Mathc complexes/07y
Installer et compiler ces fichiers dans votre répertoire de travail.
|
c00f.c |
|---|
/* ------------------------------------ */
/* Save as : c00f.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
#define RXY R5
#define CXY C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double xy[RXY*CXY] ={
1, -2,
2, -2,
3, 3,
4, -9,
5, 4 };
double ab[RA*(CA+Cb)]={
/* x**4 x**3 x**2 x**1 x**0 y */
+1, +1, +1, +1, +1, -2,
+16, +8, +4, +2, +1, -2,
+81, +27, +9, +3, +1, +3,
+256, +64, +16, +4, +1, -9,
+625, +125, +25, +5, +1, +4,
};
double **XY = ca_A_mRZ(xy,i_mZ(RA,C2));
double **Ab = ca_A_mRZ(ab,i_Abr_Ac_bc_mZ(RA,CA,Cb));
double **A = c_Ab_A_mZ(Ab,i_mZ(RA,CA));
double **b = c_Ab_b_mZ(Ab,i_mZ(RA,Cb));
double **A_T = i_mZ(CA,RA);
double **A_TA = i_mZ(CA,CA); // A_T*A
double **invA_TA = i_mZ(CA,CA); // inv(A_T*A)
double **invA_TAA_T = i_mZ(CA,RA); // inv(A_T*A)*A_T
double **x = i_mZ(CA,Cb); // x = inv(A_T*A)*A_T*b
clrscrn();
printf("\n");
printf(" Find the coefficients a, b, c of the curve \n\n");
printf(" y = ax**4 + bx**3 + cx**2 + dx + e \n\n");
printf(" that passes through the points. \n\n");
printf(" x y");
p_mRZ(XY,S5,P0,C6);
printf("\n");
printf(" Using the given points, we obtain this matrix.\n");
printf(" x**4 x**3 x**2 x**1 x**0 y");
p_mRZ(Ab,S7,P2,C6);
stop();
clrscrn();
printf(" A_T :");
p_mRZ(transpose_mZ(A,A_T),S10,P2,C7);
printf(" A_TA :");
p_mRZ(mul_mZ(A_T,A,A_TA),S10,P2,C7);
stop();
clrscrn();
printf(" inv(A_TA) :");
p_mRZ(inv_mZ(A_TA,invA_TA),S10,P4,C7);
printf(" inv(A_TA)*A_T :");
p_mRZ(mul_mZ(invA_TA,A_T,invA_TAA_T),S10,P4,C7);
printf("\n x = inv(A_TA)*A_T*b :");
p_mRZ(mul_mZ(invA_TAA_T,b,x),S10,P4,C7);
stop();
clrscrn();
printf("\n x = inv(A_TA)*A_T*b :");
p_mRZ(x,S10,P2,C7);
printf("\n The coefficients a, b, c of the curve are : \n\n"
" y = %+.2fx**4 %+.2fx**3 %+.2fx**2 %+.2fx %+.2f\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][C1],x[R5][C1]);
stop();
f_mZ(XY);
f_mZ(A);
f_mZ(b);
f_mZ(Ab);
f_mZ(A_T);
f_mZ(A_TA); // A_T*A
f_mZ(invA_TA); // inv(A_T*A)
f_mZ(invA_TAA_T); // inv(A_T*A)*A_T
f_mZ(x);
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
Find the coefficients a, b, c of the curve
y = ax**4 + bx**3 + cx**2 + dx + e
that passes through the points.
x y
+1 -2
+2 -2
+3 +3
+4 -9
+5 +4
Using the given points, we obtain this matrix.
x**4 x**3 x**2 x**1 x**0 y
+1.00 +1.00 +1.00 +1.00 +1.00 -2.00
+16.00 +8.00 +4.00 +2.00 +1.00 -2.00
+81.00 +27.00 +9.00 +3.00 +1.00 +3.00
+256.00 +64.00 +16.00 +4.00 +1.00 -9.00
+625.00 +125.00 +25.00 +5.00 +1.00 +4.00
Press return to continue.
A_T :
+1.00 +16.00 +81.00 +256.00 +625.00
+1.00 +8.00 +27.00 +64.00 +125.00
+1.00 +4.00 +9.00 +16.00 +25.00
+1.00 +2.00 +3.00 +4.00 +5.00
+1.00 +1.00 +1.00 +1.00 +1.00
A_TA :
+462979.00 +96825.00 +20515.00 +4425.00 +979.00
+96825.00 +20515.00 +4425.00 +979.00 +225.00
+20515.00 +4425.00 +979.00 +225.00 +55.00
+4425.00 +979.00 +225.00 +55.00 +15.00
+979.00 +225.00 +55.00 +15.00 +5.00
Press return to continue.
inv(A_TA) :
+0.1215 -1.4583 +6.0243 -9.8958 +5.2500
-1.4583 +17.5694 -72.9167 +120.3889 -64.1667
+6.0243 -72.9167 +304.3299 -505.7292 +271.2500
-9.8958 +120.3889 -505.7292 +847.1528 -458.3333
+5.2500 -64.1667 +271.2500 -458.3333 +251.0000
inv(A_TA)*A_T :
+0.0417 -0.1667 +0.2500 -0.1667 +0.0417
-0.5833 +2.1667 -3.0000 +1.8333 -0.4167
+2.9583 -9.8333 +12.2500 -6.8333 +1.4583
-6.4167 +17.8333 -19.5000 +10.1667 -2.0833
+5.0000 -10.0000 +10.0000 -5.0000 +1.0000
x = inv(A_TA)*A_T*b :
+2.6667
-30.3333
+117.8333
-181.1667
+89.0000
Press return to continue.
x = inv(A_TA)*A_T*b :
+2.67
-30.33
+117.83
-181.17
+89.00
The coefficients a, b, c of the curve are :
y = +2.67x**4 -30.33x**3 +117.83x**2 -181.17x +89.00
Press return to continue.