solve_henon_eqs.c

/*------------------------------------------------------------------------

エノン写像とヤコビ行列（線形化したエノン写像）

Henon map and the Jacobian matrix (linearized Henon map)

solve_henon_eqs.c

------------------------------------------------------------------------*/

#include "henon_lyap.h"

void henon_eqs( double (*x), double (*y), double (*detJ), double u[DIM][DIM] )

{

int i, j, k;

double xx;

double yy;

double d2;

double df[DIM][DIM];

double dfu[DIM][DIM];

// エノン写像

// Henon map

xx = 1.0 - A * (*x) * (*x) + (*y);

yy = B * (*x);

// (*x): x[t],  (*y): y[t]

//   xx: x[t+1],  yy: y[t+1]

// ヤコビ行列

// Jacobian  matrix

df[0][0] = -2.0 * A * (*x);

df[0][1] = 1.0;

df[1][0] = B;

df[1][1] = 0.0;

(*x) = xx;

(*y) = yy;

/*

｜ df[0][0]  df[0][1] ｜

df = ｜ ｜

｜ df[1][0]  df[1][1] ｜

*/

// ヤコビアン行列式

// Jacobian determinant

(*detJ) = fabs( df[0][0] * df[1][1] - df[0][1] * df[1][0] );

// ヤコビ行列を用いて微小変位ベクトルを計算

// calculate the micro-displacement vector using the Jacobian matrix

for ( i = 0; i < DIM; i++ ) {

for ( j = 0; j < DIM; j++ ) {

d2 = 0.0;

for ( k = 0; k < DIM; k++ ) {

d2 += df[i][k] * u[k][j];

}

dfu[i][j] = d2;

}

}

for ( i = 0; i < DIM; i++ ) {

for ( j = 0; j < DIM; j++ ) {

u[i][j] = dfu[i][j];

}

}

}