Define some often used mathematical functions. More...

#include <algorithm>
#include <numeric>
#include <cmath>
#include <utility>
#include <dune/common/typetraits.hh>
#include <dune/common/fvector.hh>
#include <dune/common/fmatrix.hh>
#include <dune/common/dynmatrix.hh>
#include <dune/common/float_cmp.hh>

Classes
struct	Dumux::InterpolationPolicy::Linear
	interpolate linearly between two given values More...

struct	Dumux::InterpolationPolicy::LinearTable
	interpolate linearly in a piecewise linear function (tabularized function) More...

Namespaces
namespace	Dumux

namespace	Dumux::InterpolationPolicy
	forward declaration of the linear interpolation policy (default)

Functions
template<class Scalar >
constexpr Scalar	Dumux::arithmeticMean (Scalar x, Scalar y, Scalar wx=1.0, Scalar wy=1.0) noexcept
	Calculate the (weighted) arithmetic mean of two scalar values. More...

template<class Scalar >
constexpr Scalar	Dumux::harmonicMean (Scalar x, Scalar y, Scalar wx=1.0, Scalar wy=1.0) noexcept
	Calculate the (weighted) harmonic mean of two scalar values. More...

template<class Scalar >
Scalar	Dumux::geometricMean (Scalar x, Scalar y) noexcept
	Calculate the geometric mean of two scalar values. More...

template<class Scalar , int m, int n>
void	Dumux::harmonicMeanMatrix (Dune::FieldMatrix< Scalar, m, n > &K, const Dune::FieldMatrix< Scalar, m, n > &Ki, const Dune::FieldMatrix< Scalar, m, n > &Kj)
	Calculate the harmonic mean of a fixed-size matrix. More...

template<class Scalar >
Scalar	Dumux::smoothMin (const Scalar a, const Scalar b, const Scalar k)
	A smoothed minimum function (using cubic interpolation) More...

template<class Scalar >
Scalar	Dumux::smoothMax (const Scalar a, const Scalar b, const Scalar k)
	A smoothed maximum function (using cubic interpolation) More...

template<class Scalar , class SolContainer >
int	Dumux::invertLinearPolynomial (SolContainer &sol, Scalar a, Scalar b)
	Invert a linear polynomial analytically. More...

template<class Scalar , class SolContainer >
int	Dumux::invertQuadraticPolynomial (SolContainer &sol, Scalar a, Scalar b, Scalar c)
	Invert a quadratic polynomial analytically. More...

template<class Scalar , class SolContainer >
int	Dumux::invertCubicPolynomial (SolContainer *sol, Scalar a, Scalar b, Scalar c, Scalar d, std::size_t numPostProcessIterations=1)
	Invert a cubic polynomial analytically. More...

template<class Scalar , int dim>
bool	Dumux::isLarger (const Dune::FieldVector< Scalar, dim > &pos, const Dune::FieldVector< Scalar, dim > &smallerVec)
	Comparison of two position vectors. More...

template<class Scalar , int dim>
bool	Dumux::isSmaller (const Dune::FieldVector< Scalar, dim > &pos, const Dune::FieldVector< Scalar, dim > &largerVec)
	Comparison of two position vectors. More...

template<class Scalar , int dim>
bool	Dumux::isBetween (const Dune::FieldVector< Scalar, dim > &pos, const Dune::FieldVector< Scalar, dim > &smallerVec, const Dune::FieldVector< Scalar, dim > &largerVec)
	Comparison of three position vectors. More...

template<class Policy = InterpolationPolicy::Linear, class Scalar , class ... Parameter>
Scalar	Dumux::interpolate (Scalar ip, Parameter &&... params)
	a generic function to interpolate given a set of parameters and an interpolation point More...

template<class Scalar >
std::vector< Scalar >	Dumux::linspace (const Scalar begin, const Scalar end, std::size_t samples, bool endPoint=true)
	Generates linearly spaced vectors. More...

template<class Scalar >
Scalar	Dumux::antoine (Scalar temperature, Scalar A, Scalar B, Scalar C)
	Evaluates the Antoine equation used to calculate the vapour pressure of various liquids. More...

