Mathc complexes/07v
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c00c.c |
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/* ------------------------------------ */
/* Save as : c00c.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R4
#define CA C4
#define Cb C1
#define RXY R4
#define CXY C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double xy[RXY*CXY] =
{ -5, -3,
-2, 0,
2, 3,
3, -2 };
double ab[RA*(CA+Cb)]={
/* x**3 x**2 x**1 x**0 y */
-125, +25, -5, +1, -3,
-8, +4, -2, +1, +0,
+8, +4, +2, +1, +3,
+27, +9, +3, +1, -2,
};
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**3 + bx**2 + cx + d \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**3 x**2 x**1 x**0 y\n");
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**3 %+.2fx**2 %+.2fx %+.2f\n\n"
,x[R1][C1],x[R2][C1],x[R3][C1],x[R4][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**3 + bx**2 + cx + d
that passes through the points.
x y
-5 -3
-2 +0
+2 +3
+3 -2
Using the given points, we obtain this matrix.
x**3 x**2 x**1 x**0 y
-125.00 +25.00 -5.00 +1.00 -3.00
-8.00 +4.00 -2.00 +1.00 +0.00
+8.00 +4.00 +2.00 +1.00 +3.00
+27.00 +9.00 +3.00 +1.00 -2.00
Press return to continue.
A_T :
-125.00 -8.00 +8.00 +27.00
+25.00 +4.00 +4.00 +9.00
-5.00 -2.00 +2.00 +3.00
+1.00 +1.00 +1.00 +1.00
A_TA :
+16482.00 -2882.00 +738.00 -98.00
-2882.00 +738.00 -98.00 +42.00
+738.00 -98.00 +42.00 -2.00
-98.00 +42.00 -2.00 +4.00
Press return to continue.
inv(A_TA) :
+0.0022 +0.0081 -0.0220 -0.0420
+0.0081 +0.0364 -0.0682 -0.2168
-0.0220 -0.0682 +0.2652 +0.3109
-0.0420 -0.2168 +0.3109 +1.6531
inv(A_TA)*A_T :
-0.0060 +0.0167 -0.0357 +0.0250
+0.0179 +0.0000 -0.1429 +0.1250
+0.0238 -0.3167 +0.3929 -0.1000
-0.0714 +0.5000 +1.0714 -0.5000
x = inv(A_TA)*A_T*b :
-0.1393
-0.7321
+1.3071
+4.4286
Press return to continue.
x = inv(A_TA)*A_T*b :
-0.14
-0.73
+1.31
+4.43
The coefficients a, b, c of the curve are :
y = -0.14x**3 -0.73x**2 +1.31x +4.43
Press return to continue.