Mathc complexes/00l

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_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                        = 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_cosh2a         = i_mZ(RCA,RCA);
double **EigsValue_TwocoshAP2mns1 = i_mZ(RCA,RCA);

double **cosh2a                   = i_mZ(RCA,RCA);
double **TwocoshAP2mns1           = 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(" 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 :
  +0.0225 +0.0051i   +0.0779 +0.0138i   -0.0945 -0.0217i 
  -0.0923 +0.0011i   -0.0101 -0.0281i   +0.0311 +0.0265i 
  -0.0476 +0.0727i   -0.0818 +0.0970i   -0.0647 +0.0755i 

 V :
 +3.8851e-01 +3.1281e-01i  -2.4670e-01 -5.7185e-01i  -6.2073e-01 +1.8526e-01i 
 +1.5785e-02 +6.6124e-02i  -4.2367e-01 +5.3807e-01i  +1.8555e-01 -5.3566e-01i 
 +8.6405e-01 +0.0000e+00i  +3.7831e-01 +0.0000e+00i  +5.0894e-01 +0.0000e+00i 

 inv(V) ... Some time the matrix is not invertible :
 +5.7288e-01 -2.8106e-01i  +3.3068e-01 -2.7999e-01i  +7.7053e-01 -1.0121e-01i 
 -4.5662e-01 +3.8366e-01i  -7.0829e-01 -4.5720e-01i  +3.2216e-01 +5.5354e-02i 
 -6.3318e-01 +1.9199e-01i  -3.4921e-02 +8.1520e-01i  +4.1723e-01 +1.3068e-01i 

 EigsValue = invV * A * V
 -1.2134e-01 +8.6469e-02i  +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +2.9878e-02 -1.2493e-01i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i  +3.9161e-02 +9.0963e-02i 

 Press return to continue. 


 cosh(2*A)        :
 +9.9863e-01-1.3628e-02i  +2.2062e-02-1.8013e-02i  +1.5567e-02-8.5442e-03i 
 -8.9704e-03+6.2120e-03i  +9.7408e-01+4.7939e-04i  +1.0280e-02+2.7482e-03i 
 +6.9753e-03-3.1922e-02i  -6.4808e-03-1.2306e-02i  +9.9872e-01-2.9622e-02i 

 2cosh(A)**2-1 :
 +9.9863e-01-1.3628e-02i  +2.2062e-02-1.8013e-02i  +1.5567e-02-8.5442e-03i 
 -8.9704e-03+6.2120e-03i  +9.7408e-01+4.7939e-04i  +1.0280e-02+2.7482e-03i 
 +6.9753e-03-3.1922e-02i  -6.4808e-03-1.2306e-02i  +9.9872e-01-2.9622e-02i 


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