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Abhinav Singh authoredAbhinav Singh authored
petsc_solver.hpp 41.98 KiB
/*
* petsc_solver.hpp
*
* Created on: Apr 26, 2016
* Author: i-bird
*/
#ifndef OPENFPM_NUMERICS_SRC_SOLVERS_PETSC_SOLVER_HPP_
#define OPENFPM_NUMERICS_SRC_SOLVERS_PETSC_SOLVER_HPP_
#include "config.h"
#ifdef HAVE_PETSC
#include "Vector/Vector.hpp"
#include <petscksp.h>
#include <petsctime.h>
#include "Plot/GoogleChart.hpp"
#include "Matrix/SparseMatrix.hpp"
#include "Vector/Vector.hpp"
#include <sstream>
#include <iomanip>
template <typename T>
std::string to_string_with_precision(const T a_value, const int n = 6)
{
std::ostringstream out;
out << std::setprecision(n) << a_value;
return out.str();
}
#define UMFPACK_NONE 0
#define REL_DOWN 1
#define REL_UP 2
#define REL_ALL 3
#define PCHYPRE_BOOMERAMG "petsc_boomeramg"
enum AMG_type
{
NONE_AMG,
HYPRE_AMG,
PETSC_AMG,
TRILINOS_ML
};
/*! \brief In case T does not match the PETSC precision compilation create a
* stub structure
*
* \param T precision
*
*/
template<typename T>
class petsc_solver
{
public:
/*! \brief Solve the linear system.
*
* In this case just return an error
*
* \param A sparse matrix
* \param b right-hand-side
*
* \return the solution
*
*/
template<typename impl> static Vector<T> solve(const SparseMatrix<T,impl> & A, const Vector<T> & b)
{ std::cerr << "Error Petsc only suppor double precision" << "/n";
}
};
#define SOLVER_NOOPTION 0
#define SOLVER_PRINT_RESIDUAL_NORM_INFINITY 1
#define SOLVER_PRINT_DETERMINANT 2
//! It contain statistic of the error of the calculated solution
struct solError
{
//! infinity norm of the error
PetscReal err_inf;
//! L1 norm of the error
PetscReal err_norm;
//! Number of iterations
PetscInt its;
};
/*! \brief This class is able to do Matrix inversion in parallel with PETSC solvers
*
* # Example of use of this class #
*
* \snippet eq_unit_test.hpp lid-driven cavity 2D
*
*/
template<>
class petsc_solver<double>
{
//! contain the infinity norm of the residual at each iteration
struct itError
{
//! Iteration
PetscInt it;
//! error norm at iteration it
PetscReal err_norm;
};
/*! \brief It contain the benchmark information for each solver
*
*
*/
struct solv_bench_info
{
//! Solver Krylov name
std::string method;
//! Method name (short form)
std::string smethod;
//! time to converge in milliseconds
double time;
//! Solution error
solError err;
//! Convergence per iteration
openfpm::vector<itError> res;
};
//! indicate if the preconditioner is set
bool is_preconditioner_set = false;
//! KSP Maximum number of iterations
PetscInt maxits;
//! Main parallel solver
KSP ksp;
//! Temporal variable used for calculation of static members
size_t tmp;
//! The full set of solvers
openfpm::vector<std::string> solvs;
//! It contain the solver benchmark results
openfpm::vector<solv_bench_info> bench;
//! Type of the algebraic multi-grid preconditioner
AMG_type atype = NONE_AMG;
//! Block size
int block_sz = 0;
/*! \brief Calculate the residual error at time t for one method
*
* \param t time
* \param slv solver
*
* \return the residual
*
*/
static double calculate_it(double t, solv_bench_info & slv)
{
double s_int = slv.time / slv.res.size();
// Calculate the discrete point in time
size_t pt = std::floor(t / s_int);
if (pt < slv.res.size())
return slv.res.get(pt).err_norm;
return slv.res.last().err_norm;
}
/*! \brief Here we write the benchmark report
*
*
*/
void write_bench_report()
{
if (create_vcluster().getProcessUnitID() != 0)
return;
openfpm::vector<std::string> x;
openfpm::vector<openfpm::vector<double>> y;
openfpm::vector<std::string> yn;
openfpm::vector<double> xd;
for (size_t i = 0 ; i < bench.size() ; i++)
x.add(bench.get(i).smethod);
// Each colum can have multiple data set (in this case 4 dataset)
// Each dataset can have a name
yn.add("Norm infinity");
yn.add("Norm average");
yn.add("Number of iterations");
// Each colums can have multiple data-set
for (size_t i = 0 ; i < bench.size() ; i++)
y.add({bench.get(i).err.err_inf,bench.get(i).err.err_norm,(double)bench.get(i).err.its});
// Google charts options
GCoptions options;
options.title = std::string("Residual error");
options.yAxis = std::string("Error");
options.xAxis = std::string("Method");
options.stype = std::string("bars");
options.more = std::string("vAxis: {scaleType: 'log'}");
GoogleChart cg;
std::stringstream ss;
cg.addHTML("<h2>Robustness</h2>");
cg.AddHistGraph(x,y,yn,options);
