Mathc matrices/c26a3
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c03.c |
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/* ------------------------------------ */
/* Save as : c03.c */
/* ------------------------------------ */
#include "v_a.h"
#include "d.h"
/* --------------------------------- */
int main(void)
{
double xy[8] ={ -5, -3,
-2, 0,
2, 3,
3, -2 };
double **XY = ca_A_mR(xy,i_mR(R4,C2));
double **A = i_mR(R4,C4);
double **b = i_mR(R4,C1);
double **Ab = i_Abr_Ac_bc_mR(R4,C4,C1);
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 \n");
p_mR(XY,S5,P0,C6);
printf("\n Using the given points, we obtain this matrix\n\n");
printf(" x**3 x**2 x**1 x**0 y\n");
i_A_b_with_XY_mR(XY,A,b);
c_A_b_Ab_mR(A,b,Ab);
p_mR(Ab,S7,P2,C6);
stop();
clrscrn();
printf(" The Gauss Jordan process will reduce this matrix to : \n");
gj_TP_mR(Ab);
p_mR(Ab,S7,P2,C6);
printf("\n The coefficients a, b, c of the curve are : \n\n");
p_eq_poly_mR(Ab);
stop();
clrscrn();
printf(" x y \n");
p_mR(XY,S5,P0,C6);
printf("\n");
printf(" Verify the result : \n\n");
verify_X_mR(Ab,XY[R1][C1]);
verify_X_mR(Ab,XY[R2][C1]);
verify_X_mR(Ab,XY[R3][C1]);
verify_X_mR(Ab,XY[R4][C1]);
printf("\n\n\n");
stop();
f_mR(XY);
f_mR(A);
f_mR(b);
f_mR(Ab);
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.
The Gauss Jordan process will reduce this matrix to :
+1.00 +0.00 +0.00 +0.00 -0.14
+0.00 +1.00 +0.00 +0.00 -0.73
+0.00 +0.00 +1.00 +0.00 +1.31
+0.00 +0.00 +0.00 +1.00 +4.43
The coefficients a, b, c of the curve are :
y = -0.139x**3 -0.732x**2 +1.307x +4.429
Press return to continue.
x y
-5 -3
-2 +0
+2 +3
+3 -2
Verify the result :
With x = -5.000, y = -3.000
With x = -2.000, y = +0.000
With x = +2.000, y = +3.000
With x = +3.000, y = -2.000
Press return to continue.