int main(int argc, char ** argv)
{
// Initialize the global VCluster
openfpm_init(&argc,&argv);
// Vcluster
Vcluster & vcl = create_vcluster();
//! [Create CartDecomposition vtk gen]
CartDecomposition<2,float> dec(vcl);
// Physical domain
Box<2,float> box({0.0,0.0},{1.0,1.0});
// division on each direction
size_t div[2] = {20,20};
// Define ghost
Ghost<2,float> g(0.01);
// boundary conditions
size_t bc[2] = {PERIODIC,PERIODIC};
// Decompose and write the decomposed graph
dec.setParameters(div,box,bc,g);
dec.decompose();
// create a ghost border
dec.calculateGhostBoxes();
// Write the decomposition
dec.write("CartDecomposition/out_");
//! [Create CartDecomposition]
// deinitialize the library
openfpm_finalize();
}
int main(int argc, char* argv[])
{
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* ## Initialization ## {#e1_st_init}
*
* Initialize the library and several objects
*
* \see \ref e0_s_initialization
*
* \snippet Grid/1_stencil/main.cpp parameters
*
*
*/
//! \cond [parameters] \endcond
openfpm_init(&argc,&argv);
// domain
Box<3,float> domain({0.0,0.0,0.0},{1.0,1.0,1.0});
// grid sizes
size_t sz[3] = {100,100,100};
// ghost extension
Ghost<3,float> g(0.03);
//! \cond [parameters] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* ## Grid create ## {#e1_st_inst}
*
* Create a distributed grid in 3D. With typedef we create an alias name for aggregate<float[3],float[3]>.
* In practice the type of grid_point == aggregate<float[3],float[3]>
*
* \see \ref e0_s_grid_inst
*
* \snippet Grid/1_stencil/main.cpp grid
*
*/
//! \cond [grid] \endcond
// a convenient alias for aggregate<...>
typedef aggregate<float,float> grid_point;
grid_dist_id<3, float, grid_point> g_dist(sz,domain,g);
//! \cond [grid] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* ## Loop over grid points ## {#e1_s_loop_gp}
*
* Get an iterator that go through the point of the domain (No ghost)
*
* \see \ref e0_s_loop_gp
*
* \snippet Grid/1_stencil/main.cpp iterator
* \snippet Grid/1_stencil/main.cpp iterator2
*
*/
//! \cond [iterator] \endcond
auto dom = g_dist.getDomainIterator();
while (dom.isNext())
{
//! \cond [iterator] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* Inside the cycle we get the local grid key
*
* \see \ref e0_s_grid_coord
*
* \snippet Grid/1_stencil/main.cpp local key
*
*/
//! \cond [local key] \endcond
auto key = dom.get();
//! \cond [local key] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* We convert the local grid position, into global position, key_g contain 3 integers that identify the position
* of the grid point in global coordinates
*
* \see \ref e0_s_grid_coord
*
* \snippet Grid/1_stencil/main.cpp global key
*
*/
//! \cond [global key] \endcond
auto key_g = g_dist.getGKey(key);
//! \cond [global key] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* we write on the grid point of position (i,j,k) the value i*i + j*j + k*k on the property A.
* Mathematically is equivalent to the function
*
* \f$ f(x,y,z) = x^2 + y^2 + z^2 \f$
*
* \snippet Grid/1_stencil/main.cpp function
*
*/
//! \cond [function] \endcond
g_dist.template get<A>(key) = key_g.get(0)*key_g.get(0) + key_g.get(1)*key_g.get(1) + key_g.get(2)*key_g.get(2);
//! \cond [function] \endcond
//! \cond [iterator2] \endcond
++dom;
}
//! \cond [iterator2] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* ## Ghost ## {#e1_s_ghost}
*
* Each sub-domain has an extended part, that is materially contained into another processor.
* In general is not synchronized
* ghost_get<A> synchronize the property A in the ghost part
*
* \snippet Grid/1_stencil/main.cpp ghost
*
*/
//! \cond [ghost] \endcond
g_dist.template ghost_get<A>();
//! \cond [ghost] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* Get again another iterator, iterate across all the domain points, calculating a Laplace stencil. Write the
* result on B
*
* \snippet Grid/1_stencil/main.cpp laplacian
*
*/
//! \cond [laplacian] \endcond
auto dom2 = g_dist.getDomainIterator();
while (dom2.isNext())
{
auto key = dom2.get();
// Laplace stencil
g_dist.template get<B>(key) = g_dist.template get<A>(key.move(x,1)) + g_dist.template get<A>(key.move(x,-1)) +
g_dist.template get<A>(key.move(y,1)) + g_dist.template get<A>(key.move(y,-1)) +
g_dist.template get<A>(key.move(z,1)) + g_dist.template get<A>(key.move(z,-1)) -
6*g_dist.template get<A>(key);
++dom2;
}
//! \cond [laplacian] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
*
* Finally we want a nice output to visualize the information stored by the distributed grid
*
* \see \ref e0_s_VTK_vis
*
* \snippet Grid/1_stencil/main.cpp output
*
*/
//! \cond [output] \endcond
g_dist.write("output");
//! \cond [output] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* Deinitialize the library
*
* \snippet Grid/1_stencil/main.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
/*!
* \page Grid_1_stencil Grid 1 stencil
*
* # Full code # {#code}
*
* \include Grid/1_stencil/main.cpp
*
*/
}
int main(int argc, char* argv[])
{
/*!
* \page Vector_5_md_vl_sym_crs Vector 5 molecular dynamic with symmetric Verlet list crossing scheme
*
* ## Simulation ## {#md_e5_sym_sim_crs}
*
* The simulation is equal to the simulation explained in the example molecular dynamic
*
* \see \ref md_e5_sym
*
* The difference is that we create a symmetric Verlet-list for crossing scheme instead of a normal one
* \snippet Vector/5_molecular_dynamic_sym_crs/main.cpp sim verlet
*
* The rest of the code remain unchanged
*
* \snippet Vector/5_molecular_dynamic_sym_crs/main.cpp simulation
*
*/
//! \cond [simulation] \endcond
double dt = 0.00025;
double sigma = 0.1;
double r_cut = 3.0*sigma;
double r_gskin = 1.3*r_cut;
double sigma12 = pow(sigma,12);
double sigma6 = pow(sigma,6);
openfpm::vector<double> x;
openfpm::vector<openfpm::vector<double>> y;
openfpm_init(&argc,&argv);
Vcluster & v_cl = create_vcluster();
// we will use it do place particles on a 10x10x10 Grid like
size_t sz[3] = {10,10,10};
// domain
Box<3,float> box({0.0,0.0,0.0},{1.0,1.0,1.0});
// Boundary conditions
size_t bc[3]={PERIODIC,PERIODIC,PERIODIC};
// ghost, big enough to contain the interaction radius
Ghost<3,float> ghost(r_gskin);
ghost.setLow(0,0.0);
ghost.setLow(1,0.0);
ghost.setLow(2,0.0);
vector_dist<3,double, aggregate<double[3],double[3]> > vd(0,box,bc,ghost,BIND_DEC_TO_GHOST);
size_t k = 0;
size_t start = vd.accum();
auto it = vd.getGridIterator(sz);
while (it.isNext())
{
vd.add();
auto key = it.get();
vd.getLastPos()[0] = key.get(0) * it.getSpacing(0);
vd.getLastPos()[1] = key.get(1) * it.getSpacing(1);
vd.getLastPos()[2] = key.get(2) * it.getSpacing(2);
vd.template getLastProp<velocity>()[0] = 0.0;
vd.template getLastProp<velocity>()[1] = 0.0;
vd.template getLastProp<velocity>()[2] = 0.0;
vd.template getLastProp<force>()[0] = 0.0;
vd.template getLastProp<force>()[1] = 0.0;
vd.template getLastProp<force>()[2] = 0.0;
k++;
++it;
}
vd.map();
vd.ghost_get<>();
timer tsim;
tsim.start();
//! \cond [sim verlet] \endcond
// Get the Cell list structure
auto NN = vd.getVerletCrs(r_gskin);;
//! \cond [sim verlet] \endcond
// calculate forces
