Mathc matrices/07f
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c00a.c |
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/* ------------------------------------ */
/* Xave as : c00a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
/* ------------------------------------ */
#define FACTOR_E +1.E-1
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double ta[RA*CA]={
/* x**2 y**2 x y e */
+1.00, +0.00, +0.00, +0.00, +0.00,
+0.00, +1.00, +0.00, +0.00, +0.00,
+1.00, +4.00, +1.00, -2.00, +1.00,
+4.00, +9.00, +2.00, -3.00, +1.00,
+9.00, +36.00, +3.00, +6.00, +1.00
};
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 +4.00 +1.00 -2.00 +1.00
+4.00 +9.00 +2.00 -3.00 +1.00
+9.00 +36.00 +3.00 +6.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Press return to continue.
U :
+0.0064 -0.0504 -0.6941 +0.6095 -0.3796
+0.0245 -0.0028 +0.1931 -0.3510 -0.9159
+0.1010 -0.4686 +0.6238 +0.6095 -0.0980
+0.2415 -0.8426 -0.3028 -0.3643 +0.0848
+0.9648 +0.2604 +0.0102 +0.0323 +0.0148
V :
+0.2497 +0.2792 -0.9087 +0.1784 -0.0458
+0.9556 +0.0155 +0.2528 -0.1027 -0.1105
+0.0890 +0.2479 +0.0373 -0.0761 +0.9610
+0.1244 -0.9079 -0.2120 +0.2305 +0.2492
+0.0335 +0.1898 +0.2530 +0.9480 +0.0133
Press return to continue.
U_TAV :
+39.0707 +0.0000 +0.0000 -0.0000 +0.0000
+0.0000 -5.5374 -0.0000 +0.0000 -0.0000
-0.0000 -0.0000 +1.3092 -0.0000 +0.0000
-0.0000 -0.0000 +0.0000 +0.2927 -0.0000
-0.0000 -0.0000 -0.0000 +0.0000 +0.1206
inv(U_TAV) :
+2.5595e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 -1.8059e-01 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +7.6385e-01 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +3.4164e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 +8.2905e+00
Pinv = V * inv(U_TAV) * U_T:
+1.0000e+00 +8.1428e-11 +1.3765e-11 -1.0077e-11 -1.1787e-12
-2.6767e-11 +1.0000e+00 -1.7148e-11 +1.1344e-11 +1.7893e-13
-3.2000e+00 -7.2000e+00 -9.0000e-01 +8.0000e-01 +1.0000e-01
-2.0000e-01 -2.2000e+00 +1.0000e-01 -2.0000e-01 +1.0000e-01
+1.8000e+00 -1.2000e+00 +2.1000e+00 -1.2000e+00 +1.0000e-01
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
+1.0000
+1.0000
-10.4000
-2.4000
+0.6000
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +1.00y**2 -10.40x -2.40y +0.60 = 0
Press return to continue.