Detailed Description

Contains all mathematical functionality used in OpenGeoSys, from defining a vector or calculating a norm to integration schemes and matrix preconditioners.

See also: detail

Namespaces
	detail

	details

	KelvinVector

	LinAlg

	Nonlinear

	ODE

Classes
class	PiecewiseLinearMonotonicCurve
	Class for strong monotonic curves. More...

class	TemplatePoint
	class-template for points can be instantiated by a numeric type. More...

struct	GaussLegendre

struct	GaussLegendrePyramid

struct	GaussLegendrePyramid< 2 >

struct	GaussLegendrePyramid< 3 >

struct	GaussLegendreTet

struct	GaussLegendreTet< 2 >

struct	GaussLegendreTet< 3 >

struct	GaussLegendreTri

struct	GaussLegendreTri< 2 >

struct	GaussLegendreTri< 3 >

struct	GaussLegendreTri< 4 >

struct	WeightedSum

class	LinearIntervalInterpolation
	Class (template) LinearIntervalInterpolation is a functional object performing an interval mapping $f: [a,b] \to [c,d]$ . More...

class	PiecewiseLinearInterpolation

class	EigenLinearSolverBase

class	EigenLinearSolver

class	EigenMatrix

struct	SetMatrixSparsity< EigenMatrix, SPARSITY_PATTERN >
	Sets the sparsity pattern of the underlying EigenMatrix. More...

struct	EigenOption
	Option for Eigen sparse solver. More...

class	EigenVector
	Global vector based on Eigen vector. More...

class	EigenLisLinearSolver

class	LisLinearSolver
	Linear solver using Lis (http://www.ssisc.org/lis/) More...

class	LisMatrix
	LisMatrix is a wrapper class for matrix types of the linear iterative solvers library. More...

struct	SetMatrixSparsity< LisMatrix, SPARSITY_PATTERN >
	Sets the sparsity pattern of the underlying LisMatrix. More...

struct	LisOption

class	LisVector
	Lis vector wrapper class. More...

struct	MatrixSpecifications

struct	MatrixVectorTraits

class	PETScLinearSolver

class	PETScMatrix
	Wrapper class for PETSc matrix routines for matrix. More...

struct	PETScMatrixOption
	This a struct data containing the configuration information to create a PETSc type matrix. More...

class	PETScVector
	Wrapper class for PETSc vector. More...

struct	RowColumnIndices

struct	SetMatrixSparsity

class	Point3dWithID

class	TemplateWeightedPoint

Typedefs
using	Point3d = MathLib::TemplatePoint< double, 3 >

template<typename IndexType >
using	SparsityPattern = std::vector< IndexType >
	A vector telling how many nonzeros there are in each global matrix row. More...

using	WeightedPoint1D = TemplateWeightedPoint< double, double, 1 >

using	WeightedPoint2D = TemplateWeightedPoint< double, double, 2 >

using	WeightedPoint3D = TemplateWeightedPoint< double, double, 3 >

Enumerations
enum	TriangleTest { GAUSS , BARYCENTRIC }

enum class	VecNormType { NORM1 , NORM2 , INFINITY_N , INVALID }
	Norm type. Not declared as class type in order to use the members as integers. More...

Functions
template<typename CurveType >
std::unique_ptr< CurveType >	createPiecewiseLinearCurve (BaseLib::ConfigTree const &config)

double	orientation3d (MathLib::Point3d const &p, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c)

double	calcTetrahedronVolume (MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c, MathLib::Point3d const &d)

double	calcTriangleArea (MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c)

bool	isPointInTetrahedron (MathLib::Point3d const &p, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c, MathLib::Point3d const &d, double eps)

bool	isPointInTriangle (MathLib::Point3d const &p, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c, double eps_pnt_out_of_plane, double eps_pnt_out_of_tri, MathLib::TriangleTest algorithm)

bool	gaussPointInTriangle (MathLib::Point3d const &q, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c, double eps_pnt_out_of_plane, double eps_pnt_out_of_tri)

bool	barycentricPointInTriangle (MathLib::Point3d const &p, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c, double eps_pnt_out_of_plane, double eps_pnt_out_of_tri)

bool	isPointInTriangleXY (MathLib::Point3d const &p, MathLib::Point3d const &a, MathLib::Point3d const &b, MathLib::Point3d const &c)

bool	dividedByPlane (const MathLib::Point3d &a, const MathLib::Point3d &b, const MathLib::Point3d &c, const MathLib::Point3d &d)

bool	isCoplanar (const MathLib::Point3d &a, const MathLib::Point3d &b, const MathLib::Point3d &c, const MathLib::Point3d &d)
	Checks if the four given points are located on a plane. More...

static std::array< std::array< double, 3 >, GaussLegendreTet< 3 >::NPoints >	initGLTet3X ()

template<typename Matrix >
Eigen::Map< Matrix >	createZeroedMatrix (std::vector< double > &data, Eigen::MatrixXd::Index rows, Eigen::MatrixXd::Index cols)

template<typename Matrix >
Eigen::Map< const Matrix >	toMatrix (std::vector< double > const &data, Eigen::MatrixXd::Index rows, Eigen::MatrixXd::Index cols)

template<typename Matrix >
Eigen::Map< Matrix >	toMatrix (std::vector< double > &data, Eigen::MatrixXd::Index rows, Eigen::MatrixXd::Index cols)

template<typename Vector >
Eigen::Map< Vector >	createZeroedVector (std::vector< double > &data, Eigen::VectorXd::Index size)

template<typename Vector >
Eigen::Map< const Vector >	toVector (std::vector< double > const &data, Eigen::VectorXd::Index size)
	Creates an Eigen mapped vector from the given data vector. More...

template<typename Vector >
Eigen::Map< Vector >	toVector (std::vector< double > &data, Eigen::VectorXd::Index size)
	Creates an Eigen mapped vector from the given data vector. More...

Eigen::Map< const Eigen::VectorXd >	toVector (std::vector< double > const &data)

Eigen::Map< Eigen::VectorXd >	toVector (std::vector< double > &data)

void	applyKnownSolution (EigenMatrix &A, EigenVector &b, EigenVector &, const std::vector< EigenMatrix::IndexType > &vec_knownX_id, const std::vector< double > &vec_knownX_x, double)

template<typename MAT_T >
bool	finalizeMatrixAssembly (MAT_T &)

template<typename VEC_T >
void	finalizeVectorAssembly (VEC_T &)
	General function to finalize the vector assembly. More...

std::string	convertVecNormTypeToString (VecNormType normType)
	convert VecNormType to string More...

VecNormType	convertStringToVecNormType (const std::string &str)
	convert string to VecNormType More...

void	ignoreOtherLinearSolvers (const BaseLib::ConfigTree &config, const std::string &solver_name)

bool	checkLisError (int err)

bool	finalizeMatrixAssembly (LisMatrix &mat)
	finish assembly to make this matrix be ready for use More...