calc_forces(vd,NN,sigma12,sigma6,r_cut);
unsigned long int f = 0;
int cnt = 0;
double max_disp = 0.0;
// MD time stepping
for (size_t i = 0; i < 10000 ; i++)
{
// Get the iterator
auto it3 = vd.getDomainIterator();
double max_displ = 0.0;
// integrate velicity and space based on the calculated forces (Step1)
while (it3.isNext())
{
auto p = it3.get();
// here we calculate v(tn + 0.5)
vd.template getProp<velocity>(p)[0] += 0.5*dt*vd.template getProp<force>(p)[0];
vd.template getProp<velocity>(p)[1] += 0.5*dt*vd.template getProp<force>(p)[1];
vd.template getProp<velocity>(p)[2] += 0.5*dt*vd.template getProp<force>(p)[2];
Point<3,double> disp({vd.template getProp<velocity>(p)[0]*dt,vd.template getProp<velocity>(p)[1]*dt,vd.template getProp<velocity>(p)[2]*dt});
// here we calculate x(tn + 1)
vd.getPos(p)[0] += disp.get(0);
vd.getPos(p)[1] += disp.get(1);
vd.getPos(p)[2] += disp.get(2);
if (disp.norm() > max_displ)
max_displ = disp.norm();
++it3;
}
if (max_disp < max_displ)
max_disp = max_displ;
// Because we moved the particles in space we have to map them and re-sync the ghost
if (cnt % 10 == 0)
{
vd.map();
vd.template ghost_get<>();
// Get the Cell list structure
vd.updateVerlet(NN,r_gskin,VL_CRS_SYMMETRIC);
}
else
{
vd.template ghost_get<>(SKIP_LABELLING);
}
cnt++;
// calculate forces or a(tn + 1) Step 2
calc_forces(vd,NN,sigma12,sigma6,r_cut);
// Integrate the velocity Step 3
auto it4 = vd.getDomainIterator();
while (it4.isNext())
{
auto p = it4.get();
// here we calculate v(tn + 1)
vd.template getProp<velocity>(p)[0] += 0.5*dt*vd.template getProp<force>(p)[0];
vd.template getProp<velocity>(p)[1] += 0.5*dt*vd.template getProp<force>(p)[1];
vd.template getProp<velocity>(p)[2] += 0.5*dt*vd.template getProp<force>(p)[2];
++it4;
}
// After every iteration collect some statistic about the confoguration
if (i % 100 == 0)
{
// We write the particle position for visualization (Without ghost)
vd.deleteGhost();
vd.write("particles_",f);
// we resync the ghost
vd.ghost_get<>();
// We calculate the energy
double energy = calc_energy(vd,NN,sigma12,sigma6,r_cut);
auto & vcl = create_vcluster();
vcl.sum(energy);
vcl.max(max_disp);
vcl.execute();
// we save the energy calculated at time step i c contain the time-step y contain the energy
x.add(i);
y.add({energy});
// We also print on terminal the value of the energy
// only one processor (master) write on terminal
if (vcl.getProcessUnitID() == 0)
std::cout << "Energy: " << energy << " " << max_disp << " " << std::endl;
max_disp = 0.0;
f++;
}
}
tsim.stop();
std::cout << "Time: " << tsim.getwct() << std::endl;
//! \cond [simulation] \endcond
// Google charts options, it store the options to draw the X Y graph
GCoptions options;
// Title of the graph
options.title = std::string("Energy with time");
// Y axis name
options.yAxis = std::string("Energy");
// X axis name
options.xAxis = std::string("iteration");
// width of the line
options.lineWidth = 1.0;
// Object that draw the X Y graph
GoogleChart cg;
// Add the graph
// The graph that it produce is in svg format that can be opened on browser
cg.AddLinesGraph(x,y,options);
// Write into html format
cg.write("gc_plot2_out.html");
//! \cond [google chart] \endcond
/*!
* \page Vector_5_md_vl_sym_crs Vector 5 molecular dynamic with symmetric Verlet list crossing scheme
*
* ## Finalize ## {#finalize_v_e5_md_sym_crs}
*
* At the very end of the program we have always to de-initialize the library
*
* \snippet Vector/5_molecular_dynamic_sym_crs/main.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
/*!
* \page Vector_5_md_vl_sym_crs Vector 5 molecular dynamic with symmetric Verlet list crossing scheme
*
* ## Full code ## {#full_code_v_e5_md_sym_crs}
*
* \include Vector/5_molecular_dynamic_sym_crs/main.cpp
*
*/
}
int main(int argc, char* argv[])
{
/*!
*
* \page Vector_4_complex_prop Vector 4 complex properties
*
*
* ## Initialization and vector creation ##
*
* We first initialize the library and define useful constants
*
* \see \ref e0_s_init
*
* \snippet Vector/4_complex_prop/main.cpp lib init
*
* We also define a custom structure
*
* \snippet Vector/4_complex_prop/main.cpp struct A
*
* After we initialize the library we can create a vector with complex properties
* with the following line
*
* \snippet Vector/4_complex_prop/main.cpp vect create
*
* In this this particular case every particle carry a scalar,
* a vector in form of float[3], a Point, a list
* in form of vector of float and a list of custom structures, and a vector of vector.
* In general particles can have properties of arbitrary complexity.
*
* \warning For arbitrary complexity mean that we can use any openfpm data structure with and arbitrary nested complexity.
* For example a openfpm::vector<aggregate<grid_cpu<openfpm::vector<aggregate<double,double[3]>>>,openfpm::vector<float>> is valid
* \verbatim
particle
*
vector
/ \
/ \
grid vector<float>
/\
/ \
double double[3]
* \endverbatim
*
* Our custom data-structure A is defined below. Note that this data-structure
* does not have pointers
*
* \snippet Vector/4_complex_prop/main.cpp struct A
*
*
* \warning custom data structure are allowed only if they does not have pointer.
* In case they have pointer we have to define how to serialize our data-structure
*
* \see \ref vector_example_cp_ser
*
*/
//! \cond [lib init] \endcond
// initialize the library
openfpm_init(&argc,&argv);
// Here we define our domain a 2D box with internals from 0 to 1.0 for x and y
Box<2,float> domain({0.0,0.0},{1.0,1.0});
// Here we define the boundary conditions of our problem
size_t bc[2]={PERIODIC,PERIODIC};
// extended boundary around the domain, and the processor domain
Ghost<2,float> g(0.01);
// the scalar is the element at position 0 in the aggregate
constexpr int scalar = 0;
// the vector is the element at position 1 in the aggregate
constexpr int vector = 1;
// the tensor is the element at position 2 in the aggregate
constexpr int point = 2;
// A list1
constexpr int list = 3;
// A listA
constexpr int listA = 4;
// A list of list
constexpr int listlist = 5;
//! \cond [lib init] \endcond
//! \cond [struct A] \endcond
// The custom structure
struct A
{
float p1;
int p2;
A() {};
A(float p1, int p2)
:p1(p1),p2(p2)
{}
};
//! \cond [struct A] \endcond
//! \cond [vect create] \endcond
vector_dist<2,float, aggregate<float,
float[3],
Point<3,double>,
openfpm::vector<float>,
openfpm::vector<A>,
openfpm::vector<openfpm::vector<float>>> >
vd(4096,domain,bc,g);
//! \cond [vect create] \endcond
/*!
*
* \page Vector_4_complex_prop Vector 4 complex properties
*
*
* ## Assign values to properties ##
*
* Assign values to properties does not changes, from the simple case. Consider
* now that each particle has a list, so when we can get the property listA for particle p
* and resize such list with **vd.getProp<listA>(p).resize(...)**. We can add new elements at the
* end with **vd.getProp<listA>(p).add(...)** and get some element of this list with **vd.getProp<listA>(p).get(i)**.
* More in general vd.getProp<listA>(p) return a reference to the openfpm::vector contained by the particle.
