXY] = {1, 6, 2, 3, 3, 5 }; double **XY = ca_A_mR(xy,i_mR(RA,CXY)); 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(" Fitting a linear Curve to Data :\n\n"); printf(" x y \n"); p_mR(XY,S5,P0,C6); printf(" A :\n x**2 x**1 x**0"); p_mR(A,S6,P2,C7); printf(" b :\n y "); p_mR(b,S6,P2,C7); stop(); clrscrn(); printf(" Inv : "); invgj_mR(A,Inv); pE_mR(Inv,S12,P4,C10); printf(" x = Inv * b "); mul_mR(Inv,b,Invb); p_mR(Invb,S10,P4,C10); printf("\n The coefficients a, b, c of the curve are : \n\n" " y = %+.2fx**2 %+.2fx %+.2f\n\n" ,Invb[R1][C1],Invb[R2][C1],Invb[R3][C1]); stop(); f_mR(XY); f_mR(b); f_mR(A); f_mR(Inv); f_mR(Invb); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ Presentation : Let's calculate the coefficients of a polynomial. y = ax**2 + bx + c Which passes through these three points. x[1], y[1] x[2], y[2] x[3], y[3] Using the points we obtain the matrix: x**2 x**1 x**0 y x[1]**2 x[1]**1 x[1]**0 y[1] x[2]**2 x[2]**1 x[2]**0 y[2] x[3]**2 x[3]**1 x[3]**0 y[3] That we can write: x**2 x 1 y x[1]**2 x[1] 1 y[1] x[2]**2 x[2] 1 y[2] x[3]**2 x[3] 1 y[3] Let's use the invgj_mR() function to solve the system that will give us the coefficients a, b, c Screen output example: Fitting a linear Curve to Data : x y +1 +6 +2 +3 +3 +5 A : x**2 x**1 x**0 +1.00 +1.00 +1.00 +4.00 +2.00 +1.00 +9.00 +3.00 +1.00 b : y +6.00 +3.00 +5.00 Press return to continue. Inv : +5.0000e-01 -1.0000e+00 +5.0000e-01 -2.5000e+00 +4.0000e+00 -1.5000e+00 +3.0000e+00 -3.0000e+00 +1.0000e+00 x = Inv * b +2.5000 -10.5000 +14.0000 The coefficients a, b, c of the curve are : y = +2.50x**2 -10.50x +14.00 Press return to continue. Copy and paste in Octave: function y = f (x) y = +2.50*x^2 -10.50*x +14.00; endfunction f (+1) f (+2) f (+3)