VEC *LTsolve(const MAT *L, const VEC *b, VEC *out, double diag)
{
unsigned int dim;
int i, i_lim;
MatrixReal **L_me, *b_ve, *out_ve, tmp, invdiag, tiny;
if ( ! L || ! b )
error(E_NULL,"LTsolve");
dim = mat_min(L->m,L->n);
if ( b->dim < dim )
error(E_SIZES,"LTsolve");
out = v_resize(out,L->n);
L_me = L->me; b_ve = b->ve; out_ve = out->ve;
tiny = (10.0/HUGE_VAL);
for ( i=dim-1; i>=0; i-- )
if ( b_ve[i] != 0.0 )
break;
i_lim = i;
if ( b != out )
{
__zero__(out_ve,out->dim);
MEM_COPY(b_ve,out_ve,(i_lim+1)*sizeof(MatrixReal));
}
if ( diag == 0.0 )
{
for ( ; i>=0; i-- )
{
tmp = L_me[i][i];
if ( fabs(tmp) <= tiny*fabs(out_ve[i]) )
error(E_SING,"LTsolve");
out_ve[i] /= tmp;
__mltadd__(out_ve,L_me[i],-out_ve[i],i);
}
}
else
{
invdiag = 1.0/diag;
for ( ; i>=0; i-- )
{
out_ve[i] *= invdiag;
__mltadd__(out_ve,L_me[i],-out_ve[i],i);
}
}
return (out);
}
VEC *UTsolve(const MAT *U, const VEC *b, VEC *out, double diag)
{
unsigned int dim, i, i_lim;
MatrixReal **U_me, *b_ve, *out_ve, tmp, invdiag, tiny;
if ( ! U || ! b )
error(E_NULL,"UTsolve");
dim = mat_min(U->m,U->n);
if ( b->dim < dim )
error(E_SIZES,"UTsolve");
out = v_resize(out,U->n);
U_me = U->me; b_ve = b->ve; out_ve = out->ve;
tiny = (10.0/HUGE_VAL);
for ( i=0; i<dim; i++ )
if ( b_ve[i] != 0.0 )
break;
else
out_ve[i] = 0.0;
i_lim = i;
if ( b != out )
{
__zero__(out_ve,out->dim);
MEM_COPY(&(b_ve[i_lim]),&(out_ve[i_lim]),(dim-i_lim)*sizeof(MatrixReal));
}
if ( diag == 0.0 )
{
for ( ; i<dim; i++ )
{
tmp = U_me[i][i];
if ( fabs(tmp) <= tiny*fabs(out_ve[i]) )
error(E_SING,"UTsolve");
out_ve[i] /= tmp;
__mltadd__(&(out_ve[i+1]),&(U_me[i][i+1]),-out_ve[i],dim-i-1);
}
}
else
{
invdiag = 1.0/diag;
for ( ; i<dim; i++ )
{
out_ve[i] *= invdiag;
__mltadd__(&(out_ve[i+1]),&(U_me[i][i+1]),-out_ve[i],dim-i-1);
}
}
return (out);
}
IGL_INLINE void igl::ears(
const Eigen::MatrixBase<DerivedF> & F,
Eigen::PlainObjectBase<Derivedear> & ear,
Eigen::PlainObjectBase<Derivedear_opp> & ear_opp)
{
assert(F.cols() == 3 && "F should contain triangles");
Eigen::Array<bool,Eigen::Dynamic,3> B;
{
Eigen::Array<bool,Eigen::Dynamic,1> I;
on_boundary(F,I,B);
}
find(B.rowwise().count() == 2,ear);
Eigen::Array<bool,Eigen::Dynamic,3> Bear;
slice(B,ear,1,Bear);
Eigen::Array<bool,Eigen::Dynamic,1> M;
mat_min(Bear,2,M,ear_opp);
}
//--------------------------------------------------------------------------
// Function to create a multilayer system replicating a standard stack
// structure cs::num_multilayers times
//
// |-----------------------| 1.0 |-----------------------| L2 M2
// | Material 2 | |-----------------------|
// |-----------------------| 0.6 x2 | | L2 M2
// | | --> |-----------------------| L1 M1
// | Material 1 | |-----------------------|
// | | | | L1 M2
// |-----------------------| 0.0 |-----------------------|
//
// The multilayers code divides the total system height into n multiples
// of the defined material heights.
