From 0a561076b3563198e8fbeed118e33369596ef19f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jakub=20Klinkovsk=C3=BD?= <klinkjak@fjfi.cvut.cz>
Date: Wed, 26 Sep 2018 10:39:21 +0200
Subject: [PATCH] Refactoring GMRES variants
---
src/TNL/Solvers/Linear/CMakeLists.txt | 2 -
src/TNL/Solvers/Linear/CWYGMRES.h | 115 ----
src/TNL/Solvers/Linear/CWYGMRES_impl.h | 633 ------------------
src/TNL/Solvers/Linear/GMRES.h | 86 ++-
src/TNL/Solvers/Linear/GMRES_impl.h | 742 +++++++++++++++------
src/TNL/Solvers/LinearSolverTypeResolver.h | 5 +-
src/TNL/Solvers/SolverConfig_impl.h | 5 -
7 files changed, 594 insertions(+), 994 deletions(-)
delete mode 100644 src/TNL/Solvers/Linear/CWYGMRES.h
delete mode 100644 src/TNL/Solvers/Linear/CWYGMRES_impl.h
diff --git a/src/TNL/Solvers/Linear/CMakeLists.txt b/src/TNL/Solvers/Linear/CMakeLists.txt
index f44f0a095f..2e33af0b8e 100644
--- a/src/TNL/Solvers/Linear/CMakeLists.txt
+++ b/src/TNL/Solvers/Linear/CMakeLists.txt
@@ -6,8 +6,6 @@ SET( headers BICGStab.h
BICGStabL_impl.h
CG.h
CG_impl.h
- CWYGMRES.h
- CWYGMRES_impl.h
GMRES.h
GMRES_impl.h
Jacobi.h
diff --git a/src/TNL/Solvers/Linear/CWYGMRES.h b/src/TNL/Solvers/Linear/CWYGMRES.h
deleted file mode 100644
index 1cccc132dd..0000000000
--- a/src/TNL/Solvers/Linear/CWYGMRES.h
+++ /dev/null
@@ -1,115 +0,0 @@
-/***************************************************************************
- CWYGMRES.h - description
- -------------------
- begin : May 13, 2016
- copyright : (C) 2016 by Tomas Oberhuber et al.
- email : tomas.oberhuber@fjfi.cvut.cz
- ***************************************************************************/
-
-/* See Copyright Notice in tnl/Copyright */
-
-// Implemented by: Jakub Klinkovsky
-
-#pragma once
-
-#include "LinearSolver.h"
-
-#include <TNL/Containers/Vector.h>
-
-namespace TNL {
-namespace Solvers {
-namespace Linear {
-
-template< typename Matrix >
-class CWYGMRES
-: public LinearSolver< Matrix >
-{
- using Base = LinearSolver< Matrix >;
-public:
- using RealType = typename Base::RealType;
- using DeviceType = typename Base::DeviceType;
- using IndexType = typename Base::IndexType;
- using VectorViewType = typename Base::VectorViewType;
- using ConstVectorViewType = typename Base::ConstVectorViewType;
-
- String getType() const;
-
- static void configSetup( Config::ConfigDescription& config,
- const String& prefix = "" );
-
- bool setup( const Config::ParameterContainer& parameters,
- const String& prefix = "" ) override;
-
- void setRestarting( IndexType rest );
-
- bool solve( ConstVectorViewType b, VectorViewType x ) override;
-
-protected:
- using DeviceVector = Containers::Vector< RealType, DeviceType, IndexType >;
- using HostVector = Containers::Vector< RealType, Devices::Host, IndexType >;
-
- void hauseholder_generate( DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& w );
-
- void hauseholder_apply_trunc( HostVector& out,
- DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& w );
-
- void hauseholder_cwy( DeviceVector& w,
- DeviceVector& Y,
- HostVector& T,
- const int& i );
-
- void hauseholder_cwy_transposed( DeviceVector& w,
- DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& z );
-
- template< typename Vector >
- void update( IndexType k,
- IndexType m,
- const HostVector& H,
- const HostVector& s,
- DeviceVector& v,
- Vector& x );
-
- void generatePlaneRotation( RealType& dx,
- RealType& dy,
- RealType& cs,
- RealType& sn );
-
- void applyPlaneRotation( RealType& dx,
- RealType& dy,
- RealType& cs,
- RealType& sn );
-
-
- void setSize( IndexType _size, IndexType m );
-
- // single vectors
- DeviceVector r, z, w, _M_tmp;
- // matrices (in column-major format)
- DeviceVector V, Y;
- // duplicate of the upper (m+1)x(m+1) submatrix of Y (it is lower triangular) for fast access
- HostVector YL, T;
- // host-only storage for Givens rotations and the least squares problem
- HostVector cs, sn, H, s;
-
- IndexType size = 0;
- IndexType ldSize = 0;
- IndexType restarting_min = 10;
- IndexType restarting_max = 10;
- IndexType restarting_step_min = 3;
- IndexType restarting_step_max = 3;
-};
-
-} // namespace Linear
-} // namespace Solvers
-} // namespace TNL
-
-#include "CWYGMRES_impl.h"
diff --git a/src/TNL/Solvers/Linear/CWYGMRES_impl.h b/src/TNL/Solvers/Linear/CWYGMRES_impl.h
deleted file mode 100644
index 4989f50207..0000000000
--- a/src/TNL/Solvers/Linear/CWYGMRES_impl.h
+++ /dev/null
@@ -1,633 +0,0 @@
-/***************************************************************************
- CWYGMRES.h - description
- -------------------
- begin : May 13, 2016
- copyright : (C) 2016 by Tomas Oberhuber et al.
- email : tomas.oberhuber@fjfi.cvut.cz
- ***************************************************************************/
-
-/* See Copyright Notice in tnl/Copyright */
-
-// Implemented by: Jakub Klinkovsky
-
-#pragma once
-
-#include <type_traits>
-#include <cmath>
-
-#include <TNL/Exceptions/CudaSupportMissing.h>
-#include <TNL/Containers/Algorithms/Multireduction.h>
-#include <TNL/Matrices/MatrixOperations.h>
-
-#include "CWYGMRES.h"
-
-namespace TNL {
-namespace Solvers {
-namespace Linear {
-
-template< typename Matrix >
-String
-CWYGMRES< Matrix >::
-getType() const
-{
- return String( "CWYGMRES< " ) +
- this->matrix -> getType() + ", " +
- this->preconditioner -> getType() + " >";
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-configSetup( Config::ConfigDescription& config,
- const String& prefix )
-{
- config.addEntry< int >( prefix + "gmres-restarting-min", "Minimal number of iterations after which the GMRES restarts.", 10 );
- config.addEntry< int >( prefix + "gmres-restarting-max", "Maximal number of iterations after which the GMRES restarts.", 10 );
- config.addEntry< int >( prefix + "gmres-restarting-step-min", "Minimal adjusting step for the adaptivity of the GMRES restarting parameter.", 3 );
- config.addEntry< int >( prefix + "gmres-restarting-step-max", "Maximal adjusting step for the adaptivity of the GMRES restarting parameter.", 3 );
-}
-
-template< typename Matrix >
-bool
-CWYGMRES< Matrix >::
-setup( const Config::ParameterContainer& parameters,
- const String& prefix )
-{
- restarting_min = parameters.getParameter< int >( "gmres-restarting-min" );
- this->setRestarting( parameters.getParameter< int >( "gmres-restarting-max" ) );
- restarting_step_min = parameters.getParameter< int >( "gmres-restarting-step-min" );
- restarting_step_max = parameters.getParameter< int >( "gmres-restarting-step-max" );
- return LinearSolver< Matrix >::setup( parameters, prefix );
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-setRestarting( IndexType rest )
-{
- if( size != 0 )
- setSize( size, rest );
- restarting_max = rest;
-}
-
-template< typename Matrix >
-bool
-CWYGMRES< Matrix >::
-solve( ConstVectorViewType b, VectorViewType x )
-{
- TNL_ASSERT_TRUE( this->matrix, "No matrix was set in CWYGMRES. Call setMatrix() before solve()." );
- if( restarting_min <= 0 || restarting_max <= 0 || restarting_min > restarting_max )
- {
- std::cerr << "Wrong value for the GMRES restarting parameters: r_min = " << restarting_min
- << ", r_max = " << restarting_max << std::endl;
- return false;
- }
- if( restarting_step_min < 0 || restarting_step_max < 0 || restarting_step_min > restarting_step_max )
- {
- std::cerr << "Wrong value for the GMRES restarting adjustment parameters: d_min = " << restarting_step_min
- << ", d_max = " << restarting_step_max << std::endl;
- return false;
- }
- setSize( this->matrix->getRows(), restarting_max );
-
- RealType normb( 0.0 ), beta( 0.0 );
- /****
- * 1. Solve r from M r = b - A x_0
- */
- if( this->preconditioner )
- {
- this->preconditioner->solve( b, _M_tmp );
- normb = _M_tmp.lpNorm( ( RealType ) 2.0 );
-
- this->matrix->vectorProduct( x, _M_tmp );
- _M_tmp.addVector( b, ( RealType ) 1.0, -1.0 );
-
- this->preconditioner->solve( _M_tmp, r );
- }
- else
