typedef struct {double re,im;} COMPLEX;
 typedef enum {false, true} LOGIC;
 #define RADIX_BASE 16
 #define EPSZ 1.0e-13

 #define CZERO cmplx(0.0,0.0)
 #define CONE cmplx(1.0,0.0)
 #define ZI cmplx(0.0,1.0)
 #define PAI 3.1415926535e+00
 #define cabs(z) sqrt(ab2((z)))


 void rep_row_c(COMPLEX *a,int n,int org, int dis, int column);
 void rep_row(COMPLEX *a,int n,int org, int dis);
 void rpe_column(COMPLEX *a,int n, int org, int dis);
 void swap(COMPLEX *a,  COMPLEX *b);
 void hesse(COMPLEX *a,int *ip,int n, double eps);
 void balance(COMPLEX *z, int n, double *bv, double *zw);
 void normalize(COMPLEX *x,int n, int nmode);
 void mat_mul(COMPLEX *za,COMPLEX *zb,COMPLEX *zc,int m, int n, int k);
 void normalize(COMPLEX *x,int n, int nmode);
 void mat_mul(COMPLEX *za,COMPLEX *zb,COMPLEX *zc,int m, int n, int k);
 void evec(COMPLEX *z, int n, COMPLEX *ev,COMPLEX *vv,double *dv, int *iq, double ep, COMPLEX *x,COMPLEX *f);
 void ith_qrcon(COMPLEX *z,int n, int low, int up, COMPLEX *vv);
 void clear_mat(COMPLEX *a,int m,int n);
 int find_max(COMPLEX *a, int n,int row,int column, double *max);
 int clu(COMPLEX *a,int n, int *is,int *ip,double epsz);
 int lcx(COMPLEX *a,COMPLEX *b,int *ip, int *is, int n,double epsz);
 int inv_mat(COMPLEX *a,COMPLEX *b,COMPLEX *w,int *ip,int n, double epsz);
 int eigen(COMPLEX *z, int n, COMPLEX *ev,COMPLEX *vv,double *dv,int *iq, COMPLEX *f,COMPLEX *x);
 int expa(COMPLEX *z,double x, COMPLEX *ea,int n, COMPLEX *vv, COMPLEX *w, COMPLEX *ev,double *dv,int *ip);
 int dka();
 
 double norm(COMPLEX z);
 double ab2(COMPLEX z);
 double norm_row(COMPLEX *z,int n,int row, double norm_dia);
 double norm_column(COMPLEX *z,int n,int column, double norm_dia);
 double length(COMPLEX za,COMPLEX zb);
 double vec_norm(COMPLEX *x,int n);
 double mat_norm(COMPLEX *x,int n);
 double hesse_norm(COMPLEX *z, int n);
 
 COMPLEX cmplx(double a, double b);
 COMPLEX cmul(COMPLEX a, COMPLEX b);
 COMPLEX cadd(COMPLEX a, COMPLEX b);
 COMPLEX csub(COMPLEX a, COMPLEX b);
 COMPLEX cdiv(COMPLEX a, COMPLEX ax);
 COMPLEX conj(COMPLEX z);
 COMPLEX zexp(COMPLEX z);
 COMPLEX csqrt(COMPLEX z);
 COMPLEX cnega(COMPLEX z);
 COMPLEX cmul_r(COMPLEX z, double r);
 COMPLEX cdiv_r(COMPLEX z, double r);
 COMPLEX org_shift(COMPLEX *pz, int n, int count);
 COMPLEX max_c_element(COMPLEX *x, int n);
 COMPLEX ccosh(COMPLEX z);
 COMPLEX csinh(COMPLEX z);
 COMPLEX zsin(COMPLEX z);
 COMPLEX zcos(COMPLEX z);
 
 LOGIC con(COMPLEX z, double epsz);  
 
 
 int dka(double a[],COMPLEX z[],int n, double eps);