Mathc complexes/00j
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 **EV_cos2A_mZ(
double **EV,
double **EV_cos2A
)
{
int r;
int c;
nb_Z cos2A;
for ( r=R1; r<EV[R_SIZE][C0]; r++)
for ( c=C1; c<EV[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
cos2A = cos_Z(i_Z(2.*EV[r][c],2.*EV[r][c+C1]));
EV_cos2A[r][c ] = cos2A.r;
EV_cos2A[r][c+C1] = cos2A.i;
}
return(EV_cos2A);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **EV_cosAP2_mns_sinAP2_mZ(
double **EV,
double **EV_cosAP2_mns_sinAP2
)
{
int r;
int c;
nb_Z cosAP2_mns_sinAP2;
nb_Z cos;
nb_Z cosP2;
nb_Z sin;
nb_Z sinP2;
for ( r=R1; r<EV[R_SIZE][C0]; r++)
for ( c=C1; c<EV[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
cos = cos_Z(i_Z(EV[r][c],EV[r][c+C1]));
cosP2 = mul_Z(cos,cos);
sin = sin_Z(i_Z(EV[r][c],EV[r][c+C1]));
sinP2 = mul_Z(sin,sin);
cosAP2_mns_sinAP2 = sub_Z(cosP2,sinP2);
EV_cosAP2_mns_sinAP2[r][c ] = cosAP2_mns_sinAP2.r;
EV_cosAP2_mns_sinAP2[r][c+C1] = cosAP2_mns_sinAP2.i;
}
return(EV_cosAP2_mns_sinAP2);
}
/* ------------------------------------ */
/* ------------------------------------ */
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 **EV = i_mZ(RCA,RCA);
double **EV_cos2a = i_mZ(RCA,RCA);
double **EV_cosAP2_mns_sinAP2 = i_mZ(RCA,RCA);
double **cos2a = i_mZ(RCA,RCA);
double **cosAP2_mns_sinAP2 = 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(" EV = invV * A * V");
mul_mZ(invV,A,T);
mul_mZ(T,V,EV);
pE_mZ(clean_eyes_mZ(EV), S12,P4, S12,P4, C3);
stop();
clrscrn();
printf(" cos(2*A) :");
EV_cos2A_mZ(EV,EV_cos2a);
mul_mZ(V,EV_cos2a,T);
mul_mZ(T,invV,cos2a);
pE_mZ(cos2a, S12,P4, S8,P4, C3);
printf(" cos(A)**2-sin(A)**2 :");
EV_cosAP2_mns_sinAP2_mZ(EV,EV_cosAP2_mns_sinAP2);
mul_mZ(V,EV_cosAP2_mns_sinAP2,T);
mul_mZ(T,invV,cosAP2_mns_sinAP2);
pE_mZ(cosAP2_mns_sinAP2, S12,P4, S8,P4, C3);
f_mZ(A);
f_mZ(V);
f_mZ(invV);
f_mZ(T);
f_mZ(EV);
f_mZ(EV_cos2a);
f_mZ(cos2a);
f_mZ(EV_cosAP2_mns_sinAP2);
f_mZ(cosAP2_mns_sinAP2);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Exemple de sortie écran :
A :
+0.0079 -0.0683i +0.0472 -0.0940i +0.0943 +0.0500i
-0.0662 -0.0341i +0.0673 +0.0078i -0.0565 -0.0033i
-0.0678 -0.0344i +0.0182 -0.0402i +0.0885 +0.0365i
V :
+6.0580e-01 +4.5086e-01i +3.1697e-01 -5.2921e-01i -2.8260e-01 +1.8510e-01i
+4.3666e-01 -2.2596e-01i +2.6245e-01 +6.3163e-01i -5.1110e-02 -8.0316e-01i
+4.3359e-01 +6.0173e-18i +3.8940e-01 +7.4493e-19i +4.8806e-01 -1.1231e-18i
inv(V) ... Some time the matrix is not invertible :
+6.7605e-01 -6.2461e-01i +6.0221e-01 +9.9447e-02i +5.3979e-02 +3.8337e-01i
-1.3294e-01 +4.6378e-01i -1.1964e-01 -6.2436e-01i +1.1139e+00 +5.6689e-02i
-4.9454e-01 +1.8487e-01i -4.3955e-01 +4.0981e-01i +1.1123e+00 -3.8582e-01i
EigsValue = invV * A * V
+2.6923e-02 -1.3203e-01i +0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +6.4033e-02 +1.0307e-01i +0.0000e+00 +0.0000e+00i
+0.0000e+00 +0.0000e+00i +0.0000e+00 +0.0000e+00i +7.2744e-02 +4.9646e-03i
Press return to continue.
cos(2*A) :
+1.0313e+00+6.2536e-03i -3.1624e-03+2.5763e-02i -1.5574e-02-1.3925e-02i
+6.7737e-03-7.2145e-03i +1.0060e+00-1.5730e-02i +2.6438e-02+1.9016e-02i
+2.0519e-02-1.7653e-03i +3.6390e-03+1.4921e-03i +9.9862e-01-4.0989e-03i
cos(A)**2-sin(A)**2 :
+1.0313e+00+6.2536e-03i -3.1624e-03+2.5763e-02i -1.5574e-02-1.3925e-02i
+6.7737e-03-7.2145e-03i +1.0060e+00-1.5730e-02i +2.6438e-02+1.9016e-02i
+2.0519e-02-1.7653e-03i +3.6390e-03+1.4921e-03i +9.9862e-01-4.0989e-03i
Press return to continue
Press X return to stop