Mathc complexes/07t
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R3
#define CA C3
#define Cb C1
#define RXY R3
#define CXY C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double xy[RXY*CXY] =
{1, 6,
2, 3,
3, 5, };
double ab[RA*(CA+Cb)]={
/* x**2 x**1 x**0 = y */
+1, +1, +1, +6,
+4, +2, +1, +3,
+9, +3, +1, +5
};
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**2 + bx + c (x**0 = 1) \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**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**2 %+.2fx %+.2f\n\n"
,x[R1][C1],x[R2][C1],x[R3][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**2 + bx + c (x**0 = 1)
that passes through the points.
x y
+1 +6
+2 +3
+3 +5
Using the given points, we obtain this matrix.
x**2 x**1 x**0 y
+1.00 +1.00 +1.00 +6.00
+4.00 +2.00 +1.00 +3.00
+9.00 +3.00 +1.00 +5.00
Press return to continue.
A_T :
+1.00 +4.00 +9.00
+1.00 +2.00 +3.00
+1.00 +1.00 +1.00
A_TA :
+98.00 +36.00 +14.00
+36.00 +14.00 +6.00
+14.00 +6.00 +3.00
Press return to continue.
inv(A_TA) :
+1.5000 -6.0000 +5.0000
-6.0000 +24.5000 -21.0000
+5.0000 -21.0000 +19.0000
inv(A_TA)*A_T :
+0.5000 -1.0000 +0.5000
-2.5000 +4.0000 -1.5000
+3.0000 -3.0000 +1.0000
x = inv(A_TA)*A_T*b :
+2.5000
-10.5000
+14.0000
Press return to continue.
x = inv(A_TA)*A_T*b :
+2.50
-10.50
+14.00
The coefficients a, b, c of the curve are :
y = +2.50x**2 -10.50x +14.00
Press return to continue.