	SPECIALIZE_MATRIX_VECTOR_TRAITS (PETScMatrix, PETScMatrix::IndexType)

	SPECIALIZE_MATRIX_VECTOR_TRAITS (PETScVector, PETScVector::IndexType)

bool	finalizeMatrixAssembly (PETScMatrix &mat, const MatAssemblyType asm_type=MAT_FINAL_ASSEMBLY)
	General interface for the matrix assembly. More...

void	applyKnownSolution (PETScMatrix &A, PETScVector &b, PETScVector &x, const std::vector< PetscInt > &vec_knownX_id, const std::vector< PetscScalar > &vec_knownX_x)
	apply known solutions to a system of linear equations More...

void	finalizeVectorAssembly (PETScVector &vec)
	Function to finalize the vector assembly. More...

template<typename MATRIX , typename SPARSITY_PATTERN >
void	setMatrixSparsity (MATRIX &matrix, SPARSITY_PATTERN const &sparsity_pattern)

void	setVector (PETScVector &v, std::initializer_list< double > values)

void	setVector (PETScVector &v, MatrixVectorTraits< PETScVector >::Index const index, double const value)

void	setMatrix (PETScMatrix &m, std::initializer_list< double > values)

void	setMatrix (PETScMatrix &m, Eigen::MatrixXd const &tmp)

void	addToMatrix (PETScMatrix &m, std::initializer_list< double > values)

double	calcProjPntToLineAndDists (Point3d const &pp, Point3d const &pa, Point3d const &pb, double &lambda, double &d0)

double	getAngle (Point3d const &p0, Point3d const &p1, Point3d const &p2)

template<typename MATRIX >
MathLib::Point3d	operator* (MATRIX const &mat, MathLib::Point3d const &p)

double	sqrDist (MathLib::Point3d const &p0, MathLib::Point3d const &p1)

double	sqrDist2d (MathLib::Point3d const &p0, MathLib::Point3d const &p1)

template<typename T , std::size_t DIM>
bool	operator== (TemplatePoint< T, DIM > const &a, TemplatePoint< T, DIM > const &b)

template<typename T , std::size_t DIM>
bool	operator< (TemplatePoint< T, DIM > const &a, TemplatePoint< T, DIM > const &b)

template<typename T , std::size_t DIM>
bool	lessEq (TemplatePoint< T, DIM > const &a, TemplatePoint< T, DIM > const &b, double eps=std::numeric_limits< double >::epsilon())

template<typename T , std::size_t DIM>
std::ostream &	operator<< (std::ostream &os, const TemplatePoint< T, DIM > &p)

template<typename T , std::size_t DIM>
std::istream &	operator>> (std::istream &is, TemplatePoint< T, DIM > &p)

Variables
static const double	p = 0.1126879257180162 / 6.

static const double	q = 0.0734930431163619 / 6.

static const double	r = 0.0425460207770812 / 6.

const Point3d	ORIGIN {{{0.0, 0.0, 0.0}}}

Typedef Documentation

◆ Point3d

typedef MathLib::TemplatePoint< double, 3 > MathLib::Point3d

Definition at line 19 of file GeometricBasics.h.

◆ SparsityPattern

template<typename IndexType >

using MathLib::SparsityPattern = typedef std::vector<IndexType>

A vector telling how many nonzeros there are in each global matrix row.

Definition at line 19 of file SparsityPattern.h.

◆ WeightedPoint1D

using MathLib::WeightedPoint1D = typedef TemplateWeightedPoint<double, double, 1>

Definition at line 34 of file TemplateWeightedPoint.h.

◆ WeightedPoint2D

using MathLib::WeightedPoint2D = typedef TemplateWeightedPoint<double, double, 2>

Definition at line 35 of file TemplateWeightedPoint.h.

◆ WeightedPoint3D

using MathLib::WeightedPoint3D = typedef TemplateWeightedPoint<double, double, 3>

Definition at line 36 of file TemplateWeightedPoint.h.

Enumeration Type Documentation

◆ TriangleTest

enum MathLib::TriangleTest

Enumerator
GAUSS
BARYCENTRIC

Definition at line 21 of file GeometricBasics.h.

 {
     GAUSS, BARYCENTRIC
 };

◆ VecNormType

enum MathLib::VecNormType

strong

Norm type. Not declared as class type in order to use the members as integers.

Enumerator
NORM1	$\sum_i \|x_i\|$
NORM2	$\sqrt(\sum_i (x_i)^2)$
INFINITY_N	$\mathrm{max}_i \|x_i\|$
INVALID

Definition at line 21 of file LinAlgEnums.h.

 {
     NORM1,        
     NORM2,        
     INFINITY_N,    
     INVALID
 };

Function Documentation

◆ addToMatrix()

void MathLib::addToMatrix	(	PETScMatrix &	m,
		std::initializer_list< double >	values
	)

Definition at line 71 of file UnifiedMatrixSetters.cpp.

 {
     using IndexType = PETScMatrix::IndexType;
  
     auto const rows = m.getNumberOfRows();
     auto const cols = m.getNumberOfColumns();
  
     assert((IndexType)values.size() == rows * cols);
  
     Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor> tmp(
         rows, cols);
  
     auto it = values.begin();
     for (IndexType r = 0; r < rows; ++r)
     {
         for (IndexType c = 0; c < cols; ++c)
         {
             tmp(r, c) = *(it++);
         }
     }
  
     std::vector<IndexType> row_idcs(rows);
     std::vector<IndexType> col_idcs(cols);
  
     std::iota(row_idcs.begin(), row_idcs.end(), 0);
     std::iota(col_idcs.begin(), col_idcs.end(), 0);
  
     m.add(row_idcs, col_idcs, tmp);
 }

References MathLib::PETScMatrix::add(), MaterialPropertyLib::c, MathLib::PETScMatrix::getNumberOfColumns(), MathLib::PETScMatrix::getNumberOfRows(), and r.

Referenced by setMatrix().

◆ applyKnownSolution() [1/2]

void MathLib::applyKnownSolution	(	EigenMatrix &	A,
		EigenVector &	b,
		EigenVector &	,
		const std::vector< EigenMatrix::IndexType > &	vec_knownX_id,
		const std::vector< double > &	vec_knownX_x,
		double	penalty_scaling = `1e+10`
	)

apply known solutions to a system of linear equations

Parameters

A	Coefficient matrix
b	RHS vector
vec_knownX_id	a vector of known solution entry IDs
vec_knownX_x	a vector of known solutions
penalty_scaling	value for scaling some matrix and right hand side entries to enforce some conditions, value ignored in the current implementation

Definition at line 17 of file EigenTools.cpp.

 {
     using SpMat = EigenMatrix::RawMatrixType;
     static_assert(SpMat::IsRowMajor, "matrix is assumed to be row major!");
  
     auto& A_eigen = A.getRawMatrix();
     auto& b_eigen = b.getRawVector();
  
     // A_eigen(k, j) = 0.
     // set row to zero
     for (auto row_id : vec_knownX_id)
     {
         for (SpMat::InnerIterator it(A_eigen, row_id); it; ++it)
         {
             if (it.col() != decltype(it.col())(row_id))
             {
                 it.valueRef() = 0.0;
             }
         }
     }
  
     SpMat AT = A_eigen.transpose();
  
     // Reserve space for at least one value (on the diagonal). For deactivated
     // subdomains some rows and columns might end empty (in the A matrix) and so
     // no space is reserved for the Dirichlet conditions in the transposed
     // matrix. Then the coeffRef call will do costly reallocations.
     AT.reserve(Eigen::VectorXi::Constant(A_eigen.rows(), 1));
  
     for (std::size_t ix = 0; ix < vec_knownX_id.size(); ix++)
     {
         SpMat::Index const row_id = vec_knownX_id[ix];
         auto const x = vec_knownX_x[ix];
  
         // b_i -= A_eigen(i,k)*val, i!=k
         // set column to zero, subtract from rhs
         for (SpMat::InnerIterator it(AT, row_id); it; ++it)
         {
             if (it.col() == row_id)
             {
                 continue;
             }
  
             b_eigen[it.col()] -= it.value() * x;
             it.valueRef() = 0.0;
         }
  
         auto& c = AT.coeffRef(row_id, row_id);
         if (c != 0.0)
         {
             b_eigen[row_id] = x * c;
         }
         else
         {
             b_eigen[row_id] = x;
             c = 1.0;
         }
     }
  
     A_eigen = AT.transpose();
 }

References MaterialPropertyLib::c, MathLib::EigenMatrix::getRawMatrix(), and MathLib::EigenVector::getRawVector().

