Mathc matrices/c09a02
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inv02.c |
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/* ------------------------------------ */
/* Save as : inv02.c */
/* ------------------------------------ */
#include "v_a.h"
/* ------------------------------------ */
/* ------------------------------------ */
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);
clrscrn();
printf("/* --------- DEBUG 1 ---------- */\n");
eye_mR(ID);
/* --------------------------- */
printf(" ID : eye_mR(ID);");
p_mR(ID,S3,P0,C6);
stop();
clrscrn();
printf(" A :");
p_mR(A,S3,P0,C6);
printf(" ID :");
p_mR(ID,S3,P0,C6);
printf(" AID :");
p_mR(AID,S3,P0,C6);
printf("/* --------- DEBUG 2 ---------- */\n");
c_A_b_Ab_mR(A,ID,AID);
/* --------------------------- */
printf(" AID : c_A_b_Ab_mR(A,ID,AID);");
p_mR(AID,S3,P0,C10);
stop();
clrscrn();
printf("/* --------- DEBUG 3 ---------- */\n");
invgj_pivot_mR(AID);
/* --------------------------- */
printf(" AID : invgj_pivot_mR(AID);");
p_mR(AID,S6,P6,C6);
stop();
clrscrn();
printf(" AID : \n");
pall_mR(AID,S6,P6,C8);
printf("/* --------- DEBUG 4 ---------- */\n\n\n");
sort_c_mR(AID);
/* --------------------------- */
printf(" AID : sort_c_mR(AID);\n");
pall_mR(AID,S6,P6,C8);
stop();
clrscrn();
printf(" AID :");
p_mR(AID,S6,P6,C6);
printf("/* --------- DEBUG 5 ---------- */\n\n");
sort_r_mR(AID);
/* --------------------------- */
printf(" AID : sort_r_mR(AID);");
p_mR(AID,S6,P6,C6);
stop();
clrscrn();
printf(" AID : ");
p_mR(AID,S6,P6,C6);
printf("/* --------- DEBUG 6 ---------- */\n");
c_Inv_A_mR(AID,invA);
/* --------------------------- */
printf(" invA : c_Inv_A_mR(AID,invA);");
p_mR(invA,S6,P6,C6);
stop();
clrscrn();
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();
printf(" A :");
p_mR(A,S3,P0,C6);
stop();
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(C3);
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
- Créer la matrice Ab (AID) avec r lignes, Ac colonnes (A) et bc colonnes (ID).
- Construire la matrice identité (ID).
- Copier la matrice A (A) et b (ID) dans Ab (AID).
- Inverser la matrice avec la méthode de gaussjordan.
- Trier les colonnes.
- Trier les lignes.
- Copier la matrice inverse dans la matrice invA.
Dans DEBUG 4 on utilise la fonction pall_mR(); pour afficher la colonne zéro et voir l'index des colonnes. Exemple de sortie écran :
------------------------------------
A :
-57 +34 +66
-61 +42 -21
-75 -95 -35
Press return to continue.
/* --------- DEBUG 1 ---------- */
ID : eye_mR(ID);
+1 +0 +0
+0 +1 +0
+0 +0 +1
Press return to continue.
A :
-57 +34 +66
-61 +42 -21
-75 -95 -35
ID :
+1 +0 +0
+0 +1 +0
+0 +0 +1
AID :
+0 +0 +0 +0 +0 +0
+0 +0 +0 +0 +0 +0
+0 +0 +0 +0 +0 +0
/* --------- DEBUG 2 ---------- */
AID : c_A_b_Ab_mR(A,ID,AID);
-57 +34 +66 +1 +0 +0
-61 +42 -21 +0 +1 +0
-75 -95 -35 +0 +0 +1
Press return to continue.
/* --------- DEBUG 3 ---------- */
AID : invgj_pivot_mR(AID);
+1.000000 +0.000000 +0.000000 +0.009033 -0.000728 -0.006793
-0.000000 +1.000000 +0.000000 -0.006607 -0.004507 -0.004534
+0.000000 +0.000000 +1.000000 -0.010360 +0.011634 -0.000416
Press return to continue.
AID :
+4.000000 +2.000000 +1.000000 +3.000000 +5.000000 +4.000000 +6.000000 <- index colonnes
+7.000000 +1.000000 +0.000000 +0.000000 +0.009033 -0.000728 -0.006793
+4.000000 -0.000000 +1.000000 +0.000000 -0.006607 -0.004507 -0.004534
+0.000000 +0.000000 +0.000000 +1.000000 -0.010360 +0.011634 -0.000416
/* --------- DEBUG 4 ---------- */
AID : sort_c_mR(AID);
+4.000000 +1.000000 +2.000000 +3.000000 +4.000000 +5.000000 +6.000000
+7.000000 +0.000000 +1.000000 +0.000000 -0.000728 +0.009033 -0.006793
+4.000000 +1.000000 -0.000000 +0.000000 -0.004507 -0.006607 -0.004534
+0.000000 +0.000000 +0.000000 +1.000000 +0.011634 -0.010360 -0.000416
Press return to continue.
AID :
+0.000000 +1.000000 +0.000000 -0.000728 +0.009033 -0.006793
+1.000000 -0.000000 +0.000000 -0.004507 -0.006607 -0.004534
+0.000000 +0.000000 +1.000000 +0.011634 -0.010360 -0.000416
/* --------- DEBUG 5 ---------- */
AID : sort_r_mR(AID);
+1.000000 -0.000000 +0.000000 -0.004507 -0.006607 -0.004534
+0.000000 +1.000000 +0.000000 -0.000728 +0.009033 -0.006793
+0.000000 +0.000000 +1.000000 +0.011634 -0.010360 -0.000416
Press return to continue.
AID :
+1.000000 -0.000000 +0.000000 -0.004507 -0.006607 -0.004534
+0.000000 +1.000000 +0.000000 -0.000728 +0.009033 -0.006793
+0.000000 +0.000000 +1.000000 +0.011634 -0.010360 -0.000416
/* --------- DEBUG 6 ---------- */
invA : c_Inv_A_mR(AID,invA);
-0.004507 -0.006607 -0.004534
-0.000728 +0.009033 -0.006793
+0.011634 -0.010360 -0.000416
Press return to continue.
Copy/Past into the octave window.
format short e
A=[
-57,+34,+66;
-61,+42,-21;
-75,-95,-35]
inv(A)
-4.5068e-03 -6.6074e-03 -4.5341e-03
-7.2837e-04 +9.0331e-03 -6.7934e-03
+1.1634e-02 -1.0360e-02 -4.1621e-04
A * inv(A)
+1.0000 -0.0000 +0.0000
-0.0000 +1.0000 -0.0000
-0.0000 +0.0000 +1.0000
Press return to continue
Press X to stop