//--------------------------------------------------------------------------
void generate_multilayers(std::vector<cs::catom_t>& catom_array){
// Load number of multilayer repeats to temporary constant
const int num_layers = cs::num_multilayers;
// Determine fractional system height for each layer
const double fractional_system_height = cs::system_dimensions[2]/double(num_layers);
// Unroll min, max and fill for performance
std::vector<double> mat_min(mp::num_materials);
std::vector<double> mat_max(mp::num_materials);
std::vector<bool> mat_fill(mp::num_materials);
for(int mat=0;mat<mp::num_materials;mat++){
mat_min[mat]=mp::material[mat].min;
mat_max[mat]=mp::material[mat].max;
// alloys generally are not defined by height, and so have max = 0.0
if(mat_max[mat]<0.0000001) mat_max[mat]=-0.1;
mat_fill[mat]=mp::material[mat].fill;
}
// Assign materials to generated atoms
for(unsigned int atom=0;atom<catom_array.size();atom++){
// loop over multilayers
for(int multi=0; multi < num_layers; ++multi){
const double multilayer_num = double(multi);
for(int mat=0;mat<mp::num_materials;mat++){
// determine mimimum and maximum heigh for this layer
const double mat_min_z = (mat_min[mat] + multilayer_num)*fractional_system_height;
const double mat_max_z = (mat_max[mat] + multilayer_num)*fractional_system_height;
const double cz=catom_array[atom].z;
// if in range then allocate to material
if((cz>=mat_min_z) && (cz<mat_max_z) && (mat_fill[mat]==false)){
catom_array[atom].material=mat;
catom_array[atom].include=true;
// Optionally recategorize heigh magnetization by layer in multilayer
if(cs::multilayer_height_category) catom_array[atom].lh_category = multi;
}
}
}
}
return;
}
VEC *Usolve(const MAT *matrix, const VEC *b, VEC *out, double diag)
{
unsigned int dim /* , j */;
int i, i_lim;
MatrixReal **mat_ent, *mat_row, *b_ent, *out_ent, *out_col, sum, tiny;
if ( matrix==MNULL || b==VNULL )
error(E_NULL,"Usolve");
dim = mat_min(matrix->m,matrix->n);
if ( b->dim < dim ){
printf("b->dim = %d; dim = %d\n", b->dim, dim);
error(E_SIZES,"Usolve");
}
if ( out==VNULL || out->dim < dim )
out = v_resize(out,matrix->n);
mat_ent = matrix->me; b_ent = b->ve; out_ent = out->ve;
tiny = (10.0/HUGE_VAL);
for ( i=dim-1; i>=0; i-- )
if ( b_ent[i] != 0.0 )
break;
else
out_ent[i] = 0.0;
i_lim = i;
for ( ; i>=0; i-- )
{
sum = b_ent[i];
mat_row = &(mat_ent[i][i+1]);
out_col = &(out_ent[i+1]);
sum -= __ip__(mat_row,out_col,i_lim-i);
if ( diag==0.0 )
{
if ( fabs(mat_ent[i][i]) <= tiny*fabs(sum) )
error(E_SING,"Usolve");
else
out_ent[i] = sum/mat_ent[i][i];
}
else
out_ent[i] = sum/diag;
}
return (out);
}
VEC *Lsolve(const MAT *matrix, const VEC *b, VEC *out, double diag)
{
unsigned int dim, i, i_lim /* , j */;
MatrixReal **mat_ent, *mat_row, *b_ent, *out_ent, *out_col, sum, tiny;
if ( matrix==(MAT *)NULL || b==(VEC *)NULL )
error(E_NULL,"Lsolve");
dim = mat_min(matrix->m,matrix->n);
if ( b->dim < dim )