- {
- this->matrix->vectorProduct( x, r );
- normb = b.lpNorm( ( RealType ) 2.0 );
- r.addVector( b, ( RealType ) 1.0, -1.0 );
- }
- beta = r.lpNorm( ( RealType ) 2.0 );
-
- //cout << "norm b = " << normb <<std::endl;
- //cout << " beta = " << beta <<std::endl;
-
-
- if( normb == 0.0 )
- normb = 1.0;
-
- this->resetIterations();
- this->setResidue( beta / normb );
-
- // parameters for the adaptivity of the restarting parameter
- RealType beta_ratio = 1; // = beta / beta_ratio (small value indicates good convergence rate)
- const RealType max_beta_ratio = 0.99; // = cos(8°) \approx 0.99
- const RealType min_beta_ratio = 0.175; // = cos(80°) \approx 0.175
- int restart_cycles = 0; // counter of restart cycles
- int m = restarting_max; // current restarting parameter
-
- DeviceVector vi, vk;
- while( this->checkNextIteration() )
- {
- // adaptivity of the restarting parameter
- // reference: A.H. Baker, E.R. Jessup, Tz.V. Kolev - A simple strategy for varying the restart parameter in GMRES(m)
- // http://www.sciencedirect.com/science/article/pii/S0377042709000132
- if( restart_cycles > 0 ) {
- if( beta_ratio > max_beta_ratio )
- // near stagnation -> set maximum
- m = restarting_max;
- else if( beta_ratio >= min_beta_ratio ) {
- // the step size is determined based on current m using linear interpolation
- // between restarting_step_min and restarting_step_max
- const int step = restarting_step_min + (float) ( restarting_step_max - restarting_step_min ) /
- ( restarting_max - restarting_min ) *
- ( m - restarting_min );
- if( m - step >= restarting_min )
- m -= step;
- else
- // set restarting_max when we hit restarting_min (see Baker et al. (2009))
- m = restarting_max;
- }
-// std::cerr << "restarting: cycle = " << restart_cycles << ", beta_ratio = " << beta_ratio << ", m = " << m << " " << std::endl;
- }
-
- /***
- * z = r / | r | = 1.0 / beta * r
- */
-// z.addVector( r, ( RealType ) 1.0 / beta, ( RealType ) 0.0 );
- z = r;
-
- H.setValue( 0.0 );
- s.setValue( 0.0 );
- T.setValue( 0.0 );
-
- // NOTE: this is unstable, s[0] is set later
-// s[ 0 ] = beta;
-
- /****
- * Starting m-loop
- */
- for( IndexType i = 0; i <= m && this->nextIteration(); i++ )
- {
-// std::cout << "==== i = " << i << " ====" <<std::endl;
-
- /****
- * Generate new Hauseholder transformation from vector z.
- */
- hauseholder_generate( Y, T, i, z );
-
- if( i == 0 ) {
- /****
- * s = e_1^T * P_i * z
- */
- hauseholder_apply_trunc( s, Y, T, i, z );
- }
- else {
- /***
- * H_{i-1} = P_i * z
- */
- HostVector h;
- h.bind( &H.getData()[ (i - 1) * (m + 1) ], m + 1 );
- hauseholder_apply_trunc( h, Y, T, i, z );
- }
-
- /***
- * Generate new basis vector v_i, using the compact WY representation:
- * v_i = (I - Y_i * T_i Y_i^T) * e_i
- */
- vi.bind( &V.getData()[ i * ldSize ], size );
- hauseholder_cwy( vi, Y, T, i );
-
- if( i < m ) {
- /****
- * Solve w from M w = A v_i
- */
- if( this->preconditioner )
- {
- this->matrix->vectorProduct( vi, _M_tmp );
- this->preconditioner->solve( _M_tmp, w );
- }
- else
- this->matrix->vectorProduct( vi, w );
-
- /****
- * Apply all previous Hauseholder transformations, using the compact WY representation:
- * z = (I - Y_i * T_i^T * Y_i^T) * w
- */
- hauseholder_cwy_transposed( z, Y, T, i, w );
- }
-
-// std::cout << "vi.norm = " << vi.lpNorm( 2.0 ) <<std::endl;
-// std::cout << "H (before rotations) = " <<std::endl;
-// for( int i = 0; i <= m; i++ ) {
-// for( int j = 0; j < m; j++ )
-// std::cout << H[ i + j * (m+1) ] << "\t";
-// std::cout <<std::endl;
-// }
-// std::cout << "s = " << s <<std::endl;
-
- /****
- * Applying the Givens rotations
- */
- if( i > 0 ) {
- for( IndexType k = 0; k < i - 1; k++ )
- applyPlaneRotation( H[ k + (i - 1) * (m + 1) ],
- H[ k + 1 + (i - 1) * (m + 1) ],
- cs[ k ],
- sn[ k ] );
-
- if( H[ i + (i - 1) * (m + 1) ] != 0.0 ) {
- generatePlaneRotation( H[ i - 1 + (i - 1) * (m + 1) ],
- H[ i + (i - 1) * (m + 1) ],
- cs[ i - 1 ],
- sn[ i - 1 ]);
- applyPlaneRotation( H[ i - 1 + (i - 1) * (m + 1) ],
- H[ i + (i - 1) * (m + 1) ],
- cs[ i - 1 ],
- sn[ i - 1 ]);
- applyPlaneRotation( s[ i - 1 ],
- s[ i ],
- cs[ i - 1 ],
- sn[ i - 1 ] );
- }
- }
-
-// std::cout << "H (after rotations) = " <<std::endl;
-// for( int i = 0; i <= m; i++ ) {
-// for( int j = 0; j < m; j++ )
-// std::cout << H[ i + j * (m+1) ] << "\t";
-// std::cout <<std::endl;
-// }
-// std::cout << "s (after rotations) = " << s <<std::endl;
-// std::cout << "residue / normb = " << std::fabs( s[ i ] ) / normb <<std::endl;
-
-// for( int k = 0; k <= i; k++ ) {
-// vk.bind( &V.getData()[ k * ldSize ], size );
-// std::cout << "(v" << k << ",v" << i << ") = " << vk.scalarProduct( vi ) <<std::endl;
-// }
-
- this->setResidue( std::fabs( s[ i ] ) / normb );
- if( ! this->checkNextIteration() ) {
- update( i - 1, m, H, s, V, x );
- this->refreshSolverMonitor( true );
- return this->checkConvergence();
- }
- else {
- this->refreshSolverMonitor();
- }
- }
- update( m - 1, m, H, s, V, x );
-
- /****
- * r = M.solve(b - A * x);
- */
- const RealType beta_old = beta;
- if( this->preconditioner )
- {
- this->matrix->vectorProduct( x, _M_tmp );
- _M_tmp.addVector( b, ( RealType ) 1.0, -1.0 );
- this->preconditioner->solve( _M_tmp, r );
- }
- else
- {
- this->matrix->vectorProduct( x, r );
- r.addVector( b, ( RealType ) 1.0, -1.0 );
- }
- beta = r.lpNorm( ( RealType ) 2.0 );
- this->setResidue( beta / normb );
-
-// std::cout << " x = " << x <<std::endl;
-// std::cout << " beta = " << beta <<std::endl;
-// std::cout << "residue = " << beta / normb <<std::endl;
-
- // update parameters for the adaptivity of the restarting parameter
- ++restart_cycles;
- beta_ratio = beta / beta_old;
- }
- this->refreshSolverMonitor( true );
- return this->checkConvergence();
-}
-
-#ifdef HAVE_CUDA
-template< typename DestinationElement,
- typename SourceElement,
- typename Index >
-__global__ void
-copyTruncatedVectorKernel( DestinationElement* destination,
- const SourceElement* source,
- const Index from,
- const Index size )
-{
- Index elementIdx = blockIdx.x * blockDim.x + threadIdx.x;
- const Index gridSize = blockDim.x * gridDim.x;
-
- while( elementIdx < from )
- {
- destination[ elementIdx ] = (DestinationElement) 0.0;
- elementIdx += gridSize;
- }
- while( elementIdx < size )
- {
- destination[ elementIdx ] = source[ elementIdx ];
- elementIdx += gridSize;
- }
-}
-#endif
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-hauseholder_generate( DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& z )
-{
- DeviceVector y_i;
- y_i.bind( &Y.getData()[ i * ldSize ], size );
-
- // XXX: the upper-right triangle of Y will be full of zeros, which can be exploited for optimization
- if( std::is_same< DeviceType, Devices::Host >::value ) {
- for( IndexType j = 0; j < size; j++ ) {
- if( j < i )
- y_i[ j ] = 0.0;
- else
- y_i[ j ] = z[ j ];
- }
- }
- if( std::is_same< DeviceType, Devices::Cuda >::value ) {
-#ifdef HAVE_CUDA
- dim3 blockSize( 256 );
- dim3 gridSize;
- gridSize.x = min( Devices::Cuda::getMaxGridSize(), Devices::Cuda::getNumberOfBlocks( size, blockSize.x ) );
-
- copyTruncatedVectorKernel<<< gridSize, blockSize >>>( y_i.getData(),
- z.getData(),
- i,
- size );
- TNL_CHECK_CUDA_DEVICE;
-#else
- throw Exceptions::CudaSupportMissing();
-#endif
- }
-
- // norm of the TRUNCATED vector z
- const RealType normz = y_i.lpNorm( 2.0 );
- const RealType y_ii = y_i.getElement( i );
- if( y_ii > 0.0 ) {
- y_i.setElement( i, y_ii + normz );
- }
- else {
- y_i.setElement( i, y_ii - normz );
- }
-
- // compute the norm of the y_i vector; equivalent to this calculation by definition:
- // const RealType norm_yi = y_i.lpNorm( 2.0 );
- const RealType norm_yi = std::sqrt( 2 * (normz * normz + std::fabs( y_ii ) * normz) );
-
- // XXX: normalization is slower, but more stable
-// y_i *= 1.0 / norm_yi;
-// const RealType t_i = 2.0;
- // assuming it's stable enough...
