Mathc complexes/00f
Fonctions matricielles dans C. Matrices Non symétriques conjugués
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c00a.c |
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/* ------------------------------------ */
/* Save as : c00a.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E +1.E-0
#define RCA RC3
/* ------------------------------------ */
/* ------------------------------------ */
double **EigsValue_cosh2A_mZ(
double **EigsValue,
double **EigsValue_cosh2A
)
{
int r;
int c;
nb_Z cosh2A;
for ( r=R1; r<EigsValue[R_SIZE][C0]; r++)
for ( c=C1; c<EigsValue[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
cosh2A = cosh_Z(i_Z(2.*EigsValue[r][c],2.*EigsValue[r][c+C1]));
EigsValue_cosh2A[r][c ] = cosh2A.r;
EigsValue_cosh2A[r][c+C1] = cosh2A.i;
}
return(EigsValue_cosh2A);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **EigsValue_coshAP2_pls_sinhAP2_mZ(
double **EigsValue,
double **EigsValue_coshAP2_pls_sinhAP2
)
{
int r;
int c;
nb_Z coshAP2_pls_sinhAP2;
nb_Z cosh;
nb_Z coshP2;
nb_Z sinh;
nb_Z sinhP2;
for ( r=R1; r<EigsValue[R_SIZE][C0]; r++)
for ( c=C1; c<EigsValue[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
cosh = cosh_Z(i_Z(EigsValue[r][c],EigsValue[r][c+C1]));
coshP2 = mul_Z(cosh,cosh);
sinh = sinh_Z(i_Z(EigsValue[r][c],EigsValue[r][c+C1]));
sinhP2 = mul_Z(sinh,sinh);
coshAP2_pls_sinhAP2 = add_Z(coshP2,sinhP2);
EigsValue_coshAP2_pls_sinhAP2[r][c ] = coshAP2_pls_sinhAP2.r;
EigsValue_coshAP2_pls_sinhAP2[r][c+C1] = coshAP2_pls_sinhAP2.i;
}
return(EigsValue_coshAP2_pls_sinhAP2);
}
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
double **A = rE_mZ(i_mZ(RCA,RCA),999,+1.E-4);
double **V = i_mZ(RCA,RCA);
double **invV = i_mZ(RCA,RCA);
double **T = i_mZ(RCA,RCA);
double **EigsValue = i_mZ(RCA,RCA);
double **EigsValue_cosh2a = i_mZ(RCA,RCA);
double **EigsValue_coshAP2_pls_sinhAP2 = i_mZ(RCA,RCA);
double **cosh2a = i_mZ(RCA,RCA);
double **coshAP2_pls_sinhAP2 = i_mZ(RCA,RCA);
clrscrn();
printf(" A :");
p_mZ(A, S9,P4, S8,P4, C3);
printf(" V :");
eigs_V_mZ(A,V,FACTOR_E);
pE_mZ(V, S12,P4, S12,P4, C3);
printf(" inv(V) ... Some time the matrix is not invertible :");
inv_mZ(V,invV);
pE_mZ(invV, S12,P4, S12,P4, C3);
printf(" EigsValue = invV * A * V");
mul_mZ(invV,A,T);
mul_mZ(T,V,EigsValue);
pE_mZ(clean_eyes_mZ(EigsValue), S12,P4, S12,P4, C3);
stop();
clrscrn();
printf(" cosh(2*A) :");
EigsValue_cosh2A_mZ(EigsValue,EigsValue_cosh2a);
mul_mZ(V,EigsValue_cosh2a,T);
mul_mZ(T,invV,cosh2a);
pE_mZ(cosh2a, S12,P4, S8,P4, C3);
printf(" cosh(A)**2+sinh(A)**2 :");
EigsValue_coshAP2_pls_sinhAP2_mZ(EigsValue,EigsValue_coshAP2_pls_sinhAP2);
mul_mZ(V,EigsValue_coshAP2_pls_sinhAP2,T);
mul_mZ(T,invV,coshAP2_pls_sinhAP2);
pE_mZ(coshAP2_pls_sinhAP2, S12,P4, S8,P4, C3);
f_mZ(A);
f_mZ(V);
f_mZ(invV);
f_mZ(T);
f_mZ(EigsValue);
f_mZ(EigsValue_cosh2a);
f_mZ(cosh2a);
f_mZ(EigsValue_coshAP2_pls_sinhAP2);
f_mZ(coshAP2_pls_sinhAP2);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
A :
-0.0059 -0.0806i -0.0845 -0.0087i +0.0988 +0.0522i
+0.0166 +0.0501i -0.0057 -0.0405i -0.0141 -0.0687i
+0.0448 +0.0881i +0.0199 +0.0717i +0.0152 +0.0594i
V :
-7.6849e-01 -2.4265e-02i +5.0021e-01 -2.6049e-01i -5.4710e-01 -7.9835e-02i
+4.9947e-01 -3.3796e-01i -1.3753e-01 -1.8362e-01i -2.3073e-02 +6.4354e-01i
+2.1246e-01 +3.9836e-18i +7.9329e-01 +0.0000e+00i +5.2880e-01 +2.8288e-19i
inv(V) ... Some time the matrix is not invertible :
-6.6537e-01 +3.0261e-01i +3.6129e-01 +7.6021e-01i +2.0685e-01 -1.9388e-01i
+4.6338e-01 +1.7900e-01i +1.1979e-01 +3.2640e-01i +8.5483e-01 +1.2360e-01i
-4.2781e-01 -3.9011e-01i -3.2487e-01 -7.9508e-01i +5.2557e-01 -1.0753e-01i
EigsValue = invV * A * V
+2.4051e-02 -1.2748e-01i +0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +8.5524e-02 +8.3205e-02i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i -1.0597e-01 -1.7422e-02i
Press return to continue.
cosh(2*A) :
+9.8486e-01+1.5303e-02i -3.6974e-03+3.6820e-02i +5.1147e-03+8.6467e-03i
+2.2548e-02-1.3790e-02i +1.0042e+00-1.2473e-02i +4.0493e-04+9.8262e-03i
-2.0382e-03+4.0611e-03i -8.3846e-03-1.3595e-02i +1.0023e+00+2.0944e-02i
cosh(A)**2+sinh(A)**2 :
+9.8486e-01+1.5303e-02i -3.6974e-03+3.6820e-02i +5.1147e-03+8.6467e-03i
+2.2548e-02-1.3790e-02i +1.0042e+00-1.2473e-02i +4.0493e-04+9.8262e-03i
-2.0382e-03+4.0611e-03i -8.3846e-03-1.3595e-02i +1.0023e+00+2.0944e-02i
Press return to continue
Press X return to stop