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Tobias Wood
2023-11-29 11:12:48 +00:00
parent 9ea520fc45
commit f38e16c193
534 changed files with 103368 additions and 116934 deletions
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165
Eigen/src/IterativeLinearSolvers/ConjugateGradient.h
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@@ -13,100 +13,92 @@
// IWYU pragma: private
#include "./InternalHeaderCheck.h"
namespace Eigen {
namespace Eigen {
namespace internal {
/** \internal Low-level conjugate gradient algorithm
* \param mat The matrix A
* \param rhs The right hand side vector b
* \param x On input and initial solution, on output the computed solution.
* \param precond A preconditioner being able to efficiently solve for an
* approximation of Ax=b (regardless of b)
* \param iters On input the max number of iteration, on output the number of performed iterations.
* \param tol_error On input the tolerance error, on output an estimation of the relative error.
*/
template<typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
EIGEN_DONT_INLINE
void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x,
const Preconditioner& precond, Index& iters,
typename Dest::RealScalar& tol_error)
{
* \param mat The matrix A
* \param rhs The right hand side vector b
* \param x On input and initial solution, on output the computed solution.
* \param precond A preconditioner being able to efficiently solve for an
* approximation of Ax=b (regardless of b)
* \param iters On input the max number of iteration, on output the number of performed iterations.
* \param tol_error On input the tolerance error, on output an estimation of the relative error.
*/
template <typename MatrixType, typename Rhs, typename Dest, typename Preconditioner>
EIGEN_DONT_INLINE void conjugate_gradient(const MatrixType& mat, const Rhs& rhs, Dest& x, const Preconditioner& precond,
Index& iters, typename Dest::RealScalar& tol_error) {
typedef typename Dest::RealScalar RealScalar;
typedef typename Dest::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> VectorType;
typedef Matrix<Scalar, Dynamic, 1> VectorType;
RealScalar tol = tol_error;
Index maxIters = iters;
Index n = mat.cols();
VectorType residual = rhs - mat * x; //initial residual
VectorType residual = rhs - mat * x; // initial residual
RealScalar rhsNorm2 = rhs.squaredNorm();
if(rhsNorm2 == 0)
{
if (rhsNorm2 == 0) {
x.setZero();
iters = 0;
tol_error = 0;
return;
}
const RealScalar considerAsZero = (std::numeric_limits<RealScalar>::min)();
RealScalar threshold = numext::maxi(RealScalar(tol*tol*rhsNorm2),considerAsZero);
RealScalar threshold = numext::maxi(RealScalar(tol * tol * rhsNorm2), considerAsZero);
RealScalar residualNorm2 = residual.squaredNorm();
if (residualNorm2 < threshold)
{
if (residualNorm2 < threshold) {
iters = 0;
tol_error = numext::sqrt(residualNorm2 / rhsNorm2);
return;
}
VectorType p(n);
p = precond.solve(residual); // initial search direction
p = precond.solve(residual); // initial search direction
VectorType z(n), tmp(n);
RealScalar absNew = numext::real(residual.dot(p)); // the square of the absolute value of r scaled by invM
Index i = 0;
while(i < maxIters)
{
tmp.noalias() = mat * p; // the bottleneck of the algorithm
while (i < maxIters) {
tmp.noalias() = mat * p; // the bottleneck of the algorithm
Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
x += alpha * p; // update solution
residual -= alpha * tmp; // update residual
Scalar alpha = absNew / p.dot(tmp); // the amount we travel on dir
x += alpha * p; // update solution
residual -= alpha * tmp; // update residual
residualNorm2 = residual.squaredNorm();
if(residualNorm2 < threshold)
break;
z = precond.solve(residual); // approximately solve for "A z = residual"
if (residualNorm2 < threshold) break;
z = precond.solve(residual); // approximately solve for "A z = residual"
RealScalar absOld = absNew;
absNew = numext::real(residual.dot(z)); // update the absolute value of r
RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
p = z + beta * p; // update search direction
absNew = numext::real(residual.dot(z)); // update the absolute value of r
RealScalar beta = absNew / absOld; // calculate the Gram-Schmidt value used to create the new search direction
p = z + beta * p; // update search direction
i++;
}
tol_error = numext::sqrt(residualNorm2 / rhsNorm2);
iters = i;
}
}
} // namespace internal
template< typename MatrixType_, int UpLo_=Lower,
template <typename MatrixType_, int UpLo_ = Lower,
typename Preconditioner_ = DiagonalPreconditioner<typename MatrixType_::Scalar> >
class ConjugateGradient;
namespace internal {
template< typename MatrixType_, int UpLo_, typename Preconditioner_>
struct traits<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
{
template <typename MatrixType_, int UpLo_, typename Preconditioner_>
struct traits<ConjugateGradient<MatrixType_, UpLo_, Preconditioner_> > {
typedef MatrixType_ MatrixType;
typedef Preconditioner_ Preconditioner;
};
}
} // namespace internal
/** \ingroup IterativeLinearSolvers_Module
* \brief A conjugate gradient solver for sparse (or dense) self-adjoint problems
@@ -125,14 +117,14 @@ struct traits<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
* The maximal number of iterations and tolerance value can be controlled via the setMaxIterations()
* and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations
* and NumTraits<Scalar>::epsilon() for the tolerance.