cg.addHTML("<h2>Speed</h2>");
y.clear();
yn.clear();
yn.add("Time in millseconds");
options.title = std::string("Time");
for (size_t i = 0 ; i < bench.size() ; i++)
y.add({bench.get(i).time});
cg.AddHistGraph(x,y,yn,options);
// Convergence in time
x.clear();
y.clear();
yn.clear();
xd.clear();
// Get the maximum in time across all the solvers
double max_time = 0.0;
for (size_t i = 0 ; i < bench.size() ; i++)
{
if (bench.get(i).time > max_time) {max_time = bench.get(i).time;}
yn.add(bench.get(i).smethod);
}
size_t n_int = maxits;
// calculate dt
double dt = max_time / n_int;
// Add
// For each solver we have a convergence plot
for (double t = dt ; t <= max_time + 0.05 * max_time ; t += dt)
{
y.add();
xd.add(t);
for (size_t j = 0 ; j < bench.size() ; j++)
y.last().add(calculate_it(t,bench.get(j)));
}
std::stringstream ss2;
ss2 << "<h2>Convergence with time</h2><br>" << std::endl;
options.title = std::string("Residual norm infinity");
options.yAxis = std::string("residual");
options.xAxis = std::string("Time in milliseconds");
options.lineWidth = 1.0;
options.more = std::string("vAxis: {scaleType: 'log'},hAxis: {scaleType: 'log'}");
cg.addHTML(ss2.str());
cg.AddLinesGraph(xd,y,yn,options);
ss << "<h2>Solvers Tested</h2><br><br>" << std::endl;
for (size_t i = 0 ; i < bench.size() ; i++)
ss << bench.get(i).smethod << " = " << bench.get(i).method << "<br>" << std::endl;
cg.addHTML(ss.str());
cg.write("gc_solver.html");
}
/*! \brief It set up the solver based on the provided options
*
* \param A_ Matrix
* \param x_ solution
* \param b_ right-hand-side
*
*/
void pre_solve_impl(const Mat & A_, const Vec & b_, Vec & x_)
{
PETSC_SAFE_CALL(KSPSetNormType(ksp,KSP_NORM_UNPRECONDITIONED));
if (atype == HYPRE_AMG)
{
PC pc;
// We set the pre-conditioner
PETSC_SAFE_CALL(KSPGetPC(ksp,&pc));
PCFactorSetShiftType(pc, MAT_SHIFT_NONZERO);
PCFactorSetShiftAmount(pc, PETSC_DECIDE);
}
}
/*! \brief Print a progress bar on standard out
*
*
*/
void print_progress_bar()
{
auto & v_cl = create_vcluster();
if (v_cl.getProcessUnitID() == 0)
std::cout << "-----------------------25-----------------------50-----------------------75----------------------100" << std::endl;
}
/*! \brief procedure print the progress of the solver in benchmark mode
*
* \param ksp Solver
* \param it Iteration number
* \param res resudual
* \param data custom pointer to data
*
* \return always zero
*
*/
static PetscErrorCode monitor_progress_residual(KSP ksp,PetscInt it,PetscReal res,void* data)
{
petsc_solver<double> * pts = (petsc_solver *)data;
pts->progress(it);
itError erri;
erri.it = it;
Mat A;
Vec Br,v,w;
PETSC_SAFE_CALL(KSPGetOperators(ksp,&A,NULL));
PETSC_SAFE_CALL(MatCreateVecs(A,&w,&v));
PETSC_SAFE_CALL(KSPBuildResidual(ksp,v,w,&Br));
PETSC_SAFE_CALL(KSPBuildResidual(ksp,v,w,&Br));
PETSC_SAFE_CALL(VecNorm(Br,NORM_INFINITY,&erri.err_norm));
itError err_fill;
size_t old_size = pts->bench.last().res.size();
pts->bench.last().res.resize(it+1);
if (old_size > 0)
err_fill = pts->bench.last().res.get(old_size-1);
else
err_fill = erri;
for (long int i = old_size ; i < (long int)it ; i++)
pts->bench.last().res.get(i) = err_fill;
// Add the error per iteration
pts->bench.last().res.get(it) = erri;
return 0;
}
/*! \brief This function print an "*" showing the progress of the solvers
*
* \param it iteration number
*
*/
void progress(PetscInt it)
{
PetscInt n_max_it;
PETSC_SAFE_CALL(KSPGetTolerances(ksp,NULL,NULL,NULL,&n_max_it));
auto & v_cl = create_vcluster();
if (std::floor(it * 100.0 / n_max_it) > tmp)
{
size_t diff = it * 100.0 / n_max_it - tmp;
tmp = it * 100.0 / n_max_it;
if (v_cl.getProcessUnitID() == 0)
{
for (size_t k = 0 ; k < diff ; k++) {std::cout << "*";}
std::cout << std::flush;
}
}
}
/*! \brief Print statistic about the solution error and method used
*
* \param err structure that contain the solution errors
*
*/
void print_stat(solError & err)
{
auto & v_cl = create_vcluster();
if (v_cl.getProcessUnitID() == 0)
{
KSPType typ;
KSPGetType(ksp,&typ);
std::cout << "Method: " << typ << " " << " pre-conditoner: " << PCJACOBI << " iterations: " << err.its << std::endl;
std::cout << "Norm of error: " << err.err_norm << " Norm infinity: " << err.err_inf << std::endl;
}
}
/*! \brief It convert the KSP type into a human read-able string *
* \param solv solver (short form)
*
* \return the name of the solver in long form
*
*/
std::string to_string_method(const std::string & solv)
{
if (solv == std::string(KSPBCGS))
{