- const RealType t_i = 2.0 / (norm_yi * norm_yi);
-
- T[ i + i * (restarting_max + 1) ] = t_i;
- if( i > 0 ) {
- // aux = Y_{i-1}^T * y_i
- RealType aux[ i ];
- Containers::Algorithms::ParallelReductionScalarProduct< RealType, RealType > scalarProduct;
- Containers::Algorithms::Multireduction< DeviceType >::reduce
- ( scalarProduct,
- i,
- size,
- Y.getData(),
- ldSize,
- y_i.getData(),
- aux );
-
- // [T_i]_{0..i-1} = - T_{i-1} * t_i * aux
- for( int k = 0; k < i; k++ ) {
- T[ k + i * (restarting_max + 1) ] = 0.0;
- for( int j = k; j < i; j++ )
- T[ k + i * (restarting_max + 1) ] -= T[ k + j * (restarting_max + 1) ] * (t_i * aux[ j ]);
- }
- }
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-hauseholder_apply_trunc( HostVector& out,
- DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& z )
-{
- DeviceVector y_i;
- y_i.bind( &Y.getData()[ i * ldSize ], size );
-
- const RealType aux = T[ i + i * (restarting_max + 1) ] * y_i.scalarProduct( z );
- if( std::is_same< DeviceType, Devices::Host >::value ) {
- for( int k = 0; k <= i; k++ )
- out[ k ] = z[ k ] - y_i[ k ] * aux;
- }
- if( std::is_same< DeviceType, Devices::Cuda >::value ) {
- // copy part of y_i to buffer on host
- // here we duplicate the upper (m+1)x(m+1) submatrix of Y on host for fast access
- RealType* host_yi = &YL[ i * (restarting_max + 1) ];
- RealType host_z[ i + 1 ];
- Containers::Algorithms::ArrayOperations< Devices::Host, Devices::Cuda >::copyMemory< RealType, RealType, IndexType >( host_yi, y_i.getData(), restarting_max + 1 );
- Containers::Algorithms::ArrayOperations< Devices::Host, Devices::Cuda >::copyMemory< RealType, RealType, IndexType >( host_z, z.getData(), i + 1 );
- for( int k = 0; k <= i; k++ )
- out[ k ] = host_z[ k ] - host_yi[ k ] * aux;
- }
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-hauseholder_cwy( DeviceVector& v,
- DeviceVector& Y,
- HostVector& T,
- const int& i )
-{
- // aux = Y_i^T * e_i
- RealType aux[ i + 1 ];
- if( std::is_same< DeviceType, Devices::Host >::value ) {
- for( int k = 0; k <= i; k++ )
- aux[ k ] = Y[ i + k * ldSize ];
- }
- if( std::is_same< DeviceType, Devices::Cuda >::value ) {
- // the upper (m+1)x(m+1) submatrix of Y is duplicated on host for fast access
- for( int k = 0; k <= i; k++ )
- aux[ k ] = YL[ i + k * (restarting_max + 1) ];
- }
-
- // aux = T_i * aux
- // Note that T_i is upper triangular, so we can overwrite the aux vector with the result in place
- for( int k = 0; k <= i; k++ ) {
- RealType aux2 = 0.0;
- for( int j = k; j <= i; j++ )
- aux2 += T[ k + j * (restarting_max + 1) ] * aux[ j ];
- aux[ k ] = aux2;
- }
-
- // v = e_i - Y_i * aux
- MatrixOperations< DeviceType >::gemv( size, i + 1,
- -1.0, Y.getData(), ldSize, aux,
- 0.0, v.getData() );
- v.setElement( i, 1.0 + v.getElement( i ) );
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-hauseholder_cwy_transposed( DeviceVector& z,
- DeviceVector& Y,
- HostVector& T,
- const int& i,
- DeviceVector& w )
-{
- // aux = Y_i^T * w
- RealType aux[ i + 1 ];
- Containers::Algorithms::ParallelReductionScalarProduct< RealType, RealType > scalarProduct;
- Containers::Algorithms::Multireduction< DeviceType >::reduce
- ( scalarProduct,
- i + 1,
- size,
- Y.getData(),
- ldSize,
- w.getData(),
- aux );
-
- // aux = T_i^T * aux
- // Note that T_i^T is lower triangular, so we can overwrite the aux vector with the result in place
- for( int k = i; k >= 0; k-- ) {
- RealType aux2 = 0.0;
- for( int j = 0; j <= k; j++ )
- aux2 += T[ j + k * (restarting_max + 1) ] * aux[ j ];
- aux[ k ] = aux2;
- }
-
- // z = w - Y_i * aux
- z = w;
- MatrixOperations< DeviceType >::gemv( size, i + 1,
- -1.0, Y.getData(), ldSize, aux,
- 1.0, z.getData() );
-}
-
-template< typename Matrix >
- template< typename Vector >
-void
-CWYGMRES< Matrix >::
-update( IndexType k,
- IndexType m,
- const HostVector& H,
- const HostVector& s,
- DeviceVector& v,
- Vector& x )
-{
-// Containers::Vector< RealType, Devices::Host, IndexType > y;
-// y.setSize( m + 1 );
- RealType y[ m + 1 ];
-
- IndexType i, j;
- for( i = 0; i <= m ; i ++ )
- y[ i ] = s[ i ];
-
- // Backsolve:
- for( i = k; i >= 0; i--) {
- if( H[ i + i * ( m + 1 ) ] == 0 ) {
-// for( int _i = 0; _i <= i; _i++ ) {
-// for( int _j = 0; _j < i; _j++ )
-// std::cout << H[ _i + _j * (m+1) ] << " ";
-// std::cout <<std::endl;
-// }
- std::cerr << "H.norm = " << H.lpNorm( 2.0 ) << std::endl;
- std::cerr << "s = " << s << std::endl;
- std::cerr << "k = " << k << ", m = " << m << std::endl;
- throw 1;
- }
- y[ i ] /= H[ i + i * ( m + 1 ) ];
- for( j = i - 1; j >= 0; j--)
- y[ j ] -= H[ j + i * ( m + 1 ) ] * y[ i ];
- }
-
- // x = V * y + x
- MatrixOperations< DeviceType >::gemv( size, k + 1,
- 1.0, v.getData(), ldSize, y,
- 1.0, x.getData() );
-}
-
-template< typename Matrix >
-void
-CWYGMRES< Matrix >::
-generatePlaneRotation( RealType& dx,
- RealType& dy,
- RealType& cs,
- RealType& sn )
-{
- if( dy == 0.0 )
- {
- cs = 1.0;
- sn = 0.0;
- }
- else
- if( std::fabs( dy ) > std::fabs( dx ) )
- {
- RealType temp = dx / dy;
- sn = 1.0 / std::sqrt( 1.0 + temp * temp );
- cs = temp * sn;
- }
- else
- {
- RealType temp = dy / dx;
- cs = 1.0 / std::sqrt( 1.0 + temp * temp );
- sn = temp * cs;
- }
-}
-
-template< typename Matrix >
-void CWYGMRES< Matrix > ::
-applyPlaneRotation( RealType& dx,