error(E_SIZES,"Lsolve");
if ( out==(VEC *)NULL || out->dim < dim )
out = v_resize(out,matrix->n);
mat_ent = matrix->me; b_ent = b->ve; out_ent = out->ve;
for ( i=0; i<dim; i++ )
if ( b_ent[i] != 0.0 )
break;
else
out_ent[i] = 0.0;
i_lim = i;
tiny = (10.0/HUGE_VAL);
for ( ; i<dim; i++ )
{
sum = b_ent[i];
mat_row = &(mat_ent[i][i_lim]);
out_col = &(out_ent[i_lim]);
sum -= __ip__(mat_row,out_col,(int)(i-i_lim));
if ( diag==0.0 )
{
if ( fabs(mat_ent[i][i]) <= tiny*fabs(sum) )
error(E_SING,"Lsolve");
else
out_ent[i] = sum/mat_ent[i][i];
}
else
out_ent[i] = sum/diag;
}
return (out);
}
VEC *Dsolve(const MAT *A, const VEC *b, VEC *x)
{
unsigned int dim, i;
MatrixReal tiny;
if ( ! A || ! b )
error(E_NULL,"Dsolve");
dim = mat_min(A->m,A->n);
if ( b->dim < dim )
error(E_SIZES,"Dsolve");
x = v_resize(x,A->n);
tiny = (10.0/HUGE_VAL);
dim = b->dim;
for ( i=0; i<dim; i++ )
if ( fabs(A->me[i][i]) <= tiny*fabs(b->ve[i]) )
error(E_SING,"Dsolve");
else
x->ve[i] = b->ve[i]/A->me[i][i];
return (x);
}
void sphere(std::vector<double>& particle_origin, std::vector<cs::catom_t> & catom_array, const int grain){
// Set particle radius
double particle_radius_squared = (cs::particle_scale*0.5)*(cs::particle_scale*0.5);
// Loop over all atoms and mark atoms in sphere
const int num_atoms = catom_array.size();
// determine order for core-shell particles
std::list<core_radius_t> material_order(0);
for(int mat=0;mat<mp::num_materials;mat++){
core_radius_t tmp;
tmp.mat=mat;
tmp.radius=mp::material[mat].core_shell_size;
material_order.push_back(tmp);
}
// sort by increasing radius
material_order.sort(compare_radius);
// Unroll min, max and fill for performance
std::vector<double> mat_min(mp::num_materials);
std::vector<double> mat_max(mp::num_materials);
std::vector<double> mat_cssize(mp::num_materials);
std::vector<int> uc_cat(mp::num_materials); // array of material -> unit cell material associations
for(int mat=0;mat<mp::num_materials;mat++){
mat_min[mat]=create::internal::mp[mat].min*cs::system_dimensions[2];
mat_max[mat]=create::internal::mp[mat].max*cs::system_dimensions[2];
mat_cssize[mat] = mp::material[mat].core_shell_size;
// alloys generally are not defined by height, and so have max = 0.0
if(mat_max[mat]<1.e-99) mat_max[mat]=-0.1;
uc_cat[mat] = create::internal::mp[mat].unit_cell_category; // unit cell category of material
}
for(int atom=0;atom<num_atoms;atom++){
double range_squared = (catom_array[atom].x-particle_origin[0])*(catom_array[atom].x-particle_origin[0]) +
(catom_array[atom].y-particle_origin[1])*(catom_array[atom].y-particle_origin[1]) +
(catom_array[atom].z-particle_origin[2])*(catom_array[atom].z-particle_origin[2]);
const double cz=catom_array[atom].z;
const int atom_uc_cat = catom_array[atom].uc_category;
if(mp::material[catom_array[atom].material].core_shell_size>0.0){
// Iterate over materials
for(std::list<core_radius_t>::iterator it = material_order.begin(); it != material_order.end(); it++){
