void RK4_step(double delta_t, double t, double *x, double *v){
double k1, k2, k3, k4;
double l1, l2, l3, l4;
double x_in;
double v_in;
x_in = *x;
v_in = *v;
k1 = deriv_x(t,x_in,v_in);
l1 = deriv_v(t,x_in,v_in);
k2 = deriv_x(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5);
l2 = deriv_v(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5) ;
k3 = deriv_x(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5);
l3 = deriv_v(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5);
k4 = deriv_x(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t);
l4 = deriv_v(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t);
x_in += (k1/6.0 + k2/3.0 + k3/3.0 + k4/6.0)*delta_t;
v_in += (l1/6.0 + l2/3.0 + l3/3.0 + l4/6.0)*delta_t;
*x = x_in;
*v = v_in;
}
void leapfrog_step(double delta_t, double t, double *x, double *v){
double x_in;
double v_in;
x_in = *x;
v_in = *v;
/*Third order*/
x_in += 1.0 * v_in * delta_t;
v_in += -1.0/24.0 * deriv_v(t, x_in, v_in) * delta_t;
x_in += -2.0/3.0 * v_in * delta_t;
v_in += 3.0/4.0 * deriv_v(t, x_in, v_in) * delta_t;
x_in += 2.0/3.0 * v_in * delta_t;
v_in += 7.0/24.0 * deriv_v(t, x_in, v_in) * delta_t;
/*Inverted
x_in += 0.5 * v_in * delta_t;
v_in += 1.0 * deriv_v(t, x_in, v_in) * delta_t;
x_in += 0.5 * v_in * delta_t;
*/
/*Normal
v_in += 0.5 * deriv_v(t, x_in, v_in) * delta_t;
x_in += 1.0 * v_in * delta_t;
v_in += 0.5 * deriv_v(t, x_in, v_in) * delta_t;
*/
*x = x_in;
*v = v_in;
}
void leapfrog_step(double delta_t, double t, double *x, double *v){
double x_in;
double v_in;
x_in = *x;
v_in = *v;
v_in += 1.0 * deriv_v(t,x_in,v_in) * delta_t;
x_in += -1.0/24.0 * v_in * delta_t;
v_in += -2.0/3.0 * deriv_v(t,x_in,v_in) * delta_t;
x_in += 3.0/4.0 * v_in * delta_t;
v_in += 2.0/3.0 * deriv_v(t,x_in,v_in) * delta_t;
x_in += 7.0/24.0 * v_in * delta_t;
/*kick*/
// v_in += 0.5 * deriv_v(t,x_in,v_in) * delta_t;
/*drift*/
// x_in += 1.0 * v_in * delta_t;
/*kick*/
// v_in += 0.5 * deriv_v(t, x_in, v_in) * delta_t;
*x = x_in;
*v = v_in;
}
void RK4_step(double delta_t, double e, double t, double *x, double *v,double *x3,double *v3){
double k1, k2, k3, k4;
double l1, l2, l3, l4;
double m1, m2, m3, m4;
double n1, n2, n3, n4;
double x_in;
double v_in;
double x3_in;
double v3_in;
x_in = *x;
v_in = *v;
x3_in = *x3;
v3_in = *v3;
k1 = deriv_x(t,x_in,v_in);
l1 = deriv_v(t,x_in,v_in,e);
k2 = deriv_x(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5);
l2 = deriv_v(t + delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5,e) ;
k3 = deriv_x(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5);
l3 = deriv_v(t + delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5,e);
k4 = deriv_x(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t);
l4 = deriv_v(t + delta_t, x_in + k3*delta_t, v_in + l3*delta_t,e);
x_in += (k1/6.0 + k2/3.0 + k3/3.0 + k4/6.0)*delta_t;
v_in += (l1/6.0 + l2/3.0 + l3/3.0 + l4/6.0)*delta_t;
m1 = deriv_x3(t,x3_in,v3_in);
n1 = deriv_v3(t,x3_in,x_in,v_in,e);
m2 = deriv_x3(t + delta_t*0.5, x3_in + m1*delta_t*0.5, v3_in + n1*delta_t*0.5);
n2 = deriv_v3(t + delta_t*0.5, x3_in + m1*delta_t*0.5, x_in + k1*delta_t*0.5, v_in + l1*delta_t*0.5,e) ;
m3 = deriv_x3(t + delta_t*0.5, x3_in + m2*delta_t*0.5, v3_in + n2*delta_t*0.5);
n3 = deriv_v3(t + delta_t*0.5, x3_in + m2*delta_t*0.5, x_in + k2*delta_t*0.5, v_in + l2*delta_t*0.5,e);
m4 = deriv_x3(t + delta_t, x3_in + m3*delta_t, v3_in + n3*delta_t);
n4 = deriv_v3(t + delta_t, x3_in + m3*delta_t, x_in + k3*delta_t, v_in + l3*delta_t,e);