- RealType& dy,
- RealType& cs,
- RealType& sn )
-{
- RealType temp = cs * dx + sn * dy;
- dy = cs * dy - sn * dx;
- dx = temp;
-}
-
-template< typename Matrix >
-void CWYGMRES< Matrix > :: setSize( IndexType _size, IndexType m )
-{
- if( size == _size && restarting_max == m )
- return;
- size = _size;
- if( std::is_same< DeviceType, Devices::Cuda >::value )
- // align each column to 256 bytes - optimal for CUDA
- ldSize = roundToMultiple( size, 256 / sizeof( RealType ) );
- else
- // on the host, we add 1 to disrupt the cache false-sharing pattern
- ldSize = roundToMultiple( size, 256 / sizeof( RealType ) ) + 1;
- restarting_max = m;
- r.setSize( size );
- z.setSize( size );
- w.setSize( size );
- V.setSize( ldSize * ( m + 1 ) );
- Y.setSize( ldSize * ( m + 1 ) );
- T.setSize( (m + 1) * (m + 1) );
- YL.setSize( (m + 1) * (m + 1) );
- cs.setSize( m + 1 );
- sn.setSize( m + 1 );
- H.setSize( ( m + 1 ) * m );
- s.setSize( m + 1 );
- _M_tmp.setSize( size );
-}
-
-} // namespace Linear
-} // namespace Solvers
-} // namespace TNL
diff --git a/src/TNL/Solvers/Linear/GMRES.h b/src/TNL/Solvers/Linear/GMRES.h
index 05c171f622..280a7ad119 100644
--- a/src/TNL/Solvers/Linear/GMRES.h
+++ b/src/TNL/Solvers/Linear/GMRES.h
@@ -1,13 +1,15 @@
/***************************************************************************
GMRES.h - description
-------------------
- begin : 2007/07/31
- copyright : (C) 2007 by Tomas Oberhuber
+ begin : May 13, 2016
+ copyright : (C) 2016 by Tomas Oberhuber et al.
email : tomas.oberhuber@fjfi.cvut.cz
***************************************************************************/
/* See Copyright Notice in tnl/Copyright */
+// Implemented by: Jakub Klinkovsky
+
#pragma once
#include "LinearSolver.h"
@@ -38,18 +40,54 @@ public:
bool setup( const Config::ParameterContainer& parameters,
const String& prefix = "" ) override;
- void setRestarting( IndexType rest );
-
bool solve( ConstVectorViewType b, VectorViewType x ) override;
protected:
- template< typename VectorT >
- void update( IndexType k,
- IndexType m,
- const Containers::Vector< RealType, Devices::Host, IndexType >& H,
- const Containers::Vector< RealType, Devices::Host, IndexType >& s,
- Containers::Vector< RealType, DeviceType, IndexType >& v,
- VectorT& x );
+ using ConstDeviceView = Containers::VectorView< const RealType, DeviceType, IndexType >;
+ using DeviceView = Containers::VectorView< RealType, DeviceType, IndexType >;
+ using HostView = Containers::VectorView< RealType, Devices::Host, IndexType >;
+ using DeviceVector = Containers::Vector< RealType, DeviceType, IndexType >;
+ using HostVector = Containers::Vector< RealType, Devices::Host, IndexType >;
+
+ enum class Variant { MGS, MGSR, CWY };
+
+ int orthogonalize_MGS( const int m, const RealType normb, const RealType beta );
+
+ int orthogonalize_CWY( const int m, const RealType normb, const RealType beta );
+
+ void compute_residue( VectorViewType r, ConstVectorViewType x, ConstVectorViewType b );
+
+ void preconditioned_matvec( DeviceVector& w, ConstDeviceView v );
+
+ void hauseholder_generate( DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& w );
+
+ void hauseholder_apply_trunc( HostView out,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& w );
+
+ void hauseholder_cwy( DeviceVector& w,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i );
+
+ void hauseholder_cwy_transposed( DeviceVector& w,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& z );
+
+ template< typename Vector >
+ void update( const int k,
+ const int m,
+ const HostVector& H,
+ const HostVector& s,
+ DeviceVector& v,
+ Vector& x );
void generatePlaneRotation( RealType& dx,
RealType& dy,
@@ -61,17 +99,29 @@ protected:
RealType& cs,
RealType& sn );
+ void apply_givens_rotations( const int i, const int m );
+
+
+ void setSize( const IndexType size );
- void setSize( IndexType _size, IndexType m );
+ // selected GMRES variant
+ Variant variant = Variant::CWY;
- Containers::Vector< RealType, DeviceType, IndexType > _r, w, _v, _M_tmp;
- Containers::Vector< RealType, Devices::Host, IndexType > _s, _cs, _sn, _H;
+ // single vectors
+ DeviceVector r, w, z, _M_tmp;
+ // matrices (in column-major format)
+ DeviceVector V, Y;
+ // (CWY only) duplicate of the upper (m+1)x(m+1) submatrix of Y (it is lower triangular) for fast access
+ HostVector YL, T;
+ // host-only storage for Givens rotations and the least squares problem
+ HostVector cs, sn, H, s;
IndexType size = 0;
- IndexType restarting_min = 10;
- IndexType restarting_max = 10;
- IndexType restarting_step_min = 3;
- IndexType restarting_step_max = 3;
+ IndexType ldSize = 0;
+ int restarting_min = 10;
+ int restarting_max = 10;
+ int restarting_step_min = 3;
+ int restarting_step_max = 3;
};
} // namespace Linear
diff --git a/src/TNL/Solvers/Linear/GMRES_impl.h b/src/TNL/Solvers/Linear/GMRES_impl.h
index 220cecf23e..4e5f0360f6 100644
--- a/src/TNL/Solvers/Linear/GMRES_impl.h
+++ b/src/TNL/Solvers/Linear/GMRES_impl.h
@@ -1,17 +1,24 @@
/***************************************************************************
GMRES_impl.h - description
-------------------
- begin : Nov 25, 2012
- copyright : (C) 2012 by Tomas Oberhuber
+ begin : May 13, 2016
+ copyright : (C) 2016 by Tomas Oberhuber et al.
