Mathc complexes/00b

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_cos2A_mZ(
double **EigsValue,
double **EigsValue_cos2A
)
{
int  r;
int  c;

nb_Z cos2A;

  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)
          {
           cos2A = cos_Z(i_Z(2.*EigsValue[r][c],2.*EigsValue[r][c+C1]));
           
           EigsValue_cos2A[r][c   ] = cos2A.r;
           EigsValue_cos2A[r][c+C1] = cos2A.i;
          }
              
 return(EigsValue_cos2A);
}
/* ------------------------------------ */
/* ------------------------------------ */
double **EigsValue_TwocosA_2mns1_mZ(
double **EigsValue,
double **EigsValue_TwocosA_2mns1
)
{
int  r;
int  c;

nb_Z cosa;
nb_Z mns1 = {1,0};

nb_Z TwocosA_2mns1;

  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)
          {
                    cosa = cos_Z(i_Z( EigsValue[r][c], EigsValue[r][c+C1]));
           TwocosA_2mns1 = sub_Z(smul_Z(2., mul_Z(cosa,cosa)),mns1); 
           
           EigsValue_TwocosA_2mns1[r][c   ] = TwocosA_2mns1.r;
           EigsValue_TwocosA_2mns1[r][c+C1] = TwocosA_2mns1.i;
          }
              
 return(EigsValue_TwocosA_2mns1);
}
/* ------------------------------------ */
/* ------------------------------------ */
void fun(void)
{                               
double **A                       = rE_mZ(i_mZ(RCA,RCA),999,+1.E-4);

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_cos2a         =       i_mZ(RCA,RCA);
double **EigsValue_TwocosA_2mns1 =       i_mZ(RCA,RCA);

double **cos2a                   =       i_mZ(RCA,RCA);
double **TwocosA_2mns1           =       i_mZ(RCA,RCA);

  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(" cos(2*A)        :");
  EigsValue_cos2A_mZ(EigsValue,EigsValue_cos2a);
   
  mul_mZ(V,EigsValue_cos2a,T);
  mul_mZ(T,invV,cos2a); 
  pE_mZ(cos2a, S12,P4, S8,P4, C3);

  printf(" 2cos(A)**2-1 :");
  EigsValue_TwocosA_2mns1_mZ(EigsValue,EigsValue_TwocosA_2mns1);
   
  mul_mZ(V,EigsValue_TwocosA_2mns1,T);
  mul_mZ(T,invV,TwocosA_2mns1); 
  pE_mZ(TwocosA_2mns1, S12,P4, S8,P4, C3);  
  
  f_mZ(A);
  
  f_mZ(V);  
  f_mZ(invV);  
  f_mZ(T);  
  
  f_mZ(EigsValue);
  
  f_mZ(EigsValue_cos2a);   
  f_mZ(cos2a); 
  
  f_mZ(EigsValue_TwocosA_2mns1);   
  f_mZ(TwocosA_2mns1);     
}
/* ------------------------------------ */
int main(void)
{
time_t t;

  srand(time(&t));

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

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

Exemple de sortie écran :

 A :
  -0.0286 +0.0042i   +0.0972 -0.0061i   -0.0644 -0.0826i 
  -0.0828 -0.0373i   +0.0421 -0.0110i   +0.0196 -0.0747i 
  -0.0084 +0.0238i   +0.0388 -0.0965i   +0.0181 +0.0877i 

 V :
 -2.3663e-01 +6.0160e-01i  +5.5634e-01 +1.8075e-01i  -2.3395e-01 -6.3154e-01i 
 -5.1858e-01 -4.0518e-02i  +7.1303e-01 -1.8652e-01i  +3.6970e-01 -5.7834e-02i 
 +5.5813e-01 +0.0000e+00i  +3.3853e-01 +2.0004e-17i  +6.3749e-01 +0.0000e+00i 

 inv(V) ... Some time the matrix is not invertible :
 +1.3849e-01 -4.0216e-01i  -6.4362e-01 +1.9729e-01i  +8.0459e-01 -1.8320e-01i 
 +3.8167e-01 -5.4317e-01i  +7.2350e-01 +5.5237e-01i  +2.0847e-01 -7.5935e-02i 
 -3.2393e-01 +6.4054e-01i  +1.7929e-01 -4.6606e-01i  +7.5351e-01 +2.0072e-01i 

 EigsValue = invV * A * V
 -4.7048e-02 +1.5540e-01i  +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +2.0141e-02 -1.0230e-01i  +0.0000e+00 +0.0000e+00i 
 +0.0000e+00 +0.0000e+00i  +0.0000e+00 +0.0000e+00i  +5.8507e-02 +2.7804e-02i 

 Press return to continue. 


 cos(2*A)        :
 +1.0099e+00+8.5302e-03i  +1.8584e-02-4.5581e-03i  -1.9660e-02+2.4930e-02i 
 -5.5410e-04-2.3265e-03i  +1.0263e+00+1.7856e-02i  -1.8412e-02-1.2661e-02i 
 +1.7946e-02-1.1055e-02i  -1.8237e-02+8.2896e-04i  +1.0227e+00+5.0901e-03i 

 2cos(A)**2-1 :
 +1.0099e+00+8.5302e-03i  +1.8584e-02-4.5581e-03i  -1.9660e-02+2.4930e-02i 
 -5.5410e-04-2.3265e-03i  +1.0263e+00+1.7856e-02i  -1.8412e-02-1.2661e-02i 
 +1.7946e-02-1.1055e-02i  -1.8237e-02+8.2896e-04i  +1.0227e+00+5.0901e-03i 


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