Mathc complexes/00e
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_TwocoshAP2mns1_mZ(
double **EigsValue,
double **EigsValue_TwocoshAP2mns1
)
{
int r;
int c;
nb_Z cosha;
nb_Z mns1 = {1,0};
nb_Z TwocoshAP2mns1;
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)
{
cosha = cosh_Z(i_Z( EigsValue[r][c], EigsValue[r][c+C1]));
TwocoshAP2mns1 = sub_Z(smul_Z(2., mul_Z(cosha,cosha)),mns1);
EigsValue_TwocoshAP2mns1[r][c ] = TwocoshAP2mns1.r;
EigsValue_TwocoshAP2mns1[r][c+C1] = TwocoshAP2mns1.i;
}
return(EigsValue_TwocoshAP2mns1);
}
/* ------------------------------------ */
/* ------------------------------------ */
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_TwocoshAP2mns1 = i_mZ(RCA,RCA);
double **cosh2a = i_mZ(RCA,RCA);
double **TwocoshAP2mns1 = 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(" 2cosh(A)**2-1 :");
EigsValue_TwocoshAP2mns1_mZ(EigsValue,EigsValue_TwocoshAP2mns1);
mul_mZ(V,EigsValue_TwocoshAP2mns1,T);
mul_mZ(T,invV,TwocoshAP2mns1);
pE_mZ(TwocoshAP2mns1, 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_TwocoshAP2mns1);
f_mZ(TwocoshAP2mns1);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
A :
+0.0372 +0.0710i +0.0626 -0.0533i -0.0692 +0.0382i
+0.0323 -0.0141i -0.0083 +0.0192i +0.0583 +0.0390i
-0.0879 +0.0934i +0.0756 +0.0769i -0.0965 -0.0218i
V :
+3.7644e-01 -3.8849e-01i -3.3837e-01 -3.8622e-01i -5.6069e-01 -5.0586e-01i
-4.1615e-01 -9.1842e-02i +5.0344e-01 +9.1015e-02i -1.3652e-01 +3.9308e-01i
+7.2509e-01 +0.0000e+00i +6.8892e-01 +3.8243e-17i +5.0654e-01 +0.0000e+00i
inv(V) ... Some time the matrix is not invertible :
+7.6906e-01 -5.6442e-01i -5.1432e-01 -3.2041e-01i +1.0277e+00 +4.5603e-01i
+3.0304e-01 +7.4472e-01i +1.3937e+00 +3.0602e-01i +2.0482e-01 +1.2790e-01i
-1.5130e+00 -2.0492e-01i -1.1593e+00 +4.2449e-02i +2.2455e-01 -8.2673e-01i
EigsValue = invV * A * V
-1.2574e-01 +2.0074e-02i +0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +4.4121e-02 +4.7789e-02i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i +1.4021e-02 +5.3752e-04i
Press return to continue.
cosh(2*A) :
+1.0002e+00-1.4361e-02i -3.1384e-03+3.3977e-03i +1.5961e-02-1.2761e-02i
-1.3160e-02+9.1032e-03i +1.0048e+00+9.0191e-03i -1.5495e-02-4.0596e-03i
+8.3216e-03-1.7013e-02i -1.6582e-02+4.5541e-03i +1.0257e+00+3.6040e-03i
2cosh(A)**2-1 :
+1.0002e+00-1.4361e-02i -3.1384e-03+3.3977e-03i +1.5961e-02-1.2761e-02i
-1.3160e-02+9.1032e-03i +1.0048e+00+9.0191e-03i -1.5495e-02-4.0596e-03i
+8.3216e-03-1.7013e-02i -1.6582e-02+4.5541e-03i +1.0257e+00+3.6040e-03i
Press return to continue
Press X return to stop