ROL
step/krylov/test_01.cpp
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43
48#include "ROL_StdVector.hpp"
49#include "ROL_GMRES.hpp"
50#include "ROL_KrylovFactory.hpp"
51#include "ROL_RandomVector.hpp"
52#include "ROL_ParameterList.hpp"
53
54#include "ROL_Stream.hpp"
55#include "Teuchos_GlobalMPISession.hpp"
56
57#include<iomanip>
58
59// Identity operator for preconditioner
60template<class Real>
61class Identity : public ROL::LinearOperator<Real> {
63public:
64 void apply( V& Hv, const V& v, Real &tol ) const {
65 Hv.set(v);
66 }
67}; // class Identity
68
69
70// Apply a tridiagonal Toeplitz matrix to a ROL::StdVector to test Krylov solvers
71template<class Real>
73
74 typedef std::vector<Real> vector;
77
78 typedef typename vector::size_type uint;
79
80private:
81
82 Real a_; // subdiagonal
83 Real b_; // diagonal
84 Real c_; // superdiagonal
85
86 ROL::LAPACK<int,Real> lapack_;
87
88public:
89
90 TridiagonalToeplitzOperator( Real &a, Real &b, Real &c ) : a_(a), b_(b), c_(c) {}
91
92 // Tridiagonal multiplication
93 void apply( V &Hv, const V &v, Real &tol ) const {
94
95
96
97 SV &Hvs = dynamic_cast<SV&>(Hv);
98 ROL::Ptr<vector> Hvp = Hvs.getVector();
99
100 const SV &vs = dynamic_cast<const SV&>(v);
101 ROL::Ptr<const vector> vp = vs.getVector();
102
103 uint n = vp->size();
104
105 (*Hvp)[0] = b_*(*vp)[0] + c_*(*vp)[1];
106
107 for(uint k=1; k<n-1; ++k) {
108 (*Hvp)[k] = a_*(*vp)[k-1] + b_*(*vp)[k] + c_*(*vp)[k+1];
109 }
110
111 (*Hvp)[n-1] = a_*(*vp)[n-2] + b_*(*vp)[n-1];
112
113 }
114
115 // Tridiagonal solve - compare against GMRES
116 void applyInverse( V &Hv, const V &v, Real &tol ) const {
117
118
119
120 SV &Hvs = dynamic_cast<SV&>(Hv);
121 ROL::Ptr<vector> Hvp = Hvs.getVector();
122
123 const SV &vs = dynamic_cast<const SV&>(v);
124 ROL::Ptr<const vector> vp = vs.getVector();
125
126 uint n = vp->size();
127
128 const char TRANS = 'N';
129 const int NRHS = 1;
130
131 vector dl(n-1,a_);
132 vector d(n,b_);
133 vector du(n-1,c_);
134 vector du2(n-2,0.0);
135
136 std::vector<int> ipiv(n);
137 int info;
138
139 Hv.set(v); // LAPACK will modify this in place
140
141 // Do Tridiagonal LU factorization
142 lapack_.GTTRF(n,&dl[0],&d[0],&du[0],&du2[0],&ipiv[0],&info);
143
144 // Solve the system with the LU factors
145 lapack_.GTTRS(TRANS,n,NRHS,&dl[0],&d[0],&du[0],&du2[0],&ipiv[0],&(*Hvp)[0],n,&info);
146
147 }
148
149}; // class TridiagonalToeplitzOperator
150
151
152
153typedef double RealT;
154
155int main(int argc, char *argv[]) {
156
157
158
159
160 typedef std::vector<RealT> vector;
161 typedef ROL::StdVector<RealT> SV;
162
163 typedef typename vector::size_type uint;
164
165 Teuchos::GlobalMPISession mpiSession(&argc, &argv);
166
167 int iprint = argc - 1;
168 ROL::Ptr<std::ostream> outStream;
169 ROL::nullstream bhs; // outputs nothing
170 if (iprint > 0)
171 outStream = ROL::makePtrFromRef(std::cout);
172 else
173 outStream = ROL::makePtrFromRef(bhs);
174
175 int errorFlag = 0;
176
177 try {
178
179 ROL::ParameterList parlist;
