Linear Algebra and the C Language/a0b9
Install and compile this file in your working directory.
/* ------------------------------------ */
/* 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;
}
/* ------------------------------------ */
/* ------------------------------------ */
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.