Mathc complexes/a340
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c00d.c |
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/* ------------------------------------ */
/* Save as : c00d.c */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define RCA RC3
#define FACTOR_E +1.E-0
/* ------------------------------------ */
/* ------------------------------------ */
double **X_Cosh2A_mZ(
double **M_Value,
double **Cosh2A_Value
)
{
int r;
int c;
nb_Z Cosh2A;
for ( r=R1; r<M_Value[R_SIZE][C0]; r++)
for ( c=C1; c<M_Value[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
Cosh2A = cosh_Z(i_Z(2.*M_Value[r][c],2.*M_Value[r][c+C1]));
Cosh2A_Value[r][c ] = Cosh2A.r;
Cosh2A_Value[r][c+C1] = Cosh2A.i;
}
return(Cosh2A_Value);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **X_CoshAP2_pls_SinAP2_mZ(
double **M_Value,
double **CoshAP2_pls_SinAP2_Value
)
{
int r;
int c;
nb_Z CoshAP2_pls_SinAP2;
nb_Z Cosh;
nb_Z CoshP2;
nb_Z Sin;
nb_Z SinP2;
for ( r=R1; r<M_Value[R_SIZE][C0]; r++)
for ( c=C1; c<M_Value[C_SIZE][C0]; c+=C2)
if(((r-R1)*C2)==c-C1)
{
Cosh = cosh_Z(i_Z(M_Value[r][c],M_Value[r][c+C1]));
CoshP2 = mul_Z(Cosh,Cosh);
Sin = sin_Z(i_Z(M_Value[r][c],M_Value[r][c+C1]));
SinP2 = mul_Z(Sin,Sin);
CoshAP2_pls_SinAP2 = add_Z(CoshP2,SinP2);
CoshAP2_pls_SinAP2_Value[r][c ] = CoshAP2_pls_SinAP2.r;
CoshAP2_pls_SinAP2_Value[r][c+C1] = CoshAP2_pls_SinAP2.i;
}
return(CoshAP2_pls_SinAP2_Value);
}
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
int r = RCA;
int c = RCA;
double **A = rE_mZ(i_mZ(r,c),99,+1.E-4);
double **A_T = ctranspose_mZ(A,i_mZ(c,r));
double **V = i_mZ(r,c);
double **V_T = i_mZ(c,r);
double **U = i_mZ(r,c);
double **U_T = i_mZ(c,r);
double **U_TA = i_mZ(c,c);
double **X = i_mZ(c,c);
double **T1 = i_mZ(c,c);
double **CoshAP2_pls_SinAP2 = i_mZ(c,c);
double **Cosh2A = i_mZ(c,c);
clrscrn();
printf(" A :");
p_mZ(A, S9,P4, S8,P4, C3);
printf(" U :");
X_U_mZ(A_T,U,FACTOR_E);
p_mZ(U, S9,P4, S8,P4, C3);
printf(" V :");
X_V_mZ(A_T,V,FACTOR_E);
p_mZ(V, S9,P4, S8,P4, C3);
ctranspose_mZ(U,U_T);
ctranspose_mZ(V,V_T);
printf(" X = U_T * A * V :");
mul_mZ(U_T, A, U_TA);
mul_mZ(U_TA, V, X);
p_mZ(X, S9,P4, S8,P4, C3);
stop();
clrscrn();
printf(" cosh(2 A) :");
X_Cosh2A_mZ(X,Cosh2A);
mul_mZ(V,Cosh2A,T1);
mul_mZ(T1,U_T,Cosh2A);
pE_mZ(Cosh2A, S12,P4, S8,P4, C3);
printf(" cosh(A)**2 + sin(A)**2 :");
X_CoshAP2_pls_SinAP2_mZ(X,CoshAP2_pls_SinAP2);
mul_mZ(V,CoshAP2_pls_SinAP2,T1);
mul_mZ(T1,U_T,CoshAP2_pls_SinAP2);
pE_mZ(CoshAP2_pls_SinAP2, S12,P4, S8,P4, C3);
f_mZ(A);
f_mZ(A_T);
f_mZ(V);
f_mZ(V_T);
f_mZ(U);
f_mZ(U_T);
f_mZ(U_TA);
f_mZ(X);
f_mZ(Cosh2A);
f_mZ(CoshAP2_pls_SinAP2);
}
/* ------------------------------------ */
int main(void)
{
time_t t;
srand(time(&t));
do
{
fun();
} while(stop_w());
return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */
Nous avons vu que :
cosh(x+y) = cosh(x) cosh(y) + sinh(x) sinh(y)
posons x = y
cosh(x+x) = cosh(x) cosh(x) + sinh(x) sinh(x)
cosh(2x) = cosh(x)**2 + sinh(x)**2
Exemple de sortie écran :
A :
+0.0088 +0.0087i +0.0089 -0.0069i +0.0039 -0.0077i
+0.0032 +0.0009i +0.0071 -0.0088i +0.0071 -0.0056i
-0.0074 -0.0028i +0.0046 +0.0054i -0.0089 -0.0062i
U :
-0.7517 -0.1144i +0.2786 -0.0609i -0.2315 +0.5357i
-0.5776 -0.0263i +0.1248 +0.1401i +0.3155 -0.7287i
+0.2960 -0.0000i +0.9399 +0.0000i +0.1700 +0.0000i
V :
+0.1730 -0.5441i +0.1834 +0.2568i -0.7342 +0.1883i
+0.6342 +0.1712i -0.3704 -0.3273i -0.0387 +0.5680i
+0.4925 +0.0000i +0.8100 +0.0000i +0.3183 +0.0000i
X = U_T * A * V :
-0.0175 +0.0159i -0.0000 -0.0000i -0.0000 +0.0000i
-0.0000 -0.0000i -0.0083 -0.0116i +0.0000 -0.0000i
-0.0000 +0.0000i -0.0000 +0.0000i -0.0007 +0.0064i
Press return to continue.
cosh(2 A) :
+2.3893e-01+8.6128e-01i -3.9521e-01-1.5026e-01i +9.8423e-02+1.1227e-01i
-2.6641e-01-2.8006e-01i -8.8912e-01+8.0224e-02i -1.6672e-01-1.6066e-01i
-2.1819e-01-6.4355e-02i -8.2888e-02+1.3176e-01i +9.6119e-01+1.3016e-04i
cosh(A)**2 + sin(A)**2 :
+2.3893e-01+8.6128e-01i -3.9521e-01-1.5026e-01i +9.8423e-02+1.1227e-01i
-2.6641e-01-2.8006e-01i -8.8912e-01+8.0224e-02i -1.6672e-01-1.6066e-01i
-2.1819e-01-6.4355e-02i -8.2888e-02+1.3176e-01i +9.6119e-01+1.3018e-04i
Press return to continue
Press X return to stop