email : tomas.oberhuber@fjfi.cvut.cz
***************************************************************************/
/* See Copyright Notice in tnl/Copyright */
+// Implemented by: Jakub Klinkovsky
+
#pragma once
+#include <type_traits>
#include <cmath>
+#include <TNL/Exceptions/CudaSupportMissing.h>
+#include <TNL/Containers/Algorithms/Multireduction.h>
+#include <TNL/Matrices/MatrixOperations.h>
+
#include "GMRES.h"
namespace TNL {
@@ -34,6 +41,10 @@ GMRES< Matrix >::
configSetup( Config::ConfigDescription& config,
const String& prefix )
{
+ config.addEntry< String >( prefix + "gmres-variant", "Minimal number of iterations after which the GMRES restarts.", "CWY" );
+ config.addEntryEnum( "MGS" );
+ config.addEntryEnum( "MGSR" );
+ config.addEntryEnum( "CWY" );
config.addEntry< int >( prefix + "gmres-restarting-min", "Minimal number of iterations after which the GMRES restarts.", 10 );
config.addEntry< int >( prefix + "gmres-restarting-max", "Maximal number of iterations after which the GMRES restarts.", 10 );
config.addEntry< int >( prefix + "gmres-restarting-step-min", "Minimal adjusting step for the adaptivity of the GMRES restarting parameter.", 3 );
@@ -46,21 +57,22 @@ GMRES< Matrix >::
setup( const Config::ParameterContainer& parameters,
const String& prefix )
{
+ const String var = parameters.getParameter< String >( "gmres-variant" );
+ if( var == "MGS" )
+ variant = Variant::MGS;
+ else if( var == "MGSR" )
+ variant = Variant::MGSR;
+ else if( var == "CWY" )
+ variant = Variant::CWY;
+ else
+ return false;
+
restarting_min = parameters.getParameter< int >( "gmres-restarting-min" );
- this->setRestarting( parameters.getParameter< int >( "gmres-restarting-max" ) );
+ restarting_max = parameters.getParameter< int >( "gmres-restarting-max" );
restarting_step_min = parameters.getParameter< int >( "gmres-restarting-step-min" );
restarting_step_max = parameters.getParameter< int >( "gmres-restarting-step-max" );
- return LinearSolver< Matrix >::setup( parameters, prefix );
-}
-template< typename Matrix >
-void
-GMRES< Matrix >::
-setRestarting( IndexType rest )
-{
- if( size != 0 )
- setSize( size, rest );
- restarting_max = rest;
+ return LinearSolver< Matrix >::setup( parameters, prefix );
}
template< typename Matrix >
@@ -69,58 +81,34 @@ GMRES< Matrix >::
solve( ConstVectorViewType b, VectorViewType x )
{
TNL_ASSERT_TRUE( this->matrix, "No matrix was set in GMRES. Call setMatrix() before solve()." );
- if( restarting_min <= 0 || restarting_max <= 0 || restarting_min > restarting_max )
- {
+ if( restarting_min <= 0 || restarting_max <= 0 || restarting_min > restarting_max ) {
std::cerr << "Wrong value for the GMRES restarting parameters: r_min = " << restarting_min
<< ", r_max = " << restarting_max << std::endl;
return false;
}
- if( restarting_step_min < 0 || restarting_step_max < 0 || restarting_step_min > restarting_step_max )
- {
+ if( restarting_step_min < 0 || restarting_step_max < 0 || restarting_step_min > restarting_step_max ) {
std::cerr << "Wrong value for the GMRES restarting adjustment parameters: d_min = " << restarting_step_min
<< ", d_max = " << restarting_step_max << std::endl;
return false;
}
- setSize( this->matrix->getRows(), restarting_max );
-
- IndexType _size = size;
-
- //RealType *w = _w.getData();
- RealType *s = _s.getData();
- RealType *cs = _cs.getData();
- RealType *sn = _sn.getData();
- RealType *v = _v.getData();
- RealType *H = _H.getData();
- RealType *M_tmp = _M_tmp.getData();
-
- RealType normb( 0.0 ), beta( 0.0 );
- /****
- * 1. Solve r from M r = b - A x_0
- */
- if( this->preconditioner )
- {
- this->preconditioner->solve( b, _M_tmp );
- normb = _M_tmp.lpNorm( ( RealType ) 2.0 );
+ setSize( this->matrix->getRows() );
- this->matrix->vectorProduct( x, _M_tmp );
- _M_tmp.addVector( b, ( RealType ) 1.0, -1.0 );
-
- this->preconditioner->solve( _M_tmp, _r );
+ // initialize the norm of the preconditioned right-hand-side
+ RealType normb;
+ if( this->preconditioner ) {
+ this->preconditioner->solve( b, _M_tmp );
+ normb = _M_tmp.lpNorm( 2.0 );
}
else
- {
- this->matrix->vectorProduct( x, _r );
- normb = b.lpNorm( ( RealType ) 2.0 );
- _r.addVector( b, ( RealType ) 1.0, -1.0 );
- }
- beta = _r.lpNorm( ( RealType ) 2.0 );
-
- //cout << "norm b = " << normb << std::endl;
- //cout << " beta = " << beta << std::endl;
-
+ normb = b.lpNorm( 2.0 );
+ if( normb == 0.0 )
+ normb = 1.0;
- if( normb == 0.0 ) normb = 1.0;
+ // r = M.solve(b - A * x);
+ compute_residue( r, x, b );
+ RealType beta = r.lpNorm( 2.0 );
+ // initialize stopping criterion
this->resetIterations();
this->setResidue( beta / normb );
@@ -131,9 +119,7 @@ solve( ConstVectorViewType b, VectorViewType x )
int restart_cycles = 0; // counter of restart cycles
int m = restarting_max; // current restarting parameter
- Containers::Vector< RealType, DeviceType, IndexType > vi, vk;
- while( this->checkNextIteration() )
- {
+ while( this->checkNextIteration() ) {
// adaptivity of the restarting parameter
// reference: A.H. Baker, E.R. Jessup, Tz.V. Kolev - A simple strategy for varying the restart parameter in GMRES(m)
// http://www.sciencedirect.com/science/article/pii/S0377042709000132
@@ -153,185 +139,471 @@ solve( ConstVectorViewType b, VectorViewType x )
// set restarting_max when we hit restarting_min (see Baker et al. (2009))
m = restarting_max;
}
-// std::cerr << "restarting: cycle = " << restart_cycles << ", beta_ratio = " << beta_ratio << ", m = " << m << " " << std::endl;
}
- for( IndexType i = 0; i < m + 1; i ++ )
- H[ i ] = s[ i ] = cs[ i ] = sn[ i ] = 0.0;
+ // orthogonalization
+ int o_steps = 0;
+ switch( variant ) {
+ case Variant::MGS:
+ case Variant::MGSR:
+ o_steps = orthogonalize_MGS( m, normb, beta );
+ break;
+ case Variant::CWY:
+ o_steps = orthogonalize_CWY( m, normb, beta );
+ break;
+ }
+
+ if( o_steps < m ) {
+ // exact solution has been reached early
+ update( o_steps, m, H, s, V, x );
+ this->refreshSolverMonitor( true );
+ return this->checkConvergence();
+ }
+
+ // update the solution approximation
+ update( m - 1, m, H, s, V, x );
+
+ // compute the new residual vector
+ compute_residue( r, x, b );
+ const RealType beta_old = beta;
+ beta = r.lpNorm( 2.0 );
+ this->setResidue( beta / normb );
+
+ // update parameters for the adaptivity of the restarting parameter
+ ++restart_cycles;
+ beta_ratio = beta / beta_old;
+ }
+ this->refreshSolverMonitor( true );
+ return this->checkConvergence();
+}
+
+template< typename Matrix >
+int
+GMRES< Matrix >::
+orthogonalize_MGS( const int m, const RealType normb, const RealType beta )
+{
+ DeviceView vi, vk;
+
+ /***
+ * v_0 = r / | r | = 1.0 / beta * r
+ */
+ vi.bind( V.getData(), ldSize );
+ vi.addVector( r, 1.0 / beta, 0.0 );
+
+ H.setValue( 0.0 );
+ s.setValue( 0.0 );
+ s[ 0 ] = beta;
+
+ /****
+ * Starting m-loop
+ */
+ for( int i = 0; i < m && this->nextIteration(); i++ ) {
+ vi.bind( &( V.getData()[ i * ldSize ] ), size );
/****
- * v = 0
+ * Solve w from M w = A v_i
*/
- _v.setValue( ( RealType ) 0.0 );
+ preconditioned_matvec( w, vi );
+
+ for( int k = 0; k <= i; k++ )
+ H[ k + i * ( m + 1 ) ] = 0.0;
+ const int reorthogonalize = (variant == Variant::MGSR) ? 2 : 1;
+ for( int l = 0; l < reorthogonalize; l++ )
+ for( int k = 0; k <= i; k++ ) {
+ vk.bind( &( V.getData()[ k * ldSize ] ), size );
+ /***
+ * H_{k,i} = ( w, v_k )
+ */
+ RealType H_k_i = w.scalarProduct( vk );
+ H[ k + i * ( m + 1 ) ] += H_k_i;
+
+ /****
+ * w = w - H_{k,i} v_k
+ */
+ w.addVector( vk, -H_k_i );
+ }
+ /***
+ * H_{i+1,i} = |w|
+ */
+ RealType normw = w.lpNorm( ( RealType ) 2.0 );
+ H[ i + 1 + i * ( m + 1 ) ] = normw;
/***
- * v_0 = r / | r | = 1.0 / beta * r
+ * v_{i+1} = w / |w|
+ */
+ vi.bind( &( V.getData()[ ( i + 1 ) * ldSize ] ), size );
+ vi.addVector( w, 1.0 / normw, 0.0 );
+
+ /****
+ * Applying the Givens rotations G_0, ..., G_i
*/
- vi.bind( _v.getData(), size );
- vi.addVector( _r, ( RealType ) 1.0 / beta );
+ apply_givens_rotations( i, m );
- _s.setValue( ( RealType ) 0.0 );
- _s[ 0 ] = beta;
+ this->setResidue( std::fabs( s[ i + 1 ] ) / normb );
+ if( ! this->checkNextIteration() )
+ return i;
+ else
+ this->refreshSolverMonitor();
+ }
+ return m;
+}
+template< typename Matrix >
+int
+GMRES< Matrix >::
+orthogonalize_CWY( const int m, const RealType normb, const RealType beta )
+{
+ DeviceVector vi, vk;
+ /***
+ * z = r / | r | = 1.0 / beta * r
+ */
+ // TODO: investigate normalization by beta and normb
+// z.addVector( r, 1.0 / beta, 0.0 );
+// z.addVector( r, 1.0 / normb, 0.0 );
+ z = r;
+
+ H.setValue( 0.0 );
+ s.setValue( 0.0 );
+ T.setValue( 0.0 );
+
+ // NOTE: this is unstable, s[0] is set later in hauseholder_apply_trunc
+// s[ 0 ] = beta;
+
+ /****
+ * Starting m-loop
+ */
+ for( int i = 0; i <= m && this->nextIteration(); i++ ) {
/****
- * Starting m-loop
+ * Generate new Hauseholder transformation from vector z.