*
* \snippet Vector/4_complex_prop/main.cpp vect assign
*
*/
//! \cond [vect assign] \endcond
auto it = vd.getDomainIterator();
while (it.isNext())
{
auto p = it.get();
// we define x, assign a random position between 0.0 and 1.0
vd.getPos(p)[0] = (float)rand() / RAND_MAX;
// we define y, assign a random position between 0.0 and 1.0
vd.getPos(p)[1] = (float)rand() / RAND_MAX;
vd.getProp<scalar>(p) = 1.0;
vd.getProp<vector>(p)[0] = 1.0;
vd.getProp<vector>(p)[1] = 1.0;
vd.getProp<vector>(p)[2] = 1.0;
vd.getProp<point>(p).get(0) = 1.0;
vd.getProp<point>(p).get(1) = 1.0;
vd.getProp<point>(p).get(2) = 1.0;
size_t n_cp = (float)10.0 * rand()/RAND_MAX;
vd.getProp<listA>(p).resize(n_cp);
for (size_t i = 0 ; i < n_cp ; i++)
{
vd.getProp<list>(p).add(i + 10);
vd.getProp<list>(p).add(i + 20);
vd.getProp<list>(p).add(i + 30);
vd.getProp<listA>(p).get(i) = A(i+10.0,i+20.0);
}
vd.getProp<listlist>(p).resize(2);
vd.getProp<listlist>(p).get(0).resize(2);
vd.getProp<listlist>(p).get(1).resize(2);
vd.getProp<listlist>(p).get(0).get(0) = 1.0;
vd.getProp<listlist>(p).get(0).get(1) = 2.0;
vd.getProp<listlist>(p).get(1).get(0) = 3.0;
vd.getProp<listlist>(p).get(1).get(1) = 4.0;
// next particle
++it;
}
//! \cond [vect assign] \endcond
/*!
*
* \page Vector_4_complex_prop Vector 4 complex properties
*
*
* ## Mapping and ghost_get ##
*
* Particles are redistributed across processors all properties are communicated but instead of
* using map we use **map_list** that we can use to select properties.
* A lot of time complex properties can be recomputed and communicate them is not a good idea.
* The same concept also apply for ghost_get. In general we choose which properties to communicate
*
*
* \see \ref e0_s_map
*
* \see \ref e1_part_ghost
*
* \snippet Vector/4_complex_prop/main.cpp vect map ghost
*
*/
//! \cond [vect map ghost] \endcond
// Particles are redistribued across the processors but only the scalar,vector, and point properties
// are transfert
vd.map_list<scalar,vector,point,list,listA,listlist>();
// Synchronize the ghost
vd.ghost_get<scalar,vector,point,listA,listlist>();
//! \cond [vect map ghost] \endcond
/*!
*
* \page Vector_4_complex_prop Vector 4 complex properties
*
*
* ## Output and VTK visualization ##
*
* Vector with complex properties can be still be visualized, because unknown properties are
* automatically excluded
*
* \see \ref e0_s_vis_vtk
*
* \snippet Vector/4_complex_prop/main.cpp vtk
*
*/
//! \cond [vtk] \endcond
vd.write("particles");
//! \cond [vtk] \endcond
/*!
*
* \page Vector_4_complex_prop Vector 4 complex properties
*
* ## Print 4 particles in the ghost area ##
*
* Here we print that the first 4 particles to show that the list of A and the list of list are filled
* and the ghosts contain the correct information
*
* \snippet Vector/4_complex_prop/main.cpp print ghost info
*
*/
//! \cond [print ghost info] \endcond
size_t fg = vd.size_local();
Vcluster & v_cl = create_vcluster();
if (v_cl.getProcessUnitID() == 0)
{
for ( ; fg < vd.size_local()+4 ; fg++)
{
std::cout << "List of A" << std::endl;
for (size_t i = 0 ; i < vd.getProp<listA>(fg).size() ; i++)
std::cout << "Element: " << i << " p1=" << vd.getProp<listA>(fg).get(i).p1 << " p2=" << vd.getProp<listA>(fg).get(i).p2 << std::endl;
std::cout << "List of list" << std::endl;
for (size_t i = 0 ; i < vd.getProp<listlist>(fg).size() ; i++)
{
for (size_t j = 0 ; j < vd.getProp<listlist>(fg).get(i).size() ; j++)
std::cout << "Element: " << i << " " << j << " " << vd.getProp<listlist>(fg).get(i).get(j) << std::endl;
}
}
}
//! \cond [print ghost info] \endcond
/*!
* \page Vector_4_complex_prop Vector 4 complex properties
*
* ## Finalize ## {#finalize}
*
* At the very end of the program we have always to de-initialize the library
*
* \snippet Vector/4_complex_prop/main.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
/*!
* \page Vector_4_complex_prop Vector 4 complex properties
*
* # Full code # {#code}
*
* \include Vector/4_complex_prop/main.cpp
*
*/
}
int main(int argc, char* argv[])
{
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* ## Initialization ## {#num_sk_inc_petsc_3D_init}
*
* After model our equation we:
* * Initialize the library
* * Define some useful constants
* * define Ghost size
* * Non-periodic boundary conditions
* * Padding domain expansion
*
* Padding and Ghost differ in the fact the padding extend the domain.
* Ghost is an extension for each sub-domain
*
* \snippet Numerics/Stoke_flow/0_2D_incompressible/main_petsc.cpp init
*
*/
//! \cond [init] \endcond
// Initialize
openfpm_init(&argc,&argv);
// velocity in the grid is the property 0, pressure is the property 1
constexpr int velocity = 0;
constexpr int pressure = 1;
// Domain
Box<3,float> domain({0.0,0.0,0.0},{3.0,1.0,1.0});
// Ghost (Not important in this case but required)
Ghost<3,float> g(0.01);
// Grid points on x=36 and y=12 z=12
long int sz[] = {36,12,12};
size_t szu[3];
szu[0] = (size_t)sz[0];
szu[1] = (size_t)sz[1];
szu[2] = (size_t)sz[2];
// We need one more point on the left and down part of the domain
// This is given by the boundary conditions that we impose.
//
Padding<3> pd({1,1,1},{0,0,0});
//! \cond [init] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* Distributed grid that store the solution
*
* \see \ref e0_s_grid_inst
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp grid inst
*
*/
//! \cond [grid inst] \endcond
grid_dist_id<3,float,aggregate<float[3],float>> g_dist(szu,domain,g);
//! \cond [grid inst] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* Solving the system above require the solution of a system like that
*
* \f$ Ax = b \quad x = A^{-1}b\f$
*
* where A is the system the discretize the left hand side of the equations + boundary conditions
* and b discretize the right hand size + boundary conditions
*
* FDScheme is the object that we use to produce the Matrix A and the vector b.
* Such object require the maximum extension of the stencil
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp fd scheme
*
*/
//! \cond [fd scheme] \endcond
// It is the maximum extension of the stencil (order 2 laplacian stencil has extension 1)
Ghost<3,long int> stencil_max(1);
// Finite difference scheme
FDScheme<lid_nn> fd(pd, stencil_max, domain, g_dist.getGridInfo(), g_dist);
//! \cond [fd scheme] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* ## Impose the equation on the domain ## {#num_sk_inc_3D_ied}
*
* Here we impose the system of equation, we start from the incompressibility Eq imposed in the bulk with the
* exception of the first point {0,0} and than we set P = 0 in {0,0}, why we are doing this is again
* mathematical to have a well defined system, an intuitive explanation is that P and P + c are both
* solution for the incompressibility equation, this produce an ill-posed problem to make it well posed
* we set one point in this case {0,0} the pressure to a fixed constant for convenience P = 0
*
* The best way to understand what we are doing is to draw a smaller example like 8x8.
* Considering that we have one additional point on the left for padding we have a grid
* 9x9. If on each point we have v_x v_y and P unknown we have
* 9x9x3 = 243 unknown. In order to fully determine and unique solution we have to
* impose 243 condition. The code under impose (in the case of 9x9) between domain
* and bulk 243 conditions.
