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/* Copyright (C) 2005-2015 Massachusetts Institute of Technology
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2, or (at your option)
% any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software Foundation,
% Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <complex>
#include "meep_internals.hpp"
using namespace std;
namespace meep {
ivec grid_volume::round_vec(const vec &p) const {
ivec result(dim);
LOOP_OVER_DIRECTIONS(dim, d)
result.set_direction(d, my_round(p.in_direction(d) * 2 * a));
return result;
}
void grid_volume::set_origin(const ivec &o) {
io = o;
origin = operator[](io); // adjust origin to match io
}
void grid_volume::set_origin(direction d, int o) {
io.set_direction(d, o);
origin = operator[](io); // adjust origin to match io
}
void grid_volume::set_origin(const vec &o) {
set_origin(round_vec(o));
}
const char *dimension_name(ndim dim) {
switch (dim) {
case D1: return "1D";
case D2: return "2D";
case D3: return "3D";
case Dcyl: return "Cylindrical";
}
return "Error in dimension_name";
}
const char *direction_name(direction d) {
switch (d) {
case X: return "x";
case Y: return "y";
case Z: return "z";
case R: return "r";
case P: return "phi";
case NO_DIRECTION: return "no_direction";
}
return "Error in direction_name";
}
const char *component_name(component c) {
if (is_derived(int(c))) return component_name(derived_component(c));
switch (c) {
case Er: return "er";
case Ep: return "ep";
case Ez: return "ez";
case Hr: return "hr";
case Hp: return "hp";
case Hz: return "hz";
case Ex: return "ex";
case Ey: return "ey";
case Hx: return "hx";
case Hy: return "hy";
case Dx: return "dx";
case Dy: return "dy";
case Dz: return "dz";
case Dr: return "dr";
case Dp: return "dp";
case Bx: return "bx";
case By: return "by";
case Bz: return "bz";
case Br: return "br";
case Bp: return "bp";
case Dielectric: return "eps";
case Permeability: return "mu";
}
return "Error in component_name";
}
const char *component_name(derived_component c) {
if (!is_derived(int(c))) return component_name(component(c));
switch (c) {
case Sr: return "sr";
case Sp: return "sp";
case Sz: return "sz";
case Sx: return "sx";
case Sy: return "sy";
case EnergyDensity: return "energy";
case D_EnergyDensity: return "denergy";
case H_EnergyDensity: return "henergy";
}
return "Error in component_name";
}
const char *component_name(int c) {
return (is_derived(c) ? component_name(derived_component(c))
: component_name(component(c)));
}
component first_field_component(field_type ft) {
switch (ft) {
case E_stuff: return Ex;
case H_stuff: return Hx;
case D_stuff: return Dx;
case B_stuff: return Bx;
default: abort("bug - only E/H/D/B stuff have components");
}
}
vec min(const vec &vec1, const vec &vec2) {
vec m(vec1.dim);
LOOP_OVER_DIRECTIONS(vec1.dim, d)
m.set_direction(d, min(vec1.in_direction(d), vec2.in_direction(d)));
return m;
}
vec max(const vec &vec1, const vec &vec2) {
vec m(vec1.dim);
LOOP_OVER_DIRECTIONS(vec1.dim, d)
m.set_direction(d, max(vec1.in_direction(d), vec2.in_direction(d)));
return m;
}
ivec min(const ivec &ivec1, const ivec &ivec2) {
ivec m(ivec1.dim);
LOOP_OVER_DIRECTIONS(ivec1.dim, d)
m.set_direction(d, min(ivec1.in_direction(d), ivec2.in_direction(d)));
return m;
}
ivec max(const ivec &ivec1, const ivec &ivec2) {
ivec m(ivec1.dim);
LOOP_OVER_DIRECTIONS(ivec1.dim, d)
m.set_direction(d, max(ivec1.in_direction(d), ivec2.in_direction(d)));
return m;
}
volume::volume(const vec &vec1, const vec &vec2) {
min_corner = min(vec1, vec2);
max_corner = max(vec1, vec2);
dim = vec1.dim;
}
volume::volume(const vec &pt) {
dim = pt.dim;
min_corner = pt;
max_corner = pt;
}
double volume::computational_volume() const {
double vol = 1.0;
LOOP_OVER_DIRECTIONS(dim,d) vol *= in_direction(d);
return vol;
}
double volume::integral_volume() const {
double vol = 1.0;
LOOP_OVER_DIRECTIONS(dim, d)
if (in_direction(d) != 0.0) vol *= in_direction(d);
if (dim == Dcyl) vol *= pi * (in_direction_max(R) + in_direction_min(R));
return vol;
}
double volume::full_volume() const {
double vol = computational_volume();
if (dim == Dcyl) vol *= pi * (in_direction_max(R) + in_direction_min(R));
return vol;
}
double volume::diameter() const {
double diam = 0.0;
LOOP_OVER_DIRECTIONS(dim,d) {
diam = max(diam, in_direction(d));
}
return diam;
}
volume volume::intersect_with(const volume &a) const {
if (a.dim != dim) abort("Can't intersect volumes of dissimilar dimensions.\n");
volume result(dim);
LOOP_OVER_DIRECTIONS(dim, d) {
double minval = max(in_direction_min(d), a.in_direction_min(d));
double maxval = min(in_direction_max(d), a.in_direction_max(d));
if (minval > maxval)
return volume(zero_vec(dim), zero_vec(dim));
result.set_direction_min(d, minval);
result.set_direction_max(d, maxval);
}
return result;
}
bool volume::intersects(const volume &a) const {
if (a.dim != dim) abort("Can't intersect volumes of dissimilar dimensions.\n");
LOOP_OVER_DIRECTIONS(dim, d) {
double minval = max(in_direction_min(d), a.in_direction_min(d));
double maxval = min(in_direction_max(d), a.in_direction_max(d));
if (minval > maxval)
return false;
}
return true;
}
// Return normal direction to grid_volume, if the grid_volume is dim-1 dimensional;
// otherwise, return NO_DIRECTION.
