void *rk4_kernel( void *args ) {
kernel_args arguments = *( (kernel_args *) args );
vector k1, k2, k3, k4, initial, direction;
vector *points_aux = NULL;
size_t n_points_aux = 0, j = 0;
set( &initial, arguments.v0[arguments.id] );
set( &direction, arguments.field[DataSet::offset( arguments.n_x, arguments.n_y,
initial.x, initial.y, initial.z )] );
points_aux = (vector *) malloc( arguments.max_points * sizeof(vector) );
while ( module( direction ) > 0 && n_points_aux < arguments.max_points ) {
n_points_aux++;
set( &(points_aux[n_points_aux - 1]), initial);
set( &k1, mult_scalar( direction, arguments.h ) );
set( &k2, mult_scalar( trilinear_interpolation( sum( initial, mult_scalar( k1, 0.5 ) ),
arguments.n_x, arguments.n_y, arguments.n_z, arguments.field ), arguments.h ) );
set( &k3, mult_scalar( trilinear_interpolation( sum( initial, mult_scalar( k2, 0.5 ) ),
arguments.n_x, arguments.n_y, arguments.n_z, arguments.field ), arguments.h ) );
set( &k4, mult_scalar( trilinear_interpolation( sum( initial, k3 ),
arguments.n_x, arguments.n_y, arguments.n_z, arguments.field ), arguments.h ) );
set( &initial, sum( initial, sum( mult_scalar( k1 , 0.166666667 ),
sum( mult_scalar( k2, 0.333333333 ), sum( mult_scalar( k3, 0.333333333 ),
mult_scalar( k4, 0.166666667 ) ) ) ) ) );
set( &direction, trilinear_interpolation( initial, arguments.n_x, arguments.n_y, arguments.n_z,
arguments.field ) );
}
(arguments.fibers)[arguments.id] = Fiber( n_points_aux );
for ( j = 0; j < n_points_aux; j++ ) {
(arguments.fibers)[arguments.id].setPoint( j, points_aux[j] );
}
free( points_aux );
return NULL;
}
void int_quad(t_inter *pt, void *e, t_ray ray, t_light *light)
{
t_quad quad;
double t;
t_vec inter;
quad = *((t_quad *)e);
t = get_dist(ray, quad);
if (t < 0)
return ;
if (pt->dist == NULL || *(pt->dist) > t)
{
if (pt->dist == NULL)
pt->dist = malloc(sizeof(double));
free_info(pt);
*(pt->dist) = t;
inter = get_inter(ray, t);
pt->normal = get_normal_quad(inter, quad);
if (scalar_prod(pt->normal, ray.dir) > 0)
pt->normal = mult_scalar(pt->normal, -1);
pt->refl = get_refl(ray, pt->normal);
pt->color = quad.color;
pt->inter = inter;
get_info(pt, light, inter);
}
}
vector trilinear_interpolation( vector v0, int n_x, int n_y, int n_z, vector_field field ) {
int x1, y1, z1, x0, y0, z0;
double xd, yd, zd;
vector P1, P2, P3, P4, P5, P6, P7, P8, X1, X2, X3, X4, Y1, Y2, final;
x1 = ceil( v0.x );
y1 = ceil( v0.y );
z1 = ceil( v0.z );
x0 = floor( v0.x );
y0 = floor( v0.y );
z0 = floor( v0.z );
xd = v0.x - x0;
yd = v0.y - y0;
zd = v0.z - z0;
if ( x1 >= n_x || y1 >= n_y || z1 >= n_z || x0 < 0 || y0 < 0 || z0 < 0 ) {
return nearest_neighbour( v0, n_x, n_y, n_z, field );
} else {
set( &P1, field[DataSet::offset( n_x, n_y, x0, y0, z0 )] );
set( &P2, field[DataSet::offset( n_x, n_y, x1, y0, z0 )] );
set( &P3, field[DataSet::offset( n_x, n_y, x0, y0, z1 )] );
set( &P4, field[DataSet::offset( n_x, n_y, x1, y0, z1 )] );
set( &P5, field[DataSet::offset( n_x, n_y, x0, y1, z0 )] );
set( &P6, field[DataSet::offset( n_x, n_y, x1, y1, z0 )] );
set( &P7, field[DataSet::offset( n_x, n_y, x0, y1, z1 )] );
set( &P8, field[DataSet::offset( n_x, n_y, x1, y1, z1 )] );
set( &X1, sum( P1, mult_scalar( subtract( P2, P1 ), xd ) ) );
set( &X2, sum( P3, mult_scalar( subtract( P4, P3 ), xd ) ) );
set( &X3, sum( P5, mult_scalar( subtract( P6, P5 ), xd ) ) );
set( &X4, sum( P7, mult_scalar( subtract( P8, P7 ), xd ) ) );
set( &Y1, sum( X1, mult_scalar( subtract( X3, X1 ), yd ) ) );
set( &Y2, sum( X2, mult_scalar( subtract( X4, X2 ), yd ) ) );
set( &final, sum( Y1, mult_scalar( subtract( Y2, Y1 ), zd ) ) );
return final;
}
}
/******************************************************************************
FUNCTION:
transform
******************************************************************************/
void transform(const int dir, const int xn[4],
const Real center[4], su2_matrix *ptau[4],
su2_matrix *psu2_link)
{
Real x[4]; /* position component */
Real norm_current; /* normalization factor at current site */
Real norm_next; /* normalization factor at next site */
complex scalar; /* scalar factor */
su2_matrix prod; /* matrix product */
su2_matrix *pprod; /* pointer to matrix product */
su2_matrix gauge; /* guage transformation matrix */
su2_matrix *pgauge; /* pointer to gauge transformation matrix*/
su2_matrix inv; /* inverse gauge transformation */
su2_matrix *pinv; /* pointer to inverse gauge transformation */
