# CG Examples [Assorted Thyra Operator/Vector Example Code]

Here we show some simple examples of using code in the Thyra package with an example ANA algorithm for the iterative solution of symmetric positive-definite linear systems using the conjugate gradient (CG) method. More...

## Modules

group  Templated Serial Implementation of the CG Method
Here is an example program that shows the use of the example serial templated matrix class `ExampleTridiagSerialLinearOp` with the example linear ANA implementation `sillyCgSolve()`.
group  Templated SPMD Implementation of the CG Method
Here is an example program that shows the use of the example SPMD templated matrix class `ExampleTridiagSpmdLinearOp` with the example linear ANA implementation `sillyCgSolve()` or `silliestCgSolve()`.

## Functions

template<class Scalar>
bool sillyCgSolve (const Thyra::LinearOpBase< Scalar > &A, const Thyra::VectorBase< Scalar > &b, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::VectorBase< Scalar > *x, std::ostream *out=NULL)
Silly little example unpreconditioned CG solver.
template<class Scalar>
bool sillierCgSolve (const Thyra::LinearOpBase< Scalar > &A_in, const Thyra::VectorBase< Scalar > &b_in, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::VectorBase< Scalar > *x_inout, std::ostream *out=NULL)
Silly little example unpreconditioned CG solver (calls templated code).
template<class Scalar>
bool silliestCgSolve (Thyra::ConstLinearOperator< Scalar > const &A, Thyra::ConstVector< Scalar > const &b, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::Vector< Scalar > &x, std::ostream *out=NULL)
Silly little example unpreconditioned CG solver that uses handles.

## Detailed Description

Here we show some simple examples of using code in the Thyra package with an example ANA algorithm for the iterative solution of symmetric positive-definite linear systems using the conjugate gradient (CG) method.

The CG ANA is implemented in the function `sillyCgSolve()` and its implementation is shown below:

```template<class Scalar>
bool sillyCgSolve(
const Thyra::LinearOpBase<Scalar>                              &A
,const Thyra::VectorBase<Scalar>                               &b
,const int                                                     maxNumIters
,const typename Teuchos::ScalarTraits<Scalar>::magnitudeType   tolerance
,Thyra::VectorBase<Scalar>                                     *x
,std::ostream                                                  *out          = NULL
)
{
// Create some typedefs and some other stuff to make the code cleaner
typedef Teuchos::ScalarTraits<Scalar> ST; typedef typename ST::magnitudeType ScalarMag;
const Scalar one = ST::one(), zero = ST::zero(); using Thyra::NOTRANS;
typedef Teuchos::RefCountPtr<const Thyra::VectorSpaceBase<Scalar> > VectorSpacePtr;
typedef Teuchos::RefCountPtr<Thyra::VectorBase<Scalar> > VectorPtr;
// Validate input
TEST_FOR_EXCEPT(x==NULL);
THYRA_ASSERT_LINEAR_OP_VEC_APPLY_SPACES("sillyCgSolve()",A,Thyra::NOTRANS,*x,&b); // Does A*x - b agree?
Teuchos::EVerbosityLevel vl = Teuchos::VERB_MEDIUM;
if(out) *out << "\nStarting CG solver ...\n" << std::scientific << "\ndescribe A:\n"<<describe(A,vl)
<< "\ndescribe b:\n"<<describe(b,vl)<<"\ndescribe x:\n"<<describe(*x,vl)<<"\n";
// Initialization
VectorSpacePtr space = A.domain();
VectorPtr r = createMember(space);
V_V(&*r,b); apply(A,NOTRANS,*x,&*r,Scalar(-one),one); // r = -A*x + b
const ScalarMag r0_nrm = norm(*r);
if(r0_nrm==zero) return true;
VectorPtr p = createMember(space), q = createMember(space);
Scalar rho_old;
// Perform the iterations
for( int iter = 0; iter <= maxNumIters; ++iter ) {
// Check convergence and output iteration
const ScalarMag r_nrm = norm(*r);
const bool isConverged = r_nrm/r0_nrm <= tolerance;
if( iter%(maxNumIters/10+1) == 0 || iter == maxNumIters || isConverged ) {
if(out) *out << "Iter = " << iter << ", ||b-A*x||/||b-A*x0|| = " << (r_nrm/r0_nrm) << std::endl;
if( r_nrm/r0_nrm < tolerance ) return true; // Success!
}
// Compute iteration
const Scalar rho = scalarProd(*r,*r);         // <r,r>              -> rho
if(iter==0) V_V(&*p,*r);                      // r                  -> p   (iter == 0)
else Vp_V( &*p, *r, Scalar(rho/rho_old) );    // r+(rho/rho_old)*p  -> p   (iter  > 0)
apply(A,NOTRANS,*p,&*q);                      // A*p                -> q
const Scalar alpha = rho/scalarProd(*p,*q);   // rho/<p,q>          -> alpha
Vp_StV( x,   Scalar(+alpha), *p );            // +alpha*p + x       -> x
Vp_StV( &*r, Scalar(-alpha), *q );            // -alpha*q + r       -> r
rho_old = rho;                                // rho                -> rho_old (remember for next iter)
}
return false; // Failure
} // end sillyCgSolve
```