*/
- for( IndexType i = 0; i < m && this->nextIteration(); i++ )
- {
- vi.bind( &( _v.getData()[ i * size ] ), size );
+ hauseholder_generate( Y, T, i, z );
+
+ if( i == 0 ) {
/****
- * Solve w from M w = A v_i
+ * s = e_1^T * P_i * z
*/
- if( this->preconditioner )
- {
- this->matrix->vectorProduct( vi, _M_tmp );
- this->preconditioner->solve( _M_tmp, w );
- }
- else
- this->matrix->vectorProduct( vi, w );
-
- //cout << " i = " << i << " vi = " << vi << std::endl;
-
- for( IndexType k = 0; k <= i; k++ )
- H[ k + i * ( m + 1 ) ] = 0.0;
- for( IndexType l = 0; l < 2; l++ )
- for( IndexType k = 0; k <= i; k++ )
- {
- vk.bind( &( _v.getData()[ k * _size ] ), _size );
- /***
- * H_{k,i} = ( w, v_k )
- */
- RealType H_k_i = w.scalarProduct( vk );
- H[ k + i * ( m + 1 ) ] += H_k_i;
-
- /****
- * w = w - H_{k,i} v_k
- */
- w.addVector( vk, -H_k_i );
-
- //cout << "H_ki = " << H_k_i << std::endl;
- //cout << "w = " << w << std::endl;
- }
+ hauseholder_apply_trunc( s, Y, T, i, z );
+ }
+ else {
/***
- * H_{i+1,i} = |w|
+ * H_{i-1} = P_i * z
*/
- RealType normw = w.lpNorm( ( RealType ) 2.0 );
- H[ i + 1 + i * ( m + 1 ) ] = normw;
+ HostView h( &H.getData()[ (i - 1) * (m + 1) ], m + 1 );
+ hauseholder_apply_trunc( h, Y, T, i, z );
+ }
- //cout << "normw = " << normw << std::endl;
-
- /***
- * v_{i+1} = w / |w|
- */
- vi.bind( &( _v.getData()[ ( i + 1 ) * size ] ), size );
- vi.addVector( w, ( RealType ) 1.0 / normw );
-
- //cout << "vi = " << vi << std::endl;
-
+ /***
+ * Generate new basis vector v_i, using the compact WY representation:
+ * v_i = (I - Y_i * T_i Y_i^T) * e_i
+ */
+ vi.bind( &V.getData()[ i * ldSize ], size );
+ hauseholder_cwy( vi, Y, T, i );
+
+ if( i < m ) {
/****
- * Applying the Givens rotations
+ * Solve w from M w = A v_i
*/
- for( IndexType k = 0; k < i; k++ )
- applyPlaneRotation( H[ k + i * ( m + 1 )],
- H[ k + 1 + i * ( m + 1 ) ],
- cs[ k ],
- sn[ k ] );
-
- generatePlaneRotation( H[ i + i * ( m + 1 ) ],
- H[ i + 1 + i * ( m + 1 ) ],
- cs[ i ],
- sn[ i ]);
- applyPlaneRotation( H[ i + i * ( m + 1 ) ],
- H[ i + 1 + i * ( m + 1 ) ],
- cs[ i ],
- sn[ i ]);
- applyPlaneRotation( s[ i ],
- s[ i + 1 ],
- cs[ i ],
- sn[ i ] );
+ preconditioned_matvec( w, vi );
- this->setResidue( std::fabs( s[ i + 1 ] ) / normb );
- if( ! this->checkNextIteration() ) {
- update( i, m, _H, _s, _v, x );
- this->refreshSolverMonitor( true );
- return this->checkConvergence();
- }
- else
- {
- this->refreshSolverMonitor();
- }
+ /****
+ * Apply all previous Hauseholder transformations, using the compact WY representation:
+ * z = (I - Y_i * T_i^T * Y_i^T) * w
+ */
+ hauseholder_cwy_transposed( z, Y, T, i, w );
}
- //cout << "x = " << x << std::endl;
- update( m - 1, m, _H, _s, _v, x );
- //cout << "x = " << x << std::endl;
/****
- * r = M.solve(b - A * x);
+ * Applying the Givens rotations G_0, ..., G_{i-1}
*/
- const RealType beta_old = beta;
- beta = 0.0;
- if( this->preconditioner )
- {
- this->matrix->vectorProduct( x, _M_tmp );
- _M_tmp.addVector( b, ( RealType ) 1.0, -1.0 );
- this->preconditioner->solve( _M_tmp, _r );
- beta = _r.lpNorm( ( RealType ) 2.0 );
- }
+ if( i > 0 )
+ apply_givens_rotations( i - 1, m );
+
+ this->setResidue( std::fabs( s[ i ] ) / normb );
+ if( ! this->checkNextIteration() )
+ return i - 1;
else
- {
- this->matrix->vectorProduct( x, _r );
- _r.addVector( b, ( RealType ) 1.0, -1.0 );
- beta = _r.lpNorm( ( RealType ) 2.0 );
+ this->refreshSolverMonitor();
+ }
+
+ return m;
+}
+
+template< typename Matrix >
+void
+GMRES< Matrix >::
+compute_residue( VectorViewType r, ConstVectorViewType x, ConstVectorViewType b )
+{
+ /****
+ * r = M.solve(b - A * x);
+ */
+ if( this->preconditioner ) {
+ this->matrix->vectorProduct( x, _M_tmp );
+ _M_tmp.addVector( b, 1.0, -1.0 );
+ this->preconditioner->solve( _M_tmp, r );
+ }
+ else {
+ this->matrix->vectorProduct( x, r );
+ r.addVector( b, 1.0, -1.0 );
+ }
+}
+
+template< typename Matrix >
+void
+GMRES< Matrix >::
+preconditioned_matvec( DeviceVector& w, ConstDeviceView v )
+{
+ /****
+ * w = M.solve(A * v_i);
+ */
+ if( this->preconditioner ) {
+ this->matrix->vectorProduct( v, _M_tmp );
+ this->preconditioner->solve( _M_tmp, w );
+ }
+ else
+ this->matrix->vectorProduct( v, w );
+}
+
+#ifdef HAVE_CUDA
+template< typename DestinationElement,
+ typename SourceElement,
+ typename Index >
+__global__ void
+copyTruncatedVectorKernel( DestinationElement* destination,
+ const SourceElement* source,
+ const Index from,
+ const Index size )
+{
+ Index elementIdx = blockIdx.x * blockDim.x + threadIdx.x;
+ const Index gridSize = blockDim.x * gridDim.x;
+
+ while( elementIdx < from ) {
+ destination[ elementIdx ] = (DestinationElement) 0.0;
+ elementIdx += gridSize;
+ }
+ while( elementIdx < size ) {
+ destination[ elementIdx ] = source[ elementIdx ];
+ elementIdx += gridSize;
+ }
+}
+#endif
+
+template< typename Matrix >
+void
+GMRES< Matrix >::
+hauseholder_generate( DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& z )
+{
+ DeviceView y_i( &Y.getData()[ i * ldSize ], size );
+
+ // XXX: the upper-right triangle of Y will be full of zeros, which can be exploited for optimization
+ if( std::is_same< DeviceType, Devices::Host >::value ) {
+ for( IndexType j = 0; j < size; j++ ) {
+ if( j < i )
+ y_i[ j ] = 0.0;
+ else
+ y_i[ j ] = z[ j ];
}
- this->setResidue( beta / normb );
+ }
+ if( std::is_same< DeviceType, Devices::Cuda >::value ) {
+#ifdef HAVE_CUDA
+ dim3 blockSize( 256 );
+ dim3 gridSize;
+ gridSize.x = min( Devices::Cuda::getMaxGridSize(), Devices::Cuda::getNumberOfBlocks( size, blockSize.x ) );
+
+ copyTruncatedVectorKernel<<< gridSize, blockSize >>>( y_i.getData(),
+ z.getData(),
+ i,
+ size );
+ TNL_CHECK_CUDA_DEVICE;
+#else
+ throw Exceptions::CudaSupportMissing();
+#endif
+ }
- //cout << " x = " << x << std::endl;
- //cout << " beta = " << beta << std::endl;
- //cout << "residue = " << beta / normb << std::endl;
+ // norm of the TRUNCATED vector z
+ const RealType normz = y_i.lpNorm( 2.0 );
+ const RealType y_ii = y_i.getElement( i );
+ if( y_ii > 0.0 )
+ y_i.setElement( i, y_ii + normz );
+ else
+ y_i.setElement( i, y_ii - normz );
+
+ // compute the norm of the y_i vector; equivalent to this calculation by definition:
+ // const RealType norm_yi = y_i.lpNorm( 2.0 );
+ const RealType norm_yi = std::sqrt( 2 * (normz * normz + std::fabs( y_ii ) * normz) );
+
+ // XXX: normalization is slower, but more stable
+// y_i *= 1.0 / norm_yi;
+// const RealType t_i = 2.0;
+ // assuming it's stable enough...