int mat = (it)->mat;
double my_radius = mat_cssize[mat];
double max_range = my_radius*my_radius*particle_radius_squared;
double maxz=mat_max[mat];
double minz=mat_min[mat];
// check for within core shell range
if(range_squared<=max_range){
if((cz>=minz) && (cz<maxz) && (atom_uc_cat == uc_cat[mat]) ){
catom_array[atom].include=true;
catom_array[atom].material=mat;
catom_array[atom].grain=grain;
}
// if set to clear atoms then remove atoms within radius
else if(cs::fill_core_shell==false){
catom_array[atom].include=false;
}
}
}
}
else if(range_squared<=particle_radius_squared) {
catom_array[atom].include=true;
catom_array[atom].grain=grain;
}
}
return;
}
/* LUfactor -- gaussian elimination with scaled partial pivoting
-- Note: returns LU matrix which is A */
MAT *LUfactor(MAT *A, PERM *pivot)
{
unsigned int i, j, m, n;
unsigned int k, k_max;
int i_max;
char MatrixTempBuffer[ 1000 ];
MatrixReal **A_v, *A_piv, *A_row;
MatrixReal max1, temp, tiny;
VEC *scale = VNULL;
if ( A==(MAT *)NULL || pivot==(PERM *)NULL ){
error(E_NULL,"LUfactor");
}
if ( pivot->size != A->m )
error(E_SIZES,"LUfactor");
m = A->m; n = A->n;
if( SET_VEC_SIZE( A->m ) <1000 )
vec_get( &scale, (void *)MatrixTempBuffer, A->m );
else
scale = v_get( A->m );
//MEM_STAT_REG(scale,TYPE_VEC);
A_v = A->me;
tiny = (MatrixReal)(10.0/HUGE_VAL);
/* initialise pivot with identity permutation */
for ( i=0; i<m; i++ )
pivot->pe[i] = i;
/* set scale parameters */
for ( i=0; i<m; i++ )
{
max1 = 0.0;
for ( j=0; j<n; j++ )
{
temp = (MatrixReal)fabs(A_v[i][j]);
max1 = mat_max(max1,temp);
}
scale->ve[i] = max1;
}
/* main loop */
k_max = mat_min(m,n)-1;
for ( k=0; k<k_max; k++ )
{
/* find best pivot row */
max1 = 0.0; i_max = -1;
for ( i=k; i<m; i++ )
if ( fabs(scale->ve[i]) >= tiny*fabs(A_v[i][k]) )
{
temp = (MatrixReal)fabs(A_v[i][k])/scale->ve[i];
if ( temp > max1 )
{ max1 = temp; i_max = i; }
}
/* if no pivot then ignore column k... */
if ( i_max == -1 )
{
/* set pivot entry A[k][k] exactly to zero,
rather than just "small" */
A_v[k][k] = 0.0;
continue;
}
/* do we pivot ? */
if ( i_max != (int)k ) /* yes we do... */
{
px_transp(pivot,i_max,k);
for ( j=0; j<n; j++ )
{
temp = A_v[i_max][j];
A_v[i_max][j] = A_v[k][j];
A_v[k][j] = temp;
}
}
/* row operations */
for ( i=k+1; i<m; i++ ) /* for each row do... */
{ /* Note: divide by zero should never happen */
temp = A_v[i][k] = A_v[i][k]/A_v[k][k];
A_piv = &(A_v[k][k+1]);
A_row = &(A_v[i][k+1]);
if ( k+1 < n )
__mltadd__(A_row,A_piv,-temp,(int)(n-(k+1)));
}
}
if( scale != (VEC *)MatrixTempBuffer ) // память выделялась, надо освободить
V_FREE(scale);
return A;
}
int create_crystal_structure(std::vector<cs::catom_t> & catom_array){
//----------------------------------------------------------
// check calling of routine if error checking is activated
//----------------------------------------------------------
