Mathc complexes/07m
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c00b.c |
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/* ------------------------------------ */
/* Save as : c00b.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
#define RA R5
#define CA C5
#define Cb C1
#define RXY R3
#define CXY C2
/* ------------------------------------ */
/* ------------------------------------ */
int main(void)
{
double xy[RXY*(CXY*C2)] ={
1, -1,
2, -9,
3, -8,0 };
double ab[RA*((CA+Cb)*C2)]={
/* x**2 y**2 x y e = +0 */
+1, +0, +0, +0, +0, +1,
+0, +1, +0, +0, +0, +1,
+1, +1, +1, -1, +1, +0,
+4, +81, +2, -9, +1, +0,
+9, +64, +3, -8, +1, +0
};
double **XY = ca_A_mRZ(xy,i_mZ(RXY,CXY));
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, d, of a circle \n\n");
printf(" ax**2 + ay**2 + bx + cy + d = 0 \n\n");
printf(" that passes through these three XY. \n\n");
printf(" x y");
p_mRZ(XY,S5,P0,C6);
printf("\n");
printf(" Using the given XY, we obtain this matrix.\n");
printf(" (a = 1. This is my choice)\n\n");
printf(" x**2 y**2 x 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(" The coefficients a, b, c, d, e, of the curve are : \n\n"
" %+.2fx**2 %+.2fy**2 %+.2fx %+.2fy %+.2f = 0\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, d, of a circle
ax**2 + ay**2 + bx + cy + d = 0
that passes through these three XY.
x y
+1 -1
+2 -9
+3 -8
Using the given XY, we obtain this matrix.
(a = 1. This is my choice)
x**2 y**2 x y
+1.00 +0.00 +0.00 +0.00 +0.00 +1.00
+0.00 +1.00 +0.00 +0.00 +0.00 +1.00
+1.00 +1.00 +1.00 -1.00 +1.00 +0.00
+4.00 +81.00 +2.00 -9.00 +1.00 +0.00
+9.00 +64.00 +3.00 -8.00 +1.00 +0.00
Press return to continue.
A_T :
+1.00 +0.00 +1.00 +4.00 +9.00
+0.00 +1.00 +1.00 +81.00 +64.00
+0.00 +0.00 +1.00 +2.00 +3.00
+0.00 +0.00 -1.00 -9.00 -8.00
+0.00 +0.00 +1.00 +1.00 +1.00
A_TA :
+99.00 +901.00 +36.00 -109.00 +14.00
+901.00 +10659.00 +355.00 -1242.00 +146.00
+36.00 +355.00 +14.00 -43.00 +6.00
-109.00 -1242.00 -43.00 +146.00 -18.00
+14.00 +146.00 +6.00 -18.00 +3.00
Press return to continue.
inv(A_TA) :
+1.0000 +0.0000 -4.7778 -0.2222 +3.5556
+0.0000 +1.0000 +6.2222 +10.7778 +3.5556
-4.7778 +6.2222 +62.9506 +68.3827 +3.8765
-0.2222 +10.7778 +68.3827 +116.2840 +37.4568
+3.5556 +3.5556 +3.8765 +37.4568 +27.6914
inv(A_TA)*A_T :
+1.0000 +0.0000 +0.0000 +0.0000 +0.0000
+0.0000 +1.0000 +0.0000 +0.0000 +0.0000
-4.7778 +6.2222 -0.1111 -0.7778 +0.8889
-0.2222 +10.7778 +0.1111 -0.2222 +0.1111
+3.5556 +3.5556 +1.2222 +0.5556 -0.7778
x = inv(A_TA)*A_T*b :
+1.0000
+1.0000
+1.4444
+10.5556
+7.1111
Press return to continue.
x = inv(A_TA)*A_T*b :
+1.00
+1.00
+1.44
+10.56
+7.11
The coefficients a, b, c, d, e, of the curve are :
+1.00x**2 +1.00y**2 +1.44x +10.56y +7.11 = 0
Press return to continue.