direction volume::normal_direction() const {
direction d = NO_DIRECTION;
switch (dim) {
case D1: d = Z; break;
case D2:
if (in_direction(X) == 0 && in_direction(Y) > 0)
d = X;
else if (in_direction(X) > 0 && in_direction(Y) == 0)
d = Y;
break;
case Dcyl:
if (in_direction(R) == 0 && in_direction(Z) > 0)
d = R;
else if (in_direction(R) > 0 && in_direction(Z) == 0)
d = Z;
break;
case D3: {
bool zx = in_direction(X) == 0;
bool zy = in_direction(Y) == 0;
bool zz = in_direction(Z) == 0;
if (zx && !zy && !zz) d = X;
else if (!zx && zy && !zz) d = Y;
else if (!zx && !zy && zz) d = Z;
break;
}
}
return d;
}
/* Used for n=0,1,2 nested loops in macros. We should arrange
the ordering so that this gives most efficient traversal of
a field array, where n=2 is the innermost loop. */
static direction yucky_dir(ndim dim, int n) {
if (dim == Dcyl)
switch (n) {
case 0: return P;
case 1: return R;
case 2: return Z;
}
else if (dim == D2)
return (direction) ((n + 2) % 3); /* n = 0,1,2 gives Z, X, Y */
return (direction) n ;
}
int ivec::yucky_val(int n) const {
if (has_direction(dim, yucky_dir(dim, n)))
return in_direction(yucky_dir(dim, n));
return 0;
}
int grid_volume::yucky_num(int n) const {
if (has_direction(dim, yucky_dir(dim, n)))
return num_direction(yucky_dir(dim, n));
return 1;
}
direction grid_volume::yucky_direction(int n) const {
return yucky_dir(dim, n);
}
volume grid_volume::surroundings() const {
return volume(operator[](little_corner()),
operator[](big_corner()));
}
volume grid_volume::interior() const {
return volume(operator[](little_corner()),
operator[](big_corner() - one_ivec(dim) * 2));
}
void grid_volume::update_ntot() {
the_ntot = 1;
LOOP_OVER_DIRECTIONS(dim, d) the_ntot *= num[d%3] + 1;
}
void grid_volume::set_num_direction(direction d, int value) {
num[d%3] = value; num_changed();
}
grid_volume::grid_volume(ndim td, double ta, int na, int nb, int nc) {
dim = td; a = ta; inva = 1.0 / ta;
num[0] = na;
num[1] = nb;
num[2] = nc;
num_changed();
set_origin(zero_vec(dim));
}
component grid_volume::eps_component() const {
switch (dim) {
case D1: return Hy;
case D2: return Hz;
case D3: return Dielectric;
case Dcyl: return Hp;
}
abort("Unsupported dimensionality eps.\n");
return Ex;
}
vec grid_volume::yee_shift(component c) const {
return operator[](iyee_shift(c));
}
/* Return array offsets to average with a given array location of c in
order to get c on the "centered" grid. Then, to get the
centered grid point i, you should average c over the four
locations: i, i+offset1, i+offset2, i+offset1+offset2.
(offset2, and possibly offset1, may be zero if only 2 or 1
locations need to be averaged). */
void grid_volume::yee2cent_offsets(component c, int &offset1, int &offset2) const {
offset1 = offset2 = 0;
LOOP_OVER_DIRECTIONS(dim,d) {
if (!iyee_shift(c).in_direction(d)) {
if (offset2)
abort("weird yee shift for component %s", component_name(c));
if (offset1) offset2 = stride(d);
else offset1 = stride(d);
}
}
}
/* Same as yee2cent_offsets, but averages centered grid to get c */
void grid_volume::cent2yee_offsets(component c, int &offset1, int &offset2) const {
yee2cent_offsets(c, offset1, offset2);
offset1 = -offset1;
offset2 = -offset2;
}
bool volume::contains(const vec &p) const {
LOOP_OVER_DIRECTIONS(dim,d) {
if (p.in_direction(d) > in_direction_max(d) ||
p.in_direction(d) < in_direction_min(d)) return false;
}
return true;
}
bool volume::contains(const volume &a) const {
return contains(a.get_min_corner()) && contains(a.get_max_corner());
}
bool grid_volume::contains(const ivec &p) const {
// containts returns true if the grid_volume has information about this grid
// point.
const ivec o = p - io;
LOOP_OVER_DIRECTIONS(dim, d)
if (o.in_direction(d) < 0 || o.in_direction(d) >= (num_direction(d)+1)*2)
return false;
return true;
}
bool grid_volume::contains(const vec &p) const {
// containts returns true if the grid_volume has any information in it
// relevant to the point p. Basically has is like owns (see below)
// except it is more lenient, in that more than one lattice may contain a
// given point.
const vec o = p - origin;
LOOP_OVER_DIRECTIONS(dim, d)
if (o.in_direction(d) < -inva || o.in_direction(d) > num_direction(d)*inva+inva)
return false;
return true;
}
/* Compute the corners (cs,ce) of the ib-th boundary for component c,
returning true if ib is a valid index (ib = 0..#boundaries-1). The
boundaries are all the points that are in but not owned by the
grid_volume, and are a set of *disjoint* regions. The main purpose of
this function is currently to support the LOOP_OVER_NOT_OWNED
macro. (In the future, it may be used for other
boundary-element-type computations, too.) */
bool grid_volume::get_boundary_icorners(component c, int ib,
ivec *cs, ivec *ce) const {
ivec cl(little_corner() + iyee_shift(c));
ivec cb(big_corner() + iyee_shift(c));
ivec clo(little_owned_corner(c));
ivec cbo(big_corner() - iyee_shift(c));
*cs = cl;
*ce = cb;
bool ib_found = false;
int jb = 0;
LOOP_OVER_DIRECTIONS(dim, d) {
if (cl.in_direction(d) < clo.in_direction(d)) {
if (jb == ib) {
ce->set_direction(d, cs->in_direction(d));
ib_found = true;
break;
}
cs->set_direction(d, clo.in_direction(d));
jb++;
}
if (cb.in_direction(d) > cbo.in_direction(d)) {
if (jb == ib) {
cs->set_direction(d, ce->in_direction(d));
ib_found = true;
break;
}
ce->set_direction(d, cbo.in_direction(d));
jb++;
}
}
if (!ib_found) { // yucky interaction here with LOOP_OVER_VOL_NOTOWNED
*cs = one_ivec(dim);
*ce = -one_ivec(dim);
}
return ib_found;
}
// first "owned" point for c in grid_volume (see also grid_volume::owns)
ivec grid_volume::little_owned_corner(component c) const {
ivec iloc(little_owned_corner0(c));
if (dim == Dcyl && origin.r() == 0.0 && iloc.r() == 2)
iloc.set_direction(R, 0);
return iloc;
}
int grid_volume::nowned(component c) const {
int n = 1;
ivec pt = big_corner() - little_owned_corner(c);
LOOP_OVER_DIRECTIONS(dim, d) n *= pt.in_direction(d) / 2 + 1;
return n;
}
bool grid_volume::owns(const ivec &p) const {
// owns returns true if the point "owned" by this grid_volume, meaning that it
// is the grid_volume that would timestep the point.
