Mathc matrices/07i
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00d.c |
|---|
/* ------------------------------------ */
/* Xave as : c00d.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, +0, +0, +0, +0,
+0, +1, +0, +0, +0,
+100, +100, +10, +10, +1,
+25, +1, -5, +1, +1,
+49, +100, +7, -10, +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
+100.00 +100.00 +10.00 +10.00 +1.00
+25.00 +1.00 -5.00 +1.00 +1.00
+49.00 +100.00 +7.00 -10.00 +1.00
b :
+1.00
+1.00
+0.00
+0.00
+0.00
Press return to continue.
U :
+0.0035 -0.0200 +0.0231 +0.6774 -0.7350
+0.0044 +0.0159 -0.0112 -0.7348 -0.6780
+0.7881 -0.4915 -0.3706 -0.0028 +0.0028
+0.0893 -0.5038 +0.8585 -0.0332 +0.0106
+0.6090 +0.7099 +0.3536 +0.0100 +0.0039
V :
+0.6200 +0.7350 +0.2013 -0.1860 -0.0128
+0.7817 -0.5818 -0.0978 +0.2018 -0.0118
+0.0654 -0.0701 -0.6345 -0.7551 +0.1343
+0.0105 +0.3410 -0.7334 +0.5878 +0.0125
+0.0083 +0.0078 +0.0967 +0.0950 +0.9907
Press return to continue.
U_TAV :
+178.8405 +0.0000 -0.0000 -0.0000 -0.0000
+0.0000 -36.7046 +0.0000 -0.0000 +0.0000
+0.0000 +0.0000 +8.7038 +0.0000 -0.0000
-0.0000 +0.0000 +0.0000 -0.2746 -0.0000
-0.0000 +0.0000 +0.0000 +0.0000 +0.0174
inv(U_TAV) :
+5.5916e-03 +0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 -2.7245e-02 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +1.1489e-01 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 -3.6411e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 +5.7478e+01
Pinv = V * inv(U_TAV) * U_T:
+1.0000e+00 +3.2235e-09 -1.3650e-11 -5.1886e-11 -1.8080e-11
-3.7958e-09 +1.0000e+00 +1.4570e-11 +5.3499e-11 +2.0450e-11
-3.8132e+00 -7.2527e+00 +4.0293e-02 -7.3260e-02 +3.2967e-02
-1.9780e+00 +1.0879e+00 +4.3956e-02 +1.0989e-02 -5.4945e-02
-4.2088e+01 -3.8352e+01 +1.5751e-01 +6.2271e-01 +2.1978e-01
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
+1.0000
+1.0000
-11.0659
-0.8901
-80.4396
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +1.00y**2 -11.07x -0.89y -80.44 = 0
Press return to continue.