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp impose eq dom
*
*
*/
//! \cond [impose eq dom] \endcond
// start and end of the bulk
fd.impose(ic_eq(),0.0, EQ_4, {0,0,0},{sz[0]-2,sz[1]-2,sz[2]-2},true);
fd.impose(Prs(), 0.0, EQ_4, {0,0,0},{0,0,0});
fd.impose(vx_eq(),0.0, EQ_1, {1,0},{sz[0]-2,sz[1]-2,sz[2]-2});
fd.impose(vy_eq(),0.0, EQ_2, {0,1},{sz[0]-2,sz[1]-2,sz[2]-2});
fd.impose(vz_eq(),0.0, EQ_3, {0,0,1},{sz[0]-2,sz[1]-2,sz[2]-2});
// v_x
// R L (Right,Left)
fd.impose(v_x(),0.0, EQ_1, {0,0,0}, {0,sz[1]-2,sz[2]-2});
fd.impose(v_x(),0.0, EQ_1, {sz[0]-1,0,0},{sz[0]-1,sz[1]-2,sz[2]-2});
// T B (Top,Bottom)
fd.impose(avg_y_vx_f(),0.0, EQ_1, {0,-1,0}, {sz[0]-1,-1,sz[2]-2});
fd.impose(avg_y_vx(),0.0, EQ_1, {0,sz[1]-1,0},{sz[0]-1,sz[1]-1,sz[2]-2});
// A F (Forward,Backward)
fd.impose(avg_z_vx_f(),0.0, EQ_1, {0,-1,-1}, {sz[0]-1,sz[1]-1,-1});
fd.impose(avg_z_vx(),0.0, EQ_1, {0,-1,sz[2]-1},{sz[0]-1,sz[1]-1,sz[2]-1});
// v_y
// R L
fd.impose(avg_x_vy_f(),0.0, EQ_2, {-1,0,0}, {-1,sz[1]-1,sz[2]-2});
fd.impose(avg_x_vy(),1.0, EQ_2, {sz[0]-1,0,0},{sz[0]-1,sz[1]-1,sz[2]-2});
// T B
fd.impose(v_y(), 0.0, EQ_2, {0,0,0}, {sz[0]-2,0,sz[2]-2});
fd.impose(v_y(), 0.0, EQ_2, {0,sz[1]-1,0},{sz[0]-2,sz[1]-1,sz[2]-2});
// F A
fd.impose(avg_z_vy(),0.0, EQ_2, {-1,0,sz[2]-1}, {sz[0]-1,sz[1]-1,sz[2]-1});
fd.impose(avg_z_vy_f(),0.0, EQ_2, {-1,0,-1}, {sz[0]-1,sz[1]-1,-1});
// v_z
// R L
fd.impose(avg_x_vz_f(),0.0, EQ_3, {-1,0,0}, {-1,sz[1]-2,sz[2]-1});
fd.impose(avg_x_vz(),1.0, EQ_3, {sz[0]-1,0,0},{sz[0]-1,sz[1]-2,sz[2]-1});
// T B
fd.impose(avg_y_vz(),0.0, EQ_3, {-1,sz[1]-1,0},{sz[0]-1,sz[1]-1,sz[2]-1});
fd.impose(avg_y_vz_f(),0.0, EQ_3, {-1,-1,0}, {sz[0]-1,-1,sz[2]-1});
// F A
fd.impose(v_z(),0.0, EQ_3, {0,0,0}, {sz[0]-2,sz[1]-2,0});
fd.impose(v_z(),0.0, EQ_3, {0,0,sz[2]-1},{sz[0]-2,sz[1]-2,sz[2]-1});
// When we pad the grid, there are points of the grid that are not
// touched by the previous condition. Mathematically this lead
// to have too many variables for the conditions that we are imposing.
// Here we are imposing variables that we do not touch to zero
//
// L R
fd.impose(Prs(), 0.0, EQ_4, {-1,-1,-1},{-1,sz[1]-1,sz[2]-1});
fd.impose(Prs(), 0.0, EQ_4, {sz[0]-1,-1,-1},{sz[0]-1,sz[1]-1,sz[2]-1});
// T B
fd.impose(Prs(), 0.0, EQ_4, {0,sz[1]-1,-1}, {sz[0]-2,sz[1]-1,sz[2]-1});
fd.impose(Prs(), 0.0, EQ_4, {0,-1 ,-1}, {sz[0]-2,-1, sz[2]-1});
// F A
fd.impose(Prs(), 0.0, EQ_4, {0,0,sz[2]-1}, {sz[0]-2,sz[1]-2,sz[2]-1});
fd.impose(Prs(), 0.0, EQ_4, {0,0,-1}, {sz[0]-2,sz[1]-2,-1});
// Impose v_x v_y v_z padding
fd.impose(v_x(), 0.0, EQ_1, {-1,-1,-1},{-1,sz[1]-1,sz[2]-1});
fd.impose(v_y(), 0.0, EQ_2, {-1,-1,-1},{sz[0]-1,-1,sz[2]-1});
fd.impose(v_z(), 0.0, EQ_3, {-1,-1,-1},{sz[0]-1,sz[1]-1,-1});
//! \cond [impose eq dom] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* ## Solve the system of equation ## {#num_sk_inc_3D_petsc_sse}
*
* Once we imposed all the equations we can retrieve the Matrix A and the vector b
* and pass these two element to the solver. In this example we are using PETSC solvers
* direct/Iterative solvers. While Umfpack
* has only one solver, PETSC wrap several solvers. The function best_solve set the solver in
* the modality to try multiple solvers to solve your system. The subsequent call to solve produce a report
* of all the solvers tried comparing them in error-convergence and speed. If you do not use
* best_solve try to solve your system with the default solver GMRES (That is the most robust iterative solver
* method)
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp solver
*
*/
//! \cond [solver] \endcond
// Create an PETSC solver
petsc_solver<double> solver;
// Warning try many solver and collect statistics require a lot of time
// To just solve you can comment this line
// solver.best_solve();
// Give to the solver A and b, return x, the solution
auto x = solver.solve(fd.getA(),fd.getB());
//! \cond [solver] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* ## Copy the solution on the grid and write on VTK ## {#num_sk_inc_3D_petsc_csg}
*
* Once we have the solution we copy it on the grid
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp copy write
*
*/
//! \cond [copy write] \endcond
// Bring the solution to grid
fd.template copy<velocity,pressure>(x,{0,0},{sz[0]-1,sz[1]-1,sz[2]-1},g_dist);
g_dist.write("lid_driven_cavity_p_petsc");
//! \cond [copy write] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* ## Finalize ## {#num_sk_inc_3D_petsc_fin}
*
* At the very end of the program we have always to de-initialize the library
*
* \snippet Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp fin lib
*
*/
//! \cond [fin lib] \endcond
openfpm_finalize();
//! \cond [fin lib] \endcond
/*!
* \page Stokes_1_3D_petsc Stokes incompressible 3D petsc
*
* # Full code # {#num_sk_inc_3D_petsc_code}
*
* \include Numerics/Stoke_flow/1_3D_incompressible/main_petsc.cpp
*
*/
}
int main(int argc, char* argv[])
{
//
// ### WIKI 2 ###
//
// Initialize the library and several objects
//
openfpm_init(&argc,&argv);
//
// ### WIKI 3 ###
//
// Get the vcluster object and the number of processor
//
Vcluster & v_cl = create_vcluster();
size_t N_prc = v_cl.getProcessingUnits();
//
// ### WIKI 3 ###
//
// We find the maximum of the processors rank, that should be the Number of
// processora minus one, only processor 0 print on terminal
//
size_t id = v_cl.getProcessUnitID();
v_cl.max(id);
v_cl.execute();
if (v_cl.getProcessUnitID() == 0)
std::cout << "Maximum processor rank: " << id << "\n";
//
// ### WIKI 4 ###
//
// We sum all the processor ranks the maximum, the result should be that should
// be $\frac{(n-1)n}{2}$, only processor 0 print on terminal
//
size_t id2 = v_cl.getProcessUnitID();
v_cl.sum(id2);
v_cl.execute();
if (v_cl.getProcessUnitID() == 0)
std::cout << "Sum of all processors rank: " << id2 << "\n";
//
// ### WIKI 5 ###
//
// we can collect information from all processors using the function gather
//
size_t id3 = v_cl.getProcessUnitID();
openfpm::vector<size_t> v;
v_cl.allGather(id3,v);
v_cl.execute();
if (v_cl.getProcessUnitID() == 0)
{
std::cout << "Collected ids: ";
for(size_t i = 0 ; i < v.size() ; i++)
std::cout << " " << v.get(i) << " ";
std::cout << "\n";
}
//
// ### WIKI 5 ###
//
// we can also send messages to specific processors, with the condition that the receiving
// processors know we want to communicate with them, if you are searching for a more
// free way to communicate where the receiving processors does not know which one processor
// want to communicate with us, see the example 1_dsde
//
std::stringstream ss_message_1;
std::stringstream ss_message_2;
ss_message_1 << "Hello from " << std::setw(8) << v_cl.getProcessUnitID() << "\n";
ss_message_2 << "Hello from " << std::setw(8) << v_cl.getProcessUnitID() << "\n";
std::string message_1 = ss_message_1.str();
std::string message_2 = ss_message_2.str();
size_t msg_size = message_1.size();
// Processor 0 send to processors 1,2 , 1 to 2,1, 2 to 0,1
v_cl.send(((id3+1)%N_prc + N_prc)%N_prc,0,message_1.c_str(),msg_size);