180 ROL::ParameterList &gList = parlist.sublist("General");
181 ROL::ParameterList &kList = gList.sublist("Krylov");
182
183 kList.set("Type","GMRES");
184 kList.set("Iteration Limit",20);
185 kList.set("Absolute Tolerance",1.e-8);
186 kList.set("Relative Tolerance",1.e-6);
187 kList.set("Use Initial Guess",false);
188
189 uint dim = 10;
190
191 ROL::Ptr<vector> xp = ROL::makePtr<vector>(dim,0.0);
192 ROL::Ptr<vector> yp = ROL::makePtr<vector>(dim,0.0);
193 ROL::Ptr<vector> zp = ROL::makePtr<vector>(dim,0.0);
194 ROL::Ptr<vector> bp = ROL::makePtr<vector>(dim,0.0);
195
196 SV x(xp); // Exact solution
197 SV y(yp); // Solution using direct solve
198 SV z(zp); // Solution using GMRES
199
200 SV b(bp); // Right-hand-side
201
202 RealT left = -1.0;
203 RealT right = 1.0;
204
205 ROL::RandomizeVector(x,left,right);
206
207 RealT sub = -1.0;
208 RealT diag = 2.0;
209 RealT super = -1.0;
210
211 TridiagonalToeplitzOperator<RealT> T(sub,diag,super);
213
214 RealT tol = 0.0;
215
216 T.apply(b,x,tol);
217
218 T.applyInverse(y,b,tol);
219
220 ROL::Ptr<ROL::Krylov<RealT> > krylov = ROL::KrylovFactory<RealT>( parlist );
221
222 int iter;
223 int flag;
224
225 krylov->run(z,T,b,I,iter,flag);
226
227 *outStream << std::setw(10) << "Exact"
228 << std::setw(10) << "LAPACK"
229 << std::setw(10) << "GMRES " << std::endl;
230 *outStream << "---------------------------------" << std::endl;
231
232 for(uint k=0;k<dim;++k) {
233 *outStream << std::setw(10) << (*xp)[k] << " "
234 << std::setw(10) << (*yp)[k] << " "
235 << std::setw(10) << (*zp)[k] << " " << std::endl;
236 }
237
238 *outStream << "GMRES performed " << iter << " iterations." << std::endl;
239
240 z.axpy(-1.0,x);
241
242 if( z.norm() > std::sqrt(ROL::ROL_EPSILON<RealT>()) ) {
243 ++errorFlag;
244 }
245
246 }
247 catch (std::logic_error& err) {
248 *outStream << err.what() << "\n";
249 errorFlag = -1000;
250 }; // end try
251
252 if (errorFlag != 0)
253 std::cout << "End Result: TEST FAILED\n";
254 else
255 std::cout << "End Result: TEST PASSED\n";
256
257 return 0;
258}
Defines a no-output stream class ROL::NullStream and a function makeStreamPtr which either wraps a re...
ROL::Vector< Real > V
void apply(V &Hv, const V &v, Real &tol) const
Apply linear operator.
Provides the interface to apply a linear operator.
Provides the ROL::Vector interface for scalar values, to be used, for example, with scalar constraint...
Ptr< const std::vector< Element > > getVector() const
Defines the linear algebra or vector space interface.
virtual void set(const Vector &x)
Set where .
void apply(V &Hv, const V &v, Real &tol) const
Apply linear operator.
TridiagonalToeplitzOperator(Real &a, Real &b, Real &c)
void applyInverse(V &Hv, const V &v, Real &tol) const
Apply inverse of linear operator.
ROL::LAPACK< int, Real > lapack_
void RandomizeVector(Vector< Real > &x, const Real &lower=0.0, const Real &upper=1.0)
Fill a ROL::Vector with uniformly-distributed random numbers in the interval [lower,...
int main(int argc, char *argv[])
double RealT
constexpr auto dim