Referenced by NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Newton >::applyKnownSolutionsNewton(), and NumLib::TimeDiscretizedODESystem< ODESystemTag::FirstOrderImplicitQuasilinear, NonlinearSolverTag::Picard >::applyKnownSolutionsPicard().

◆ applyKnownSolution() [2/2]

void MathLib::applyKnownSolution	(	PETScMatrix &	A,
		PETScVector &	b,
		PETScVector &	x,
		const std::vector< PetscInt > &	vec_knownX_id,
		const std::vector< PetscScalar > &	vec_knownX_x
	)

apply known solutions to a system of linear equations

Parameters

A	Coefficient matrix
b	RHS vector
x	Solution vector
vec_knownX_id	A vector of known solution entry IDs
vec_knownX_x	A vector of known solutions

Definition at line 21 of file PETScTools.cpp.

 {
     A.finalizeAssembly();
  
     A.setRowsColumnsZero(vec_knownX_id);
     A.finalizeAssembly();
  
     x.finalizeAssembly();
     b.finalizeAssembly();
     if (vec_knownX_id.size() > 0)
     {
         x.set(vec_knownX_id, vec_knownX_x);
         b.set(vec_knownX_id, vec_knownX_x);
     }
  
     x.finalizeAssembly();
     b.finalizeAssembly();
 }

References MathLib::PETScVector::finalizeAssembly(), MathLib::PETScMatrix::finalizeAssembly(), MathLib::PETScVector::set(), and MathLib::PETScMatrix::setRowsColumnsZero().

◆ barycentricPointInTriangle()

bool MathLib::barycentricPointInTriangle	(	MathLib::Point3d const &	p,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c,
		double	eps_pnt_out_of_plane = `std::numeric_limits< float >::epsilon()`,
		double	eps_pnt_out_of_tri = `std::numeric_limits< float >::epsilon()`
	)

Tests if the given point p is within the triangle, defined by its edge nodes a, b and c. Using two eps-values it is possible to test an 'epsilon' neighbourhood around the triangle as well as an 'epsilon' outside the triangles plane. Algorithm based on "Fundamentals of Computer Graphics" by Peter Shirley.

Parameters

p	test point
a	edge node of triangle
b	edge node of triangle
c	edge node of triangle
eps_pnt_out_of_plane	eps allowing for p to be slightly off the plane spanned by abc
eps_pnt_out_of_tri	eps allowing for p to be slightly off outside of abc

Returns: true if the test point p is within the 'epsilon'-neighbourhood of the triangle

Definition at line 162 of file GeometricBasics.cpp.

 {
     if (std::abs(MathLib::orientation3d(p, a, b, c)) > eps_pnt_out_of_plane)
     {
         return false;
     }
  
     auto const vp = Eigen::Map<Eigen::Vector3d const>(p.getCoords());
     auto const va = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const vb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const vc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
     Eigen::Vector3d const pa = va - vp;
     Eigen::Vector3d const pb = vb - vp;
     Eigen::Vector3d const pc = vc - vp;
     double const area_x_2(calcTriangleArea(a, b, c) * 2);
  
     double const alpha((pb.cross(pc).norm()) / area_x_2);
     if (alpha < -eps_pnt_out_of_tri || alpha > 1 + eps_pnt_out_of_tri)
     {
         return false;
     }
     double const beta((pc.cross(pa).norm()) / area_x_2);
     if (beta < -eps_pnt_out_of_tri || beta > 1 + eps_pnt_out_of_tri)
     {
         return false;
     }
     double const gamma(1 - alpha - beta);
     return !(gamma < -eps_pnt_out_of_tri || gamma > 1 + eps_pnt_out_of_tri);
 }

References MaterialPropertyLib::alpha, MaterialPropertyLib::beta, MaterialPropertyLib::c, calcTriangleArea(), MathLib::TemplatePoint< T, DIM >::getCoords(), orientation3d(), and p.

Referenced by isPointInTriangle().

◆ calcProjPntToLineAndDists()

double MathLib::calcProjPntToLineAndDists	(	MathLib::Point3d const &	pp,
		MathLib::Point3d const &	pa,
		MathLib::Point3d const &	pb,
		double &	lambda,
		double &	d0
	)

calcProjPntToLineAndDists computes the orthogonal projection of a point p to the line described by the points a and b, $g(\lambda) = a + \lambda (b - a)$ , the distance between p and the projected point and the distances between the projected point and the end points pa, pb of the line

Parameters

pp	the (mesh) point
pa	first point of line
pb	second point of line
lambda	the projected point described by the line equation above
d0	distance to the line point a

Returns: the distance between pp and the orthogonal projection of pp

Definition at line 19 of file MathTools.cpp.

 {
     auto const a = Eigen::Map<Eigen::Vector3d const>(pa.getCoords());
     auto const b = Eigen::Map<Eigen::Vector3d const>(pb.getCoords());
     auto const p = Eigen::Map<Eigen::Vector3d const>(pp.getCoords());
  
     // g(lambda) = a + lambda v, v = b-a
     Eigen::Vector3d const v = b - a;
  
     // orthogonal projection: (p - g(lambda))^T * v = 0
     // <=> (a-p - lambda (b-a))^T * (b-a) = 0
     // <=> (a-p)^T * (b-a) = lambda (b-a)^T ) (b-a)
     lambda = (((p - a).transpose() * v) / v.squaredNorm())(0, 0);
  
     // compute projected point
     Eigen::Vector3d const proj_pnt = a + lambda * v;
  
     d0 = (proj_pnt - a).norm();
  
     return (p - proj_pnt).norm();
 }

References MathLib::TemplatePoint< T, DIM >::getCoords(), MathLib::LinAlg::norm(), and p.

Referenced by GeoLib::Polyline::getDistanceAlongPolyline(), and MeshLib::LineRule2::isPntInElement().

◆ calcTetrahedronVolume()

double MathLib::calcTetrahedronVolume	(	MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c,
		MathLib::Point3d const &	d
	)

Calculates the volume of a tetrahedron. The formula is V=1/6*|a(b x c)| with a=x1->x2, b=x1->x3 and c=x1->x4.

Definition at line 35 of file GeometricBasics.cpp.

 {
     auto const va = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const vb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const vc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
     auto const vd = Eigen::Map<Eigen::Vector3d const>(d.getCoords());
     Eigen::Vector3d const w = vb - va;
     Eigen::Vector3d const u = vc - va;
     Eigen::Vector3d const v = vd - va;
     return std::abs(u.cross(v).dot(w)) / 6.0;
 }

References MaterialPropertyLib::c, and MathLib::TemplatePoint< T, DIM >::getCoords().

