Mathc matrices/c22r
Application ou QR décomposition
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
void fun(int r)
{
double **A = i_mR(r,r);
double **b = i_mR(r,C1);
double **Ab = i_Abr_Ac_bc_mR(r,r,C1);
double **Q = i_mR(r,r);
double **R = i_mR(r,r);
double **Q_T = i_mR(r,r);
double **invR = i_mR(r,r);
double **invR_Q_T = i_mR(r,r);
double **x = i_mR(r,C1); // x invR * Q_T * b
do
{
r_mR(A,999.);
printf(".");
}while(!det_R(A));
clrscrn();
printf(" A :");
p_mR(A,S8,P0,C7);
printf(" b :");
r_mR(b,999.);
p_mR(b,S8,P0,C7);
printf(" Ab :");
c_A_b_Ab_mR(A,b,Ab);
p_mR(Ab,S8,P0,C7);
stop();
clrscrn();
QR_mR(A,Q,R);
printf(" Q :");
p_mR(Q,S3,P4,C6);
printf(" R :");
p_mR(R,S10,P4,C6);
stop();
clrscrn();
transpose_mR(Q,Q_T);
printf(" Q_T :");
pE_mR(Q_T,S3,P4,C6);
inv_mR(R,invR);
printf(" invR :");
pE_mR(invR,S10,P4,C6);
stop();
clrscrn();
printf(" Copy/Past into the octave window.\n\n");
p_Octave_mR(Ab,"Ab",P0);
printf(" rref(Ab,.00000000001)\n\n");
stop();
clrscrn();
printf(" gj_TP_mR(Ab) :");
gj_TP_mR(Ab);
p_mR(Ab,S10,P4,C7);
mul_mR(invR,Q_T,invR_Q_T);
mul_mR(invR_Q_T,b,x);
printf(" x = invR * Q_T * b :");
p_mR(x,S10,P4,C6);
f_mR(A);
f_mR(b);
f_mR(Ab);
f_mR(Q);
f_mR(Q_T);
f_mR(R);
f_mR(invR);
f_mR(invR_Q_T);
f_mR(x);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun(rp_I(RC5)+R1);
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
On obtient le même résultat qu'avec la méthode de gauss jordan Exemple de sortie écran :
-----------------------------------
A :
+303 +668 +458 +849 +842
+160 -201 +648 -117 -704
+531 +986 -696 +611 -443
-153 -265 -901 -208 -589
-306 +39 +119 -82 +364
b :
-393
+296
+381
-64
-477
Ab :
+303 +668 +458 +849 +842 -393
+160 -201 +648 -117 -704 +296
+531 +986 -696 +611 -443 +381
-153 -265 -901 -208 -589 -64
-306 +39 +119 -82 +364 -477
Press return to continue.
-----------------------------------
Q :
+0.4216 +0.3386 +0.4293 +0.7050 -0.1621
+0.2226 -0.5892 +0.3447 -0.2125 -0.6628
+0.7389 +0.3372 -0.4144 -0.3846 -0.1437
-0.2129 -0.0707 -0.6873 +0.4615 -0.5141
-0.4258 +0.6477 +0.2299 -0.3112 -0.4994
R :
+718.6202 +1005.2890 -35.7393 +862.6031 -158.6568
+0.0000 +721.0832 -320.6643 +524.0055 +827.8365
+0.0000 -0.0000 +1354.9698 +195.0440 +790.8400
+0.0000 +0.0000 -0.0000 +317.9480 +528.4995
-0.0000 +0.0000 +0.0000 +0.0000 +514.8021
Press return to continue.
-----------------------------------
Q_T :
+4.2164e-01 +2.2265e-01 +7.3892e-01 -2.1291e-01 -4.2582e-01
+3.3856e-01 -5.8915e-01 +3.3724e-01 -7.0680e-02 +6.4773e-01
+4.2926e-01 +3.4469e-01 -4.1436e-01 -6.8730e-01 +2.2988e-01
+7.0502e-01 -2.1251e-01 -3.8461e-01 +4.6154e-01 -3.1119e-01
-1.6211e-01 -6.6284e-01 -1.4371e-01 -5.1407e-01 -4.9944e-01
invR :
+1.3916e-03 -1.9400e-03 -4.2242e-04 -3.1889e-04 +4.5248e-03
+0.0000e+00 +1.3868e-03 +3.2820e-04 -2.4869e-03 -1.8118e-04
+0.0000e+00 -0.0000e+00 +7.3802e-04 -4.5274e-04 -6.6897e-04
+0.0000e+00 -0.0000e+00 +0.0000e+00 +3.1452e-03 -3.2289e-03
-0.0000e+00 +0.0000e+00 -0.0000e+00 -0.0000e+00 +1.9425e-03
Press return to continue.
-----------------------------------
Copy/Past into the octave window.
Ab=[
+303,+668,+458,+849,+842,-393;
+160,-201,+648,-117,-704,+296;
+531,+986,-696,+611,-443,+381;
-153,-265,-901,-208,-589,-64;
-306,+39,+119,-82,+364,-477]
rref(Ab,.00000000001)
Press return to continue.
-----------------------------------
gj_TP_mR(Ab) :
+1.0000 -0.0000 -0.0000 +0.0000 -0.0000 +2.1117
+0.0000 +1.0000 +0.0000 +0.0000 +0.0000 +0.1334
+0.0000 +0.0000 +1.0000 +0.0000 +0.0000 -0.1039
+0.0000 +0.0000 +0.0000 +1.0000 +0.0000 -1.4271
-0.0000 +0.0000 +0.0000 +0.0000 +1.0000 +0.1630
x = invR * Q_T * b :
+2.1117
+0.1334
-0.1039
-1.4271
+0.1630
Press return to continue
Press X to stop