return std::string("BiCGStab (Stabilized version of BiConjugate Gradient Squared)");
}
else if (solv == std::string(KSPIBCGS))
{
return std::string("IBiCGStab (Improved Stabilized version of BiConjugate Gradient Squared)");
}
else if (solv == std::string(KSPFBCGS))
{
return std::string("FBiCGStab (Flexible Stabilized version of BiConjugate Gradient Squared)");
}
else if (solv == std::string(KSPFBCGSR))
{
return std::string("FBiCGStab-R (Modified Flexible Stabilized version of BiConjugate Gradient Squared)");
}
else if (solv == std::string(KSPBCGSL))
{
return std::string("BiCGStab(L) (Stabilized version of BiConjugate Gradient Squared with L search directions)");
}
else if (solv == std::string(KSPGMRES))
{
return std::string("GMRES(M) (Generalized Minimal Residual method with restart)");
}
else if (solv == std::string(KSPFGMRES))
{
return std::string("FGMRES(M) (Flexible Generalized Minimal Residual with restart)");
}
else if (solv == std::string(KSPLGMRES))
{
return std::string("LGMRES(M) (Augment Generalized Minimal Residual method with restart)");
}
else if (solv == std::string(KSPPGMRES))
{
return std::string("PGMRES(M) (Pipelined Generalized Minimal Residual method)");
}
else if (solv == std::string(KSPGCR))
{
return std::string("GCR (Generalized Conjugate Residual)");
}
return std::string("UNKNOWN");
}
/*! \brief Allocate a new benchmark slot for a method
*
* \param str Method name
*
*/
void new_bench(const std::string & str)
{
// Add a new benchmark result
bench.add();
bench.last().method = to_string_method(str);
bench.last().smethod = std::string(str);
}
/*! \brief Copy the solution if better
*
* \param res Residual of the solution
* \param sol solution
* \param best_res residual of the best solution * \param best_sol best solution
*
*/
void copy_if_better(double res, Vec & sol, double & best_res, Vec & best_sol)
{
if (res < best_res)
{
VecCopy(sol,best_sol);
best_res = res;
}
}
/*! \brief Try to solve the system x=inv(A)*b using all the Krylov solvers with simple Jacobi pre-conditioner
*
* It try to solve the system using JACOBI pre-conditioner and all the Krylov solvers available at the end it write
* a report
*
* \param A_ Matrix
* \param b_ vector of coefficents
* \param x_ solution
*
*/
void try_solve_simple(const Mat & A_, const Vec & b_, Vec & x_)
{
Vec best_sol;
PETSC_SAFE_CALL(VecDuplicate(x_,&best_sol));
// Best residual
double best_res = std::numeric_limits<double>::max();
// Create a new VCluster
auto & v_cl = create_vcluster();
destroyKSP();
// for each solver
for (size_t i = 0 ; i < solvs.size() ; i++)
{
initKSPForTest();
// Here we solve without preconditioner
PC pc;
// We set the pre-conditioner to none
PETSC_SAFE_CALL(KSPGetPC(ksp,&pc));
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_type",PCNONE));
setSolver(solvs.get(i).c_str());
// Setup for BCGSL, GMRES
if (solvs.get(i) == std::string(KSPBCGSL))
{
// we try from 2 to 6 as search direction
for (size_t j = 2 ; j < 6 ; j++)
{
new_bench(solvs.get(i));
if (v_cl.getProcessUnitID() == 0)
std::cout << "L = " << j << std::endl;
bench.last().smethod += std::string("(") + std::to_string(j) + std::string(")");
searchDirections(j);
bench_solve_simple(A_,b_,x_,bench.last());
copy_if_better(bench.last().err.err_inf,x_,best_res,best_sol);
}
}
else if (solvs.get(i) == std::string(KSPGMRES) ||
solvs.get(i) == std::string(std::string(KSPFGMRES)) ||
solvs.get(i) == std::string(std::string(KSPLGMRES)) )
{ // we try from 2 to 6 as search direction
for (size_t j = 50 ; j < 300 ; j += 50)
{
// Add a new benchmark result
new_bench(solvs.get(i));
if (v_cl.getProcessUnitID() == 0)
std::cout << "Restart = " << j << std::endl;
bench.last().smethod += std::string("(") + std::to_string(j) + std::string(")");
setRestart(j);
bench_solve_simple(A_,b_,x_,bench.last());
copy_if_better(bench.last().err.err_inf,x_,best_res,best_sol);
}
}
else
{
// Add a new benchmark result
new_bench(solvs.get(i));
bench_solve_simple(A_,b_,x_,bench.last());
copy_if_better(bench.last().err.err_inf,x_,best_res,best_sol);
}
destroyKSP();
}
write_bench_report();
// Copy the best solution to x
PETSC_SAFE_CALL(VecCopy(best_sol,x_));
PETSC_SAFE_CALL(VecDestroy(&best_sol));
}
/*! \brief Benchmark solve simple solving x=inv(A)*b
*
* \param A_ Matrix A
* \param b_ vector b
* \param x_ solution x
* \param bench structure that store the benchmark information
*
*/
void bench_solve_simple(const Mat & A_, const Vec & b_, Vec & x_, solv_bench_info & bench)