Referenced by MeshLib::HexRule8::computeVolume(), MeshLib::PrismRule6::computeVolume(), MeshLib::PyramidRule5::computeVolume(), and MeshLib::TetRule4::computeVolume().

◆ calcTriangleArea()

double MathLib::calcTriangleArea	(	MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c
	)

Calculates the area of the triangle defined by its edge nodes a, b and c. The formula is $A= \frac{1}{2} \cdot |u \times v|$ , i.e. half of the area of the parallelogram specified by the vectors $u=b-a$ and $v=c-a$ .

Definition at line 50 of file GeometricBasics.cpp.

 {
     auto const va = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const vb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const vc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
     Eigen::Vector3d const u = vc - va;
     Eigen::Vector3d const v = vb - va;
     Eigen::Vector3d const w = u.cross(v);
     return 0.5 * w.norm();
 }

References MaterialPropertyLib::c, and MathLib::TemplatePoint< T, DIM >::getCoords().

Referenced by barycentricPointInTriangle(), MeshLib::QuadRule4::computeVolume(), MeshLib::TriRule3::computeVolume(), and GeoLib::IO::TINInterface::readTIN().

◆ checkLisError()

bool MathLib::checkLisError ( int err )

inline

check Lis error codes

Parameters

err	Lis error code

Returns: success or not

Definition at line 32 of file LisCheck.h.

 {
     bool ok = (err == LIS_SUCCESS);
     if (!ok) {
         ERR("***ERROR: Lis error code = {:d}", err);
     }
     return ok;
 }

References ERR().

Referenced by MathLib::LisMatrix::LisMatrix(), MathLib::LisMatrix::~LisMatrix(), MathLib::SetMatrixSparsity< LisMatrix, SPARSITY_PATTERN >::operator()(), MathLib::LisMatrix::setZero(), MathLib::LisVector::size(), and MathLib::LisLinearSolver::solve().

◆ convertStringToVecNormType()

VecNormType MathLib::convertStringToVecNormType ( const std::string & str )

convert string to VecNormType

Definition at line 32 of file LinAlgEnums.cpp.

 {
     if (str == "NORM1")
     {
         return VecNormType::NORM1;
     }
     if (str == "NORM2")
     {
         return VecNormType::NORM2;
     }
     if (str == "INFINITY_N")
     {
         return VecNormType::INFINITY_N;
     }
     return VecNormType::INVALID;
 }

References INFINITY_N, INVALID, NORM1, and NORM2.

Referenced by NumLib::createConvergenceCriterionDeltaX(), NumLib::createConvergenceCriterionPerComponentDeltaX(), NumLib::createConvergenceCriterionPerComponentResidual(), and NumLib::createConvergenceCriterionResidual().

◆ convertVecNormTypeToString()

std::string MathLib::convertVecNormTypeToString ( VecNormType normType )

convert VecNormType to string

Definition at line 17 of file LinAlgEnums.cpp.

 {
     switch (normType)
     {
         case VecNormType::NORM1:
             return "NORM1";
         case VecNormType::NORM2:
             return "NORM2";
         case VecNormType::INFINITY_N:
             return "INFINITY_N";
         default:
             return "INVALID";
     }
 }

References INFINITY_N, NORM1, and NORM2.

◆ createPiecewiseLinearCurve()

template<typename CurveType >

std::unique_ptr< CurveType > MathLib::createPiecewiseLinearCurve ( BaseLib::ConfigTree const & config )

Create a curve

Parameters

config ConfigTree object has a tag of <curve>

Input File Parameter:: curve__coords

Input File Parameter:: curve__values

Definition at line 21 of file CreatePiecewiseLinearCurve-impl.h.

 {
     auto x =
         config.getConfigParameter<std::vector<double>>("coords");
     auto y =
         config.getConfigParameter<std::vector<double>>("values");
  
     if (x.empty() || y.empty())
     {
         OGS_FATAL("The given coordinates or values vector is empty.");
     }
     if (x.size() != y.size())
     {
         OGS_FATAL(
             "The given coordinates and values vector sizes are "
             "different.");
     }
     return std::make_unique<CurveType>(std::move(x), std::move(y));
 }

References BaseLib::ConfigTree::getConfigParameter(), and OGS_FATAL.

Referenced by MaterialLib::PorousMedium::createCapillaryPressureModel(), MaterialLib::PorousMedium::createRelativePermeabilityModel(), and ProjectData::parseCurves().

◆ createZeroedMatrix()

template<typename Matrix >

Eigen::Map< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > > MathLib::createZeroedMatrix	(	std::vector< double > &	data,
		Eigen::MatrixXd::Index	rows,
		Eigen::MatrixXd::Index	cols
	)

inline

Creates an Eigen mapped matrix having its entries stored in the given data vector.

Returns: An Eigen mapped matrix of the given size. All values of the matrix are set to zero.

Precondition: The passed data vector must have zero size.

Postcondition: The data has size rows * cols.

Note: The data vector will have the same storage order (row or column major) as the requested matrix type.

Creates an Eigen mapped matrix having its entries stored in the given data vector.

This is a convenience method which makes the specification of dynamically allocated Eigen matrices as return type easier.

Definition at line 32 of file EigenMapTools.h.

 {
     static_assert(Matrix::IsRowMajor || Matrix::IsVectorAtCompileTime,
                   "The default storage order in OGS is row major storage for "
                   "dense matrices.");
     assert(Matrix::RowsAtCompileTime == Eigen::Dynamic ||
            Matrix::RowsAtCompileTime == rows);
     assert(Matrix::ColsAtCompileTime == Eigen::Dynamic ||
            Matrix::ColsAtCompileTime == cols);
     assert(data.empty());  // in order that resize fills the vector with zeros.
  
     data.resize(rows * cols);
     return {data.data(), rows, cols};
 }

◆ createZeroedVector()

template<typename Vector >

Eigen::Map<Vector> MathLib::createZeroedVector	(	std::vector< double > &	data,
		Eigen::VectorXd::Index	size
	)

Creates an Eigen mapped vector having its entries stored in the given data vector.

Returns: An Eigen mapped vector of the given size. All values of the vector are set to zero.

Precondition: The passed data vector must have zero size.

Postcondition: The data has size size.

Definition at line 153 of file EigenMapTools.h.

 {
     static_assert(Vector::IsVectorAtCompileTime, "A vector type is required.");
     assert(Vector::SizeAtCompileTime == Eigen::Dynamic ||
            Vector::SizeAtCompileTime == size);
     assert(data.empty());  // in order that resize fills the vector with zeros.
  
     data.resize(size);
     return {data.data(), size};
 }

◆ dividedByPlane()

bool MathLib::dividedByPlane	(	const MathLib::Point3d &	a,
		const MathLib::Point3d &	b,
		const MathLib::Point3d &	c,
		const MathLib::Point3d &	d
	)

Checks if a and b can be placed on a plane such that c and d lie on different sides of said plane. (In 2D space this checks if c and d are on different sides of a line through a and b.)

Parameters

a	first point on plane
b	second point on plane
c	first point to test
d	second point to test

Returns: true, if such a plane can be found, false otherwise

Definition at line 217 of file GeometricBasics.cpp.

