cg_blas.h (flens/examples/cg

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#ifndef FLENS_EXAMPLES_CG_BLAS_H

#define FLENS_EXAMPLES_CG_BLAS_H 1

#include <flens/flens.h>

#include <cxxstd/limits.h>

template <typename MA, typename VX, typename VB>

int

cg(const MA &A, const VB &b, VX &&x,

   double tol = std::numeric_limits<double>::epsilon(),

   int    maxIterations = std::numeric_limits<int>::max())

{

    using namespace flens;

    typedef typename VB::ElementType  ElementType;

    typedef typename VB::IndexType    IndexType;

    typedef typename VB::NoView       VectorType;

    ElementType  alpha, beta, rNormSquare, rNormSquarePrev;

    VectorType   Ap, r, p;

    const ElementType  Zero(0), One(1);

///

/// `r = b - A*x;`

///

    blas::copy(b, r);

    blas::mv(NoTrans, -One, A, x, One, r);

///

/// `p = r;`

///

    blas::copy(r, p);

///

/// `rNormSquare = r*r;`

///

    rNormSquare = blas::dot(r, r);

    for (int k=1; k<=maxIterations; ++k) {

        if (sqrt(rNormSquare)<=tol) {

            return k-1;

        }

///

///     `Ap = A*p;`

///

        blas::mv(NoTrans, One, A, p, Zero, Ap);

///

///     `alpha = rNormSquare/(p * Ap);`

///

        alpha = rNormSquare/blas::dot(p, Ap);

///

///     `x += alpha*p;`

///

        blas::axpy(alpha, p, x);

///

///     `r -= alpha*Ap;`

///

        blas::axpy(-alpha, Ap, r);

        rNormSquarePrev = rNormSquare;

///

///     `rNormSquare = r*r;`

///

        rNormSquare = blas::dot(r, r);

        beta = rNormSquare/rNormSquarePrev;

///

///     `p = beta*p + r;`

///

        blas::scal(beta, p);

        blas::axpy(One, r, p);

    }

    return maxIterations;

}

#endif // FLENS_EXAMPLES_CG_BLAS_H