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/*
* Copyright 2011 The Regents of the University of California
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <cusp/array1d.h>
#include <cusp/blas.h>
#include <cusp/multiply.h>
#include <cusp/monitor.h>
#include <cusp/linear_operator.h>
namespace blas = cusp::blas;
namespace cusp
{
namespace krylov
{
template <typename ValueType>
void ApplyPlaneRotation(ValueType& dx,
ValueType& dy,
ValueType& cs,
ValueType& sn)
{
ValueType temp = cs * dx + sn *dy;
dy = -sn*dx+cs*dy;
dx = temp;
}
template <typename ValueType>
void GeneratePlaneRotation(ValueType& dx,
ValueType& dy,
ValueType& cs,
ValueType& sn)
{
if(dy == ValueType(0.0)){
cs = 1.0;
sn = 0.0;
}else if (abs(dy) > abs(dx)) {
ValueType tmp = dx / dy;
sn = ValueType(1.0) / sqrt(ValueType(1.0) + tmp*tmp);
cs = tmp*sn;
}else {
ValueType tmp = dy / dx;
cs = ValueType(1.0) / sqrt(ValueType(1.0) + tmp*tmp);
sn = tmp*cs;
}
}
template <class LinearOperator,typename ValueType>
void PlaneRotation(LinearOperator& H,
ValueType& cs,
ValueType& sn,
ValueType& s,
int i)
{
for (int k = 0; k < i; k++){
ApplyPlaneRotation(H(k,i), H(k+1,i), cs[k], sn[k]);
}
GeneratePlaneRotation(H(i,i), H(i+1,i), cs[i], sn[i]);
ApplyPlaneRotation(H(i,i), H(i+1,i), cs[i], sn[i]);
ApplyPlaneRotation(s[i], s[i+1], cs[i], sn[i]);
}
template <class LinearOperator,
class Vector>
void gmres(LinearOperator& A,
Vector& x,
Vector& b,
const size_t restart)
{
typedef typename LinearOperator::value_type ValueType;
cusp::default_monitor<ValueType> monitor(b);
cusp::krylov::gmres(A, x, b, restart, monitor);
}
template <class LinearOperator,
class Vector,
class Monitor>
void gmres(LinearOperator& A,
Vector& x,
Vector& b,
const size_t restart,
Monitor& monitor)
{
typedef typename LinearOperator::value_type ValueType;
typedef typename LinearOperator::memory_space MemorySpace;
cusp::identity_operator<ValueType,MemorySpace> M(A.num_rows, A.num_cols);
cusp::krylov::gmres(A, x, b, restart, monitor, M);
}
template <class LinearOperator,
class Vector,
class Monitor,
class Preconditioner>
void gmres(LinearOperator& A,
Vector& x,
Vector& b,
const size_t restart,
Monitor& monitor,
Preconditioner& M)
{
typedef typename LinearOperator::value_type ValueType;
typedef typename LinearOperator::memory_space MemorySpace;
typedef typename norm_type<ValueType>::type NormType;
assert(A.num_rows == A.num_cols); // sanity check
const size_t N = A.num_rows;
const int R = restart;
int i, j, k;
NormType beta = 0;
cusp::array1d<NormType,cusp::host_memory> resid(1);
//allocate workspace
cusp::array1d<ValueType,MemorySpace> w(N);
cusp::array1d<ValueType,MemorySpace> V0(N); //Arnoldi matrix pos 0
cusp::array2d<ValueType,MemorySpace,cusp::column_major> V(N,R+1,ValueType(0.0)); //Arnoldi matrix
//duplicate copy of s on GPU
cusp::array1d<ValueType,MemorySpace> sDev(R+1);
//HOST WORKSPACE
cusp::array2d<ValueType,cusp::host_memory,cusp::column_major> H(R+1, R); //Hessenberg matrix
cusp::array1d<ValueType,cusp::host_memory> s(R+1);
cusp::array1d<ValueType,cusp::host_memory> cs(R);
cusp::array1d<ValueType,cusp::host_memory> sn(R);
do{
// compute initial residual and its norm //
cusp::multiply(A, x, w); // V(0) = A*x //
blas::axpy(b,w,ValueType(-1)); // V(0) = V(0) - b //
cusp::multiply(M,w,w); // V(0) = M*V(0) //
beta = blas::nrm2(w); // beta = norm(V(0)) //
blas::scal(w, ValueType(-1.0/beta)); // V(0) = -V(0)/beta //
blas::copy(w,V.column(0));
//s = 0 //
blas::fill(s,ValueType(0.0));
s[0] = beta;
i = -1;
resid[0] = abs(s[0]);
if (monitor.finished(resid)){
break;
}
do{
++i;
++monitor;
//apply preconditioner
//can't pass in ref to column in V so need to use copy (w)
cusp::multiply(A,w,V0);
//V(i+1) = A*w = M*A*V(i) //
cusp::multiply(M,V0,w);
for (k = 0; k <= i; k++){
// H(k,i) = <V(i+1),V(k)> //
H(k, i) = blas::dotc(w, V.column(k));
// V(i+1) -= H(k, i) * V(k) //
blas::axpy(V.column(k),w,-H(k,i));
}
H(i+1,i) = blas::nrm2(w);
// V(i+1) = V(i+1) / H(i+1, i) //
blas::scal(w,ValueType(1.0)/H(i+1,i));
blas::copy(w,V.column(i+1));
PlaneRotation(H,cs,sn,s,i);
resid[0] = abs(s[i+1]);
//check convergence condition
if (monitor.finished(resid)){
break;
}
}while (i+1 < R && monitor.iteration_count()+1 <= monitor.iteration_limit());
// solve upper triangular system in place //
for (j = i; j >= 0; j--){
s[j] /= H(j,j);
//S(0:j) = s(0:j) - s[j] H(0:j,j)
for (k = j-1; k >= 0; k--){
s[k] -= H(k,j) * s[j];
}
}
// update the solution //
//copy s to gpu
blas::copy(s,sDev);
// x= V(1:N,0:i)*s(0:i)+x //
for (j = 0; j <= i; j++){
// x = x + s[j] * V(j) //
blas::axpy(V.column(j),x,s[j]);
}
} while (!monitor.finished(resid));
}
} // end namespace krylov
} // end namespace cusp
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