*
*
* The tolerance corresponds to the relative residual error: |Ax-b|/|b|
*
*
* \b Performance: Even though the default value of \c UpLo_ is \c Lower, significantly higher performance is
* achieved when using a complete matrix and \b Lower|Upper as the \a UpLo_ template parameter. Moreover, in this
* case multi-threading can be exploited if the user code is compiled with OpenMP enabled.
* See \ref TopicMultiThreading for details.
*
*
* This class can be used as the direct solver classes. Here is a typical usage example:
\code
int n = 10000;
@@ -147,71 +139,67 @@ struct traits<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
// update b, and solve again
x = cg.solve(b);
\endcode
*
*
* By default the iterations start with x=0 as an initial guess of the solution.
* One can control the start using the solveWithGuess() method.
*
* ConjugateGradient can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example \endlink.
*
* ConjugateGradient can also be used in a matrix-free context, see the following \link MatrixfreeSolverExample example
\endlink.
*
* \sa class LeastSquaresConjugateGradient, class SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner
*/
template< typename MatrixType_, int UpLo_, typename Preconditioner_>
class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<MatrixType_,UpLo_,Preconditioner_> >
{
template <typename MatrixType_, int UpLo_, typename Preconditioner_>
class ConjugateGradient : public IterativeSolverBase<ConjugateGradient<MatrixType_, UpLo_, Preconditioner_> > {
typedef IterativeSolverBase<ConjugateGradient> Base;
using Base::matrix;
using Base::m_error;
using Base::m_iterations;
using Base::m_info;
using Base::m_isInitialized;
public:
using Base::m_iterations;
using Base::matrix;
public:
typedef MatrixType_ MatrixType;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef Preconditioner_ Preconditioner;
enum {
UpLo = UpLo_
};
public:
enum { UpLo = UpLo_ };
public:
/** Default constructor. */
ConjugateGradient() : Base() {}
/** Initialize the solver with matrix \a A for further \c Ax=b solving.
*
* This constructor is a shortcut for the default constructor followed
* by a call to compute().
*
* \warning this class stores a reference to the matrix A as well as some
* precomputed values that depend on it. Therefore, if \a A is changed
* this class becomes invalid. Call compute() to update it with the new
* matrix A, or modify a copy of A.
*/
template<typename MatrixDerived>
*
* This constructor is a shortcut for the default constructor followed
* by a call to compute().
*
* \warning this class stores a reference to the matrix A as well as some
* precomputed values that depend on it. Therefore, if \a A is changed
* this class becomes invalid. Call compute() to update it with the new
* matrix A, or modify a copy of A.
*/
template <typename MatrixDerived>
explicit ConjugateGradient(const EigenBase<MatrixDerived>& A) : Base(A.derived()) {}
~ConjugateGradient() {}
/** \internal */
template<typename Rhs,typename Dest>
void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const
{
template <typename Rhs, typename Dest>
void _solve_vector_with_guess_impl(const Rhs& b, Dest& x) const {
typedef typename Base::MatrixWrapper MatrixWrapper;
typedef typename Base::ActualMatrixType ActualMatrixType;
enum {
TransposeInput = (!MatrixWrapper::MatrixFree)
&& (UpLo==(Lower|Upper))
&& (!MatrixType::IsRowMajor)
&& (!NumTraits<Scalar>::IsComplex)
TransposeInput = (!MatrixWrapper::MatrixFree) && (UpLo == (Lower | Upper)) && (!MatrixType::IsRowMajor) &&
(!NumTraits<Scalar>::IsComplex)
};
typedef std::conditional_t<TransposeInput,Transpose<const ActualMatrixType>, ActualMatrixType const&> RowMajorWrapper;
EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree,UpLo==(Lower|Upper)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
typedef std::conditional_t<UpLo==(Lower|Upper),
RowMajorWrapper,
typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type
> SelfAdjointWrapper;
typedef std::conditional_t<TransposeInput, Transpose<const ActualMatrixType>, ActualMatrixType const&>
RowMajorWrapper;
EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree, UpLo == (Lower | Upper)),
MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);
typedef std::conditional_t<UpLo == (Lower | Upper), RowMajorWrapper,
typename MatrixWrapper::template ConstSelfAdjointViewReturnType<UpLo>::Type>
SelfAdjointWrapper;
m_iterations = Base::maxIterations();
m_error = Base::m_tolerance;
@@ -221,10 +209,9 @@ public:
m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;
}
protected:
protected:
};
} // end namespace Eigen
} // end namespace Eigen
#endif // EIGEN_CONJUGATE_GRADIENT_H
#endif // EIGEN_CONJUGATE_GRADIENT_H