{
// timer for benchmark
timer t;
t.start();
// Enable progress monitor
tmp = 0;
PETSC_SAFE_CALL(KSPMonitorCancel(ksp));
PETSC_SAFE_CALL(KSPMonitorSet(ksp,monitor_progress_residual,this,NULL));
print_progress_bar();
solve_simple(A_,b_,x_);
// New line
if (create_vcluster().getProcessUnitID() == 0)
std::cout << std::endl;
t.stop();
bench.time = t.getwct() * 1000.0;
// calculate error statistic about the solution and print
solError err = statSolutionError(A_,b_,x_,ksp);
print_stat(err);
bench.err = err;
// New line if (create_vcluster().getProcessUnitID() == 0)
std::cout << std::endl;
}
/*! \brief solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner
*
* \param A_ SparseMatrix
* \param b_ right-hand-side
* \param x_ solution
*
*/
void solve_simple(const Mat & A_, const Vec & b_, Vec & x_)
{
// PETSC_SAFE_CALL(KSPSetType(ksp,s_type));
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;
PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));
// We set the Matrix operators
PETSC_SAFE_CALL(KSPSetOperators(ksp,A_,A_));
// if we are on on best solve set-up a monitor function
PETSC_SAFE_CALL(KSPSetFromOptions(ksp));
//PETSC_SAFE_CALL(KSPSetUp(ksp));
// Solve the system
PETSC_SAFE_CALL(KSPSolve(ksp,b_,x_));
}
/*! \brief solve simple use a Krylov solver + Simple selected Parallel Pre-conditioner
*
* \param b_ right hand side
* \param x_ solution
*
*/
void solve_simple(const Vec & b_, Vec & x_)
{
// Solve the system
PETSC_SAFE_CALL(KSPSolve(ksp,b_,x_));
}
/*! \brief Calculate statistic on the error solution
*
* \param A_ Matrix of the system
* \param b_ Right hand side of the matrix
* \param x_ Solution
* \param ksp Krylov solver
*
* \return the solution error
*
*/
static solError statSolutionError(const Mat & A_, const Vec & b_, Vec & x_, KSP ksp)
{
solError err;
err = getSolNormError(A_,b_,x_);
PetscInt its;
PETSC_SAFE_CALL(KSPGetIterationNumber(ksp,&its));
err.its = its;
return err;
}
/*! \brief initialize the KSP object
*
*
*/
void initKSP()
{
PETSC_SAFE_CALL(KSPCreate(PETSC_COMM_WORLD,&ksp));
}
/*! \brief initialize the KSP object for solver testing
*
*
*/
void initKSPForTest()
{
PETSC_SAFE_CALL(KSPCreate(PETSC_COMM_WORLD,&ksp));
setMaxIter(maxits);
}
/*! \brief Destroy the KSP object
*
*
*/
void destroyKSP()
{
KSPDestroy(&ksp);
}
/*! \brief Return the norm error of the solution
*
* \param x_ the solution
* \param b_ the right-hand-side
* \param ksp Krylov solver
*
* \return the solution error
*
*/
static solError getSolNormError(const Vec & b_, const Vec & x_,KSP ksp)
{
Mat A_;
Mat P_;
KSPGetOperators(ksp,&A_,&P_);
return getSolNormError(A_,b_,x_);
}
/*! \brief Return the norm error of the solution
*
* \param A_ the matrix that identity the linear system
* \param x_ the solution
* \param b_ the right-hand-side
*
* \return the solution error
*
*/
static solError getSolNormError(const Mat & A_, const Vec & b_, const Vec & x_)
{
PetscScalar neg_one = -1.0;
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;
PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));
/*
Here we calculate the residual error
*/
PetscReal norm;
PetscReal norm_inf;
// Get a vector r for the residual
Vector<double,PETSC_BASE> r(row,row_loc);
Vec & r_ = r.getVec();
PETSC_SAFE_CALL(MatMult(A_,x_,r_));
PETSC_SAFE_CALL(VecAXPY(r_,neg_one,b_));
PETSC_SAFE_CALL(VecNorm(r_,NORM_1,&norm));
PETSC_SAFE_CALL(VecNorm(r_,NORM_INFINITY,&norm_inf));
solError err;
err.err_norm = norm / col;
err.err_inf = norm_inf;
err.its = 0;
return err;
}
public:
//! Type of the solution object
typedef Vector<double,PETSC_BASE> return_type;
~petsc_solver()
{
PETSC_SAFE_CALL(KSPDestroy(&ksp));
}
petsc_solver()
:maxits(300),tmp(0)
{
initKSP();
// Add the solvers
solvs.add(std::string(KSPBCGS));
// solvs.add(std::string(KSPIBCGS)); <--- Produce invalid argument
// solvs.add(std::string(KSPFBCGS));
// solvs.add(std::string(KSPFBCGSR)); <--- Nan production problems
solvs.add(std::string(KSPBCGSL));
solvs.add(std::string(KSPGMRES));
solvs.add(std::string(KSPFGMRES));
solvs.add(std::string(KSPLGMRES));
// solvs.add(std::string(KSPPGMRES)); <--- Take forever
// solvs.add(std::string(KSPGCR));
//setSolver(KSPGMRES);
}
/*! \brief Print the preconditioner used by the solver
*
*
*/
void print_preconditioner()
{
auto & v_cl = create_vcluster();
if (v_cl.getProcessUnitID() == 0)
{
PC pc;
PCType type_pc;
// We set the pre-conditioner PETSC_SAFE_CALL(KSPGetPC(ksp,&pc));
PETSC_SAFE_CALL(PCGetType(pc,&type_pc));