if(err::check==true){std::cout << "cs::create_crystal_structure has been called" << std::endl;}
int min_bounds[3];
int max_bounds[3];
#ifdef MPICF
if(vmpi::mpi_mode==0){
min_bounds[0] = int(vmpi::min_dimensions[0]/unit_cell.dimensions[0]);
min_bounds[1] = int(vmpi::min_dimensions[1]/unit_cell.dimensions[1]);
min_bounds[2] = int(vmpi::min_dimensions[2]/unit_cell.dimensions[2]);
max_bounds[0] = vmath::iceil(vmpi::max_dimensions[0]/unit_cell.dimensions[0]);
max_bounds[1] = vmath::iceil(vmpi::max_dimensions[1]/unit_cell.dimensions[1]);
max_bounds[2] = vmath::iceil(vmpi::max_dimensions[2]/unit_cell.dimensions[2]);
}
else{
min_bounds[0]=0;
min_bounds[1]=0;
min_bounds[2]=0;
max_bounds[0]=cs::total_num_unit_cells[0];
max_bounds[1]=cs::total_num_unit_cells[1];
max_bounds[2]=cs::total_num_unit_cells[2];
}
#else
min_bounds[0]=0;
min_bounds[1]=0;
min_bounds[2]=0;
max_bounds[0]=cs::total_num_unit_cells[0];
max_bounds[1]=cs::total_num_unit_cells[1];
max_bounds[2]=cs::total_num_unit_cells[2];
#endif
cs::local_num_unit_cells[0]=max_bounds[0]-min_bounds[0];
cs::local_num_unit_cells[1]=max_bounds[1]-min_bounds[1];
cs::local_num_unit_cells[2]=max_bounds[2]-min_bounds[2];
int num_atoms=cs::local_num_unit_cells[0]*cs::local_num_unit_cells[1]*cs::local_num_unit_cells[2]*unit_cell.atom.size();
// set catom_array size
catom_array.reserve(num_atoms);
// Initialise atoms number
int atom=0;
// find maximum height lh_category
unsigned int maxlh=0;
for(unsigned int uca=0;uca<unit_cell.atom.size();uca++) if(unit_cell.atom[uca].hc > maxlh) maxlh = unit_cell.atom[uca].hc;
maxlh+=1;
const double cff = 1.e-9; // Small numerical correction for atoms exactly on the borderline between processors
// Duplicate unit cell
for(int z=min_bounds[2];z<max_bounds[2];z++){
for(int y=min_bounds[1];y<max_bounds[1];y++){
for(int x=min_bounds[0];x<max_bounds[0];x++){
// need to change this to accept non-orthogonal lattices
// Loop over atoms in unit cell
for(unsigned int uca=0;uca<unit_cell.atom.size();uca++){
double cx = (double(x)+unit_cell.atom[uca].x)*unit_cell.dimensions[0]+cff;
double cy = (double(y)+unit_cell.atom[uca].y)*unit_cell.dimensions[1]+cff;
double cz = (double(z)+unit_cell.atom[uca].z)*unit_cell.dimensions[2]+cff;
#ifdef MPICF
if(vmpi::mpi_mode==0){
// only generate atoms within allowed dimensions
if( (cx>=vmpi::min_dimensions[0] && cx<vmpi::max_dimensions[0]) &&
(cy>=vmpi::min_dimensions[1] && cy<vmpi::max_dimensions[1]) &&
(cz>=vmpi::min_dimensions[2] && cz<vmpi::max_dimensions[2])){
#endif
if((cx<cs::system_dimensions[0]) && (cy<cs::system_dimensions[1]) && (cz<cs::system_dimensions[2])){
catom_array.push_back(cs::catom_t());
catom_array[atom].x=cx;
catom_array[atom].y=cy;
catom_array[atom].z=cz;
//std::cout << atom << "\t" << cx << "\t" << cy <<"\t" << cz << std::endl;
catom_array[atom].material=unit_cell.atom[uca].mat;
catom_array[atom].uc_id=uca;
catom_array[atom].lh_category=unit_cell.atom[uca].hc+z*maxlh;
