Linear Algebra and the C Language/a0b8
Install and compile this file in your working directory.
/* ------------------------------------ */
/* 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;
}
/* ------------------------------------ */
/* ------------------------------------ */
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.