Mathc matrices/c09a11
Installer et compiler ces fichiers dans votre répertoire de travail.
|
inv11.c |
|---|
/* ------------------------------------ */
/* Save as : inv11.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
double **xx_sort_r_mR(
double **Ab
)
{
double pivot;
int c;
int r;
int r_pivot = R1;
clrscrn();
printf(" Ab");
pE_mR(Ab,S12,P4,C6);
stop();
clrscrn();
for ( c=C1; c<Ab[C_SIZE_A][C0]; c++)
{
r = r_pivot;
pivot = 0.;
while( (pivot<ERROR_E) && r<Ab[R_SIZE][C0] )
{
pivot = fabs( Ab[r][c] );
clrscrn();
printf("/* --------- DEBUG 1 ---------- */\n\n");
printf(" Ab : pivot[%d][%d] = %f ",r,c,pivot);
p_mR(Ab,S8,P4,C8);
if(pivot>ERROR_E)
{
swapR_mR(Ab, r, r_pivot);
r_pivot++;
}
printf(" Ab");
p_mR(Ab,S8,P4,C8);
stop();
clrscrn();
/* --------- DEBUG 1 ---------- */
r++;
}
}
return(Ab);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **XX_invgj_mR(
double **A,
double **invA
)
{
double **ID = i_RC_mR(A[R_SIZE][C0],A[C_SIZE][C0]);
double **AID;
int r = A[R_SIZE][C0];
r--;
AID = i_Abr_Ac_bc_mR(r,r,r);
eye_mR(ID);
c_A_b_Ab_mR(A,ID,AID);
invgj_pivot_mR(AID);
sort_c_mR(AID);
xx_sort_r_mR(AID);
c_Inv_A_mR(AID,invA);
f_mR(AID);
f_mR(ID);
return(invA);
}
/* ------------------------------------ */
/* ------------------------------------ */
void fun(int r)
{
double **A = r_mR( i_mR(r,r), 99.);
double **Inv = i_mR(r,r);
double **AInv = i_mR(r,r);
clrscrn();
XX_invgj_mR(A,Inv);
printf(" Copy/Past into the octave window.\n\n");
printf("format short e\n");
p_Octave_mR(A,"A",P0);
printf(" inv(A)");
pE_mR(Inv,S12,P4,C6);
printf(" A * inv(A)");
mul_mR(A,Inv,AInv);
p_mR(AInv,S12,P4,C6);
f_mR(AInv);
f_mR(Inv);
f_mR(A);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun(C4);
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
On commence par regarder le premier pivot (R1xC1), si il est nulle on descend dans la colonne pour trouver un pivot non nul. Lorsque le pivot non nul est trouver on échange la ligne avec la ligne du pivot. Puis on passe à la colonne suivante (R2xC2). Exemple de sortie écran :
------------------------------------
Ab
+0.0000e+00 +0.0000e+00 +0.0000e+00 +1.0000e+00 +4.0500e-03 -8.0479e-04
+1.0000e+00 +0.0000e+00 +0.0000e+00 +0.0000e+00 -5.6074e-03 +6.9059e-03
+0.0000e+00 +1.0000e+00 +0.0000e+00 +0.0000e+00 +1.0105e-02 +4.9401e-03
-0.0000e+00 -0.0000e+00 +1.0000e+00 -0.0000e+00 +3.5346e-03 -6.3411e-03
-1.4045e-02 -1.7865e-03
+2.3002e-03 +4.6525e-03
+7.0962e-03 +1.0533e-02
-1.2066e-02 +6.2204e-03
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[1][1] = 0.000000
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[2][1] = 1.000000
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[2][2] = 0.000000
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[3][2] = 1.000000
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[3][3] = 0.000000
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[4][3] = 1.000000
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
Press return to continue.
/* --------- DEBUG 1 ---------- */
Ab : pivot[4][4] = 1.000000
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
Ab
+1.0000 +0.0000 +0.0000 +0.0000 -0.0056 +0.0069 +0.0023 +0.0047
+0.0000 +1.0000 +0.0000 +0.0000 +0.0101 +0.0049 +0.0071 +0.0105
-0.0000 -0.0000 +1.0000 -0.0000 +0.0035 -0.0063 -0.0121 +0.0062
+0.0000 +0.0000 +0.0000 +1.0000 +0.0041 -0.0008 -0.0140 -0.0018
Press return to continue.
Copy/Past into the octave window.
format short e
A=[
-65,+56,-33,+46;
+68,+28,-73,+88;
-29,+12,-15,-57;
+50,+20,+76,-47]
inv(A)
-5.6074e-03 +6.9059e-03 +2.3002e-03 +4.6525e-03
+1.0105e-02 +4.9401e-03 +7.0962e-03 +1.0533e-02
+3.5346e-03 -6.3411e-03 -1.2066e-02 +6.2204e-03
+4.0500e-03 -8.0479e-04 -1.4045e-02 -1.7865e-03
A * inv(A)
+1.0000 -0.0000 +0.0000 +0.0000
+0.0000 +1.0000 +0.0000 +0.0000
+0.0000 +0.0000 +1.0000 -0.0000
+0.0000 +0.0000 +0.0000 +1.0000
Press return to continue
Press X to stop