 {
     for (unsigned x = 0; x < 3; ++x)
     {
         const unsigned y = (x + 1) % 3;
         const double abc =
             (b[x] - a[x]) * (c[y] - a[y]) - (b[y] - a[y]) * (c[x] - a[x]);
         const double abd =
             (b[x] - a[x]) * (d[y] - a[y]) - (b[y] - a[y]) * (d[x] - a[x]);
  
         if ((abc > 0 && abd < 0) || (abc < 0 && abd > 0))
         {
             return true;
         }
     }
     return false;
 }

References MaterialPropertyLib::c.

Referenced by MeshLib::QuadRule4::validate().

◆ finalizeMatrixAssembly() [1/3]

bool MathLib::finalizeMatrixAssembly ( LisMatrix & mat )

finish assembly to make this matrix be ready for use

Definition at line 123 of file LisMatrix.cpp.

 {
     LIS_MATRIX& A = mat.getRawMatrix();
  
     if (!mat.isAssembled())
     {
         int ierr =
             lis_matrix_set_type(A, static_cast<int>(mat.getMatrixType()));
         checkLisError(ierr);
         ierr = lis_matrix_assemble(A);
         checkLisError(ierr);
         mat.is_assembled_ = true;
     }
     return true;
 }

◆ finalizeMatrixAssembly() [2/3]

template<typename MAT_T >

bool MathLib::finalizeMatrixAssembly ( MAT_T & )

Definition at line 18 of file FinalizeMatrixAssembly.h.

 {
     return true;
 }

Referenced by ProcessLib::LiquidFlow::LiquidFlowProcess::assembleConcreteProcess(), ProcessLib::HeatConduction::HeatConductionProcess::assembleConcreteProcess(), MathLib::LisLinearSolver::solve(), and ProcessLib::ComponentTransport::ComponentTransportProcess::solveReactionEquation().

◆ finalizeMatrixAssembly() [3/3]

bool MathLib::finalizeMatrixAssembly	(	PETScMatrix &	mat,
		const MatAssemblyType	asm_type = `MAT_FINAL_ASSEMBLY`
	)

General interface for the matrix assembly.

Parameters

mat	The matrix to be finalized.
asm_type	Assmebly type, either MAT_FLUSH_ASSEMBLY or MAT_FINAL_ASSEMBLY.

Definition at line 152 of file PETScMatrix.cpp.

 {
     mat.finalizeAssembly(asm_type);
     return true;
 }

◆ finalizeVectorAssembly() [1/2]

void MathLib::finalizeVectorAssembly ( PETScVector & vec )

Function to finalize the vector assembly.

Definition at line 320 of file PETScVector.cpp.

 {
     vec.finalizeAssembly();
 }

◆ finalizeVectorAssembly() [2/2]

template<typename VEC_T >

void MathLib::finalizeVectorAssembly ( VEC_T & )

General function to finalize the vector assembly.

Definition at line 19 of file FinalizeVectorAssembly.h.

20 {

21 }

Referenced by ProcessLib::LiquidFlow::LiquidFlowProcess::assembleConcreteProcess(), ProcessLib::HeatConduction::HeatConductionProcess::assembleConcreteProcess(), NumLib::PETScNonlinearSolver::solve(), and ProcessLib::ComponentTransport::ComponentTransportProcess::solveReactionEquation().

◆ gaussPointInTriangle()

bool MathLib::gaussPointInTriangle	(	MathLib::Point3d const &	q,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c,
		double	eps_pnt_out_of_plane = `std::numeric_limits< float >::epsilon()`,
		double	eps_pnt_out_of_tri = `std::numeric_limits< float >::epsilon()`
	)

Tests if the given point q is within the triangle, defined by its edge nodes a, b and c. Using two eps-values it is possible to test an 'epsilon' neighbourhood around the triangle as well as an 'epsilon' outside the triangles plane.

Parameters

q	test point
a	edge node of triangle
b	edge node of triangle
c	edge node of triangle
eps_pnt_out_of_plane	eps allowing for p to be slightly off the plane spanned by abc ((orthogonal distance to the plane spaned by triangle)
eps_pnt_out_of_tri	eps allowing for p to be slightly off outside of abc

Returns: true if the test point p is within the 'epsilon'-neighbourhood of the triangle

Definition at line 120 of file GeometricBasics.cpp.

 {
     auto const pa = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const pb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const pc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
     Eigen::Vector3d const v = pb - pa;
     Eigen::Vector3d const w = pc - pa;
  
     Eigen::Matrix2d mat;
     mat(0, 0) = v.squaredNorm();
     mat(0, 1) = v[0] * w[0] + v[1] * w[1] + v[2] * w[2];
     mat(1, 0) = mat(0, 1);
     mat(1, 1) = w.squaredNorm();
     Eigen::Vector2d y(
         v[0] * (q[0] - a[0]) + v[1] * (q[1] - a[1]) + v[2] * (q[2] - a[2]),
         w[0] * (q[0] - a[0]) + w[1] * (q[1] - a[1]) + w[2] * (q[2] - a[2]));
  
     y = mat.partialPivLu().solve(y);
  
     const double lower(eps_pnt_out_of_tri);
     const double upper(1 + lower);
  
     if (-lower <= y[0] && y[0] <= upper && -lower <= y[1] && y[1] <= upper &&
         y[0] + y[1] <= upper)
     {
         MathLib::Point3d const q_projected(std::array<double, 3>{
             {a[0] + y[0] * v[0] + y[1] * w[0], a[1] + y[0] * v[1] + y[1] * w[1],
              a[2] + y[0] * v[2] + y[1] * w[2]}});
         if (MathLib::sqrDist(q, q_projected) <= eps_pnt_out_of_plane)
         {
             return true;
         }
     }
  
     return false;
 }

References MaterialPropertyLib::c, MathLib::TemplatePoint< T, DIM >::getCoords(), q, and sqrDist().

Referenced by isPointInTriangle().

◆ getAngle()

double MathLib::getAngle	(	Point3d const &	p0,
		Point3d const &	p1,
		Point3d const &	p2
	)

Let $p_0, p_1, p_2 \in R^3$ . The function getAngle computes the angle between the edges $(p_0,p_1)$ and $(p_1,p_2)$

Parameters

p0	start point of edge 0
p1	end point of edge 0 and start point of edge 1
p2	end point of edge 1

Returns: the angle between the edges

Definition at line 42 of file MathTools.cpp.

 {
     auto const a = Eigen::Map<Eigen::Vector3d const>(p0.getCoords());
     auto const b = Eigen::Map<Eigen::Vector3d const>(p1.getCoords());
     auto const c = Eigen::Map<Eigen::Vector3d const>(p2.getCoords());
     Eigen::Vector3d const v0 = a - b;
     Eigen::Vector3d const v1 = c - b;
  
     // apply Cauchy Schwarz inequality
     return std::acos(v0.dot(v1) / (v0.norm() * v1.norm()));
 }

References MaterialPropertyLib::c, and MathLib::TemplatePoint< T, DIM >::getCoords().

Referenced by MeshLib::anonymous_namespace{AngleSkewMetric.cpp}::getMinMaxAngle().

◆ ignoreOtherLinearSolvers()

void MathLib::ignoreOtherLinearSolvers	(	BaseLib::ConfigTree const &	config,
		std::string const &	solver_name
	)

Ignore linear solver settings not needed for the selected one.