v_cl.send(((id3+2)%N_prc + N_prc)%N_prc,0,message_2.c_str(),msg_size);
openfpm::vector<char> v_one;
v_one.resize(msg_size);
openfpm::vector<char> v_two(msg_size);
v_two.resize(msg_size);
v_cl.recv(((id3-1)%N_prc + N_prc)%N_prc,0,(void *)v_one.getPointer(),msg_size);
v_cl.recv(((id3-2)%N_prc + N_prc)%N_prc,0,(void *)v_two.getPointer(),msg_size);
v_cl.execute();
if (v_cl.getProcessUnitID() == 0)
{
for (size_t i = 0 ; i < msg_size ; i++)
std::cout << v_one.get(i);
for (size_t i = 0 ; i < msg_size ; i++)
std::cout << v_two.get(i);
}
//
// ### WIKI 5 ###
//
// we can also do what we did before in one shot
//
id = v_cl.getProcessUnitID();
id2 = v_cl.getProcessUnitID();
id3 = v_cl.getProcessUnitID();
v.clear();
// convert the string into a vector
openfpm::vector<char> message_1_v(msg_size);
openfpm::vector<char> message_2_v(msg_size);
for (size_t i = 0 ; i < msg_size ; i++)
message_1_v.get(i) = message_1[i];
for (size_t i = 0 ; i < msg_size ; i++)
message_2_v.get(i) = message_2[i];
v_cl.max(id);
v_cl.sum(id2);
v_cl.allGather(id3,v);
// in the case of vector we have special functions that avoid to specify the size
v_cl.send(((id+1)%N_prc + N_prc)%N_prc,0,message_1_v);
v_cl.send(((id+2)%N_prc + N_prc)%N_prc,0,message_2_v);
v_cl.recv(((id-1)%N_prc + N_prc)%N_prc,0,v_one);
v_cl.recv(((id-2)%N_prc + N_prc)%N_prc,0,v_two);
v_cl.execute();
if (v_cl.getProcessUnitID() == 0)
{
std::cout << "Maximum processor rank: " << id << "\n";
std::cout << "Sum of all processors rank: " << id << "\n";
std::cout << "Collected ids: ";
for(size_t i = 0 ; i < v.size() ; i++)
std::cout << " " << v.get(i) << " ";
std::cout << "\n";
for (size_t i = 0 ; i < msg_size ; i++)
std::cout << v_one.get(i);
for (size_t i = 0 ; i < msg_size ; i++)
std::cout << v_two.get(i);
}
openfpm_finalize();
}
int main(int argc, char* argv[])
{
/*!
*
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
*
* ## Initialization and vector creation ##
*
* After we initialize the library we can create a vector with complex properties
* with the following line
*
* \snippet Vector/4_complex_prop/main.cpp vect create
*
* In this this particular case every particle carry two my_struct object
*
*/
// initialize the library
openfpm_init(&argc,&argv);
// Here we define our domain a 2D box with internals from 0 to 1.0 for x and y
Box<2,float> domain({0.0,0.0},{1.0,1.0});
// Here we define the boundary conditions of our problem
size_t bc[2]={PERIODIC,PERIODIC};
// extended boundary around the domain, and the processor domain
Ghost<2,float> g(0.01);
// my_struct at position 0 in the aggregate
constexpr int my_s1 = 0;
// my_struct at position 1 in the aggregate
constexpr int my_s2 = 1;
//! \cond [vect create] \endcond
vector_dist<2,float, aggregate<my_struct,my_struct>>
vd(4096,domain,bc,g);
std::cout << "HAS PACK: " << has_pack_agg<aggregate<my_struct,my_struct>>::result::value << std::endl;
//! \cond [vect create] \endcond
/*!
*
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
*
* ## Assign values to properties ##
*
* In this loop we assign position to particles and we fill the two my_struct
* that each particle contain. As demostration the first my_struct is filled
* with the string representation of the particle coordinates. The second my struct
* is filled with the string representation of the particle position multiplied by 2.0.
* The the vectors of the two my_struct are filled respectively with the sequence
* 1,2,3 and 1,2,3,4
*
*
*
* \snippet Vector/4_complex_prop/main_ser.cpp vect assign
*
*/
//! \cond [vect assign] \endcond
auto it = vd.getDomainIterator();
while (it.isNext())
{
auto p = it.get();
// we define x, assign a random position between 0.0 and 1.0
vd.getPos(p)[0] = (float)rand() / RAND_MAX;
// we define y, assign a random position between 0.0 and 1.0
vd.getPos(p)[1] = (float)rand() / RAND_MAX;
// Get the particle position as point
Point<2,float> pt = vd.getPos(p);
// create a C string from the particle coordinates
// and copy into my struct
vd.getProp<my_s1>(p).size = 32;
vd.getProp<my_s1>(p).ptr = new char[32];
strcpy(vd.getProp<my_s1>(p).ptr,pt.toString().c_str());
// create a C++ string from the particle coordinates
vd.getProp<my_s1>(p).str = std::string(pt.toString());
vd.getProp<my_s1>(p).v.add(1);
vd.getProp<my_s1>(p).v.add(2);
vd.getProp<my_s1>(p).v.add(3);
pt = pt * 2.0;
// create a C string from the particle coordinates multiplied by 2.0
// and copy into my struct
vd.getProp<my_s2>(p).size = 32;
vd.getProp<my_s2>(p).ptr = new char[32];
strcpy(vd.getProp<my_s2>(p).ptr,pt.toString().c_str());
// create a C++ string from the particle coordinates
vd.getProp<my_s2>(p).str = std::string(pt.toString());
vd.getProp<my_s2>(p).v.add(1);
vd.getProp<my_s2>(p).v.add(2);
vd.getProp<my_s2>(p).v.add(3);
vd.getProp<my_s2>(p).v.add(4);
// next particle
++it;
}
//! \cond [vect assign] \endcond
/*!
*
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
*
* ## Mapping and ghost_get ##
*
* Particles are redistributed across processors and we also synchronize the ghost
*
* \see \ref e0_s_map
*
* \see \ref e1_part_ghost
*
* \snippet Vector/4_complex_prop/main_ser.cpp vect map ghost
*
*/
//! \cond [vect map ghost] \endcond
// Particles are redistribued across the processors
vd.map();
// Synchronize the ghost
vd.ghost_get<my_s1,my_s2>();
//! \cond [vect map ghost] \endcond
/*!
*
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
*
* ## Output and VTK visualization ##
*
* Vector with complex properties can be still be visualized, because unknown properties are
* automatically excluded
*
* \see \ref e0_s_vis_vtk
*
* \snippet Vector/4_complex_prop/main.cpp vtk
*
*/
//! \cond [vtk] \endcond
vd.write("particles");
//! \cond [vtk] \endcond
/*!
*
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
* ## Print 4 particles in the ghost area ##
*
* Here we print that the first 4 particles to show that the two my_struct contain the
* right information
*
* \snippet Vector/4_complex_prop/main_ser.cpp print ghost info
*
*/
//! \cond [print ghost info] \endcond
size_t fg = vd.size_local();
Vcluster & v_cl = create_vcluster();
// Only the master processor print
if (v_cl.getProcessUnitID() == 0)
{
// Print 4 particles
for ( ; fg < vd.size_local()+4 ; fg++)
{
// Print my struct1 information
std::cout << "my_struct1:" << std::endl;
std::cout << "C-string: " << vd.getProp<my_s1>(fg).ptr << std::endl;
std::cout << "Cpp-string: " << vd.getProp<my_s1>(fg).str << std::endl;
for (size_t i = 0 ; i < vd.getProp<my_s1>(fg).v.size() ; i++)
std::cout << "Element: " << i << " " << vd.getProp<my_s1>(fg).v.get(i) << std::endl;
// Print my struct 2 information
std::cout << "my_struct2" << std::endl;
std::cout << "C-string: " << vd.getProp<my_s2>(fg).ptr << std::endl;
std::cout << "Cpp-string: " << vd.getProp<my_s2>(fg).str << std::endl;
for (size_t i = 0 ; i < vd.getProp<my_s2>(fg).v.size() ; i++)
std::cout << "Element: " << i << " " << vd.getProp<my_s2>(fg).v.get(i) << std::endl;
}
}
//! \cond [print ghost info] \endcond
/*!