+ const RealType t_i = 2.0 / (norm_yi * norm_yi);
+
+ T[ i + i * (restarting_max + 1) ] = t_i;
+ if( i > 0 ) {
+ // aux = Y_{i-1}^T * y_i
+ RealType aux[ i ];
+ Containers::Algorithms::ParallelReductionScalarProduct< RealType, RealType > scalarProduct;
+ Containers::Algorithms::Multireduction< DeviceType >::reduce
+ ( scalarProduct,
+ i,
+ size,
+ Y.getData(),
+ ldSize,
+ y_i.getData(),
+ aux );
+
+ // [T_i]_{0..i-1} = - T_{i-1} * t_i * aux
+ for( int k = 0; k < i; k++ ) {
+ T[ k + i * (restarting_max + 1) ] = 0.0;
+ for( int j = k; j < i; j++ )
+ T[ k + i * (restarting_max + 1) ] -= T[ k + j * (restarting_max + 1) ] * (t_i * aux[ j ]);
+ }
+ }
+}
- // update parameters for the adaptivity of the restarting parameter
- ++restart_cycles;
- beta_ratio = beta / beta_old;
+template< typename Matrix >
+void
+GMRES< Matrix >::
+hauseholder_apply_trunc( HostView out,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& z )
+{
+ DeviceView y_i( &Y.getData()[ i * ldSize ], size );
+
+ const RealType aux = T[ i + i * (restarting_max + 1) ] * y_i.scalarProduct( z );
+ if( std::is_same< DeviceType, Devices::Host >::value ) {
+ for( int k = 0; k <= i; k++ )
+ out[ k ] = z[ k ] - y_i[ k ] * aux;
+ }
+ if( std::is_same< DeviceType, Devices::Cuda >::value ) {
+ // copy part of y_i to buffer on host
+ // here we duplicate the upper (m+1)x(m+1) submatrix of Y on host for fast access
+ RealType* host_yi = &YL[ i * (restarting_max + 1) ];
+ RealType host_z[ i + 1 ];
+ Containers::Algorithms::ArrayOperations< Devices::Host, Devices::Cuda >::copyMemory< RealType, RealType, IndexType >( host_yi, y_i.getData(), restarting_max + 1 );
+ Containers::Algorithms::ArrayOperations< Devices::Host, Devices::Cuda >::copyMemory< RealType, RealType, IndexType >( host_z, z.getData(), i + 1 );
+ for( int k = 0; k <= i; k++ )
+ out[ k ] = host_z[ k ] - host_yi[ k ] * aux;
}
- this->refreshSolverMonitor( true );
- return this->checkConvergence();
}
template< typename Matrix >
- template< typename VectorT >
void
GMRES< Matrix >::
-update( IndexType k,
- IndexType m,
- const Containers::Vector< RealType, Devices::Host, IndexType >& H,
- const Containers::Vector< RealType, Devices::Host, IndexType >& s,
- Containers::Vector< RealType, DeviceType, IndexType >& v,
- VectorT& x )
+hauseholder_cwy( DeviceVector& v,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i )
{
- Containers::Vector< RealType, Devices::Host, IndexType > y;
- y.setSize( m + 1 );
+ // aux = Y_i^T * e_i
+ RealType aux[ i + 1 ];
+ if( std::is_same< DeviceType, Devices::Host >::value ) {
+ for( int k = 0; k <= i; k++ )
+ aux[ k ] = Y[ i + k * ldSize ];
+ }
+ if( std::is_same< DeviceType, Devices::Cuda >::value ) {
+ // the upper (m+1)x(m+1) submatrix of Y is duplicated on host for fast access
+ for( int k = 0; k <= i; k++ )
+ aux[ k ] = YL[ i + k * (restarting_max + 1) ];
+ }
+
+ // aux = T_i * aux
+ // Note that T_i is upper triangular, so we can overwrite the aux vector with the result in place
+ for( int k = 0; k <= i; k++ ) {
+ RealType aux2 = 0.0;
+ for( int j = k; j <= i; j++ )
+ aux2 += T[ k + j * (restarting_max + 1) ] * aux[ j ];
+ aux[ k ] = aux2;
+ }
- IndexType i, j;
- for( i = 0; i <= m ; i ++ )
+ // v = e_i - Y_i * aux
+ MatrixOperations< DeviceType >::gemv( size, i + 1,
+ -1.0, Y.getData(), ldSize, aux,
+ 0.0, v.getData() );
+ v.setElement( i, 1.0 + v.getElement( i ) );
+}
+
+template< typename Matrix >
+void
+GMRES< Matrix >::
+hauseholder_cwy_transposed( DeviceVector& z,
+ DeviceVector& Y,
+ HostVector& T,
+ const int i,
+ DeviceVector& w )
+{
+ // aux = Y_i^T * w
+ RealType aux[ i + 1 ];
+ Containers::Algorithms::ParallelReductionScalarProduct< RealType, RealType > scalarProduct;
+ Containers::Algorithms::Multireduction< DeviceType >::reduce
+ ( scalarProduct,
+ i + 1,
+ size,
+ Y.getData(),
+ ldSize,
+ w.getData(),
+ aux );
+
+ // aux = T_i^T * aux
+ // Note that T_i^T is lower triangular, so we can overwrite the aux vector with the result in place
+ for( int k = i; k >= 0; k-- ) {
+ RealType aux2 = 0.0;
+ for( int j = 0; j <= k; j++ )
+ aux2 += T[ j + k * (restarting_max + 1) ] * aux[ j ];
+ aux[ k ] = aux2;
+ }
+
+ // z = w - Y_i * aux
+ z = w;
+ MatrixOperations< DeviceType >::gemv( size, i + 1,
+ -1.0, Y.getData(), ldSize, aux,
+ 1.0, z.getData() );
+}
+
+template< typename Matrix >
+ template< typename Vector >
+void
+GMRES< Matrix >::
+update( const int k,
+ const int m,
+ const HostVector& H,
+ const HostVector& s,
+ DeviceVector& v,
+ Vector& x )
+{
+ RealType y[ m + 1 ];
+
+ for( int i = 0; i <= m ; i ++ )
y[ i ] = s[ i ];
// Backsolve:
- for( i = k; i >= 0; i--)
- {
- //cout << " y = " << y << std::endl;
+ for( int i = k; i >= 0; i--) {
+ if( H[ i + i * ( m + 1 ) ] == 0 ) {
+// for( int _i = 0; _i <= i; _i++ ) {
+// for( int _j = 0; _j < i; _j++ )
+// std::cout << H[ _i + _j * (m+1) ] << " ";
+// std::cout << std::endl;
+// }
+ std::cerr << "H.norm = " << H.lpNorm( 2.0 ) << std::endl;
+ std::cerr << "s = " << s << std::endl;
+ std::cerr << "k = " << k << ", m = " << m << std::endl;
+ throw 1;
+ }
y[ i ] /= H[ i + i * ( m + 1 ) ];
- for( j = i - 1; j >= 0; j--)
+ for( int j = i - 1; j >= 0; j--)
y[ j ] -= H[ j + i * ( m + 1 ) ] * y[ i ];
}
- Containers::Vector< RealType, DeviceType, IndexType > vi;
- for( i = 0; i <= k; i++)
- {
- vi.bind( &( v.getData()[ i * this->size ] ), x.getSize() );
- x.addVector( vi, y[ i ] );
- }
+ // x = V * y + x
+ MatrixOperations< DeviceType >::gemv( size, k + 1,
+ 1.0, v.getData(), ldSize, y,
+ 1.0, x.getData() );
}
template< typename Matrix >