The project files support specifying linear solver options for all known solver libraries (currently PETSC, LIS, Eigen) even though for a specific build only one of those settings is used. That clearly conflicts with the requirement of the config tree that each setting present in the project file must be read exactly once.

The purpose of this function is to explicitly ignore all the settings that are not relevant for the currently used linear solver

Parameters

config	The config tree snippet for the linear solver.
solver_name	The tag under which the relevant configuration is found. All other configurations will be ignored.

This function is currently used in the option parsing code of our EigenLinearSolver, LisOption and PETScLinearSolver

Definition at line 12 of file LinearSolverOptions.cpp.

 {
     for (auto const& s : known_linear_solvers)
     {
         if (s != solver_name)
         {
             config.ignoreConfigParameter(s);
         }
     }
 }

References BaseLib::ConfigTree::ignoreConfigParameter(), and known_linear_solvers.

Referenced by MathLib::LisOption::LisOption(), MathLib::PETScLinearSolver::PETScLinearSolver(), and MathLib::EigenLinearSolver::setOption().

◆ initGLTet3X()

static std::array<std::array<double, 3>, GaussLegendreTet<3>::NPoints> MathLib::initGLTet3X ( )

static

Definition at line 31 of file GaussLegendreTet.cpp.

 {
     // Cf. Gellert, M., Harbord, R., 1991. Moderate degree cubature formulas for
     // 3-D tetrahedral finite-element approximations. Communications in Applied
     // Numerical Methods 7, 487-495. doi:10.1002/cnm.1630070609
     const double a = 0.0673422422100983;
     const double b = 0.3108859192633005;
     const double c = 0.7217942490673264;
     const double d = 0.0927352503108912;
     const double e = 0.4544962958743506;
     const double f = 0.045503704125649;
  
     return {{{{a, b, b}},
              {{b, a, b}},
              {{b, b, a}},
              {{b, b, b}},
              {{c, d, d}},
              {{d, c, d}},
              {{d, d, c}},
              {{d, d, d}},
              {{e, e, f}},
              {{e, f, e}},
              {{e, f, f}},
              {{f, e, e}},
              {{f, e, f}},
              {{f, f, e}}}};
 }

References MaterialPropertyLib::c.

◆ isCoplanar()

bool MathLib::isCoplanar	(	const MathLib::Point3d &	a,
		const MathLib::Point3d &	b,
		const MathLib::Point3d &	c,
		const MathLib::Point3d &	d
	)

Checks if the four given points are located on a plane.

Definition at line 236 of file GeometricBasics.cpp.

 {
     auto const pa = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const pb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const pc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
     auto const pd = Eigen::Map<Eigen::Vector3d const>(d.getCoords());
  
     Eigen::Vector3d const ab = pb - pa;
     Eigen::Vector3d const ac = pc - pa;
     Eigen::Vector3d const ad = pd - pa;
  
     auto const eps_squared =
         std::pow(std::numeric_limits<double>::epsilon(), 2);
     if (ab.squaredNorm() < eps_squared || ac.squaredNorm() < eps_squared ||
         ad.squaredNorm() < eps_squared)
     {
         return true;
     }
  
     // In exact arithmetic <ac*ad^T, ab> should be zero
     // if all four points are coplanar.
     const double sqr_scalar_triple(std::pow(ac.cross(ad).dot(ab), 2));
     // Due to evaluating the above numerically some cancellation or rounding
     // can occur. For this reason a normalisation factor is introduced.
     const double normalisation_factor =
         (ab.squaredNorm() * ac.squaredNorm() * ad.squaredNorm());
  
     // tolerance 1e-11 is chosen such that
     // a = (0,0,0), b=(1,0,0), c=(0,1,0) and d=(1,1,1e-6) are considered as
     // coplanar
     // a = (0,0,0), b=(1,0,0), c=(0,1,0) and d=(1,1,1e-5) are considered as not
     // coplanar
     return (sqr_scalar_triple / normalisation_factor < 1e-11);
 }

References MaterialPropertyLib::c, and MathLib::TemplatePoint< T, DIM >::getCoords().

Referenced by GeoLib::MinimalBoundingSphere::MinimalBoundingSphere(), MeshLib::MeshRevision::constructFourNodeElement(), GeoLib::Polyline::isCoplanar(), GeoLib::lineSegmentIntersect(), MeshLib::MeshRevision::reducePrism(), and MeshLib::QuadRule4::validate().

◆ isPointInTetrahedron()

bool MathLib::isPointInTetrahedron	(	MathLib::Point3d const &	p,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c,
		MathLib::Point3d const &	d,
		double	eps = `std::numeric_limits< double >::epsilon()`
	)

Tests if the given point p is located within a tetrahedron spanned by points a, b, c, d. If the tet specified by a, b, c, d is degenerated (i.e. all points are coplanar) the function will return false because there is no meaningful concept of "inside" for such elements.

Parameters

p	test point
a	edge node of tetrahedron
b	edge node of tetrahedron
c	edge node of tetrahedron
d	edge node of tetrahedron
eps	Accounts for numerical inaccuracies by allowing a point to be slightly outside of the element and still be regarded as inside.

Returns: true if the test point p is not located outside of abcd (i.e. inside or on a plane/edge).

Definition at line 62 of file GeometricBasics.cpp.

 {
     double const d0(MathLib::orientation3d(d, a, b, c));
     // if tetrahedron is not coplanar
     if (std::abs(d0) > std::numeric_limits<double>::epsilon())
     {
         bool const d0_sign(d0 > 0);
         // if p is on the same side of bcd as a
         double const d1(MathLib::orientation3d(d, p, b, c));
         if (!(d0_sign == (d1 >= 0) || std::abs(d1) < eps))
         {
             return false;
         }
         // if p is on the same side of acd as b
         double const d2(MathLib::orientation3d(d, a, p, c));
         if (!(d0_sign == (d2 >= 0) || std::abs(d2) < eps))
         {
             return false;
         }
         // if p is on the same side of abd as c
         double const d3(MathLib::orientation3d(d, a, b, p));
         if (!(d0_sign == (d3 >= 0) || std::abs(d3) < eps))
         {
             return false;
         }
         // if p is on the same side of abc as d
         double const d4(MathLib::orientation3d(p, a, b, c));
         return d0_sign == (d4 >= 0) || std::abs(d4) < eps;
     }
     return false;
 }

References MaterialPropertyLib::c, orientation3d(), and p.

Referenced by MeshLib::HexRule8::isPntInElement(), MeshLib::PrismRule6::isPntInElement(), MeshLib::PyramidRule5::isPntInElement(), and MeshLib::TetRule4::isPntInElement().

◆ isPointInTriangle()

bool MathLib::isPointInTriangle	(	MathLib::Point3d const &	p,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c,
		double	eps_pnt_out_of_plane = `std::numeric_limits< float >::epsilon()`,
		double	eps_pnt_out_of_tri = `std::numeric_limits< float >::epsilon()`,
		MathLib::TriangleTest	algorithm = `MathLib::GAUSS`
	)

Tests if the given point p is within the triangle, defined by its edge nodes a, b and c.Using two eps-values it is possible to test an 'epsilon' neighbourhood around the triangle as well as an 'epsilon' outside the triangles plane.