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
* ## Finalize ## {#finalize}
*
* At the very end of the program we have always to de-initialize the library
*
* \snippet Vector/4_complex_prop/main_ser.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
/*!
* \page Vector_4_complex_prop_ser Vector 4 property serialization
*
* # Full code # {#code}
*
* \include Vector/4_complex_prop/main_ser.cpp
*
*/
}
int main(int argc, char* argv[])
{
//
// ### WIKI 2 ###
//
// Here we Initialize the library, than we create a uniform random generator between 0 and 1 to to generate particles
// randomly in the domain, we create a Box that define our domain, boundary conditions, and ghost
//
// initialize the library
openfpm_init(&argc,&argv);
// Here we define our domain a 2D box with internals from 0 to 1.0 for x and y
Box<2,float> domain({0.0,0.0},{1.0,1.0});
// Here we define the boundary conditions of our problem
size_t bc[2]={PERIODIC,PERIODIC};
// extended boundary around the domain, and the processor domain
Ghost<2,float> g(0.01);
//
// ### WIKI 3 ###
//
// Here we are creating a distributed vector defined by the following parameters
//
// * 2 is the Dimensionality of the space where the objects live
// * float is the type used for the spatial coordinate of the particles
// * float,float[3],float[3][3] is the information stored by each particle a scalar float, a vector float[3] and a tensor of rank 2 float[3][3]
// the list of properties must be put into an aggregate data astructure aggregate<prop1,prop2,prop3, ... >
//
// vd is the instantiation of the object
//
// The Constructor instead require:
//
// * Number of particles 4096 in this case
// * Domain where is defined this structure
// * bc boundary conditions
// * g Ghost
//
// The following construct a vector where each processor has 4096 / N_proc (N_proc = number of processor)
// objects with an undefined position in space. This non-space decomposition is also called data-driven
// decomposition
//
vector_dist<2,float, aggregate<float,float[3],float[3][3]> > vd(4096,domain,bc,g);
// the scalar is the element at position 0 in the aggregate
const int scalar = 0;
// the vector is the element at position 1 in the aggregate
const int vector = 1;
// the tensor is the element at position 2 in the aggregate
const int tensor = 2;
//
// ### WIKI 5 ###
//
// Get an iterator that go through the 4096 particles, in an undefined position state and define its position
//
auto it = vd.getDomainIterator();
while (it.isNext())
{
auto key = it.get();
// we define x, assign a random position between 0.0 and 1.0
vd.getPos(key)[0] = rand() / RAND_MAX;
// we define y, assign a random position between 0.0 and 1.0
vd.getPos(key)[1] = rand() / RAND_MAX;
// next particle
++it;
}
//
// ### WIKI 6 ###
//
// Once we define the position, we distribute them according to the default space decomposition
// The default decomposition is created even before assigning the position to the object. It determine
// which part of space each processor manage
//
vd.map();
//
// ### WIKI 7 ###
//
// We get the object that store the decomposition, than we iterate again across all the objects, we count them
// and we confirm that all the particles are local
//
//Counter we use it later
size_t cnt = 0;
// Get the space decomposition
auto & ct = vd.getDecomposition();
// Get a particle iterator
it = vd.getDomainIterator();
// For each particle ...
while (it.isNext())
{
// ... p
auto p = it.get();
// we set the properties of the particle p
// the scalar property
vd.template getProp<scalar>(p) = 1.0;
vd.template getProp<vector>(p)[0] = 1.0;
vd.template getProp<vector>(p)[1] = 1.0;
vd.template getProp<vector>(p)[2] = 1.0;
vd.template getProp<tensor>(p)[0][0] = 1.0;
vd.template getProp<tensor>(p)[0][1] = 1.0;
vd.template getProp<tensor>(p)[0][2] = 1.0;
vd.template getProp<tensor>(p)[1][0] = 1.0;
vd.template getProp<tensor>(p)[1][1] = 1.0;
vd.template getProp<tensor>(p)[1][2] = 1.0;
vd.template getProp<tensor>(p)[2][0] = 1.0;
vd.template getProp<tensor>(p)[2][1] = 1.0;
vd.template getProp<tensor>(p)[2][2] = 1.0;
// increment the counter
cnt++;
// next particle
++it;
}
//
// ### WIKI 8 ###
//
// cnt contain the number of object the local processor contain, if we are interested to count the total number across the processor
// we can use the function add, to sum across processors. First we have to get an instance of Vcluster, queue an operation of add with
// the variable count and finaly execute. All the operations are asynchronous, execute work like a barrier and ensure that all the
// queued operations are executed
//
auto & v_cl = create_vcluster();
v_cl.sum(cnt);
v_cl.execute();
//
// ### WIKI 9 ###
//
// Output the particle position for each processor
//
vd.write("output",VTK_WRITER);
//
// ### WIKI 10 ###
//
// Deinitialize the library
//
openfpm_finalize();
}
int main(int argc, char* argv[])
{
/*!
*
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* ## Initialization ##
*
* The initialization is the same as the molecular dynamic example. The differences are in the
* parameters. We will use a bigger system, with more particles. The delta time for integration
* is chosen in order to keep the system stable.
*
* \see \ref e3_md_init
*
* \snippet Vector/4_reorder/main_comp_ord.cpp vect create
*
*/
//! \cond [vect create] \endcond
double dt = 0.0001;
float r_cut = 0.03;
double sigma = r_cut/3.0;
double sigma12 = pow(sigma,12);
double sigma6 = pow(sigma,6);
openfpm::vector<double> x;
openfpm::vector<openfpm::vector<double>> y;
openfpm_init(&argc,&argv);
Vcluster & v_cl = create_vcluster();
// we will use it do place particles on a 40x40x40 Grid like
size_t sz[3] = {40,40,40};
// domain
Box<3,float> box({0.0,0.0,0.0}, {1.0,1.0,1.0});
// Boundary conditions
size_t bc[3]= {PERIODIC,PERIODIC,PERIODIC};
// ghost, big enough to contain the interaction radius
Ghost<3,float> ghost(r_cut);
vector_dist<3,double, aggregate<double[3],double[3]> > vd(0,box,bc,ghost);
//! \cond [vect create] \endcond
/*!
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* ## Particles on a grid like position ##
*
* Here we place the particles on a grid like manner
*
* \see \ref e3_md_gl
*
* \snippet Vector/4_reorder/main_comp_ord.cpp vect grid
*
*/
//! \cond [vect grid] \endcond
auto it = vd.getGridIterator(sz);
while (it.isNext())
{
vd.add();
auto key = it.get();
vd.getLastPos()[0] = key.get(0) * it.getSpacing(0);
vd.getLastPos()[1] = key.get(1) * it.getSpacing(1);
vd.getLastPos()[2] = key.get(2) * it.getSpacing(2);
vd.template getLastProp<velocity>()[0] = 0.0;
vd.template getLastProp<velocity>()[1] = 0.0;
vd.template getLastProp<velocity>()[2] = 0.0;
vd.template getLastProp<force>()[0] = 0.0;
vd.template getLastProp<force>()[1] = 0.0;
vd.template getLastProp<force>()[2] = 0.0;
++it;
}
//! \cond [vect grid] \endcond
/*!
*
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* ## Molecular dynamic steps ##
*
* Here we do 30000 MD steps using verlet integrator the cycle is the same as the
* molecular dynamic example. with the following changes.
*
* ### Cell lists ###
*
* Instead of getting the normal cell list we get an hilbert curve cell-list. Such cell list has a
* function called **getIterator** used inside the function **calc_forces** and **calc_energy**
* that iterate across all the particles but in a smart-way. In practice
* given an r-cut a cell-list is constructed with the provided spacing. Suppose to have a cell-list
* \f$ m \times n \f$, an hilbert curve \f$ 2^k \times 2^k \f$ is contructed with \f$ k = ceil(log_2(max(m,n))) \f$.
* Cell-lists are explored according to this Hilbert curve, If a cell does not exist is simply skipped.