std::cout << "The precoditioner is: " << type_pc << std::endl;
}
}
/*! \brief Print the ksp_type used by the solver
*
*
*/
void print_ksptype()
{
auto & v_cl = create_vcluster();
if (v_cl.getProcessUnitID() == 0)
{
KSPType type_ksp;
// We get the KSP_type
PETSC_SAFE_CALL(KSPGetType(ksp,&type_ksp));
std::cout << "The ksp_type is: " << type_ksp << std::endl;
}
}
/*! \brief Add a test solver
*
* The try solve function use the most robust solvers in PETSC, if you want to add
* additionally solver like KSPIBCGS,KSPFBCGSR,KSPPGMRES, use addTestSolver(std::string(KSPIBCGS))
*
* \param solver additional solver solver to test
*
*/
void addTestSolver(std::string & solver)
{
solvs.add(solver);
}
/*! \brief Remove a test solver
*
* The try solve function use the most robust solvers in PETSC, if you want to remove
* a solver like use removeTestSolver(std::string(KSPIBCGS))
*
* \param solver remove solver to test
*
*/
void removeTestSolver(const std::string & solver)
{
// search for the test solver and remove it
for (size_t i = 0 ; i < solvs.size() ; i++)
{
if (solvs.get(i) == solver)
return;
}
}
/*! \brief Set the Petsc solver
*
* \see KSPType in PETSC manual for a list of all PETSC solvers
*
*/
void log_monitor()
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-ksp_monitor",0));
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_print_statistics","2"));
}
/*! \brief Set the Petsc solver
*
* \see KSPType in PETSC manual for a list of all PETSC solvers
*
* \param type petsc solver type
*
*/
void setSolver(KSPType type)
{
PetscOptionsSetValue(NULL,"-ksp_type",type);
}
/*! \brief Set the relative tolerance as stop criteria
*
* \see PETSC manual KSPSetTolerances for an explanation
*
* \param rtol_ Relative tolerance
*
*/
void setRelTol(PetscReal rtol_)
{
PetscReal rtol;
PetscReal abstol;
PetscReal dtol;
PetscInt maxits;
PETSC_SAFE_CALL(KSPGetTolerances(ksp,&rtol,&abstol,&dtol,&maxits));
PETSC_SAFE_CALL(KSPSetTolerances(ksp,rtol_,abstol,dtol,maxits));
}
/*! \brief Set the absolute tolerance as stop criteria
*
* \see PETSC manual KSPSetTolerances for an explanation
*
* \param abstol_ Absolute tolerance
*
*/
void setAbsTol(PetscReal abstol_)
{
PetscReal rtol;
PetscReal abstol;
PetscReal dtol;
PetscInt maxits;
PETSC_SAFE_CALL(KSPGetTolerances(ksp,&rtol,&abstol,&dtol,&maxits));
PETSC_SAFE_CALL(KSPSetTolerances(ksp,rtol,abstol_,dtol,maxits));
}
/*! \brief Set the divergence tolerance
*
* \see PETSC manual KSPSetTolerances for an explanation
*
* \param dtol_ tolerance
*
*/
void setDivTol(PetscReal dtol_)
{
PetscReal rtol;
PetscReal abstol;
PetscReal dtol;
PetscInt maxits;
PETSC_SAFE_CALL(KSPGetTolerances(ksp,&rtol,&abstol,&dtol,&maxits));
PETSC_SAFE_CALL(KSPSetTolerances(ksp,rtol,abstol,dtol_,maxits));
}
/*! \brief Set the maximum number of iteration for Krylov solvers
*
* \param n maximum number of iterations
* */
void setMaxIter(PetscInt n)
{
PetscReal rtol;
PetscReal abstol;
PetscReal dtol;
PetscInt maxits;
PETSC_SAFE_CALL(KSPGetTolerances(ksp,&rtol,&abstol,&dtol,&maxits));
PETSC_SAFE_CALL(KSPSetTolerances(ksp,rtol,abstol,dtol,n));
this->maxits = n;
}
/*! For the BiCGStab(L) it define the number of search directions
*
* BiCG Methods can fail for base break-down (or near break-down). BiCGStab(L) try
* to avoid this problem. Such method has a parameter L (2 by default) Bigger is L
* more the system will try to avoid the breakdown
*
* \param l Increasing L should reduce the probability of failure of the solver because of break-down of the base
*
*/
void searchDirections(PetscInt l)
{
PetscOptionsSetValue(NULL,"-ksp_bcgsl_ell",std::to_string(l).c_str());
}
/*! \brief For GMRES based method, the number of Krylov directions to orthogonalize against
*
* \param n number of directions
*
*/
void setRestart(PetscInt n)
{
PetscOptionsSetValue(NULL,"-ksp_gmres_restart",std::to_string(n).c_str());
}
/*! \brief Set the preconditioner of the linear solver
*
* The preconditoner that can be set are the same as PETSC
*
* For a full list please visit
* Please visit: http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/PC/PCType.html#PCType
*
* An exception is PCHYPRE with BOOMERAMG in this case use
* PCHYPRE_BOOMERAMG. Many preconditioners has default values, but many
* times the default values are not good. Here we list some interesting case
*
* ## Algebraic-multi-grid based preconditioners##
*
* Parameters for this type of preconditioner can be set using
* setPreconditionerAMG_* functions.
