Mathc complexes/08b
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c00c.c |
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/* ------------------------------------ */
/* Save as : c00c.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_Ipls2sinhA_2_mZ(
double **M_Value,
double **Ipls2sinhA_2_Value
)
{
int r;
int c;
nb_Z sinha;
nb_Z Ipls = {1,0};
nb_Z Ipls2sinhA_2;
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)
{
sinha = cosh_Z(i_Z( M_Value[r][c], M_Value[r][c+C1]));
Ipls2sinhA_2 = sub_Z(Ipls,smul_Z(2., mul_Z(sinha,sinha)));
Ipls2sinhA_2_Value[r][c ] = Ipls2sinhA_2.r;
Ipls2sinhA_2_Value[r][c+C1] = Ipls2sinhA_2.i;
}
return(Ipls2sinhA_2_Value);
}
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{
int r = RCA;
int c = RCA;
double **A = rE_mZ(i_mZ(r,c),999,+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 **cosh2A = i_mZ(c,c);
double **Ipls2sinhA_2 = 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(" 1 + 2 sinhA**2:");
X_Ipls2sinhA_2_mZ(X,Ipls2sinhA_2);
mul_mZ(V,Ipls2sinhA_2,T1);
mul_mZ(T1,U_T,Ipls2sinhA_2);
pE_mZ(Ipls2sinhA_2, 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(Ipls2sinhA_2);
}
/* ------------------------------------ */
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 cosh(x)**2-sinh(x)**2 = 1
cosh(x)**2 = 1+sinh(x)**2
cosh(2x) = (1+sinh(x)**2) + sinh(x)**2
cosh(2x) = 1 + 2*sinh(x)**2
Exemple de sortie écran :
A :
+0.0678 -0.0865i +0.0151 +0.0733i +0.0381 -0.0345i
+0.0146 -0.0550i +0.0680 +0.0171i +0.0750 -0.0946i
-0.0124 +0.0836i +0.0111 +0.0829i -0.0283 -0.0217i
U :
-0.3450 -0.5734i +0.0274 +0.0845i +0.5747 +0.4626i
-0.6243 -0.3464i +0.1841 +0.0807i -0.6637 -0.0961i
+0.2059 +0.0000i +0.9755 +0.0000i +0.0770 +0.0000i
V :
+0.6111 +0.2421i -0.3977 +0.3679i -0.2620 -0.4537i
+0.1214 -0.4619i -0.7080 +0.0489i +0.3668 +0.3657i
+0.5830 +0.0000i +0.4503 +0.0000i +0.6763 +0.0000i
X = U_T * A * V :
-0.0227 +0.1961i -0.0000 -0.0000i +0.0000 -0.0000i
+0.0000 +0.0000i -0.0517 -0.1084i -0.0000 -0.0000i
+0.0000 -0.0000i +0.0000 -0.0000i -0.0546 +0.0457i
Press return to continue.
cosh(2*A) :
-6.6241e-01+1.6006e-01i -2.5381e-01+4.3542e-01i -2.9229e-01+3.5285e-01i
+5.7485e-01+3.0442e-01i -3.2311e-01+1.6127e-01i -6.2918e-01-2.9049e-02i
+2.1896e-01-4.1610e-02i -6.9998e-01+2.2891e-01i +5.9449e-01+7.1913e-03i
1 + 2 sinhA**2:
+6.6241e-01-1.6006e-01i +2.5381e-01-4.3542e-01i +2.9229e-01-3.5285e-01i
-5.7485e-01-3.0442e-01i +3.2311e-01-1.6127e-01i +6.2918e-01+2.9049e-02i
-2.1896e-01+4.1610e-02i +6.9998e-01-2.2891e-01i -5.9449e-01-7.1913e-03i
Press return to continue
Press X return to stop