Mathc matrices/07m
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c00d.c |
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/* ------------------------------------ */
/* Xave as : c00d.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
/* ------------------------------------ */
#define FACTOR_E +1.E-2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double ta[RA*CA]={
/* x**2 y**2 x y e */
+1, +0, +0, +0, +0,
+1, +16, +1, +4, +1,
+4, +25, +2, +5, +1,
+9, +49, +3, -7, +1,
+16, +25, +4, +5, +1,
};
double tb[RA*C1]={
/* = 0 */
+1,
+0,
+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
+1.00 +16.00 +1.00 +4.00 +1.00
+4.00 +25.00 +2.00 +5.00 +1.00
+9.00 +49.00 +3.00 -7.00 +1.00
+16.00 +25.00 +4.00 +5.00 +1.00
b :
+1.00
+0.00
+0.00
+0.00
+0.00
Press return to continue.
U :
+0.0038 +0.0524 +0.0822 +0.3335 -0.9377
+0.2443 +0.0601 -0.6059 +0.7251 +0.2091
+0.3913 +0.1571 -0.6311 -0.5979 -0.2576
+0.7709 -0.5601 +0.3010 +0.0351 +0.0107
+0.4391 +0.8095 +0.3705 +0.0649 +0.1026
V :
+0.2441 +0.6734 -0.6777 +0.0840 -0.1436
+0.9661 -0.1805 +0.1773 -0.0138 -0.0492
+0.0788 +0.1504 -0.0627 -0.4203 +0.8892
-0.0041 +0.7001 +0.7075 -0.0408 -0.0875
+0.0286 +0.0363 +0.0686 +0.9025 +0.4228
Press return to continue.
U_TAV :
+64.6364 +0.0000 +0.0000 -0.0000 +0.0000
+0.0000 +12.8479 +0.0000 -0.0000 +0.0000
-0.0000 +0.0000 -8.2453 +0.0000 +0.0000
-0.0000 -0.0000 -0.0000 +0.2518 +0.0000
-0.0000 -0.0000 +0.0000 +0.0000 +0.1531
inv(U_TAV) :
+1.5471e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +7.7834e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 -1.2128e-01 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +3.9718e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 +6.5301e+00
Pinv = V * inv(U_TAV) * U_T:
+1.0000e+00 -4.7052e-10 +3.8688e-10 -2.2504e-11 -4.1605e-11
+2.8030e-01 -9.0909e-02 +1.3258e-01 +7.5758e-03 -4.9242e-02
-6.0000e+00 +2.9160e-09 -5.0000e-01 +1.3977e-10 +5.0000e-01
+4.7727e-01 -1.8182e-01 +3.0682e-01 -6.8182e-02 -5.6818e-02
-1.3939e+00 +3.1818e+00 -2.8485e+00 +1.5152e-01 +5.1515e-01
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
+1.0000
+0.2803
-6.0000
+0.4773
-1.3939
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +0.28y**2 -6.00x +0.48y -1.39 = 0
Press return to continue.