*
* * Number of levels set by setPreconditionerAMG_nl
* * Maximum number of cycles setPreconditionerAMG_maxit
* * Smooth or relax method setPreconditionerAMG_smooth,setPreconditionerAMG_relax
* * Cycle type and number of sweep (relaxation steps) when going up or down setPreconditionerAMG_cycleType
* * Coarsening method setPreconditionerAMG_coarsen
* * interpolation schemes setPreconditionerAMG_interp
*
*
* \param type of the preconditioner
*
*/
void setPreconditioner(PCType type)
{
is_preconditioner_set = true;
if (std::string(type) == PCHYPRE_BOOMERAMG) {
PC pc;
// We set the pre-conditioner
PETSC_SAFE_CALL(KSPGetPC(ksp,&pc));
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_type",PCHYPRE));
PETSC_SAFE_CALL(PCFactorSetShiftType(pc, MAT_SHIFT_NONZERO));
PETSC_SAFE_CALL(PCFactorSetShiftAmount(pc, PETSC_DECIDE));
#ifdef PETSC_HAVE_HYPRE
PETSC_SAFE_CALL(PCHYPRESetType(pc, "boomeramg"));
#endif
atype = HYPRE_AMG;
}
else
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_type",type));
}
}
/*! \brief Set the number of levels for the algebraic-multigrid preconditioner
*
* In case you select an algebraic preconditioner like PCHYPRE or PCGAMG you can
* set the number of levels using this function
*
* \param nl number of levels
*
*/
void setPreconditionerAMG_nl(int nl)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_max_levels",std::to_string(nl).c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set the maximum number of V or W cycle for algebraic-multi-grid
*
* \param nit number of levels
*
*/
void setPreconditionerAMG_maxit(int nit)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_max_iter",std::to_string(nit).c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set the relaxation method for the algebraic-multi-grid preconditioner
*
* Possible values for relazation can be
* "Jacobi","sequential-Gauss-Seidel","seqboundary-Gauss-Seidel",
* "SOR/Jacobi","backward-SOR/Jacobi",hybrid chaotic Gauss-Seidel (works only with OpenMP),
* "symmetric-SOR/Jacobi","l1scaled-SOR/Jacobi","Gaussian-elimination","CG","Chebyshev",
* "FCF-Jacobi","l1scaled-Jacobi"
*
*
*
* * Every smooth operator can have additional parameters to be set in order to
* correctly work.
*
*
* \param type of relax method
* \param k where is applied REL_UP,REL_DOWN,REL_ALL (default is all)
*
*/
void setPreconditionerAMG_relax(const std::string & type, int k = REL_ALL)
{
if (atype == HYPRE_AMG)
{
if (k == REL_ALL)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_relax_type_all",type.c_str()));}
else if (k == REL_UP)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_relax_type_up",type.c_str()));}
else if (k == REL_DOWN)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_relax_type_down",type.c_str()));}
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief It set the type of cycle and optionally the number of sweep
*
* This function set the cycle type for the multigrid methods.
* Possible values are:
* * V cycle
* * W cycle
*
* Optionally you can set the number of sweep or relaxation steps
* on each grid when going up and when going down
*
* \param cycle_type cycle type
* \param sweep_up
* \param sweep_dw
* \param sweep_crs speep at the coarse level
*
*/
void setPreconditionerAMG_cycleType(const std::string & cycle_type, int sweep_up = -1, int sweep_dw = -1, int sweep_crs = -1)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_cycle_type",cycle_type.c_str()));
if (sweep_dw != -1)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_grid_sweeps_down",std::to_string(sweep_up).c_str()));}
if (sweep_up != -1)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_grid_sweeps_up",std::to_string(sweep_dw).c_str()));}
if (sweep_crs != -1)
{PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_grid_sweeps_coarse",std::to_string(sweep_crs).c_str()));}
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set the coarsening method for the algebraic-multi-grid preconditioner
*
* Possible values can be
* "CLJP","Ruge-Stueben","modifiedRuge-Stueben","Falgout", "PMIS", "HMIS"
*
* \warning in case of big problem use PMIS or HMIS otherwise the AMG can hang (take a lot of time) in setup
*
* \param type of the preconditioner smoothing operator *
*/
void setPreconditionerAMG_coarsen(const std::string & type)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_coarsen_type",type.c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set the interpolation method for the algebraic-multi-grid preconditioner
*
* Possible values can be
* "classical", "direct", "multipass", "multipass-wts", "ext+i",
* "ext+i-cc", "standard", "standard-wts", "FF", "FF1"
*
*
* \param type of the interpolation scheme
*
*/
void setPreconditionerAMG_interp(const std::string & type)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_interp_type",type.c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set the block coarsening norm type.
*
* The use of this function make sanse if you specify
* the degree of freedom for each node using setBlockSize
*
* * 0 (default each variable treat independently)
* * 1 Frobenius norm
* * 2 sum of absolute values of elements in each block
* * 3 largest element in each block (not absolute value)
* * 4 row-sum norm
* * 6 sum of all values in each block
*
* In case the matrix represent a system of equations in general
*
* \param norm type
*
*/
void setPreconditionerAMG_coarsenNodalType(int norm)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_nodal_coarsen",std::to_string(norm).c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Indicate the number of levels in the ILU(k) for the Euclid smoother
*
* \param k number of levels for the Euclid smoother
*
*/ void setPreconditionerAMG_interp_eu_level(int k)
{
if (atype == HYPRE_AMG)
{
PETSC_SAFE_CALL(PetscOptionsSetValue(NULL,"-pc_hypre_boomeramg_eu_level",std::to_string(k).c_str()));
}
else
{
std::cout << __FILE__ << ":" << __LINE__ << "Warning: the selected preconditioner does not support this option" << std::endl;
}
}
/*! \brief Set how many degree of freedom each node has
*
* In case you are solving a system of equations this function,
* help in setting the degree of freedom each grid point has.