const ivec o = p - io;
if (dim == Dcyl) {
if (origin.r() == 0.0 && o.z() > 0 && o.z() <= nz()*2 &&
o.r() == 0) return true;
return o.r() > 0 && o.z() > 0 &&
o.r() <= nr()*2 && o.z() <= nz()*2;
} else if (dim == D3) {
return
o.x() > 0 && o.x() <= nx()*2 &&
o.y() > 0 && o.y() <= ny()*2 &&
o.z() > 0 && o.z() <= nz()*2;
} else if (dim == D2) {
return
o.x() > 0 && o.x() <= nx()*2 &&
o.y() > 0 && o.y() <= ny()*2;
} else if (dim == D1) {
return o.z() > 0 && o.z() <= nz()*2;
} else {
abort("Unsupported dimension in owns.\n");
return false;
}
}
int grid_volume::has_boundary(boundary_side b,direction d) const {
switch (dim) {
case Dcyl: return d == Z || (d == R && (b == High || get_origin().r() > 0));
case D1: return d == Z;
case D2: return d == X || d == Y;
case D3: return d == X || d == Y || d == Z;
}
return 0; // This should never be reached.
}
int grid_volume::index(component c, const ivec &p) const {
const ivec offset = p - io - iyee_shift(c);
int idx = 0;
LOOP_OVER_DIRECTIONS(dim,d) idx += offset.in_direction(d)/2*stride(d);
return idx;
}
void grid_volume::set_strides() {
FOR_DIRECTIONS(d) the_stride[d] = 0; // Yuck yuck yuck.
LOOP_OVER_DIRECTIONS(dim,d)
switch(d) {
case Z: the_stride[d] = 1; break;
case R: the_stride[d] = nz()+1; break;
case X: the_stride[d] = (nz()+1)*(ny() + 1); break;
case Y: the_stride[d] = nz() + 1; break;
case P: break; // There is no phi stride...
case NO_DIRECTION: break; // no stride here, either
}
}
static inline void stupidsort(int *ind, double *w, int l) {
while (l) {
if (fabs(w[0]) < 2e-15) {
w[0] = w[l-1];
ind[0] = ind[l-1];
w[l-1] = 0.0;
ind[l-1] = 0;
} else {
w += 1;
ind += 1;
}
l -= 1;
}
}
static inline void stupidsort(ivec *locs, double *w, int l) {
while (l) {
if (fabs(w[0]) < 2e-15) {
w[0] = w[l-1];
locs[0] = locs[l-1];
w[l-1] = 0.0;
locs[l-1] = 0;
} else {
w += 1;
locs += 1;
}
l -= 1;
}
}
void grid_volume::interpolate(component c, const vec &p,
int indices[8], double weights[8]) const {
ivec locs[8];
interpolate(c, p, locs, weights);
for (int i=0;i<8&&weights[i];i++)
if (!owns(locs[i])) weights[i] = 0.0;
stupidsort(locs, weights, 8);
for (int i=0;i<8&&weights[i];i++)
indices[i] = index(c, locs[i]);
if (!contains(p) && weights[0]) {
printf("Error at point %g %g\n", p.r(), p.z());
printf("Interpolated to point %d %d\n", locs[0].r(), locs[0].z());
printf("Or in other words... %g %g\n",
operator[](locs[0]).r(), operator[](locs[0]).z());
printf("I %s own the interpolated point.\n",
owns(locs[0])?"actually":"don't");
print();
abort("Error made in interpolation of %s--fix this bug!!!\n",
component_name(c));
}
// Throw out out of range indices:
for (int i=0;i<8&&weights[i];i++)
if (indices[0] < 0 || indices[0] >= ntot()) weights[i] = 0.0;
// Stupid very crude code to compactify arrays:
stupidsort(indices, weights, 8);
if (!contains(p) && weights[0]) {
printf("Error at point %g %g\n", p.r(), p.z());
printf("Interpolated to point %d %d\n", locs[0].r(), locs[0].z());
print();
abort("Error made in interpolation of %s--fix this bug!!!\n",
component_name(c));
}
}
void grid_volume::interpolate(component c, const vec &pc,
ivec locs[8], double weights[8]) const {
const double SMALL = 1e-13;
const vec p = (pc - yee_shift(c))*a;
ivec middle(dim);
LOOP_OVER_DIRECTIONS(dim,d)
middle.set_direction(d, ((int) floor(p.in_direction(d)))*2+1);
middle += iyee_shift(c);
const vec midv = operator[](middle);
const vec dv = (pc - midv)*(2*a);
int already_have = 1;
for (int i=0;i<8;i++) {
locs[i] = round_vec(midv);
weights[i] = 1.0;
}
LOOP_OVER_DIRECTIONS(dim,d) {
for (int i=0;i<already_have;i++) {
locs[already_have+i] = locs[i];
weights[already_have+i] = weights[i];
locs[i].set_direction(d,middle.in_direction(d)-1);
weights[i] *= 0.5*(1.0-dv.in_direction(d));
locs[already_have+i].set_direction(d,middle.in_direction(d)+1);
weights[already_have+i] *= 0.5*(1.0+dv.in_direction(d));
}
already_have *= 2;
}
for (int i=already_have;i<8;i++) weights[i] = 0.0;
double total_weight = 0.0;
for (int i=0;i<already_have;i++) total_weight += weights[i];
for (int i=0;i<already_have;i++)
weights[i] += (1.0 - total_weight)*(1.0/already_have);
for (int i=0;i<already_have;i++) {
if (weights[i] < 0.0) {
if (-weights[i] >= SMALL * 1e5)
abort("large negative interpolation weight[%d] = %e\n", i, weights[i]);
weights[i] = 0.0;
}
else if (weights[i] < SMALL)
weights[i] = 0.0;
}
stupidsort(locs, weights, already_have);
// The rest of this code is a crude hack to get the weights right when we
// are exactly between a few grid points. i.e. to eliminate roundoff
// error.
