Linear Algebra and the C Language/a0b8

__NOTOC__ Install and compile this file in your working directory. thumb| /* ------------------------------------ */ /* Save as : c00b.c */ /* ------------------------------------ */ #include "v_a.h" /* ------------------------------------ */ /* ------------------------------------ */ #define RA R8 #define CA C6 #define Cb C1 /* ------------------------------------ */ int main(void) { double ta[RA*(CA+Cb)]={ // I1 I2 I3 I4 I5 I6 +1, -1, -1, +0, +0, +0, +0, +0, +1, -1, -1, +0, +0, +1, +0, +0, +1, -1, -1, +0, +0, +1, +0, +1, +0, -50, +0, +0, +0, -20, +0, +50, -20, +0, -10, +0, +0, +0, +0, -50, +10, +20, +0, +0, -20, -50, +0, +0, }; double tb[RA*(CA+Cb)]={ 0, 0, 0, 0, -90, 0, 0, -90, }; 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"); stop(); clrscrn(); 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,P3, C6); invgj_mR(R,invR); printf(" invR :"); pE_mR(invR,S9,P3, 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,P4 ,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,-1,+0,+0,+0; +0,+0,+1,-1,-1,+0; +0,+1,+0,+0,+1,-1; -1,+0,+0,+1,+0,+1; +0,-50,+0,+0,+0,-20; +0,+50,-20,+0,-10,+0; +0,+0,+0,-50,+10,+20; +0,+0,-20,-50,+0,+0] [Q, R] = qr (a,0) Press return to continue. Q : +0.7071 -0.0071 -0.0245 +0.0259 +0.1704 +0.4687 +0.0000 +0.0000 +0.0408 -0.0460 -0.8338 -0.2257 +0.0000 +0.0141 +0.0081 -0.0057 +0.4931 -0.7117 -0.7071 -0.0071 -0.0245 +0.0259 +0.1704 +0.4687 +0.0000 -0.7070 -0.4073 +0.2866 -0.0253 -0.0385 +0.0000 +0.7070 -0.4080 +0.2872 -0.0317 -0.0149 +0.0000 +0.0000 +0.0000 -0.8645 +0.0386 +0.0337 +0.0000 +0.0000 -0.8153 -0.2908 -0.0185 -0.0198 R : +1.4142 -0.7071 -0.7071 -0.7071 +0.0000 -0.7071 +0.0000 +70.7213 -14.1329 -0.0071 -7.0559 +14.1188 +0.0000 -0.0000 +24.5308 +40.6999 +4.0472 +8.1139 +0.0000 +0.0000 +0.0000 +57.8362 -11.4767 -22.9897 +0.0000 +0.0000 +0.0000 -0.0000 +2.0299 +0.9540 +0.0000 -0.0000 +0.0000 -0.0000 -0.0000 +2.6246 Press return to continue. Q_T : +7.071e-01 +0.000e+00 +0.000e+00 -7.071e-01 +0.000e+00 +0.000e+00 -7.070e-03 +0.000e+00 +1.414e-02 -7.070e-03 -7.070e-01 +7.070e-01 -2.446e-02 +4.077e-02 +8.146e-03 -2.446e-02 -4.073e-01 -4.080e-01 +2.585e-02 -4.598e-02 -5.731e-03 +2.585e-02 +2.866e-01 +2.872e-01 +1.704e-01 -8.338e-01 +4.931e-01 +1.704e-01 -2.528e-02 -3.174e-02 +4.687e-01 -2.257e-01 -7.117e-01 +4.687e-01 -3.854e-02 -1.493e-02 +0.000e+00 +0.000e+00 +0.000e+00 +0.000e+00 +0.000e+00 -8.153e-01 -8.645e-01 -2.908e-01 +3.855e-02 -1.847e-02 +3.368e-02 -1.979e-02 invR : +7.071e-01 +7.070e-03 +2.446e-02 -8.564e-03 -7.260e-02 +2.824e-02 +0.000e+00 +1.414e-02 +8.146e-03 -5.731e-03 +5.057e-04 -1.516e-01 +0.000e+00 +0.000e+00 +4.077e-02 -2.869e-02 -2.435e-01 -2.888e-01 -0.000e+00 -0.000e+00 -0.000e+00 +1.729e-02 +9.775e-02 +1.159e-01 -0.000e+00 -0.000e+00 -0.000e+00 +0.000e+00 +4.926e-01 -1.791e-01 -0.000e+00 -0.000e+00 -0.000e+00 +0.000e+00 -0.000e+00 +3.810e-01 Press return to continue. Solving this system yields a unique least squares solution, namely x = invR * Q_T * b : +3.0000 +1.0000 +2.0000 +1.0000 +1.0000 +2.0000 Press return to continue.