* Setting this parameter to the number of variables for each
* grid point it should improve the convergenve of the solvers
* in particular using algebraic-multi-grid
*
* \param block_sz number of degree of freedom
*
*/
void setBlockSize(int block_sz)
{
this->block_sz = block_sz;
}
/*! \brief Here we invert the matrix and solve the system
*
* \warning umfpack is not a parallel solver, this function work only with one processor
*
* \note if you want to use umfpack in a NON parallel, but on a distributed data, use solve with triplet
*
* \tparam impl Implementation of the SparseMatrix
*
* \param A sparse matrix
* \param b vector
* \param initial_guess true if x has the initial guess
*
* \return the solution
*
*/
Vector<double,PETSC_BASE> solve(SparseMatrix<double,int,PETSC_BASE> & A, const Vector<double,PETSC_BASE> & b, bool initial_guess = false)
{
Mat & A_ = A.getMat();
const Vec & b_ = b.getVec();
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_FALSE));
PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));
Vector<double,PETSC_BASE> x(row,row_loc);
Vec & x_ = x.getVec();
pre_solve_impl(A_,b_,x_);
solve_simple(A_,b_,x_);
x.update();
return x;
}
/*! \brief Here we invert the matrix and solve the system
*
* \param A sparse matrix
* \param b vector
* \param x solution and initial guess
*
* \return true if succeed
*
*/
Vector<double,PETSC_BASE> solve(SparseMatrix<double,int,PETSC_BASE> & A, Vector<double,PETSC_BASE> & x, const Vector<double,PETSC_BASE> & b)
{
Mat & A_ = A.getMat();
const Vec & b_ = b.getVec();
Vec & x_ = x.getVec();
/* // We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;*/
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_TRUE));
/*PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));*/
pre_solve_impl(A_,b_,x_);
solve_simple(A_,b_,x_);
x.update();
return x;
/*pre_solve_impl(A_,b_,x_);
solve_simple(A_,b_,x_);
x.update();
return true;*/
}
/*! \brief Here we invert the matrix and solve the system with previous operator
*
* \param A sparse matrix
* \param b vector
* \param x solution and initial guess
*
* \return true if succeed
*
*/
Vector<double,PETSC_BASE> solve_successive(const Vector<double,PETSC_BASE> & b,bool initial_guess = false)
{
const Vec & b_ = b.getVec();
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt row_loc;
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_FALSE));
PETSC_SAFE_CALL(VecGetSize(b_,&row));
PETSC_SAFE_CALL(VecGetLocalSize(b_,&row_loc));
Vector<double,PETSC_BASE> x(row,row_loc);
Vec & x_ = x.getVec();
PETSC_SAFE_CALL(KSPSetNormType(ksp,KSP_NORM_UNPRECONDITIONED));
solve_simple(b_,x_);
x.update();
return x;
/*pre_solve_impl(A_,b_,x_);
solve_simple(A_,b_,x_);
x.update();
return true;*/
}
/*! \brief Here we invert the matrix and solve the system with previous operator and initial guess
*
* \param A sparse matrix
* \param b vector
* \param x solution and initial guess
*
* \return true if succeed
*
*/
Vector<double,PETSC_BASE> solve_successive(Vector<double,PETSC_BASE> & x, const Vector<double,PETSC_BASE> & b)
{
const Vec & b_ = b.getVec();
Vec & x_ = x.getVec();
/* // We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;*/
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_TRUE));
/*PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));*/
PETSC_SAFE_CALL(KSPSetNormType(ksp,KSP_NORM_UNPRECONDITIONED));
solve_simple(b_,x_);
x.update();
return x;
/*pre_solve_impl(A_,b_,x_);
solve_simple(A_,b_,x_);
x.update();
return true;*/
}
/*! \brief Here we invert the matrix and solve the system using a Nullspace for Neumann BC
*
* \warning umfpack is not a parallel solver, this function work only with one processor
*
* \note if you want to use umfpack in a NON parallel, but on a distributed data, use solve with triplet
*
* \tparam impl Implementation of the SparseMatrix
*
* \param A sparse matrix
* \param b vector
* \param initial_guess true if x has the initial guess
*
* \return the solution
*
*/
Vector<double,PETSC_BASE> with_nullspace_solve(SparseMatrix<double,int,PETSC_BASE> & A, const Vector<double,PETSC_BASE> & b, bool initial_guess = false,bool symmetric = false)
{
#ifndef __arm64__
Mat & A_ = A.getMat();
const Vec & b_ = b.getVec();
// We set the size of x according to the Matrix A
PetscInt row; PetscInt col;
PetscInt row_loc;
PetscInt col_loc;
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_FALSE));
PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));
Vector<double,PETSC_BASE> x(row,row_loc);
Vec & x_ = x.getVec();
PETSC_SAFE_CALL(KSPSetFromOptions(ksp));
PETSC_SAFE_CALL(KSPSetOperators(ksp,A_,A_));
PETSC_SAFE_CALL(KSPSolve(ksp,b_,x_));
Mat F, work, V;
PetscInt N, rows;
/* Determine factorability */