*
*
* \verbatim
+------+------+------+------+ Example of Hilbert curve running on a 3 x 3 Cell
| | | | | An hilbert curve of k = ceil(log_2(3)) = 4
| X+---->X | X +---> X |
| ^ | + | ^ | + |
***|******|******|****---|--+ *******
* + | v | + * v | * *
* 7 | 8+---->9 * X | * * = Domain
* ^ | | * + | * *
*--|-----------------*---|--+ *******
* + | | * v |
* 4<----+5 | 6<---+ X |
* | ^ | + * |
*---------|-------|--*------+
* | + | v * |
* 1+---->2 | 3+---> X |
* | | * |
**********************------+
this mean that we will iterate the following cells
1,2,5,4,7,8,9,6,3
Suppose now that the particles are ordered like described
Particles id Cell
0 1
1 7
2 8
3 1
4 9
5 9
6 6
7 7
8 3
9 2
10 4
11 3
The iterator of the cell-list will explore the particles in the following way
Cell 1 2 5 4 7 8 9 6 3
| | | | | | | | | |
0,3,9,,10,1,7,2,4,5,6,8
* \endverbatim
*
* We cannot explain here what is a cache, but in practice is a fast memory in the CPU able
* to store chunks of memory. The cache in general is much smaller than RAM, but the big advantage
* is its speed. Retrieve data from the cache is much faster than RAM. Unfortunately the factors
* that determine what is on cache and what is not are multiples: Type of cache, algorithm ... .
* Qualitatively all caches will tend to load chunks of data that you read multiple-time, or chunks
* of data that probably you will read based on pattern analysis. A small example is a linear memory copy where
* you read consecutively memory and you write on consecutive memory.
* Modern CPU recognize such pattern and decide to load on cache the consecutive memory before
* you actually require it.
*
*
* Iterating the vector in the way described above has the advantage that when we do computation on particles
* and its neighborhood with the sequence described above it will happen that:
*
* * If to process a particle A we read some neighborhood particles to process the next particle A+1
* we will probably read most of the previous particles.
*
*
* In order to show in practice what happen we first show the graph when we do not reorder
*
* \htmlinclude Vector/4_reorder/no_reorder.html
*
* The measure has oscillation but we see an asymptotic behavior from 0.04 in the initial condition to
* 0.124 . Below we show what happen when we use iterator from the Cell list hilbert
*
* \htmlinclude Vector/4_reorder/comp_reord.html
*
* In cases where particles does not move or move very slowly consider to use data-reordering, because it can
* give **8-10% speedup**
*
* \see \ref e4_reo
*
* ## Timers ##
*
* In order to collect the time of the force calculation we insert two timers around the function
* calc_force. The overall performance is instead calculated with another timer around the time stepping
*
* \snippet Vector/4_reorder/main_data_ord.cpp timer start
* \snippet Vector/4_reorder/main_data_ord.cpp timer stop
*
* \see \ref e3_md_vi
*
*
*/
//! \cond [md steps] \endcond
// Get the Cell list structure
auto NN = vd.getCellList_hilb(r_cut);
// calculate forces
calc_forces(vd,NN,sigma12,sigma6);
unsigned long int f = 0;
timer time2;
time2.start();
#ifndef TEST_RUN
size_t Nstep = 30000;
#else
size_t Nstep = 300;
#endif
// MD time stepping
for (size_t i = 0; i < Nstep ; i++)
{
// Get the iterator
auto it3 = vd.getDomainIterator();
// integrate velicity and space based on the calculated forces (Step1)
while (it3.isNext())
{
auto p = it3.get();
// here we calculate v(tn + 0.5)
vd.template getProp<velocity>(p)[0] += 0.5*dt*vd.template getProp<force>(p)[0];
vd.template getProp<velocity>(p)[1] += 0.5*dt*vd.template getProp<force>(p)[1];
vd.template getProp<velocity>(p)[2] += 0.5*dt*vd.template getProp<force>(p)[2];
// here we calculate x(tn + 1)
vd.getPos(p)[0] += vd.template getProp<velocity>(p)[0]*dt;
vd.getPos(p)[1] += vd.template getProp<velocity>(p)[1]*dt;
vd.getPos(p)[2] += vd.template getProp<velocity>(p)[2]*dt;
++it3;
}
// Because we mooved the particles in space we have to map them and re-sync the ghost
vd.map();
vd.template ghost_get<>();
timer time;
if (i % 10 == 0)
time.start();
// calculate forces or a(tn + 1) Step 2
calc_forces(vd,NN,sigma12,sigma6);
if (i % 10 == 0)
{
time.stop();
x.add(i);
y.add({time.getwct()});
}
// Integrate the velocity Step 3
auto it4 = vd.getDomainIterator();
while (it4.isNext())
{
auto p = it4.get();
// here we calculate v(tn + 1)
vd.template getProp<velocity>(p)[0] += 0.5*dt*vd.template getProp<force>(p)[0];
vd.template getProp<velocity>(p)[1] += 0.5*dt*vd.template getProp<force>(p)[1];
vd.template getProp<velocity>(p)[2] += 0.5*dt*vd.template getProp<force>(p)[2];
++it4;
}
// After every iteration collect some statistic about the confoguration
if (i % 100 == 0)
{
// We write the particle position for visualization (Without ghost)
vd.deleteGhost();
vd.write("particles_",f);
// we resync the ghost
vd.ghost_get<>();
// We calculate the energy
double energy = calc_energy(vd,NN,sigma12,sigma6);
auto & vcl = create_vcluster();
vcl.sum(energy);
vcl.execute();
// We also print on terminal the value of the energy
// only one processor (master) write on terminal
if (vcl.getProcessUnitID() == 0)
std::cout << std::endl << "Energy: " << energy << std::endl;
f++;
}
}
time2.stop();
std::cout << "Performance: " << time2.getwct() << std::endl;
//! \cond [md steps] \endcond
/*!
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* ## Plotting graphs ##
*
* After we terminate the MD steps our vector x contains at which iteration we benchmark the force
* calculation time, while y contains the measured time at that time-step. We can produce a graph X Y
*
* \note The graph produced is an svg graph that can be view with a browser. From the browser we can
* also easily save the graph into pure svg format
*
* \snippet Vector/4_reorder/main_comp_ord.cpp google chart
*
*/
//! \cond [google chart] \endcond
// Google charts options, it store the options to draw the X Y graph
GCoptions options;
// Title of the graph
options.title = std::string("Force calculation time");
// Y axis name
options.yAxis = std::string("Time");
// X axis name
options.xAxis = std::string("iteration");
// width of the line
options.lineWidth = 1.0;
// Object that draw the X Y graph
GoogleChart cg;
// Add the graph
// The graph that it produce is in svg format that can be opened on browser
cg.AddLinesGraph(x,y,options);
// Write into html format
cg.write("gc_plot2_out.html");
//! \cond [google chart] \endcond
/*!
*
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* ## Finalize ##
*
* At the very end of the program we have always to de-initialize the library
*
* \snippet Vector/4_reorder/main_comp_ord.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
/*!
*
* \page Vector_4_comp_reo Vector 4 computational reordering and cache friendliness
*
* # Full code #
*
* \include Vector/4_reorder/main_comp_ord.cpp
*
*/
}
int main(int argc, char* argv[])
{
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
* ## Initialization ##
*
* Here we Initialize the library, and we check the we are on a single processor. GoogleChart
* cannot do parallel IO or write big files. So or we collect all data on one processor, or each
* processor write a distinct file. In this particular example we simply stop if the program start
* on more than one processor
*
* \snippet Plot/0_simple_graph/main.cpp initialize
*
*/
//! \cond [initialize] \endcond
openfpm_init(&argc,&argv);
auto & v_cl = create_vcluster();
// Google chart is only single processor
if (v_cl.getProcessingUnits() > 1)
{
std::cerr << "Error: only one processor is allowed" << "\n";
return 1;
}
//! \cond [initialize] \endcond
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
* ## Graph data ##
*
* Here we have the vectors that will contain the information about the graph.
*
* \snippet Plot/0_simple_graph/main.cpp datas vector
*
*/
//! \cond [datas vector] \endcond
openfpm::vector<std::string> x;
openfpm::vector<openfpm::vector<double>> y;
openfpm::vector<std::string> yn;
//! \cond [datas vector] \endcond
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
* We will try now to produce the following situation. Six values on **x** each of them having 4 values on **y**
*
* This mean that for each x value we have to define 4 y values. Having multiple values on on x can be used for
* several purpose.