Parameters

p	test point
a	edge node of triangle
b	edge node of triangle
c	edge node of triangle
eps_pnt_out_of_plane	eps allowing for p to be slightly off the plane spanned by abc
eps_pnt_out_of_tri	eps allowing for p to be slightly off outside of abc
algorithm	defines the method to use

Returns: true if the test point p is within the 'epsilon'-neighbourhood of the triangle

Definition at line 96 of file GeometricBasics.cpp.

 {
     switch (algorithm)
     {
         case MathLib::GAUSS:
             return gaussPointInTriangle(p, a, b, c, eps_pnt_out_of_plane,
                                         eps_pnt_out_of_tri);
         case MathLib::BARYCENTRIC:
             return barycentricPointInTriangle(p, a, b, c, eps_pnt_out_of_plane,
                                               eps_pnt_out_of_tri);
         default:
             ERR("Selected algorithm for point in triangle testing not found, "
                 "falling back on default.");
     }
     return gaussPointInTriangle(p, a, b, c, eps_pnt_out_of_plane,
                                 eps_pnt_out_of_tri);
 }

References BARYCENTRIC, barycentricPointInTriangle(), MaterialPropertyLib::c, ERR(), GAUSS, gaussPointInTriangle(), and p.

Referenced by GeoLib::Triangle::containsPoint(), GeoLib::EarClippingTriangulation::isEar(), MeshLib::QuadRule4::isPntInElement(), and MeshLib::TriRule3::isPntInElement().

◆ isPointInTriangleXY()

bool MathLib::isPointInTriangleXY	(	MathLib::Point3d const &	p,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c
	)

Checks if the point $p'$ is in the triangle defined by the points $a', b', c'$ , where the $p', a', b', c'$ are the orthogonal projections to the $x$ - $y$ plane of the points $p, a, b, c$ , respectively.

Definition at line 197 of file GeometricBasics.cpp.

 {
     // criterion: p-a = u0 * (b-a) + u1 * (c-a); 0 <= u0, u1 <= 1, u0+u1 <= 1
     Eigen::Matrix2d mat;
     mat(0, 0) = b[0] - a[0];
     mat(0, 1) = c[0] - a[0];
     mat(1, 0) = b[1] - a[1];
     mat(1, 1) = c[1] - a[1];
     Eigen::Vector2d y;
     y << p[0] - a[0], p[1] - a[1];
  
     y = mat.partialPivLu().solve(y);
  
     // check if u0 and u1 fulfills the condition
     return 0 <= y[0] && y[0] <= 1 && 0 <= y[1] && y[1] <= 1 && y[0] + y[1] <= 1;
 }

References MaterialPropertyLib::c, and p.

Referenced by MeshLib::isPointInElementXY().

◆ lessEq()

template<typename T , std::size_t DIM>

bool MathLib::lessEq	(	TemplatePoint< T, DIM > const &	a,
		TemplatePoint< T, DIM > const &	b,
		double	eps = `std::numeric_limits<double>::epsilon()`
	)

Lexicographic comparison of points taking an epsilon into account.

Parameters

a	first input point.
b	second input point.
eps	tolerance used in comparison of coordinates.

Returns: true, if a is smaller then or equal to b according to the following test $|a_i - b_i| > \epsilon \cdot \min (|a_i|, |b_i|)$ and $|a_i - b_i| > \epsilon$ for all coordinates $0 \le i < \textrm{DIM}$ .

Definition at line 148 of file TemplatePoint.h.

 {
     auto coordinateIsLargerEps = [&eps](T const u, T const v) -> bool
     {
         return std::abs(u - v) > eps * std::min(std::abs(v), std::abs(u)) &&
                std::abs(u - v) > eps;
     };
  
     for (std::size_t i = 0; i < DIM; ++i)
     {
         // test a relative and an absolute criterion
         if (coordinateIsLargerEps(a[i], b[i]))
         {
             return static_cast<bool>(a[i] <= b[i]);
         }
         // a[i] ~= b[i] up to an epsilon. Compare next dimension.
     }
  
     // all coordinates are equal up to an epsilon.
     return true;
 }

◆ operator*()

template<typename MATRIX >

MathLib::Point3d MathLib::operator*	(	MATRIX const &	mat,
		MathLib::Point3d const &	p
	)

inline

rotation of points

Parameters

mat	a rotation matrix
p	a point to be transformed

Returns: a rotated point

Definition at line 34 of file Point3d.h.

 {
     MathLib::Point3d new_p;
     for (std::size_t i(0); i<3; ++i) {
         for (std::size_t j(0); j<3; ++j) {
             new_p[i] += mat(i,j)*p[j];
         }
     }
     return new_p;
 }

References p.

◆ operator<()

template<typename T , std::size_t DIM>

bool MathLib::operator<	(	TemplatePoint< T, DIM > const &	a,
		TemplatePoint< T, DIM > const &	b
	)

Definition at line 117 of file TemplatePoint.h.

 {
     for (std::size_t i = 0; i < DIM; ++i)
     {
         if (a[i] > b[i]) {
             return false;
         }
         if (a[i] < b[i])
         {
             return true;
             }
  
         // continue with next dimension, because a[0] == b[0]
     }
  
     // The values in all dimenisions are equal.
     return false;
 }

◆ operator<<()

template<typename T , std::size_t DIM>

std::ostream& MathLib::operator<<	(	std::ostream &	os,
		const TemplatePoint< T, DIM > &	p
	)

overload the output operator for class Point

Definition at line 173 of file TemplatePoint.h.

 {
     p.write (os);
     return os;
 }

References p.

◆ operator==()

template<typename T , std::size_t DIM>

bool MathLib::operator==	(	TemplatePoint< T, DIM > const &	a,
		TemplatePoint< T, DIM > const &	b
	)

Equality of TemplatePoint's up to an epsilon.

Definition at line 109 of file TemplatePoint.h.

 {
     T const sqr_dist(sqrDist(a,b));
     auto const eps = std::numeric_limits<T>::epsilon();
     return (sqr_dist < eps*eps);
 }

References sqrDist().

◆ operator>>()

template<typename T , std::size_t DIM>

std::istream& MathLib::operator>>	(	std::istream &	is,
		TemplatePoint< T, DIM > &	p
	)

overload the input operator for class Point

Definition at line 181 of file TemplatePoint.h.

 {
     p.read (is);
     return is;
 }

References p.

◆ orientation3d()

double MathLib::orientation3d	(	MathLib::Point3d const &	p,
		MathLib::Point3d const &	a,
		MathLib::Point3d const &	b,
		MathLib::Point3d const &	c
	)

Checks if a point p is on the left or right side of a plane spanned by three points a, b, c.

Parameters

p	point to test
a	first point on plane
b	second point on plane
c	third point on plane

Returns: If the triangle abc is ordered counterclockwise when viewed from p, the method will return a negative value, otherwise it will return a positive value. If p is coplanar with abc, the function will return 0.

Definition at line 19 of file GeometricBasics.cpp.