Another version of this CG algorithm is demonstrated in the below function:

```template<class Scalar>
bool silliestCgSolve(
Thyra::ConstLinearOperator<Scalar>                           const& A
,Thyra::ConstVector<Scalar>                                  const& b
,const int                                                          maxNumIters
,const typename Teuchos::ScalarTraits<Scalar>::magnitudeType        tolerance
,Thyra::Vector<Scalar>                                            & x
,std::ostream                                                     * out = NULL
)
{
// Create some typedefs and inject some names into local namespace
typedef Teuchos::ScalarTraits<Scalar> ST;
typedef typename ST::magnitudeType ScalarMag;
const Scalar one = ST::one(), zero = ST::zero();
using Thyra::VectorSpace;
using Thyra::Vector;
// Initialization of the algorithm
const VectorSpace<Scalar>     space = A.domain();
Vector<Scalar>                r = b - A*x;
ScalarMag                     r0_nrm = norm(r);
if(r0_nrm==zero) return true;
Vector<Scalar>                p(space), q(space);
Scalar                        rho_old = -one;
// Perform the iterations
for( int iter = 0; iter <= maxNumIters; ++iter ) {
// Check convergence and output iteration
const ScalarMag    r_nrm = norm(r);
const bool         isConverged = ( (r_nrm/r0_nrm) <= tolerance );
if( ( iter%(maxNumIters/10+1) == 0 || iter == maxNumIters || isConverged ) && out )
*out<<"Iter = "<<iter<<", ||b-A*x||/||b-A*x0|| = "<<(r_nrm/r0_nrm)<<std::endl;
if( r_nrm/r0_nrm < tolerance ) return true; // Success!
// Compute the iteration
const Scalar      rho = inner(r,r);
if(iter==0)       copyInto(r,p);
else              p = Scalar(rho/rho_old)*p + r;
q = A*p;
const Scalar      alpha = rho/inner(p,q);
x += Scalar(+alpha)*p;
r += Scalar(-alpha)*q;
rho_old = rho;
}
return false; // Failure
} // end silliestCgSolve
```

This above templated functions are used in the following various example implementations which use several different scalar types:

## Function Documentation

 template bool sillyCgSolve ( const Thyra::LinearOpBase< Scalar > & A, const Thyra::VectorBase< Scalar > & b, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::VectorBase< Scalar > * x, std::ostream * out = `NULL` )
 Silly little example unpreconditioned CG solver. This little function is just a silly little ANA that implements the CG (conjugate gradient) method for solving symmetric positive definite systems using the foundational Thyra operator/vector interfaces. This function is small and is meant to be looked at so study its implementation by clicking on the below link to its definition. Examples: sillyCgSolve.hpp, sillyCgSolve_mpi.cpp, and sillyCgSolve_serial.cpp. Definition at line 48 of file sillyCgSolve.hpp.

 template bool sillierCgSolve ( const Thyra::LinearOpBase< Scalar > & A_in, const Thyra::VectorBase< Scalar > & b_in, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::VectorBase< Scalar > * x_inout, std::ostream * out = `NULL` )
 Silly little example unpreconditioned CG solver (calls templated code). This little function is just a silly little ANA that implements the CG (conjugate gradient) method for solving symmetric positive definite systems using the foundational Thyra operator/vector interfaces. This function is small and is meant to be looked at so study its implementation by clicking on the below link to its definition. Examples: sillierCgSolve.hpp, and sillyCgSolve_serial.cpp. Definition at line 50 of file sillierCgSolve.hpp.

 template bool silliestCgSolve ( Thyra::ConstLinearOperator< Scalar > const & A, Thyra::ConstVector< Scalar > const & b, const int maxNumIters, const typename Teuchos::ScalarTraits< Scalar >::magnitudeType tolerance, Thyra::Vector< Scalar > & x, std::ostream * out = `NULL` )
 Silly little example unpreconditioned CG solver that uses handles. This little function is just a silly little ANA that implements the CG (conjugate gradient) method for solving symmetric positive definite systems using the foundational Thyra operator/vector interfaces. This function is small and is meant to be looked at so study its implementation by clicking on the below link to its definition. Examples: sillierCgSolve.hpp, and silliestCgSolve.hpp. Definition at line 49 of file silliestCgSolve.hpp.

Generated on Thu Sep 18 12:32:32 2008 for Thyra Operator/Vector Support by  1.3.9.1