Mathc matrices/07l
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00c.c |
|---|
/* ------------------------------------ */
/* Xave as : c00c.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, +64, +1, -8, +1,
+4, +4, +2, +2, +1,
+9, +1, +3, +1, +1,
+16, +4, +4, +2, +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 +64.00 +1.00 -8.00 +1.00
+4.00 +4.00 +2.00 +2.00 +1.00
+9.00 +1.00 +3.00 +1.00 +1.00
+16.00 +4.00 +4.00 +2.00 +1.00
b :
+1.00
+0.00
+0.00
+0.00
+0.00
U :
+0.0006 +0.0480 +0.1301 +0.1826 -0.9734
+0.9956 -0.0821 +0.0412 -0.0204 -0.0018
+0.0609 +0.2346 -0.9600 +0.1001 -0.0980
+0.0202 +0.4835 +0.0428 -0.8640 -0.1324
+0.0688 +0.8379 +0.2407 +0.4580 +0.1595
V :
+0.0389 +0.9469 -0.2718 -0.1452 +0.0826
+0.9918 -0.0245 +0.0955 -0.0806 -0.0137
+0.0224 +0.2633 +0.3771 +0.7290 -0.5065
-0.1186 +0.1667 +0.8260 -0.5223 -0.0554
+0.0177 +0.0748 +0.3042 +0.4101 +0.8564
Press return to continue.
U_TAV :
+64.7886 +0.0000 -0.0000 +0.0000 -0.0000
-0.0000 +19.7086 +0.0000 +0.0000 -0.0000
-0.0000 -0.0000 -2.0886 -0.0000 +0.0000
-0.0000 -0.0000 -0.0000 -0.7954 +0.0000
+0.0000 -0.0000 -0.0000 -0.0000 -0.0849
inv(U_TAV) :
+1.5435e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +5.0739e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 -4.7879e-01 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 -1.2572e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 -1.1785e+01
Pinv = V * inv(U_TAV) * U_T:
+1.0000e+00 +3.2773e-15 -5.9119e-15 +1.3642e-13 -8.3211e-14
-1.4444e-01 +1.1111e-02 +3.8889e-02 -1.1111e-01 +6.1111e-02
-6.0000e+00 -2.8980e-14 -5.0000e-01 -1.2146e-12 +5.0000e-01
-5.6667e-01 -3.3333e-02 +3.8333e-01 -6.6667e-01 +3.1667e-01
+9.7111e+00 +2.2222e-02 +1.0778e+00 +1.7778e+00 -1.8778e+00
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
+1.0000
-0.1444
-6.0000
-0.5667
+9.7111
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 -0.14y**2 -6.00x -0.57y +9.71 = 0
Press return to continue.