catom_array[atom].uc_category=unit_cell.atom[uca].lc;
catom_array[atom].scx=x;
catom_array[atom].scy=y;
catom_array[atom].scz=z;
atom++;
}
#ifdef MPICF
}
}
else{
if((cx<cs::system_dimensions[0]) && (cy<cs::system_dimensions[1]) && (cz<cs::system_dimensions[2])){
catom_array.push_back(cs::catom_t());
catom_array[atom].x=cx;
catom_array[atom].y=cy;
catom_array[atom].z=cz;
catom_array[atom].material=unit_cell.atom[uca].mat;
catom_array[atom].uc_id=uca;
catom_array[atom].lh_category=unit_cell.atom[uca].hc+z*maxlh;
catom_array[atom].uc_category=unit_cell.atom[uca].lc;
catom_array[atom].scx=x;
catom_array[atom].scy=y;
catom_array[atom].scz=z;
catom_array[atom].include=false; // assume no atoms until classification complete
atom++;
}
}
#endif
}
}
}
}
// Check to see if actual and expected number of atoms agree, if not trim the excess
if(atom!=num_atoms){
std::vector<cs::catom_t> tmp_catom_array(num_atoms);
tmp_catom_array=catom_array;
catom_array.resize(atom);
for(int a=0;a<atom;a++){
catom_array[a]=tmp_catom_array[a];
}
tmp_catom_array.resize(0);
}
// If z-height material selection is enabled then do so
if(cs::SelectMaterialByZHeight==true){
// Check for interfacial roughness and call custom material assignment routine
if(cs::interfacial_roughness==true) cs::roughness(catom_array);
// Check for multilayer system and if required generate multilayers
else if(cs::multilayers) cs::generate_multilayers(catom_array);
// Otherwise perform normal assignement of materials
else{
// determine z-bounds for materials
std::vector<double> mat_min(mp::num_materials);
std::vector<double> mat_max(mp::num_materials);
std::vector<bool> mat_fill(mp::num_materials);
// Unroll min, max and fill for performance
for(int mat=0;mat<mp::num_materials;mat++){
mat_min[mat]=mp::material[mat].min*cs::system_dimensions[2];
mat_max[mat]=mp::material[mat].max*cs::system_dimensions[2];
// alloys generally are not defined by height, and so have max = 0.0
if(mat_max[mat]<0.0000001) mat_max[mat]=-0.1;
mat_fill[mat]=mp::material[mat].fill;
}
// Assign materials to generated atoms
for(unsigned int atom=0;atom<catom_array.size();atom++){
for(int mat=0;mat<mp::num_materials;mat++){
const double cz=catom_array[atom].z;
if((cz>=mat_min[mat]) && (cz<mat_max[mat]) && (mat_fill[mat]==false)){
catom_array[atom].material=mat;
catom_array[atom].include=true;
}
}
}
}
// Delete unneeded atoms
clear_atoms(catom_array);
}
// Check to see if any atoms have been generated
if(atom==0){
terminaltextcolor(RED);
std::cout << "Error - no atoms have been generated, increase system dimensions!" << std::endl;
terminaltextcolor(WHITE);
zlog << zTs() << "Error: No atoms have been generated. Increase system dimensions." << std::endl;
err::vexit();
}
// Now unselect all atoms by default for particle shape cutting
for(unsigned int atom=0;atom<catom_array.size();atom++){
catom_array[atom].include=false;
}
return EXIT_SUCCESS;
}