su2_matrix temp; /* holding matrix */
su2_matrix *ptemp; /* pointer to holding matrix */
int k; /* index over forward directions */
int p; /* index over matrix row */
int q; /* index over matrix column */
/* set position components of current site relative to instanton center */
for (k = 0; k < 4; k++)
{
x[k] = (Real)xn[k] - center[k];
}
/* set normalization factor of current site */
norm_current = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2] + x[3] * x[3]);
/* initialize pointers to matrices */
pprod = ∏
pgauge = &gauge;
pinv = &inv;
ptemp = &temp;
/* set instanton link value */
switch (dir)
{
case 0:
norm_next = sqrt((x[0] + 1.0) * (x[0] + 1.0) + x[1] * x[1] + x[2] * x[2]
+ x[3] * x[3]);
scalar.real = 0.0;
scalar.imag = (x[0] + 1.0) / norm_next;
mult_scalar(pgauge, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = x[1] / norm_next;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = x[2] / norm_next;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pgauge, pprod);
scalar.real = x[3] / norm_next;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = -x[0] / norm_current;
mult_scalar(pinv, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = -x[1] / norm_current;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pinv, pprod);
scalar.real = 0.0;
scalar.imag = -x[2] / norm_current;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pinv, pprod);
scalar.real = x[3] / norm_current;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pinv, pprod);
break;
case 1:
norm_next = sqrt(x[0] * x[0] + (x[1] + 1.0) * (x[1] + 1.0) + x[2] * x[2]
+ x[3] * x[3]);
scalar.real = 0.0;
scalar.imag = x[0] / norm_next;
mult_scalar(pgauge, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = (x[1] + 1.0) / norm_next;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = x[2] / norm_next;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pgauge, pprod);
scalar.real = x[3] / norm_next;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = -x[0] / norm_current;
mult_scalar(pinv, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = -x[1] / norm_current;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pinv, pprod);
scalar.real = 0.0;
scalar.imag = -x[2] / norm_current;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pinv, pprod);
scalar.real = x[3] / norm_current;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pinv, pprod);
break;
case 2:
norm_next = sqrt(x[0] * x[0] + x[1] * x[1] + (x[2] + 1.0) * (x[2] + 1.0)
+ x[3] * x[3]);
scalar.real = 0.0;
scalar.imag = x[0] / norm_next;
mult_scalar(pgauge, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = x[1] / norm_next;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = (x[2] + 1.0) / norm_next;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pgauge, pprod);
scalar.real = x[3] / norm_next;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = -x[0] / norm_current;
mult_scalar(pinv, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = -x[1] / norm_current;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pinv, pprod);
scalar.real = 0.0;
scalar.imag = -x[2] / norm_current;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pinv, pprod);
scalar.real = x[3] / norm_current;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pinv, pprod);
break;
case 3:
norm_next = sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]
+ (x[3] + 1.0) * (x[3] + 1.0));
scalar.real = 0.0;
scalar.imag = x[0] / norm_next;
mult_scalar(pgauge, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = x[1] / norm_next;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = x[2] / norm_next;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pgauge, pprod);
scalar.real = (x[3] + 1.0) / norm_next;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pgauge, pprod);
scalar.real = 0.0;
scalar.imag = -x[0] / norm_current;
mult_scalar(pinv, scalar, ptau[0]);
scalar.real = 0.0;
scalar.imag = -x[1] / norm_current;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(pinv, pprod);
scalar.real = 0.0;
scalar.imag = -x[2] / norm_current;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(pinv, pprod);
scalar.real = x[3] / norm_current;
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(pinv, pprod);
break;
}
for (p = 0; p < 2; p++)
{
for (q = 0; q < 2; q++)
{
ptemp->e[p][q].real = psu2_link->e[p][q].real;
ptemp->e[p][q].imag = psu2_link->e[p][q].imag;
}
}
mult_su2(psu2_link, ptemp, pgauge);
for (p = 0; p < 2; p++)
{
for (q = 0; q < 2; q++)
{
