Mathc complexes/a301
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c00b.c |
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/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
void fun(int r,int rn)
{
double **A = i_mZ(r+rn,r);
double **b = i_mZ(r+rn,C1);
double **Ab = i_Abr_Ac_bc_mZ(r+rn,r,C1);
double **Q = i_mZ(r+rn,r);
double **R = i_mZ(r,r);
double **invR = i_mZ(r,r);
double **Q_T = i_mZ(r,r+rn);
double **invR_Q_T = i_mZ(r,r+rn);
double **x = i_mZ(r,C1); // x invR * Q_T * b
clrscrn();
printf(" Find the unique Least Squares Solution :\n\n");
printf(" A :");
p_mZ(r_mZ(A,99.),S6,P0,S4,P0,C6);
printf(" b :");
p_mZ(r_mZ(b,99.),S6,P0,S4,P0,C6);
printf(" Ab :");
c_A_b_Ab_mZ(A,b,Ab);
p_mZ(Ab,S6,P0,S4,P0,C6);
stop();
clrscrn();
QR_mZ(A,Q,R);
printf(" Q :");
p_mZ(Q,S11,P5,S9,P5,C6);
printf(" R :");
p_mZ(R,S11,P5,S9,P5,C6);
stop();
clrscrn();
ctranspose_mZ(Q,Q_T);
printf(" Q_T :");
pE_mZ(Q_T,S9,P5,S7,P5,C3);
inv_mZ(R,invR);
printf(" invR :");
pE_mZ(invR,S9,P5,S7,P5,C6);
stop();
clrscrn();
printf(" Solving this system yields a unique\n"
" least squares solution, namely \n\n");
mul_mZ(invR,Q_T,invR_Q_T);
mul_mZ(invR_Q_T,b,x);
printf(" x = invR * Q_T * b :");
p_mZ(x,S9,P5,S7,P5,C6);
stop();
clrscrn();
printf(" Copy/Past into the octave window.\n\n");
p_Octave_mZ(Ab,"Ab",P0,P0);
printf(" rref(Ab,.00000000001)\n\n");
stop();
clrscrn();
p_Octave_mZ(A,"A",P0,P0);
p_Octave_mZ(b,"b",P0,P0);
printf(" format short e;\n");
printf(" [Q, R] = qr (A,0)\n");
printf(" inv(R)*Q'*b\n\n");
printf(" x = invR * Q_T * b :");
pE_mZ(x,S9,P5,S7,P5,C6);
getchar();
f_mZ(A);
f_mZ(b);
f_mZ(Ab);
f_mZ(Q);
f_mZ(Q_T);
f_mZ(R);
f_mZ(invR);
f_mZ(invR_Q_T);
f_mZ(x);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun(R3,R2);
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Ici le nombre de lignes doit être supérieurs aux nombres de colonnes. La fonction Gauss-Jordan ne fonctionne pas dans cette situation.
Exemple de sortie écran :
Find the unique Least Squares Solution :
A :
-94.000 -7.00i +84.000 -7.00i
+35.000 +67.00i +46.000 -82.00i
+54.000 +52.00i +39.000 +77.00i
+22.000 -84.00i -39.000 +74.00i
+61.000 -58.00i +21.000 +1.00i
b :
-666.000-506.00i
-668.000+634.00i
-389.000 -45.00i
+255.000+384.00i
-934.000+476.00i
Ab :
-94.000 -7.00i +84.000 -7.00i -666.000-506.00i
+35.000 +67.00i +46.000 -82.00i -668.000+634.00i
+54.000 +52.00i +39.000 +77.00i -389.000 -45.00i
+22.000 -84.00i -39.000 +74.00i +255.000+384.00i
+61.000 -58.00i +21.000 +1.00i -934.000+476.00i
Press return to continue.
Q :
-0.504 -0.04i +0.328 -0.11i
+0.188 +0.36i +0.317 -0.35i
+0.289 +0.28i +0.320 +0.60i
+0.118 -0.45i -0.151 +0.29i
+0.327 -0.31i +0.281 -0.08i
R :
+186.665 +0.00i -61.458 -15.78i
-0.000 +0.00i +163.732 -0.00i
Press return to continue.
Q_T :
-5.036e-01-3.75e-02i +1.875e-01+3.59e-01i +2.893e-01+2.79e-01i
+3.276e-01-1.05e-01i +3.167e-01-3.48e-01i +3.199e-01+6.03e-01i
+1.179e-01-4.50e-01i +3.268e-01-3.11e-01i
-1.506e-01+2.94e-01i +2.809e-01-7.90e-02i
invR :
+5.357e-03-3.08e-20i +2.011e-03+5.16e-04i
-0.000e+00+0.00e+00i +6.108e-03+3.13e-20i
Press return to continue.
Solving this system yields a unique
least squares solution, namely
x = invR * Q_T * b :
-2.129 +2.47i
-4.495 +1.92i
Press return to continue
Press X return to stop