bool all_same = true;
for (int i=0;i<8&&weights[i];i++)
if (weights[i] != weights[0]) all_same = false;
if (all_same) {
int num_weights = 0;
for (int i=0;i<8&&weights[i];i++) num_weights++;
for (int i=0;i<8&&weights[i];i++) weights[i] = 1.0/num_weights;
}
}
volume empty_volume(ndim dim) {
volume out(dim);
LOOP_OVER_DIRECTIONS(dim,d) {
out.set_direction_max(d,0.0);
out.set_direction_min(d,0.0);
}
return out;
}
volume grid_volume::dV(const ivec &here, double diameter) const {
const double hinva = 0.5*inva * diameter;
const grid_volume &gv = *this;
const vec h = gv[here];
volume out(dim);
LOOP_OVER_DIRECTIONS(dim,d) {
out.set_direction_max(d,h.in_direction(d)+hinva);
out.set_direction_min(d,h.in_direction(d)-hinva);
}
if (dim == Dcyl && here.r() == 0) {
out.set_direction_min(R,0.0);
}
return out;
}
volume grid_volume::dV(component c, int ind) const {
if (!owns(iloc(c, ind))) return empty_volume(dim);
return dV(iloc(c,ind));
}
double grid_volume::xmax() const {
const double qinva = 0.25*inva;
return origin.x() + nx()*inva + qinva;
}
double grid_volume::xmin() const {
const double qinva = 0.25*inva;
return origin.x() + qinva;
}
double grid_volume::ymax() const {
const double qinva = 0.25*inva;
return origin.y() + ny()*inva + qinva;
}
double grid_volume::ymin() const {
const double qinva = 0.25*inva;
return origin.y() + qinva;
}
double grid_volume::zmax() const {
const double qinva = 0.25*inva;
return origin.z() + nz()*inva + qinva;
}
double grid_volume::zmin() const {
const double qinva = 0.25*inva;
return origin.z() + qinva;
}
double grid_volume::rmax() const {
const double qinva = 0.25*inva;
if (dim == Dcyl) return origin.r() + nr()*inva + qinva;
abort("No rmax in these dimensions.\n");
return 0.0; // This is never reached.
}
double grid_volume::rmin() const {
const double qinva = 0.25*inva;
if (dim == Dcyl) {
if (origin.r() == 0.0) {
return 0.0;
} else {
return origin.r() + qinva;
}
}
abort("No rmin in these dimensions.\n");
return 0.0; // This is never reached.
}
double vec::project_to_boundary(direction d, double boundary_loc) {
return fabs(boundary_loc - in_direction(d));
}
double grid_volume::boundary_location(boundary_side b, direction d) const {
// Returns the location of metallic walls...
if (b == High) switch (d) {
case X: return loc(Ez,ntot()-1).x();
case Y: return loc(Ez,ntot()-1).y();
case R: return loc(Ep,ntot()-1).r();
case Z: if (dim == Dcyl) return loc(Ep,ntot()-1).z();
else return loc(Ex,ntot()-1).z();
case P: abort("P has no boundary!\n");
case NO_DIRECTION: abort("NO_DIRECTION has no boundary!\n");
}
else switch (d) {
case X: return loc(Ez,0).x();
case Y: return loc(Ez,0).y();
case R: return loc(Ep,0).r();
case Z: if (dim == Dcyl) return loc(Ep,0).z();
else return loc(Ex,0).z();
case P: abort("P has no boundary!\n");
case NO_DIRECTION: abort("NO_DIRECTION has no boundary!\n");
}
return 0.0;
}
ivec grid_volume::big_corner() const {
switch (dim) {
case D1: return io + ivec(nz())*2;
case D2: return io + ivec(nx(),ny())*2;
case D3: return io + ivec(nx(),ny(),nz())*2;
case Dcyl: return io + iveccyl(nr(),nz())*2;
}
return ivec(0); // This is never reached.
