Mathc complexes/00m
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 = i_mZ(RCA,RCA);
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);
do
{
rE_mZ(A,999,+1.E-4);
eigs_V_mZ(A,V,FACTOR_E);
}while(!det_Z(V).r);
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 :
+0.0631 -0.0058i +0.0825 +0.0468i +0.0862 -0.0453i
-0.0571 +0.0469i -0.0689 +0.0290i +0.0960 -0.0539i
+0.0488 +0.0110i -0.0587 +0.0919i +0.0777 +0.0401i
V :
-1.9061e-01 -7.1959e-01i +7.3448e-01 -4.0806e-01i -1.8452e-01 -2.4072e-01i
+5.1565e-01 -2.3206e-01i +1.2721e-01 +1.8056e-01i +8.7213e-02 +7.9767e-01i
+3.5512e-01 +1.9713e-17i +4.9522e-01 +0.0000e+00i +5.1392e-01 -1.9746e-18i
inv(V) ... Some time the matrix is not invertible :
-4.9168e-01 +3.1511e-01i +6.8143e-01 +6.1835e-01i +5.1999e-01 -1.2798e+00i
+8.9119e-01 -1.0436e-01i -4.0095e-01 +3.7864e-01i +1.0246e+00 +9.3803e-01i
-5.1901e-01 -1.1717e-01i -8.4504e-02 -7.9213e-01i +5.9920e-01 -1.9592e-02i
EigsValue = invV * A * V
+4.8615e-02 +1.0711e-01i +0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +1.1056e-01 +1.8408e-02i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i -8.7270e-02 -6.2222e-02i
Press return to continue.
cosh(2*A) :
+1.0036e+00-1.6439e-03i -5.0415e-03+2.4424e-02i +4.8360e-02-6.5205e-03i
+9.1007e-03-6.2711e-03i +9.9261e-01+1.8343e-02i +3.3921e-03+2.5588e-02i
+1.1150e-02-9.5216e-03i -6.6912e-03-1.1782e-04i +1.0168e+00+3.3984e-02i
cosh(A)**2+sinh(A)**2 :
+1.0036e+00-1.6439e-03i -5.0415e-03+2.4424e-02i +4.8360e-02-6.5205e-03i
+9.1007e-03-6.2711e-03i +9.9261e-01+1.8343e-02i +3.3921e-03+2.5588e-02i
+1.1150e-02-9.5216e-03i -6.6912e-03-1.1782e-04i +1.0168e+00+3.3984e-02i
Press return to continue
Press X return to stop