*
* * Define multiple lines. For example if we connect all the points # we obtain one line. If we connect
* all the @ points we obtain another line, an so on ... (figure below)
*
* * Define error bands
*
* * Visualize different observables/parameters for the same value x
*
*
* \verbatim
y ^ $ dataset1
| * dataset2
0.9 | # dataset3
| @ @ dataset4
| #
0.6 | * * @ *
| $ # @ # #
| @ $ $ @ @
0.3 | # * $ #
| $ *
| * $
0 |_________________________________
o t t f f s x
n w h o i i
e o r u v x
e r e
e
\endverbatim
*
* We start from the first case (Define multiple lines)
*
* \snippet Plot/0_simple_graph/main.cpp data fill
*
*/
//! \cond [data fill] \endcond
// Fill the x values
x.add("one");
x.add("two");
x.add("three");
x.add("four");
x.add("five");
x.add("six");
// we have 4 dataset or lines
yn.add("dataset1");
yn.add("dataset2");
yn.add("dataset3");
yn.add("dataset4");
// Because we have 6 points on x each containing 4 lines or dataset, we have to provides
// 6 point with 4 values at each x point
y.add({2,3,5,6});
y.add({5,6,1,6});
y.add({2,1,6,9});
y.add({1,6,3,2});
y.add({3,3,0,6});
y.add({2,1,4,6});
//! \cond [data fill] \endcond
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
* ## Graph options ##
*
* We can specify several options for the graphs.
*
* * Title of the graph
* * Title of the y axis
* * Title of the x axis
*
*
* \snippet Plot/0_simple_graph/main.cpp google chart
*
*/
//! \cond [google chart] \endcond
GCoptions options;
options.title = std::string("Example");
options.yAxis = std::string("Y Axis");
options.xAxis = std::string("X Axis");
options.lineWidth = 5;
//! \cond [google chart] \endcond
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
* ## Graph write ##
*
* We create the object to create plots with Google Charts
*
* A writer can produce several graphs optionally interleaved with HTML code.
* Here we write in HTML a description of the graph, than we output the graph
*
* AddLinesGraph create a typical graph with lines
*
* \snippet Plot/0_simple_graph/main.cpp google chart write1
*
* \htmlonly
<div id="chart_div0" style="width: 900px; height: 500px;"></div>
\endhtmlonly
*
*/
//! \cond [google chart write1] \endcond
GoogleChart cg;
//
cg.addHTML("<h2>First graph</h2>");
cg.AddLinesGraph(x,y,yn,options);
//! \cond [google chart write1] \endcond
/*!
*
* \page Plot_0_cg Plot 0 Google Chart
*
* ## Hist graph ##
*
* Hist graph is instead a more flexible Graph writer. In particular we can specify
* how to draw each dataset. With the option
*
* * **stype** specify how to draw each dataset
* * **stypeext** we can override the default stype option. In this case we say that the third dataset
* in must be reppresented as a line instead of a bars
*
* To note that we can reuse the same Google chart writer to write multiple
* Graph on the same page, interleaved with HTML code
*
* \snippet Plot/0_simple_graph/main.cpp google chart write2
*
* \htmlonly
<div id="chart_div1" style="width: 900px; height: 500px;"></div>
\endhtmlonly
*
*
*/
//! \cond [google chart write2] \endcond
options.stype = std::string("bars");
// it say that the dataset4 must me represented with a line
options.stypeext = std::string("{3: {type: 'line'}}");
cg.addHTML("<h2>Second graph</h2>");
cg.AddHistGraph(x,y,yn,options);
//! \cond [google chart write2] \endcond
/*!
*
* \page Plot_0_cg Plot 0 Google Chart
*
* ## %Error bars ##
*
* Here we show how to draw error bars. %Error bars are drawn specifying intervals with a min and a max.
* Intervals in general does not have to encapsulate any curve. First we construct the vector y with 3
* values the first value contain the curve points, the second and third contain the min,max interval.
*
* \snippet Plot/0_simple_graph/main.cpp google chart write3
*
* \htmlonly
<div id="chart_div2" style="width: 900px; height: 500px;"></div>
\endhtmlonly
*
*
*/
//! \cond [google chart write3] \endcond
cg.addHTML("<h2>Third graph</h2>");
// The first colum are the values of a line while the other 2 values
// are the min and max of an interval, as we can see interval does not
// have to encapsulate any curve
y.clear();
y.add({0.10,0.20,0.19});
y.add({0.11,0.21,0.18});
y.add({0.12,0.22,0.21});
y.add({0.15,0.25,0.20});
y.add({0.09,0.29,0.25});
y.add({0.08,0.28,0.27});
// Here we mark that the the colum 2 and 3 are intervals
yn.clear();
yn.add("line1");
yn.add("interval");
yn.add("interval");
cg.AddLinesGraph(x,y,yn,options);
//! \cond [google chart write3] \endcond
/*!
*
* \page Plot_0_cg Plot 0 Google Chart
*
* The style of each interval can be controlled, and the definition of intervals can be interleaved with definition of
* other lines. In this example we show how to define 3 lines and 3 intervals, controlling the style of the last interval
*
* \snippet Plot/0_simple_graph/main.cpp google chart write4
*
* \htmlonly
<div id="chart_div3" style="width: 900px; height: 500px;"></div>
\endhtmlonly
*
*
*/
//! \cond [google chart write4] \endcond
cg.addHTML("<h2>Four graph</h2>");
// again 6 point but 9 values
y.clear();
y.add({0.10,0.20,0.19,0.22,0.195,0.215,0.35,0.34,0.36});
y.add({0.11,0.21,0.18,0.22,0.19,0.215,0.36,0.35,0.37});
y.add({0.12,0.22,0.21,0.23,0.215,0.225,0.35,0.34,0.36});
y.add({0.15,0.25,0.20,0.26,0.22,0.255,0.36,0.35,0.37});
y.add({0.09,0.29,0.25,0.30,0.26,0.295,0.35,0.34,0.36});
y.add({0.08,0.28,0.27,0.29,0.275,0.285,0.36,0.35,0.37});
// colum 0 and 1 are lines
// colums 2-3 and 4-5 are intervals
// colum 6 is a line
// colum 7-8 is an interval
yn.add("line1");
yn.add("line2");
yn.add("interval");
yn.add("interval");
yn.add("interval");
yn.add("interval");
yn.add("line3");
yn.add("interval");
yn.add("interval");
// Intervals are enumerated with iX, for example in this case with 3 intervals we have i0,i1,i2
// with this line we control the style of the intervals. In particular we change from the default
// values
options.intervalext = std::string("{'i2': { 'color': '#4374E0', 'style':'bars', 'lineWidth':4, 'fillOpacity':1 } }");
cg.AddLinesGraph(x,y,yn,options);
//! \cond [google chart write4] \endcond
/*!
*
* \page Plot_0_cg Plot 0 Google Chart
*
* ## More options ##
*
* In this last example we also show how to:
*
*
* * Make the graph bigger, setting **width** and **height** options
* * Give the possibility to to zoom-in and zoom-out with **GC_EXPLORER**
* * Use lines instead a smooth function to connect points
* * Use logaritmic scale
*
* \note For more options refer to doxygen and Google Charts
*
* \snippet Plot/0_simple_graph/main.cpp google chart write5
*
*
* \htmlonly
<div id="chart_div4" style="width: 1280px; height: 700px;"></div>
\endhtmlonly
*
*/
//! \cond [google chart write5] \endcond
openfpm::vector<double> xn;
xn.add(1.0);
xn.add(2.0);
xn.add(3.0);
xn.add(4.0);
xn.add(5.0);
xn.add(6.0);
options.intervalext = "";
options.width = 1280;
options.heigh = 720;
options.curveType = "line";
options.more = GC_ZOOM + "," + GC_X_LOG + "," + GC_Y_LOG;
cg.AddLinesGraph(xn,y,yn,options);
cg.write("gc_out.html");
//! \cond [google chart write5] \endcond
/*!
* \page Plot_0_cg Plot 0 Google Chart
*
*
* ## Finalize ## {#finalize}
*
* At the very end of the program we have always de-initialize the library
*
* \snippet Plot/0_simple_graph/main.cpp finalize
*
*/
//! \cond [finalize] \endcond
openfpm_finalize();
//! \cond [finalize] \endcond
}
~ut_start() { BOOST_TEST_MESSAGE("Delete global VClster"); openfpm_finalize(); }