}
vec grid_volume::corner(boundary_side b) const {
if (b == Low) return origin; // Low corner
vec tmp = origin;
LOOP_OVER_DIRECTIONS(dim, d)
tmp.set_direction(d, tmp.in_direction(d) + num_direction(d) * inva);
return tmp; // High corner
}
void grid_volume::print() const {
LOOP_OVER_DIRECTIONS(dim, d)
printf("%s =%5g - %5g (%5g) \t",
direction_name(d), origin.in_direction(d),
origin.in_direction(d)+num_direction(d)/a, num_direction(d)/a);
printf("\n");
}
bool grid_volume::intersect_with(const grid_volume &vol_in, grid_volume *intersection, grid_volume *others, int *num_others) const {
int temp_num[3] = {0,0,0};
ivec new_io(dim);
LOOP_OVER_DIRECTIONS(dim, d) {
int minval = max(little_corner().in_direction(d), vol_in.little_corner().in_direction(d));
int maxval = min(big_corner().in_direction(d), vol_in.big_corner().in_direction(d));
if (minval >= maxval)
return false;
temp_num[d%3] = (maxval - minval)/2;
new_io.set_direction(d, minval);
}
if (intersection != NULL) {
*intersection = grid_volume(dim, a, temp_num[0], temp_num[1], temp_num[2]); // fix me : ugly, need new constructor
intersection->set_origin(new_io);
}
if (others != NULL) {
int counter = 0;
grid_volume vol_containing = *this;
LOOP_OVER_DIRECTIONS(dim, d) {
if (vol_containing.little_corner().in_direction(d)
< vol_in.little_corner().in_direction(d)) {
// shave off lower slice from vol_containing and add it to others
grid_volume other = vol_containing;
const int thick = (vol_in.little_corner().in_direction(d)
- vol_containing.little_corner().in_direction(d))/2;
other.set_num_direction(d, thick);
others[counter] = other;
counter++;
vol_containing.shift_origin(d, thick*2);
vol_containing.set_num_direction(d, vol_containing.num_direction(d)
- thick);
if (vol_containing.little_corner().in_direction(d)
< vol_in.little_corner().in_direction(d))
abort("intersect_with: little corners differ by odd integer?");
}
if (vol_containing.big_corner().in_direction(d)
> vol_in.big_corner().in_direction(d)) {
// shave off upper slice from vol_containing and add it to others
grid_volume other = vol_containing;
const int thick = (vol_containing.big_corner().in_direction(d)
- vol_in.big_corner().in_direction(d))/2;
other.set_num_direction(d, thick);
other.shift_origin(d, (vol_containing.num_direction(d) - thick)*2);
others[counter] = other;
counter++;
vol_containing.set_num_direction(d, vol_containing.num_direction(d)
- thick);
if (vol_containing.big_corner().in_direction(d)
< vol_in.big_corner().in_direction(d))
abort("intersect_with: big corners differ by odd integer?");
}
}
*num_others = counter;
int initial_points = 1;
LOOP_OVER_DIRECTIONS(dim, d) initial_points *= num_direction(d);
int final_points , temp = 1;
LOOP_OVER_DIRECTIONS(dim, d) temp *= intersection->num_direction(d);
final_points = temp;
for (int j=0; j<*num_others; j++) {
temp = 1;
LOOP_OVER_DIRECTIONS(dim, d) temp *= others[j].num_direction(d);
final_points += temp;
}
if (initial_points != final_points)
abort("intersect_with: initial_points != final_points, %d, %d\n",
initial_points, final_points);
}
return true;
}
vec grid_volume::loc_at_resolution(int index, double res) const {
vec where = origin;
for (int dd=X;dd<=R;dd++) {
const direction d = (direction) dd;
if (has_boundary(High,d)) {
const double dist = boundary_location(High,d)-boundary_location(Low,d);
const int nhere = max(1,(int)floor(dist*res+0.5));
where.set_direction(d,origin.in_direction(d) +
((index % nhere)+0.5)*(1.0/res));
index /= nhere;
}
}
return where;
}
int grid_volume::ntot_at_resolution(double res) const {
int mytot = 1;
for (int d=X;d<=R;d++)
if (has_boundary(High,(direction)d)) {
const double dist = boundary_location(High,(direction)d)
- boundary_location(Low,(direction)d);
mytot *= max(1,(int)(dist*res+0.5));
}
return mytot;
}
vec grid_volume::loc(component c, int ind) const {
return operator[](iloc(c,ind));
}
ivec grid_volume::iloc(component c, int ind) const {
ivec out(dim);
LOOP_OVER_DIRECTIONS(dim,d) {
int ind_over_stride = ind/stride(d);
while (ind_over_stride < 0) ind_over_stride += num_direction(d)+1;
out.set_direction(d, 2*(ind_over_stride%(num_direction(d)+1)));
}
return out + iyee_shift(c) + io;
}
vec grid_volume::dr() const {
switch (dim) {
case Dcyl: return veccyl(inva, 0.0);
case D1: case D2: case D3: abort("Error in dr\n");
}
return vec(0); // This is never reached.
}
vec grid_volume::dx() const {
switch (dim) {
case D3: return vec(inva,0,0);
case D2: return vec(inva,0);
case D1: case Dcyl: abort("Error in dx.\n");
}
return vec(0); // This is never reached.
}
vec grid_volume::dy() const {
switch (dim) {
case D3: return vec(0,inva,0);
case D2: return vec(0,inva);
case D1: case Dcyl: abort("Error in dy.\n");
}
return vec(0); // This is never reached.
}
vec grid_volume::dz() const {
switch (dim) {
case Dcyl: return veccyl(0.0,inva);
case D3: return vec(0,0,inva);
case D1: return vec(inva);
case D2: abort("dz doesn't exist in 2D\n");
}
return vec(0); // This is never reached.
}
grid_volume volone(double zsize, double a) {
return grid_volume(D1, a, 0, 0, (int) (zsize*a + 0.5));
}
grid_volume voltwo(double xsize, double ysize, double a) {
return grid_volume(D2, a, (xsize==0)?1:(int) (xsize*a + 0.5),
(ysize==0)?1:(int) (ysize*a + 0.5),0);
}
grid_volume vol1d(double zsize, double a) {
return volone(zsize, a);
}
grid_volume vol2d(double xsize, double ysize, double a) {
return voltwo(xsize, ysize, a);
}
grid_volume vol3d(double xsize, double ysize, double zsize, double a) {
return grid_volume(D3, a,(xsize==0)?1:(int) (xsize*a + 0.5),
(ysize==0)?1:(int) (ysize*a + 0.5),
(zsize==0)?1:(int) (zsize*a + 0.5));
}
grid_volume volcyl(double rsize, double zsize, double a) {
if (zsize == 0.0) return grid_volume(Dcyl, a, (int) (rsize*a + 0.5), 0, 1);
else return grid_volume(Dcyl, a, (int) (rsize*a + 0.5), 0, (int) (zsize*a + 0.5));
}
grid_volume grid_volume::split(int n, int which) const {
if (n > nowned_min())
abort("Cannot split %d grid points into %d parts\n", nowned_min(), n);
if (n == 1) return *this;
// Try to get as close as we can...
