Mathc complexes/074
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c00c.c |
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/* ------------------------------------ */
/* Xave as : c00c.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RA R4
#define CA C4
#define Cb C1
/* ------------------------------------ */
#define FACTOR_E +1.E-2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double ta[RA*CA]={
/* x**3 x**2 x**1 x**0 */
-125, +25, -5, +1,
-8, +4, -2, +1,
+8, +4, +2, +1,
+27, +9, +3, +1,
};
double tb[RA*C1]={
/* y */
-3.00 ,
+0.00,
+3.00,
-2.00,
};
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);
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,P3, C6);
printf(" The coefficients a, b, c, d of the curve are : \n\n"
" y = %+.3fx**3 %+.3fx**2 %+.3fx %+.3f\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][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 :
-125.00 +25.00 -5.00 +1.00
-8.00 +4.00 -2.00 +1.00
+8.00 +4.00 +2.00 +1.00
+27.00 +9.00 +3.00 +1.00
b :
-3.00
+0.00
+3.00
-2.00
U :
-0.9775 +0.1872 +0.0836 +0.0502
-0.0664 +0.1549 -0.9338 -0.3157
+0.0556 +0.3659 +0.3479 -0.8614
+0.1925 +0.8984 +0.0019 +0.3948
V :
-0.9837 +0.1662 +0.0633 -0.0265
+0.1743 +0.9701 +0.1068 -0.1310
-0.0438 +0.1425 -0.9665 +0.2091
+0.0061 +0.1049 +0.2248 +0.9687
Press return to continue.
U_TAV :
-130.4844 +0.0000 -0.0000 -0.0000
+0.0000 +15.3066 -0.0000 -0.0000
-0.0000 -0.0000 -2.2259 +0.0000
-0.0000 +0.0000 -0.0000 -0.7558
inv(U_TAV) :
-7.6638e-03 +0.0000e+00 +0.0000e+00 +0.0000e+00
+0.0000e+00 +6.5331e-02 +0.0000e+00 +0.0000e+00
+0.0000e+00 +0.0000e+00 -4.4926e-01 +0.0000e+00
+0.0000e+00 +0.0000e+00 +0.0000e+00 -1.3231e+00
Pinv = V * inv(U_TAV) * U_T:
-5.9524e-03 +1.6667e-02 -3.5714e-02 +2.5000e-02
+1.7857e-02 -2.4321e-14 -1.4286e-01 +1.2500e-01
+2.3810e-02 -3.1667e-01 +3.9286e-01 -1.0000e-01
-7.1429e-02 +5.0000e-01 +1.0714e+00 -5.0000e-01
Press return to continue.
A x = b
Pinv A x = Pinv b
Ide x = Pinv b
x = Pinv b
-0.139
-0.732
+1.307
+4.429
The coefficients a, b, c, d of the curve are :
y = -0.139x**3 -0.732x**2 +1.307x +4.429
Press return to continue.