template<class ValueType >
constexpr int	Dumux::sign (const ValueType &value) noexcept
	Sign or signum function. More...

template<class Scalar >
Dune::FieldVector< Scalar, 3 >	Dumux::crossProduct (const Dune::FieldVector< Scalar, 3 > &vec1, const Dune::FieldVector< Scalar, 3 > &vec2)
	Cross product of two vectors in three-dimensional Euclidean space. More...

template<class Scalar >
Scalar	Dumux::crossProduct (const Dune::FieldVector< Scalar, 2 > &vec1, const Dune::FieldVector< Scalar, 2 > &vec2)
	Cross product of two vectors in two-dimensional Euclidean space retuning scalar. More...

template<class Scalar >
Scalar	Dumux::tripleProduct (const Dune::FieldVector< Scalar, 3 > &vec1, const Dune::FieldVector< Scalar, 3 > &vec2, const Dune::FieldVector< Scalar, 3 > &vec3)
	Triple product of three vectors in three-dimensional Euclidean space retuning scalar. More...

template<class Scalar , int m, int n>
Dune::FieldMatrix< Scalar, n, m >	Dumux::getTransposed (const Dune::FieldMatrix< Scalar, m, n > &M)
	Transpose a FieldMatrix. More...

template<class Scalar >
Dune::DynamicMatrix< Scalar >	Dumux::getTransposed (const Dune::DynamicMatrix< Scalar > &M)
	Transpose a DynamicMatrix. More...

template<class Scalar >
Dune::DynamicMatrix< Scalar >	Dumux::multiplyMatrices (const Dune::DynamicMatrix< Scalar > &M1, const Dune::DynamicMatrix< Scalar > &M2)
	Multiply two dynamic matrices. More...

template<class Scalar , int rows1, int cols1, int cols2>
Dune::FieldMatrix< Scalar, rows1, cols2 >	Dumux::multiplyMatrices (const Dune::FieldMatrix< Scalar, rows1, cols1 > &M1, const Dune::FieldMatrix< Scalar, cols1, cols2 > &M2)
	Multiply two field matrices. More...

template<class MatrixType >
Dune::DenseMatrix< MatrixType >::field_type	Dumux::trace (const Dune::DenseMatrix< MatrixType > &M)
	Trace of a dense matrix. More...

template<class MAT , class V >
Dune::DenseVector< V >::derived_type	Dumux::mv (const Dune::DenseMatrix< MAT > &M, const Dune::DenseVector< V > &v)
	Returns the result of the projection of a vector v with a Matrix M. More...

template<class FieldScalar , class V >
std::enable_if_t< Dune::IsNumber< FieldScalar >::value, typename Dune::DenseVector< V >::derived_type >	Dumux::mv (const FieldScalar m, const Dune::DenseVector< V > &v)
	Returns the result of a vector v multiplied by a scalar m. More...

template<class V1 , class MAT , class V2 >
Dune::DenseMatrix< MAT >::value_type	Dumux::vtmv (const Dune::DenseVector< V1 > &v1, const Dune::DenseMatrix< MAT > &M, const Dune::DenseVector< V2 > &v2)
	Evaluates the scalar product of a vector v2, projected by a matrix M, with a vector v1. More...

template<class V1 , class FieldScalar , class V2 >
std::enable_if_t< Dune::IsNumber< FieldScalar >::value, FieldScalar >	Dumux::vtmv (const Dune::DenseVector< V1 > &v1, const FieldScalar m, const Dune::DenseVector< V2 > &v2)
	Evaluates the scalar product of a vector v2, scaled by a scalar m, with a vector v1. More...

template<class Scalar >
std::array< Scalar, 2 >	Dumux::linearRegression (const std::vector< Scalar > &x, const std::vector< Scalar > &y)
	Returns the [intercept, slope] of the regression line fitted to a set of (x, y) data points. More...

Include dependency graph for math.hh:

Classes

Namespaces

Functions