int biglen = 0;
for (int i=0;i<3;i++) if (num[i] > biglen) biglen = num[i];
const int split_point = (int)(biglen*(n/2)/(double)n + 0.5);
const int num_low = (int)(split_point*n/(double)biglen + 0.5);
if (which < num_low)
return split_at_fraction(false, split_point).split(num_low,which);
else
return split_at_fraction(true, split_point).split(n-num_low,which-num_low);
}
grid_volume grid_volume::split_by_effort(int n, int which, int Ngv, const grid_volume *v, double *effort) const {
const int grid_points_owned = nowned_min();
if (n > grid_points_owned)
abort("Cannot split %d grid points into %d parts\n", nowned_min(), n);
if (n == 1) return *this;
int biglen = 0;
direction splitdir = NO_DIRECTION;
LOOP_OVER_DIRECTIONS(dim, d) if (num_direction(d) > biglen) { biglen = num_direction(d); splitdir = d; }
double best_split_measure = 1e20, left_effort_fraction = 0;
int best_split_point = 0;
vec corner = zero_vec(dim);
LOOP_OVER_DIRECTIONS(dim, d) corner.set_direction(d, origin.in_direction(d) + num_direction(d)/a);
for (int split_point = 1; split_point < biglen; split_point+=1) {
grid_volume v_left = *this;
v_left.set_num_direction(splitdir, split_point);
grid_volume v_right = *this;
v_right.set_num_direction(splitdir, num_direction(splitdir) - split_point);
v_right.shift_origin(splitdir, split_point*2);
double total_left_effort = 0, total_right_effort = 0;
grid_volume vol;
if (Ngv == 0) {
total_left_effort = v_left.ntot();
total_right_effort = v_right.ntot();
}
else {
for (int j = 0; j<Ngv; j++) {
if (v_left.intersect_with(v[j], &vol))
total_left_effort += effort[j] * vol.ntot();
if (v_right.intersect_with(v[j], &vol))
total_right_effort += effort[j] * vol.ntot();
}
}
double split_measure = max(total_left_effort/(n/2), total_right_effort/(n-n/2));
if (split_measure < best_split_measure) {
best_split_measure = split_measure;
best_split_point = split_point;
left_effort_fraction = total_left_effort/(total_left_effort + total_right_effort);
}
}
const int split_point = best_split_point;
const int num_low = (int)(left_effort_fraction *n + 0.5);
// Revert to split() when effort method gives less grid points than chunks
if (num_low > best_split_point*(grid_points_owned/biglen) ||
(n-num_low) > (grid_points_owned - best_split_point*(grid_points_owned/biglen)))
return split(n, which);
if (which < num_low)
return split_at_fraction(false, split_point).split_by_effort(num_low,which, Ngv,v,effort);
else
return split_at_fraction(true, split_point).split_by_effort(n-num_low,which-num_low, Ngv,v,effort);
}
grid_volume grid_volume::split_at_fraction(bool want_high, int numer) const {
int bestd = -1, bestlen = 1;
for (int i=0;i<3;i++)
if (num[i] > bestlen) {
bestd = i;
bestlen = num[i];
}
if (bestd == -1) {
for (int i=0;i<3;i++) master_printf("num[%d] = %d\n", i, num[i]);
abort("Crazy weird splitting error.\n");
}
grid_volume retval(dim, a, 1,1,1);
for (int i=0;i<3;i++) retval.num[i] = num[i];
if (numer >= num[bestd])
abort("Aaack bad bug in split_at_fraction.\n");
direction d = (direction) bestd;
if (dim == Dcyl && d == X) d = R;
retval.set_origin(io);
if (want_high)
retval.shift_origin(d,numer*2);
if (want_high) retval.num[bestd] -= numer;
else retval.num[bestd] = numer;
retval.num_changed();
return retval;
}
// Halve the grid_volume for symmetry exploitation...must contain icenter!
grid_volume grid_volume::halve(direction d) const {
grid_volume retval(*this);
// note that icenter-io is always even by construction of grid_volume::icenter
retval.set_num_direction(d, (icenter().in_direction(d)
- io.in_direction(d)) / 2);
return retval;
}
grid_volume grid_volume::pad(direction d) const {
grid_volume gv(*this);
gv.pad_self(d);
return gv;
}
void grid_volume::pad_self(direction d) {
num[d%3]+=2; // Pad in both directions by one grid point.
num_changed();
shift_origin(d, -2);
}
ivec grid_volume::icenter() const {
/* Find the center of the user's cell. This will be used as the
symmetry point, and therefore icenter-io must be *even*
in all components in order that rotations preserve the Yee lattice. */
switch (dim) {
case D1: return io + ivec(nz()).round_up_to_even();
case D2: return io + ivec(nx(), ny()).round_up_to_even();
case D3: return io + ivec(nx(), ny(), nz()).round_up_to_even();
case Dcyl: return io + iveccyl(0, nz()).round_up_to_even();
}
abort("Can't do symmetry with these dimensions.\n");
return ivec(0); // This is never reached.
