Mathc matrices/07g
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00b.c |
|---|
/* ------------------------------------ */
/* Xave as : c00b.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
/* ------------------------------------ */
#define FACTOR_E +0.5E-1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double ta[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+0, +1, +0, +0, +0,
+1, +1, +1, -1, +1,
+4, +81, +2, -9, +1,
+9, +64, +3, -8, +1,
};
double tb[RA*C1]={
/* b */
+1,
+1,
+0,
+0,
+0,
};
double **A = ca_A_mRZ(ta,i_mZ(RA,CA));
double **A_T = ctranspose_mZ(A, i_mZ(CA,RA));
double **b = ca_A_mRZ(tb, i_mZ(RA,C1));
double **x = i_mZ(CA,C1);
double **V = i_mZ(CA,CA);
double **V_T = i_mZ(CA,CA);
double **U = i_mZ(RA,CA);
double **U_T = i_mZ(CA,RA);
double **U_TA = i_mZ(CA,CA); // CA,RA RA,CA :CA,CA
double **U_TAV = i_mZ(CA,CA); // CA,CA CA,CA :CA,CA
double **invU_TAV = i_mZ(CA,CA); // :CA,CA
double **V_invU_TAV = i_mZ(CA,CA); // CA,CA CA,CA :CA,CA
double **Pinv = i_mZ(CA,RA);
// Pinv = V_invU_TAV * U_T // CA,CA CA,RA :CA,RA
clrscrn();
printf(" A :");
p_mRZ(A, S10,P2, C6);
printf(" b :");
p_mRZ(b, S10,P2, C6);
stop();
clrscrn();
printf(" U :");
X_U_mZ(A_T,U,FACTOR_E);
p_mRZ(U, S10,P4, C6);
printf(" V :");
X_V_mZ(A_T,V,FACTOR_E);
p_mRZ(V, S10,P4, C6);
ctranspose_mZ(U,U_T);
ctranspose_mZ(V,V_T);
stop();
clrscrn();
printf(" U_TAV :");
mul_mZ(U_T, A, U_TA); // U_TA CA,RA RA,CA :CA,CA
mul_mZ(U_TA, V, U_TAV ); // V :CA,CA
p_mRZ(U_TAV, S11,P4, C6); // U_TAV CA,CA CA,CA :CA,CA
printf(" inv(U_TAV) :");
X_inv_mZ(U_TAV, invU_TAV);
pE_mRZ(invU_TAV, S10,P4, C6);
printf(" Pinv = V * inv(U_TAV) * U_T:");
mul_mZ(V, invU_TAV, V_invU_TAV);
mul_mZ(V_invU_TAV, U_T, Pinv);
pE_mRZ(Pinv, S13,P4, C6);
stop();
clrscrn();
printf(" A x = b \n"
" Pinv A x = Pinv b \n"
" Ide x = Pinv b \n\n"
" x = Pinv b ");
mul_mZ(Pinv, b, x);
p_mRZ(x, S12,P4, C6);
printf(" The coefficients a, b, c, d, e, of the curve are : \n\n"
" %+.2fx**2 %+.2fy**2 %+.2fx %+.2fy %+.2f = 0\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][C1],x[R5][C1]);
stop();
f_mZ(A);
f_mZ(A_T);
f_mZ(b);
f_mZ(x);
f_mZ(V);
f_mZ(V_T);
f_mZ(U);
f_mZ(U_T);
f_mZ(U_TA);
f_mZ(invU_TAV);
f_mZ(V_invU_TAV);
f_mZ(Pinv);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
A :
+1.00 +0.00 +0.00 +0.00 +0.00
+0.00 +1.00 +0.00 +0.00 +0.00
+1.00 +1.00 +1.00 -1.00 +1.00
+4.00 +81.00 +2.00 -9.00 +1.00
+9.00 +64.00 +3.00 -8.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Press return to continue.
U :
+0.0008 +0.1880 +0.2090 -0.9487 -0.1445
+0.0095 -0.0218 +0.0431 -0.1453 +0.9882
+0.0118 +0.2675 -0.9498 -0.1599 +0.0237
+0.7815 -0.5917 -0.1341 -0.1408 -0.0354
+0.6237 +0.7365 +0.1851 +0.1829 +0.0290
V :
+0.0839 +0.9418 -0.2852 +0.1569 -0.0110
+0.9891 -0.1090 -0.0588 +0.0240 +0.0754
+0.0330 +0.2583 +0.4857 -0.6481 +0.5256
-0.1153 -0.1665 -0.4952 +0.2185 +0.8161
+0.0136 +0.0823 +0.6588 +0.7121 +0.2279
Press return to continue.
U_TAV :
+104.3744 -0.0000 -0.0000 +0.0000 -0.0000
+0.0000 +5.0091 -0.0000 +0.0000 -0.0000
+0.0000 +0.0000 -1.3642 -0.0000 +0.0000
+0.0000 +0.0000 -0.0000 -0.1654 +0.0000
+0.0000 -0.0000 -0.0000 -0.0000 +0.0763
inv(U_TAV) :
+9.5809e-03 +0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +1.9964e-01 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 -7.3301e-01 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 -6.0465e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 +1.3107e+01
Pinv = V * inv(U_TAV) * U_T:
+1.0000e+00 -1.8424e-09 +8.3717e-10 +6.9737e-10 -8.6707e-10
-3.5773e-08 +1.0000e+00 -6.0148e-09 -5.2960e-09 +6.8851e-09
-4.7778e+00 +6.2222e+00 -1.1111e-01 -7.7778e-01 +8.8889e-01
-2.2222e-01 +1.0778e+01 +1.1111e-01 -2.2222e-01 +1.1111e-01
+3.5556e+00 +3.5556e+00 +1.2222e+00 +5.5556e-01 -7.7778e-01
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
+1.0000
+1.0000
+1.4444
+10.5556
+7.1111
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +1.00y**2 +1.44x +10.56y +7.11 = 0
Press return to continue.