x3_in += (m1/6.0 + m2/3.0 + m3/3.0 + m4/6.0)*delta_t;
v3_in += (n1/6.0 + n2/3.0 + n3/3.0 + n4/6.0)*delta_t;
*x = x_in;
*v = v_in;
*x3 = x3_in;
*v3 = v3_in;
}
void leapfrog_step(double delta_t,double e, double t, double *x, double *v,double *x3,double *v3){
double x_in,x3_in;
double v_in,v3_in;
x_in = *x;
v_in = *v;
x3_in=*x3;
v3_in=*v3;
x_in += 1/(2*(2-pow(2,1/3)))* v_in * delta_t;
v_in += 1/(2-pow(2,1/3)) * deriv_v(t,x_in,v_in,e) * delta_t;
x_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v_in * delta_t;
v_in += -pow(2,1/3)/(2-pow(2,1/3)) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v_in * delta_t;
v_in += 1/(2-pow(2,1/3)) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += 1/(2*(2-pow(2,1/3))) * v_in * delta_t;
x3_in += 1/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += 1/(2-pow(2,1/3)) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += -pow(2,1/3)/(2-pow(2,1/3)) * deriv_v3(t, x3_in,x_in, v_in,e) * delta_t;
x3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * v3_in * delta_t;
v3_in += 1/(2-pow(2,1/3)) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2*(2-pow(2,1/3))) * v3_in * delta_t;
/*v_in += 1/(2*(2-pow(2,1/3)))* deriv_v(t,x_in,v_in,e) * delta_t;
x_in += 1/(2-pow(2,1/3)) * v_in * delta_t;
v_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += -pow(2,1/3)/(2-pow(2,1/3)) * v_in * delta_t;
v_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v(t, x_in, v_in,e) * delta_t;
x_in += 1/(2-pow(2,1/3)) * v_in * delta_t;
v_in += 1/(2*(2-pow(2,1/3)))* deriv_v(t, x_in, v_in,e) * delta_t;
v3_in += 1/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v3(t, x3_in,x_in, v_in,e) * delta_t;
x3_in += -pow(2,1/3)/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += (1-pow(2,1/3))/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;
x3_in += 1/(2-pow(2,1/3)) * v3_in * delta_t;
v3_in += 1/(2*(2-pow(2,1/3))) * deriv_v3(t,x3_in,x_in,v_in,e) * delta_t;*/
*x = x_in;
*v = v_in;
*x3=x3_in;
*v3=v3_in;
}
/* for findSplit */
void AzReg_TsrSib::reset_forNewLeaf(const AzTrTree_ReadOnly *inp_tree,
const AzRegDepth *inp_reg_depth)
{
tree = inp_tree;
forNewLeaf = true;
focus_nx = -1;
reg_depth = inp_reg_depth;
int node_num = tree->nodeNum();
/*--- set v ---*/
v_v.reform(node_num);
int nx;
for (nx = 0; nx < node_num; ++nx) {
if (!tree->node(nx)->isLeaf()) continue;
deriv_v(tree, nx, false, NULL, &v_v);
}
reset_values();
}
/* for findSplit */
void AzReg_TsrSib::reset_forNewLeaf(int inp_focus_nx,
const AzTrTree_ReadOnly *inp_tree,
const AzRegDepth *inp_reg_depth)
{
tree = inp_tree;
forNewLeaf = true;
focus_nx = inp_focus_nx;
reg_depth = inp_reg_depth;
int node_num = tree->nodeNum();
/*--- set derivatives w.r.t. the weight of the new leaf ---*/
av_dv.reset(node_num);
AzSvect *v_dv = av_dv.point_u(focus_nx);
deriv_v(tree, focus_nx, forNewLeaf, v_dv, NULL);
if (v_v.rowNum() != node_num) {
throw new AzException("AzReg_TsrSib::sib_reset_forNewLeaf",
"v_v is not initialized");
}
update();
}
/* for optimization */
void AzReg_TsrSib::reset(const AzTrTree_ReadOnly *inp_tree,
const AzRegDepth *inp_reg_depth)
{
tree = inp_tree;
forNewLeaf = false;
focus_nx = -1;
reg_depth = inp_reg_depth;
if (tree == NULL) {
throw new AzException("AzReg_TsrSib::reset", "null tree");
}
int node_num = tree->nodeNum();
av_dv.reset(node_num);
v_v.reform(node_num);
int nx;
for (nx = 0; nx < node_num; ++nx) {
if (!tree->node(nx)->isLeaf()) continue;
deriv_v(tree, nx, false, av_dv.point_u(nx), &v_v);
}
reset_values();
}