}
vec grid_volume::center() const {
return operator[](icenter());
}
symmetry rotate4(direction axis, const grid_volume &gv) {
symmetry s = identity();
if (axis > 2) abort("Can only rotate4 in 2D or 3D.\n");
s.g = 4;
FOR_DIRECTIONS(d) {
s.S[d].d = d;
s.S[d].flipped = false;
}
s.S[(axis+1)%3].d = (direction)((axis+2)%3);
s.S[(axis+1)%3].flipped = true;
s.S[(axis+2)%3].d = (direction)((axis+1)%3);
s.symmetry_point = gv.center();
s.i_symmetry_point = gv.icenter();
return s;
}
symmetry rotate2(direction axis, const grid_volume &gv) {
symmetry s = identity();
if (axis > 2) abort("Can only rotate2 in 2D or 3D.\n");
s.g = 2;
s.S[(axis+1)%3].flipped = true;
s.S[(axis+2)%3].flipped = true;
s.symmetry_point = gv.center();
s.i_symmetry_point = gv.icenter();
return s;
}
symmetry mirror(direction axis, const grid_volume &gv) {
symmetry s = identity();
s.g = 2;
s.S[axis].flipped = true;
s.symmetry_point = gv.center();
s.i_symmetry_point = gv.icenter();
return s;
}
symmetry r_to_minus_r_symmetry(double m) {
symmetry s = identity();
s.g = 2;
s.S[R].flipped = true;
s.S[P].flipped = true;
s.symmetry_point = zero_vec(Dcyl);
s.i_symmetry_point = zero_ivec(Dcyl);
if (m == int(m)) // phase is purely real (+/- 1) when m an integer
s.ph = (int(m) & 1) ? -1.0 : 1.0;
else
s.ph = polar(1.0, m * pi); // general case
return s;
}
symmetry identity() {
return symmetry();
}
symmetry::symmetry() {
g = 1;
ph = 1.0;
FOR_DIRECTIONS(d) {
S[d].d = d;
S[d].flipped = false;
}
next = NULL;
}
symmetry::symmetry(const symmetry &s) {
g = s.g;
FOR_DIRECTIONS(d) {
S[d].d = s.S[d].d;
S[d].flipped = s.S[d].flipped;
}
ph = s.ph;
symmetry_point = s.symmetry_point;
i_symmetry_point = s.i_symmetry_point;
if (s.next) next = new symmetry(*s.next);
else next = NULL;
}
void symmetry::operator=(const symmetry &s) {
g = s.g;
FOR_DIRECTIONS(d) {
S[d].d = s.S[d].d;
S[d].flipped = s.S[d].flipped;
}
ph = s.ph;
symmetry_point = s.symmetry_point;
i_symmetry_point = s.i_symmetry_point;
if (s.next) next = new symmetry(*s.next);
else next = NULL;
}
bool symmetry::operator==(const symmetry &sym) const {
int gtot = multiplicity();
if (gtot != sym.multiplicity())
return false;
for (int sn = 1; sn < gtot; ++sn)
FOR_DIRECTIONS(d)
if (transform(d, sn) != sym.transform(d, sn))
return false;
return true;
}
symmetry::~symmetry() {
delete next;
}
int symmetry::multiplicity() const {
if (next) return g*next->multiplicity();
else return g;
}
symmetry symmetry::operator+(const symmetry &b) const {
// The following optimization ignores identity when adding symmetries
// together. This is important because identity has an undefined
// symmetry point.
if (multiplicity() == 1) return b;
else if (b.multiplicity() == 1) return *this;
symmetry s = *this;
symmetry *sn = &s;
for (; sn->next; sn = sn->next) ;
sn->next = new symmetry(b);
return s;
}
symmetry symmetry::operator*(complex<double> p) const {
symmetry s = *this;
s.ph *= p;
return s;
}
signed_direction signed_direction::operator*(complex<double> p) {
signed_direction sd = *this;
sd.phase *= p;
return sd;
}
signed_direction symmetry::transform(direction d, int n) const {
// Returns transformed direction + phase/flip; -n indicates inverse transform
if (n == 0 || d == NO_DIRECTION) return signed_direction(d);
int nme, nrest;
if (n < 0) {
nme = (g - (-n) % g) % g;
nrest = -((-n) / g);
} else {
nme = n % g;
nrest = n / g;
}
if (nme == 0) {
if (nrest == 0) return signed_direction(d);
else return next->transform(d,nrest);
} else {
signed_direction sd;
if (nme == 1) sd = S[d];
if (S[d].flipped) sd = flip(transform(S[d].d, nme-1));
else sd = transform(S[d].d, nme-1);
if (next && nrest) {
if (sd.flipped) return flip(next->transform(sd.d, nrest))*ph;
else return next->transform(sd.d, nrest)*ph;
} else {
return sd*ph;
}
}
}
ivec symmetry::transform(const ivec &ov, int n) const {
if (n == 0) return ov;
ivec out = ov;
LOOP_OVER_DIRECTIONS(ov.dim, d) {
const signed_direction s = transform(d,n);
const int sp_d = i_symmetry_point.in_direction(d);
const int sp_sd = i_symmetry_point.in_direction(s.d);
const int delta = ov.in_direction(d) - sp_d;
if (s.flipped) out.set_direction(s.d, sp_sd - delta);
else out.set_direction(s.d, sp_sd + delta);
}
return out;
}
ivec symmetry::transform_unshifted(const ivec &ov, int n) const {
if (n == 0) return ov;
ivec out(ov.dim);
LOOP_OVER_DIRECTIONS(ov.dim, d) {
const signed_direction s = transform(d,n);
if (s.flipped) out.set_direction(s.d, -ov.in_direction(d));
else out.set_direction(s.d, ov.in_direction(d));
}
return out;
}
vec symmetry::transform(const vec &ov, int n) const {
if (n == 0) return ov;
vec delta = ov;
LOOP_OVER_DIRECTIONS(ov.dim, d) {
const signed_direction s = transform(d,n);
double deltad = ov.in_direction(d) - symmetry_point.in_direction(d);
if (s.flipped) delta.set_direction(s.d, -deltad);
else delta.set_direction(s.d, deltad);
}
return symmetry_point + delta;
}
volume symmetry::transform(const volume &v, int n) const {
return volume(transform(v.get_min_corner(),n),
transform(v.get_max_corner(),n));
}
component symmetry::transform(component c, int n) const {
return direction_component(c,transform(component_direction(c),n).d);
}
derived_component symmetry::transform(derived_component c, int n) const {
return direction_component(c,transform(component_direction(c),n).d);
}
int symmetry::transform(int c, int n) const {
return (is_derived(c) ? int(transform(derived_component(c), n))
: int(transform(component(c), n)));
}
complex<double> symmetry::phase_shift(component c, int n) const {
if (c == Dielectric || c == Permeability) return 1.0;
complex<double> phase = transform(component_direction(c),n).phase;
// flip tells us if we need to flip the sign. For vectors (E), it is
// just this simple:
bool flip = transform(component_direction(c),n).flipped;
if (is_magnetic(c) || is_B(c)) {
// Because H is a pseudovector, here we have to figure out if the
// transformation changes the handedness of the basis.
