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fun(rp_I(R2)+R2);
} while(stop_w());
return 0;
/* ------------------------------------ */
Si i est différent de j alors :
<Orth_Normal_T(i), orth_Normal(j)> == 0
Orth_Normal * Orth_Normal_T == ID :
+0.5065 -0.1560 -0.1689 -0.8310 +0.5065 -0.3618 +0.4341 -0.6512
-0.3618 -0.9212 +0.1234 -0.0727 -0.1560 -0.9212 -0.0582 +0.3517
+0.4341 -0.0582 +0.8941 +0.0939 * -0.1689 +0.1234 +0.8941 +0.3961 ==
-0.6512 +0.3517 +0.3961 -0.5434 -0.8310 -0.0727 +0.0939 -0.5434
+1.0000 +0.0000 -0.0000 +0.0000
+0.0000 +1.0000 -0.0000 +0.0000
-0.0000 -0.0000 +1.0000 -0.0000
+0.0000 +0.0000 -0.0000 +1.0000
Exemple de sortie écran :
U :
+7.0000 -4.0000 -3.0000 -7.0000
-5.0000 -3.0000 -9.0000 +1.0000
+6.0000 -3.0000 +7.0000 +7.0000
-9.0000 +6.0000 +7.0000 -9.0000
Orth :
+7.0000 -0.8848 -1.4231 -9.3842
-5.0000 -5.2251 +1.0399 -0.8205
+6.0000 -0.3298 +7.5346 +1.0598
-9.0000 +1.9948 +3.3385 -6.1365
Press return to continue.
-------------------------------
Orth_Normal :
+0.5065 -0.1560 -0.1689 -0.8310
-0.3618 -0.9212 +0.1234 -0.0727
+0.4341 -0.0582 +0.8941 +0.0939
-0.6512 +0.3517 +0.3961 -0.5434
Orth_Normal_T :
+0.5065 -0.3618 +0.4341 -0.6512
-0.1560 -0.9212 -0.0582 +0.3517
-0.1689 +0.1234 +0.8941 +0.3961
-0.8310 -0.0727 +0.0939 -0.5434
Orth_Normal_T * Orth_Normal :
+1.0000 +0.0000 -0.0000 +0.0000
+0.0000 +1.0000 -0.0000 +0.0000
-0.0000 -0.0000 +1.0000 -0.0000
+0.0000 +0.0000 -0.0000 +1.0000
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Mathc matrices/a233
Application
Installer et compiler ces fichiers dans votre répertoire de travail.
/* Save as : c01a.c */
void fun(int r)
double **u = r_mR( i_mR(r,C1),9.);
double **v = r_mR( i_mR(r,C1),9.);
double **umnsv = sub_mR(u, v, i_mR(r,C1) );
clrscrn();
printf(" u :");
p_mR(u,S3,P0,C6);
printf(" v :");
p_mR(v,S3,P0,C6);
printf(" ||u||^2 + ||v||^2 - ||u - v||^2 = %.0f \n\n",
pow(norm_uv_R( u),2.)
+ pow(norm_uv_R( v),2.)
- pow(norm_uv_R(umnsv),2.));
printf(" 2 * <u,v> = %.0f \n\n", 2 * dot_uv_R(u,v) );
f_mR(u);
f_mR(v);
f_mR(umnsv);
/* ------------------------------------ */
int main(void)
time_t t;
srand(time(&t));
do
fun(rp_I(R3)+R2);
} while(stop_w());
return 0;
/* ------------------------------------ */
Nous vérifions une des propriétés de la norme : norm_uv_R(u);
Exemple de sortie écran :
u :
+6
-2
+9
-3
+7
v :
+1
-6
-1
+5
+7
||u||^2 + ||v||^2 - ||u - v||^2 = 86
2 * <u,v> = 86
Press return to continue
Press X return to stop