Mathc complexes/00k

Fonctions matricielles dans C. Matrices Non symétriques conjugués

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	c00a.c

/* ------------------------------------ */
/*  Save as :   c00a.c                  */
/* ------------------------------------ */
#include "w_a.h"
/* ------------------------------------ */
#define FACTOR_E    +1.E-0         
#define RCA          RC3  
/* ------------------------------------ */
/* ------------------------------------ */
double **EigsValue_sinh2A_mZ(
double **EigsValue,
double **EigsValue_sinh2A
)
{
int  r;
int  c;
nb_Z sinh2A;

  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)
          {
           sinh2A = sinh_Z(i_Z(2.*EigsValue[r][c],2.*EigsValue[r][c+C1]));
           
           EigsValue_sinh2A[r][c   ] = sinh2A.r;
           EigsValue_sinh2A[r][c+C1] = sinh2A.i;
          }
              
 return(EigsValue_sinh2A);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **EigsValue_TwocoshAsinhA_mZ(
double **EigsValue,
double **EigsValue_TwocoshAsinhA
)
{
int  r;
int  c;

nb_Z cosha;
nb_Z sinha;

nb_Z TwocoshAsinhA;

  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]));
           sinha = sinh_Z(i_Z( EigsValue[r][c], EigsValue[r][c+C1]));
             
           TwocoshAsinhA = smul_Z(2., mul_Z(cosha,sinha) ); 
           
           EigsValue_TwocoshAsinhA[r][c   ] = TwocoshAsinhA.r;
           EigsValue_TwocoshAsinhA[r][c+C1] = TwocoshAsinhA.i;     
          }
              
 return(EigsValue_TwocoshAsinhA);
}
/* ------------------------------------ */    
/* ------------------------------------ */
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_sinh2A        = i_mZ(RCA,RCA);
double **EigsValue_TwocoshAsinhA = i_mZ(RCA,RCA);

double **sinh2A                  = i_mZ(RCA,RCA);
double **TwocoshAsinhA           = 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(" sinh(2*A)        :");
  EigsValue_sinh2A_mZ(EigsValue,EigsValue_sinh2A);
   
  mul_mZ(V,EigsValue_sinh2A,T);
  mul_mZ(T,invV,sinh2A); 
  pE_mZ(sinh2A, S12,P4, S8,P4, C3);

  printf(" 2 cosh(A)sinh(A) :");
  EigsValue_TwocoshAsinhA_mZ(EigsValue,EigsValue_TwocoshAsinhA);
   
  mul_mZ(V,EigsValue_TwocoshAsinhA,T);
  mul_mZ(T,invV,TwocoshAsinhA); 
  pE_mZ(TwocoshAsinhA, S12,P4, S8,P4, C3);  
  
  f_mZ(A);
  
  f_mZ(V);  
  f_mZ(invV);  
  f_mZ(T);  
  
  f_mZ(EigsValue);
  
  f_mZ(EigsValue_sinh2A);   
  f_mZ(sinh2A); 
  
  f_mZ(EigsValue_TwocoshAsinhA);   
  f_mZ(TwocoshAsinhA);     
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

do
{
    fun();
    
} while(stop_w());

  return 0;
}
/* ------------------------------------ */
/* ------------------------------------ */

Exemple de sortie écran :

 A :
  +0.0255 -0.0832i   -0.0272 +0.0408i   -0.0747 -0.0754i 
  +0.0269 -0.0200i   +0.0518 +0.0331i   +0.0874 -0.0067i 
  +0.0746 +0.0486i   -0.0223 +0.0870i   +0.0712 +0.0577i 

 V :
 -1.8265e-01 +1.3961e-01i  -4.0748e-01 -7.9646e-01i  -4.2445e-01 +5.2710e-01i 
 +3.3651e-01 -5.4931e-01i  +1.2439e-01 +5.5202e-02i  -5.5288e-01 +8.8787e-03i 
 +7.2950e-01 +0.0000e+00i  +4.2554e-01 +1.1811e-17i  +4.8606e-01 +1.4041e-17i 

 inv(V) ... Some time the matrix is not invertible :
 +3.0616e-01 -2.6567e-01i  +6.1174e-01 +5.6963e-01i  +6.8549e-01 +7.2765e-02i 
 -2.7774e-01 +8.1404e-01i  -9.6267e-02 -5.1873e-01i  +5.2125e-01 +4.2376e-01i 
 -2.1633e-01 -3.1395e-01i  -8.3384e-01 -4.0079e-01i  +5.7219e-01 -4.8021e-01i 

 EigsValue = invV * A * V
 +9.8446e-02 +1.1673e-01i  +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +7.2925e-02 -1.0592e-01i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i  -2.2870e-02 -3.2085e-03i 

 Press return to continue. 


 sinh(2*A)        :
 +4.8685e-02-1.6702e-01i  -5.2362e-02+8.0674e-02i  -1.4977e-01-1.4993e-01i 
 +5.4865e-02-3.9233e-02i  +1.0172e-01+6.8204e-02i  +1.7448e-01-1.1565e-02i 
 +1.4930e-01+9.7654e-02i  -4.7449e-02+1.7400e-01i  +1.3972e-01+1.1573e-01i 

 2 cosh(A)sinh(A) :
 +4.8685e-02-1.6702e-01i  -5.2362e-02+8.0674e-02i  -1.4977e-01-1.4993e-01i 
 +5.4865e-02-3.9233e-02i  +1.0172e-01+6.8204e-02i  +1.7448e-01-1.1565e-02i 
 +1.4930e-01+9.7654e-02i  -4.7449e-02+1.7400e-01i  +1.3972e-01+1.1573e-01i 


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