Linear Algebra and the C Language/a0b3

__NOTOC__ Install and compile this file in your working directory. thumb| /* ------------------------------------ */ /* Save as : c00a.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ /* ------------------------------------ */ #define RA R4 #define CA C3 #define Cb C1 /* ------------------------------------ */ /* ------------------------------------ */ int main(void) { double ta[RA*(CA+Cb)]={ // x1 x2 x3 +1, +1, +0,// A +0, -1, -1,// B +0, +0, +1,// C -1, +0, +0 // D }; double tb[RA*(CA+Cb)]={ +50, // A -40, // B +20 -10, // C -30 +10 // D }; double **A = ca_A_mR(ta,i_mR(RA,CA)); double **b = ca_A_mR(tb,i_mR(RA,Cb)); double **Q = i_mR(RA,CA); double **Q_T = i_mR(CA,RA); double **R = i_mR(CA,CA); double **invR = i_mR(CA,CA); double **invR_Q_T = i_mR(CA,RA); double **x = i_mR(CA,C1); clrscrn(); printf(" Copy/Paste into the octave windows \n\n"); p_Octave_mR(A,"a",P0); printf(" [Q, R] = qr (a,0) \n\n"); QR_mR(A,Q,R); printf(" Q :"); p_mR(Q, S10,P4, C10); printf(" R :"); p_mR(R, S10,P4, C10); stop(); clrscrn(); transpose_mR(Q,Q_T); printf(" Q_T :"); pE_mR(Q_T,S9,P5, C3); invgj_mR(R,invR); printf(" invR :"); pE_mR(invR,S9,P5, C6); stop(); clrscrn(); printf(" Solving this system yields a unique\n" " least squares solution, namely \n\n"); mul_mR(invR,Q_T,invR_Q_T); mul_mR(invR_Q_T,b,x); printf(" x = invR * Q_T * b :"); p_mR(x,S9,P5 ,C6); stop(); f_mR(A); f_mR(b); f_mR(Q); f_mR(Q_T); f_mR(R); f_mR(invR); f_mR(x); return 0; } /* ------------------------------------ */ /* ------------------------------------ */ thumb| Screen output example: Copy/Paste into the octave windows a=[ +1,+1,+0; +0,-1,-1; +0,+0,+1; -1,+0,+0] [Q, R] = qr (a,0) Q : +0.7071 +0.4082 -0.2887 +0.0000 -0.8165 -0.2887 +0.0000 +0.0000 +0.8660 -0.7071 +0.4082 -0.2887 R : +1.4142 +0.7071 +0.0000 +0.0000 +1.2247 +0.8165 +0.0000 +0.0000 +1.1547 Press return to continue. Q_T : +7.07107e-01 +0.00000e+00 +0.00000e+00 +4.08248e-01 -8.16497e-01 +0.00000e+00 -2.88675e-01 -2.88675e-01 +8.66025e-01 -7.07107e-01 +4.08248e-01 -2.88675e-01 invR : +7.07107e-01 -4.08248e-01 +2.88675e-01 -0.00000e+00 +8.16497e-01 -5.77350e-01 -0.00000e+00 -0.00000e+00 +8.66025e-01 Press return to continue. Solving this system yields a unique least squares solution, namely x = invR * Q_T * b : +20.00000 +30.00000 +10.00000 Press return to continue.