ptemp->e[p][q].real = psu2_link->e[p][q].real;
ptemp->e[p][q].imag = psu2_link->e[p][q].imag;
}
}
mult_su2(psu2_link, pinv, ptemp);
}
/******************************************************************************
FUNCTION:
calc_su2_instanton_link
******************************************************************************/
void calc_su2_instanton_link(const int dir, const int xn[4],
const Real center[4], const Real rho,
su2_matrix *ptau[4], su2_matrix *psu2_link)
{
Real x[4]; /* position component */
Real normalization; /* normalization for unit 3-vector */
Real shape; /* shape factor, averaged over link */
Real theta; /* parameter in SU(2) exponential */
complex scalar; /* scalar factor */
su2_matrix prod; /* matrix product */
su2_matrix *pprod; /* pointer to matrix product */
int k; /* index over forward directions */
int p; /* index over matrix row */
int q; /* index over matrix column */
int m; /* index over link increments */
/* initialize link to zero */
for (p = 0; p < 2; p++)
{
for (q = 0; q < 2; q++)
{
psu2_link->e[p][q].real = 0.0;
psu2_link->e[p][q].imag = 0.0;
}
}
/* set position components of current site relative to instanton center */
for (k = 0; k < 4; k++)
{
x[k] = (Real)xn[k] - center[k];
}
/* initialize shape factor */
shape = 0.0;
/* initialize pointer to matrix product */
pprod = ∏
/* set instanton link value */
switch (dir)
{
case 0:
normalization = 1.0 / sqrt(x[1] * x[1] + x[2] * x[2] + x[3] * x[3]);
for (m = 0; m < SUBLINK; m++)
{
shape += 1.0
/ ((x[0] + m / (SUBLINK - 1.0)) * (x[0] + m / (SUBLINK - 1.0))
+ x[1] * x[1] + x[2] * x[2] + x[3] * x[3] + rho * rho);
}
shape /= (Real)SUBLINK;
theta = - shape / normalization;
scalar.real = 0.0;
scalar.imag = x[3] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[0]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = -x[2] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[1] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(psu2_link, pprod);
scalar.real = cos(theta);
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(psu2_link, pprod);
break;
case 1:
normalization = 1.0 / sqrt(x[0] * x[0] + x[2] * x[2] + x[3] * x[3]);
for (m = 0; m < SUBLINK; m++)
{
shape += 1.0
/ (x[0] * x[0]
+ (x[1] + m / (SUBLINK - 1.0)) * (x[1] + m / (SUBLINK - 1.0))
+ x[2] * x[2] + x[3] * x[3] + rho * rho);
}
shape /= (Real)SUBLINK;
theta = - shape / normalization;
scalar.real = 0.0;
scalar.imag = x[2] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[0]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[3] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = -x[0] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(psu2_link, pprod);
scalar.real = cos(theta);
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(psu2_link, pprod);
break;
case 2:
normalization = 1.0 / sqrt(x[0] * x[0] + x[1] * x[1] + x[3] * x[3]);
for (m = 0; m < SUBLINK; m++)
{
shape += 1.0
/ (x[0] * x[0] + x[1] * x[1]
+ (x[2] + m / (SUBLINK - 1.0)) * (x[2] + m / (SUBLINK - 1.0))
+ x[3] * x[3] + rho * rho);
}
shape /= (Real)SUBLINK;
theta = - shape / normalization;
scalar.real = 0.0;
scalar.imag = -x[1] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[0]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[0] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[3] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(psu2_link, pprod);
scalar.real = cos(theta);
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(psu2_link, pprod);
break;
case 3:
normalization = 1.0 / sqrt(x[0] * x[0] + x[1] * x[1] + x[2] * x[2]);
for (m = 0; m < SUBLINK; m++)
{
shape += 1.0 / (x[0] * x[0] + x[1] * x[1] + x[2] * x[2]
+ (x[3] + m / (SUBLINK - 1.0))
* (x[3] + m / (SUBLINK - 1.0)) + rho * rho);
}
shape /= (Real)SUBLINK;
theta = + shape / normalization;
scalar.real = 0.0;
scalar.imag = x[0] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[0]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[1] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[1]);
sum_su2(psu2_link, pprod);
scalar.real = 0.0;
scalar.imag = x[2] * sin(theta) * normalization;
mult_scalar(pprod, scalar, ptau[2]);
sum_su2(psu2_link, pprod);
scalar.real = cos(theta);
scalar.imag = 0.0;
mult_scalar(pprod, scalar, ptau[3]);
sum_su2(psu2_link, pprod);
break;
}
}
Vector*
Util::normal(Vector *v){
double mag = Util::mag(v);
double n = mag == 0 ? HUGE_VAL : 1 / mag;
return mult_scalar(v, n);
}
double distance( vector x, vector y ) {
return module( sum( x, mult_scalar( y, -1.0 ) ) );
}