bool have_one = false, have_two = false;
FOR_DIRECTIONS(d) {
if (transform(d,n).flipped) flip = !flip;
int shift = (transform(d,n).d - d + 6) % 3;
if (shift == 1) have_one = true;
if (shift == 2) have_two = true;
}
if (have_one && have_two) flip = !flip;
}
if (flip) return -phase;
else return phase;
}
complex<double> symmetry::phase_shift(derived_component c, int n) const {
if (is_poynting(c)) {
signed_direction ds = transform(component_direction(c),n);
complex<double> ph = conj(ds.phase) * ds.phase; // E x H gets |phase|^2
return (ds.flipped ? -ph : ph);
}
else /* energy density */
return 1.0;
}
complex<double> symmetry::phase_shift(int c, int n) const {
return (is_derived(c) ? phase_shift(derived_component(c), n)
: phase_shift(component(c), n));
}
bool symmetry::is_primitive(const ivec &p) const {
// This is only correct if p is somewhere on the yee lattice.
if (multiplicity() == 1) return true;
for (int i=1;i<multiplicity();i++) {
const ivec pp = transform(p,i);
switch (p.dim) {
case D2:
if (pp.x()+pp.y() < p.x()+p.y()) return false;
if (pp.x()+pp.y() == p.x()+p.y() &&
p.y() > p.x() && pp.y() <= pp.x()) return false;
break;
case D3:
if (pp.x()+pp.y()+pp.z() < p.x()+p.y()+p.z()) return false;
if (pp.x()+pp.y()+pp.z() == p.x()+p.y()+p.z() &&
pp.x()+pp.y()-pp.z() < p.x()+p.y()-p.z()) return false;
if (pp.x()+pp.y()+pp.z() == p.x()+p.y()+p.z() &&
pp.x()+pp.y()-pp.z() == p.x()+p.y()-p.z() &&
pp.x()-pp.y()-pp.z() < p.x()-p.y()-p.z()) return false;
break;
case D1: case Dcyl:
if (pp.z() < p.z()) return false;
break;
}
}
return true;
}
/* given a list of geometric volumes, produce a new list with appropriate
weights that is minimized according to the symmetry. */
volume_list *symmetry::reduce(const volume_list *gl) const {
volume_list *glnew = 0;
for (const volume_list *g = gl; g; g = g->next) {
int sn;
for (sn = 0; sn < multiplicity(); ++sn) {
volume gS(transform(g->v, sn));
int cS = transform(g->c, sn);
volume_list *gn;
for (gn = glnew; gn; gn = gn->next)
if (gn->c == cS && gn->v.round_float() == gS.round_float())
break;
if (gn) { // found a match
gn->weight += g->weight * phase_shift(g->c, sn);
break;
}
}
if (sn == multiplicity() && g->weight != 0.0) { // no match, add to glnew
volume_list *gn =
new volume_list(g->v, g->c, g->weight, glnew);
glnew = gn;
}
}
// reduce v's redundant with themselves & delete elements with zero weight:
volume_list *gprev = 0, *g = glnew;
while (g) {
// first, see if g->v is redundant with itself
bool halve[5] = {false,false,false,false,false};
complex<double> weight = g->weight;
for (int sn = 1; sn < multiplicity(); ++sn)
if (g->c == transform(g->c, sn) &&
g->v.round_float() == transform(g->v, sn).round_float()) {
LOOP_OVER_DIRECTIONS(g->v.dim, d)
if (transform(d,sn).flipped) {
halve[d] = true;
break;
}
g->weight += weight * phase_shift(g->c, sn);
}
LOOP_OVER_DIRECTIONS(g->v.dim, d)
if (halve[d])
g->v.set_direction_max(d, g->v.in_direction_min(d) +
0.5 * g->v.in_direction(d));
// now, delete it if it has zero weight
if (g->weight == 0.0) {
if (gprev)
gprev->next = g->next;
else // g == glnew
glnew = g->next;
g->next = 0; // necessary so that g->next is not deleted recursively
delete g;
g = gprev ? gprev->next : glnew;
}
else
g = (gprev = g)->next;
}
return glnew;
}
/***************************************************************************/
static double poynting_fun(const complex<double> *fields,
const vec &loc, void *data_)
{
(void) loc; // unused
(void) data_; // unused
return (real(conj(fields[0]) * fields[1])
- real(conj(fields[2])*fields[3]));
}
static double energy_fun(const complex<double> *fields,
const vec &loc, void *data_)
{
(void) loc; // unused
int nfields = *((int *) data_) / 2;
double sum = 0;
for (int k = 0; k < nfields; ++k)
sum += real(conj(fields[2*k]) * fields[2*k+1]);
return sum * 0.5;
}
field_rfunction derived_component_func(derived_component c, const grid_volume &gv,
int &nfields, component cs[12]) {
switch (c) {
case Sx: case Sy: case Sz: case Sr: case Sp:
switch (c) {
case Sx: cs[0] = Ey; cs[1] = Hz; break;
case Sy: cs[0] = Ez; cs[1] = Hx; break;
case Sz: cs[0] = Ex; cs[1] = Hy; break;
case Sr: cs[0] = Ep; cs[1] = Hz; break;
case Sp: cs[0] = Ez; cs[1] = Hr; break;
default: break; // never reached
}
nfields = 4;
cs[2] = direction_component(Ex, component_direction(cs[1]));
cs[3] = direction_component(Hx, component_direction(cs[0]));
return poynting_fun;
case EnergyDensity: case D_EnergyDensity: case H_EnergyDensity:
nfields = 0;
if (c != H_EnergyDensity)
FOR_ELECTRIC_COMPONENTS(c0) if (gv.has_field(c0)) {
cs[nfields++] = c0;
cs[nfields++] = direction_component(Dx, component_direction(c0));
}
if (c != D_EnergyDensity)
FOR_MAGNETIC_COMPONENTS(c0) if (gv.has_field(c0)) {
cs[nfields++] = c0;
cs[nfields++] = direction_component(Bx, component_direction(c0));
}
if (nfields > 12) abort("too many field components");
return energy_fun;
default:
abort("unknown derived_component in derived_component_func");
}
return 0;
}
/***************************************************************************/
} // namespace meep
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