Linear Algebra and the C Language/a0b9

__NOTOC__ Install and compile this file in your working directory. thumb| /* ------------------------------------ */ /* Save as : c00c.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, +0, +0, -1, +1, +1, +1, -1, +0, +0, +0, -1, +15, +60, +0, +0, +0, +0, +0, -60, +15, +15, +0, +15, +0, +0, +0, -15, -60, +0, +15, +0, +15, +0, -60, +15 }; double tb[RA*(CA+Cb)]={ +0, +0, +0, +0, +90, +0, -90, +0 }; 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,+0,+0,-1,+1,+1; +1,-1,+0,+0,+0,-1; +15,+60,+0,+0,+0,+0; +0,-60,+15,+15,+0,+15; +0,+0,+0,-15,-60,+0; +15,+0,+15,+0,-60,+15] [Q, R] = qr (a,0) Press return to continue. Q : -0.0470 +0.0406 +0.8125 +0.0160 -0.1464 -0.2537 +0.0000 +0.0000 -0.3633 +0.0631 -0.7414 +0.2537 +0.0000 +0.0000 +0.0000 -0.0575 +0.5581 +0.6597 +0.0470 -0.0406 -0.4492 -0.0216 +0.3297 -0.6597 +0.7055 +0.4103 +0.0210 +0.2881 +0.0177 +0.0101 +0.0000 -0.8151 +0.0421 +0.2888 +0.0098 +0.0169 +0.0000 +0.0000 +0.0000 -0.8625 -0.0769 -0.0101 +0.7055 -0.4049 +0.0631 -0.2856 -0.0494 +0.0169 R : +21.2603 +42.2384 +10.5361 +0.0000 -42.3324 +10.5361 -0.0000 +73.6065 -18.2596 -12.2272 +24.2920 -18.2596 -0.0000 -0.0000 +2.7528 +0.2675 -3.4216 +2.0262 -0.0000 -0.0000 -0.0000 +17.3904 +68.7702 +0.0112 -0.0000 -0.0000 +0.0000 -0.0000 +8.8776 -0.3666 -0.0000 -0.0000 -0.0000 +0.0000 +0.0000 +1.8269 Press return to continue. Q_T : -4.704e-02 +0.000e+00 +0.000e+00 +4.704e-02 +7.055e-01 +0.000e+00 +4.058e-02 +0.000e+00 +0.000e+00 -4.058e-02 +4.103e-01 -8.151e-01 +8.125e-01 -3.633e-01 +0.000e+00 -4.492e-01 +2.103e-02 +4.205e-02 +1.603e-02 +6.309e-02 -5.750e-02 -2.162e-02 +2.881e-01 +2.888e-01 -1.464e-01 -7.414e-01 +5.581e-01 +3.297e-01 +1.769e-02 +9.757e-03 -2.537e-01 +2.537e-01 +6.597e-01 -6.597e-01 +1.015e-02 +1.692e-02 +0.000e+00 +7.055e-01 +0.000e+00 -4.049e-01 +0.000e+00 +6.308e-02 -8.625e-01 -2.856e-01 -7.688e-02 -4.943e-02 -1.015e-02 +1.692e-02 invR : +4.704e-02 -2.699e-02 -3.591e-01 -1.345e-02 +2.640e-01 -8.974e-02 -0.000e+00 +1.359e-02 +9.012e-02 +8.166e-03 -6.570e-02 +2.260e-02 +0.000e+00 -0.000e+00 +3.633e-01 -5.589e-03 +1.833e-01 -3.661e-01 +0.000e+00 -0.000e+00 +0.000e+00 +5.750e-02 -4.454e-01 -8.974e-02 -0.000e+00 +0.000e+00 -0.000e+00 -0.000e+00 +1.126e-01 +2.260e-02 -0.000e+00 +0.000e+00 -0.000e+00 -0.000e+00 +0.000e+00 +5.474e-01 Press return to continue. Solving this system yields a unique least squares solution, namely x = invR * Q_T * b : +2.0000 +1.0000 +1.0000 +2.0000 +1.0000 +1.0000 Press return to continue.