@@ -342,24 +614,20 @@ generatePlaneRotation( RealType& dx,
RealType& cs,
RealType& sn )
{
- if( dy == 0.0 )
- {
+ if( dy == 0.0 ) {
cs = 1.0;
sn = 0.0;
}
- else
- if( std::fabs( dy ) > std::fabs( dx ) )
- {
- RealType temp = dx / dy;
- sn = 1.0 / std::sqrt( 1.0 + temp * temp );
- cs = temp * sn;
- }
- else
- {
- RealType temp = dy / dx;
- cs = 1.0 / std::sqrt( 1.0 + temp * temp );
- sn = temp * cs;
- }
+ else if( std::fabs( dy ) > std::fabs( dx ) ) {
+ const RealType temp = dx / dy;
+ sn = 1.0 / std::sqrt( 1.0 + temp * temp );
+ cs = temp * sn;
+ }
+ else {
+ const RealType temp = dy / dx;
+ cs = 1.0 / std::sqrt( 1.0 + temp * temp );
+ sn = temp * cs;
+ }
}
template< typename Matrix >
@@ -370,28 +638,68 @@ applyPlaneRotation( RealType& dx,
RealType& cs,
RealType& sn )
{
- RealType temp = cs * dx + sn * dy;
- dy = cs * dy - sn * dx;
+ const RealType temp = cs * dx + sn * dy;
+ dy = cs * dy - sn * dx;
dx = temp;
}
template< typename Matrix >
void
GMRES< Matrix >::
-setSize( IndexType _size, IndexType m )
+apply_givens_rotations( int i, int m )
+{
+ for( int k = 0; k < i; k++ )
+ applyPlaneRotation( H[ k + i * (m + 1) ],
+ H[ k + 1 + i * (m + 1) ],
+ cs[ k ],
+ sn[ k ] );
+
+ if( H[ i + 1 + i * (m + 1) ] != 0.0 ) {
+ generatePlaneRotation( H[ i + i * (m + 1) ],
+ H[ i + 1 + i * (m + 1) ],
+ cs[ i ],
+ sn[ i ]);
+ applyPlaneRotation( H[ i + i * (m + 1) ],
+ H[ i + 1 + i * (m + 1) ],
+ cs[ i ],
+ sn[ i ]);
+ applyPlaneRotation( s[ i ],
+ s[ i + 1 ],
+ cs[ i ],
+ sn[ i ] );
+ }
+}
+
+template< typename Matrix >
+void
+GMRES< Matrix >::
+setSize( const IndexType size )
{
- if( size == _size && restarting_max == m )
- return;
- size = _size;
- restarting_max = m;
- _r.setSize( size );
+ this->size = size;
+ if( std::is_same< DeviceType, Devices::Cuda >::value )
+ // align each column to 256 bytes - optimal for CUDA
+ ldSize = roundToMultiple( size, 256 / sizeof( RealType ) );
+ else
+ // on the host, we add 1 to disrupt the cache false-sharing pattern
+ ldSize = roundToMultiple( size, 256 / sizeof( RealType ) ) + 1;
+
+ const int m = restarting_max;
+ r.setSize( size );
w.setSize( size );
- _s.setSize( m + 1 );
- _cs.setSize( m + 1 );
- _sn.setSize( m + 1 );
- _v.setSize( size * ( m + 1 ) );
- _H.setSize( ( m + 1 ) * m );
+ V.setSize( ldSize * ( m + 1 ) );
+ cs.setSize( m + 1 );
+ sn.setSize( m + 1 );
+ H.setSize( ( m + 1 ) * m );
+ s.setSize( m + 1 );
_M_tmp.setSize( size );
+
+ // CWY-specific storage
+ if( variant == Variant::CWY ) {
+ z.setSize( size );
+ Y.setSize( ldSize * ( m + 1 ) );
+ T.setSize( (m + 1) * (m + 1) );
+ YL.setSize( (m + 1) * (m + 1) );
+ }
}
} // namespace Linear
diff --git a/src/TNL/Solvers/LinearSolverTypeResolver.h b/src/TNL/Solvers/LinearSolverTypeResolver.h
index 8842038009..61a141f504 100644
--- a/src/TNL/Solvers/LinearSolverTypeResolver.h
+++ b/src/TNL/Solvers/LinearSolverTypeResolver.h
@@ -19,7 +19,6 @@
#include <TNL/Solvers/Linear/BICGStab.h>
#include <TNL/Solvers/Linear/BICGStabL.h>
#include <TNL/Solvers/Linear/GMRES.h>
-#include <TNL/Solvers/Linear/CWYGMRES.h>
#include <TNL/Solvers/Linear/TFQMR.h>
#include <TNL/Solvers/Linear/UmfpackWrapper.h>
#include <TNL/Solvers/Linear/Preconditioners/Diagonal.h>
@@ -45,8 +44,6 @@ getLinearSolver( const Config::ParameterContainer& parameters )
return std::make_shared< Linear::BICGStabL< MatrixType > >();
if( discreteSolver == "gmres" )
return std::make_shared< Linear::GMRES< MatrixType > >();
- if( discreteSolver == "cwygmres" )
- return std::make_shared< Linear::CWYGMRES< MatrixType > >();
if( discreteSolver == "tfqmr" )
return std::make_shared< Linear::TFQMR< MatrixType > >();
#ifdef HAVE_UMFPACK
@@ -54,7 +51,7 @@ getLinearSolver( const Config::ParameterContainer& parameters )
return std::make_shared< Linear::UmfpackWrapper< MatrixType > >();
#endif
- std::cerr << "Unknown semi-implicit discrete solver " << discreteSolver << ". It can be only: sor, cg, bicgstab, bicgstabl, gmres, cwygmres, tfqmr";
+ std::cerr << "Unknown semi-implicit discrete solver " << discreteSolver << ". It can be only: sor, cg, bicgstab, bicgstabl, gmres, tfqmr";
#ifdef HAVE_UMFPACK
std::cerr << ", umfpack"
#endif
diff --git a/src/TNL/Solvers/SolverConfig_impl.h b/src/TNL/Solvers/SolverConfig_impl.h
index bc86767e16..598cee285a 100644
--- a/src/TNL/Solvers/SolverConfig_impl.h
+++ b/src/TNL/Solvers/SolverConfig_impl.h
@@ -21,7 +21,6 @@
#include <TNL/Solvers/Linear/BICGStab.h>
#include <TNL/Solvers/Linear/BICGStabL.h>
#include <TNL/Solvers/Linear/GMRES.h>
-#include <TNL/Solvers/Linear/CWYGMRES.h>
#include <TNL/Solvers/Linear/TFQMR.h>
#include <TNL/Solvers/Linear/UmfpackWrapper.h>
#include <TNL/Solvers/Linear/Preconditioners/Diagonal.h>
@@ -135,7 +134,6 @@ bool SolverConfig< ConfigTag, ProblemConfig >::configSetup( Config::ConfigDescri
config.addEntryEnum( "cg" );
config.addEntryEnum( "bicgstab" );
config.addEntryEnum( "bicgstabl" );
- config.addEntryEnum( "cwygmres" );
config.addEntryEnum( "gmres" );
config.addEntryEnum( "tfqmr" );
config.addEntryEnum( "sor" );
@@ -174,10 +172,7 @@ bool SolverConfig< ConfigTag, ProblemConfig >::configSetup( Config::ConfigDescri
Linear::CG< MatrixType >::configSetup( config );
Linear::BICGStab< MatrixType >::configSetup( config );
Linear::BICGStabL< MatrixType >::configSetup( config );
-
- // GMRES and CWYGMRES have the same options
Linear::GMRES< MatrixType >::configSetup( config );
-
Linear::TFQMR< MatrixType >::configSetup( config );
Linear::SOR< MatrixType >::configSetup( config );
--
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