//PETSC_SAFE_CALL(MatGetFactor(A_, MATSOLVERMUMPS, MAT_FACTOR_LU, &F));
//PETSC_SAFE_CALL(MatGetLocalSize(A_, &rows, NULL));
/* Set MUMPS options, see MUMPS documentation for more information */
//PETSC_SAFE_CALL(MatMumpsSetIcntl(F, 24, 1));
//PETSC_SAFE_CALL(MatMumpsSetIcntl(F, 25, 1));
/* Perform factorization */
//PETSC_SAFE_CALL(MatLUFactorSymbolic(F, A_, NULL, NULL, NULL));
//PETSC_SAFE_CALL(MatLUFactorNumeric(F, A_, NULL));
/* This is the dimension of the null space */
//PETSC_SAFE_CALL(MatMumpsGetInfog(F, 28, &N));
/* This will contain the null space in the columns */
PETSC_SAFE_CALL(MatCreateDense(PETSC_COMM_WORLD, rows, N, PETSC_DETERMINE, PETSC_DETERMINE, NULL, &V));
PETSC_SAFE_CALL(MatDuplicate(V, MAT_DO_NOT_COPY_VALUES, &work));
PETSC_SAFE_CALL(MatMatSolve(F, work, V));
std::cout<<"Dimension:" << N;
Vec nvec[N];
for(int i=0;i<N;i++)
{
PETSC_SAFE_CALL(MatGetColumnVector(V,nvec[i],i));
}
MatNullSpace nullspace;
PETSC_SAFE_CALL(MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,N,nvec,&nullspace));
PETSC_SAFE_CALL(MatSetTransposeNullSpace(A_,nullspace));
PETSC_SAFE_CALL(MatSetNullSpace(A_,nullspace));
PETSC_SAFE_CALL(MatNullSpaceDestroy(&nullspace));
PETSC_SAFE_CALL(KSPSetOperators(ksp,A_,A_));
PETSC_SAFE_CALL(KSPSetFromOptions(ksp));
PETSC_SAFE_CALL(KSPSolve(ksp,b_,x_));
x.update();
return x;
#endif
}
/*! \brief Return the KSP solver
*
* In case you want to do fine tuning of the KSP solver before
* solve your system whith this function you can retrieve the
* KSP object
*
* \return the Krylov solver
*
*/
KSP getKSP()
{ return ksp;
}
/*! \brief It return the resiual error
*
* \param A Sparse matrix
* \param x solution
* \param b right-hand-side
*
* \return the solution error norms
*
*/
solError get_residual_error(SparseMatrix<double,int,PETSC_BASE> & A, const Vector<double,PETSC_BASE> & x, const Vector<double,PETSC_BASE> & b)
{
return getSolNormError(A.getMat(),b.getVec(),x.getVec());
}
/*! \brief It return the resiual error
*
* \param x solution
* \param b right-hand-side
*
* \return the solution error norms
*
*/
solError get_residual_error(const Vector<double,PETSC_BASE> & x, const Vector<double,PETSC_BASE> & b)
{
return getSolNormError(b.getVec(),x.getVec(),ksp);
}
/*! \brief Here we invert the matrix and solve the system
*
* \param b vector
*
* \return true if succeed
*
*/
Vector<double,PETSC_BASE> solve(const Vector<double,PETSC_BASE> & b)
{
const Vec & b_ = b.getVec();
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt row_loc;
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_FALSE));
PETSC_SAFE_CALL(VecGetSize(b_,&row));
PETSC_SAFE_CALL(VecGetLocalSize(b_,&row_loc));
Vector<double,PETSC_BASE> x(row,row_loc);
Vec & x_ = x.getVec();
solve_simple(b_,x_);
x.update();
return x;
}
/*! \brief Here we invert the matrix and solve the system
*
* In this call we are interested in solving the system
* with multiple right-hand-side and the same Matrix.
* We do not set the Matrix again and this give us the
* possibility to-skip the preconditioning setting that
* in some case like Algebraic-multi-grid can be expensive
*
* \param b vector
* \param x solution and initial guess
*
* \return true if succeed *
*/
bool solve(Vector<double,PETSC_BASE> & x, const Vector<double,PETSC_BASE> & b)
{
const Vec & b_ = b.getVec();
Vec & x_ = x.getVec();
solve_simple(b_,x_);
x.update();
return true;
}
/*! \brief this function give you the possibility to set PETSC options
*
* this function call PetscOptionsSetValue
*
* \param name the name of the option
* \param value the value of the option
*
*/
void setPetscOption(const char * name, const char * value)
{
PetscOptionsSetValue(NULL,name,value);
}
/*! \brief Try to solve the system using all the solvers and generate a report
*
* In this mode the system will try different Solvers, Preconditioner and
* combination of solvers in order to find the best solver in speed, and
* precision. As output it will produce a performance report
*
* \param A Matrix to invert
* \param b right hand side
* \return the solution
*
*/
Vector<double,PETSC_BASE> try_solve(SparseMatrix<double,int,PETSC_BASE> & A, const Vector<double,PETSC_BASE> & b)
{
Mat & A_ = A.getMat();
const Vec & b_ = b.getVec();
// We set the size of x according to the Matrix A
PetscInt row;
PetscInt col;
PetscInt row_loc;
PetscInt col_loc;
PETSC_SAFE_CALL(KSPSetInitialGuessNonzero(ksp,PETSC_FALSE));
PETSC_SAFE_CALL(MatGetSize(A_,&row,&col));
PETSC_SAFE_CALL(MatGetLocalSize(A_,&row_loc,&col_loc));
Vector<double,PETSC_BASE> x(row,row_loc);
Vec & x_ = x.getVec();
pre_solve_impl(A_,b_,x_);
try_solve_simple(A_,b_,x_);
x.update();
return x;
}
};
#endif
#endif /* OPENFPM_NUMERICS_SRC_SOLVERS_PETSC_SOLVER_HPP_ */