 {
     auto const pp = Eigen::Map<Eigen::Vector3d const>(p.getCoords());
     auto const pa = Eigen::Map<Eigen::Vector3d const>(a.getCoords());
     auto const pb = Eigen::Map<Eigen::Vector3d const>(b.getCoords());
     auto const pc = Eigen::Map<Eigen::Vector3d const>(c.getCoords());
  
     Eigen::Vector3d const u = pp - pa;
     Eigen::Vector3d const v = pp - pb;
     Eigen::Vector3d const w = pp - pc;
     return u.cross(v).dot(w);
 }

References MaterialPropertyLib::c, MathLib::TemplatePoint< T, DIM >::getCoords(), and p.

Referenced by barycentricPointInTriangle(), and isPointInTetrahedron().

◆ setMatrix() [1/2]

void MathLib::setMatrix	(	PETScMatrix &	m,
		Eigen::MatrixXd const &	tmp
	)

Definition at line 48 of file UnifiedMatrixSetters.cpp.

 {
     using IndexType = PETScMatrix::IndexType;
  
     auto const rows = tmp.rows();
     auto const cols = tmp.cols();
  
     assert(rows == m.getNumberOfRows() && cols == m.getNumberOfColumns());
  
     m.setZero();
     std::vector<IndexType> row_idcs(rows);
     std::vector<IndexType> col_idcs(cols);
  
     std::iota(row_idcs.begin(), row_idcs.end(), 0);
     std::iota(col_idcs.begin(), col_idcs.end(), 0);
  
     // PETSc wants row-major
     Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>
         tmp_ = tmp;
  
     m.add(row_idcs, col_idcs, tmp_);
 }

References MathLib::PETScMatrix::add(), MathLib::PETScMatrix::getNumberOfColumns(), MathLib::PETScMatrix::getNumberOfRows(), and MathLib::PETScMatrix::setZero().

◆ setMatrix() [2/2]

void MathLib::setMatrix	(	PETScMatrix &	m,
		std::initializer_list< double >	values
	)

Definition at line 42 of file UnifiedMatrixSetters.cpp.

 {
     m.setZero();
     addToMatrix(m, values);
 }

References addToMatrix(), and MathLib::PETScMatrix::setZero().

◆ setMatrixSparsity()

template<typename MATRIX , typename SPARSITY_PATTERN >

void MathLib::setMatrixSparsity	(	MATRIX &	matrix,
		SPARSITY_PATTERN const &	sparsity_pattern
	)

Sets the sparsity pattern of the underlying matrix. To allow partial specialization a SetMatrixSparsity template is instantiated, to which the matrix and the sparsity_pattern are passed.

Definition at line 31 of file SetMatrixSparsity.h.

 {
     SetMatrixSparsity<MATRIX, SPARSITY_PATTERN> set_sparsity;
     set_sparsity(matrix, sparsity_pattern);
 }

◆ setVector() [1/2]

void MathLib::setVector	(	PETScVector &	v,
		MatrixVectorTraits< PETScVector >::Index const	index,
		double const	value
	)

Definition at line 35 of file UnifiedMatrixSetters.cpp.

 {
     v.set(index, value);  // TODO handle negative indices
 }

References MathLib::PETScVector::set().

◆ setVector() [2/2]

void MathLib::setVector	(	PETScVector &	v,
		std::initializer_list< double >	values
	)

Definition at line 26 of file UnifiedMatrixSetters.cpp.

 {
     std::vector<double> const vals(values);
     std::vector<PETScVector::IndexType> idcs(vals.size());
     std::iota(idcs.begin(), idcs.end(), 0);
  
     v.set(idcs, vals);
 }

References MathLib::PETScVector::set().

Referenced by detail::applyKnownSolutions().

◆ SPECIALIZE_MATRIX_VECTOR_TRAITS() [1/2]

MathLib::SPECIALIZE_MATRIX_VECTOR_TRAITS	(	PETScMatrix	,
		PETScMatrix::IndexType
	)

◆ SPECIALIZE_MATRIX_VECTOR_TRAITS() [2/2]

MathLib::SPECIALIZE_MATRIX_VECTOR_TRAITS	(	PETScVector	,
		PETScVector::IndexType
	)

◆ sqrDist()

double MathLib::sqrDist	(	MathLib::Point3d const &	p0,
		MathLib::Point3d const &	p1
	)

inline

Computes the squared dist between the two points p0 and p1.

Definition at line 48 of file Point3d.h.

 {
     return (Eigen::Map<Eigen::Vector3d>(const_cast<double*>(p0.getCoords())) -
             Eigen::Map<Eigen::Vector3d>(const_cast<double*>(p1.getCoords())))
         .squaredNorm();
 }

References MathLib::TemplatePoint< T, DIM >::getCoords().

Referenced by MeshGeoToolsLib::BoundaryElementsAtPoint::BoundaryElementsAtPoint(), MeshLib::EdgeRatioMetric::calculateQuality(), MeshLib::MeshRevision::collapseNodeIndices(), MeshLib::computeSqrEdgeLengthRange(), MeshLib::computeSqrNodeDistanceRange(), MeshLib::LineRule2::computeVolume(), GeoLib::Polygon::containsSegment(), createPoints(), MeshGeoToolsLib::createSubSegmentsForElement(), MeshLib::findElementsWithinRadius(), gaussPointInTriangle(), GeoLib::Polyline::getLocationOfPoint(), MeshGeoToolsLib::MeshNodeSearcher::getMeshNodeIDs(), MeshLib::PointRule1::isPntInElement(), GeoLib::lineSegmentIntersect(), main(), MeshGeoToolsLib::mapLineSegment(), GeoLib::operator==(), operator==(), GeoLib::MinimalBoundingSphere::pointDistanceSquared(), GeoLib::pointsAreIdentical(), and GeoLib::sortSegments().

◆ sqrDist2d()

double MathLib::sqrDist2d	(	MathLib::Point3d const &	p0,
		MathLib::Point3d const &	p1
	)

inline

Computes the squared distance between the orthogonal projection of the two points p0 and p1 onto the $xy$ -plane.

Definition at line 58 of file Point3d.h.

 {
     return (p0[0]-p1[0])*(p0[0]-p1[0]) + (p0[1]-p1[1])*(p0[1]-p1[1]);
 }

Referenced by MeshLib::isPointInElementXY(), GeoLib::lineSegmentIntersect2d(), and MeshGeoToolsLib::snapPointToElementNode().

◆ toMatrix() [1/2]

template<typename Matrix >

Eigen::Map< Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > > MathLib::toMatrix	(	std::vector< double > &	data,
		Eigen::MatrixXd::Index	rows,
		Eigen::MatrixXd::Index	cols
	)

inline

Creates an Eigen mapped matrix from the given data vector.

Attention: The data vector must have the same storage order (row or column major) as the requested matrix type.

Creates an Eigen mapped matrix from the given data vector.

This is a convenience method which makes the specification of dynamically allocated Eigen matrices as return type easier.

Definition at line 111 of file EigenMapTools.h.

 {
     static_assert(Matrix::IsRowMajor || Matrix::IsVectorAtCompileTime,
                   "The default storage order in OGS is row major storage for "
                   "dense matrices.");
     assert(Matrix::RowsAtCompileTime == Eigen::Dynamic ||
            Matrix::RowsAtCompileTime == rows);
     assert(Matrix::ColsAtCompileTime == Eigen::Dynamic ||
            Matrix::ColsAtCompileTime == cols);
     assert(static_cast<Eigen::MatrixXd::Index>(data.size()) == rows * cols);
  
     return {data.data(), rows, cols};
 }

◆ toMatrix() [2/2]

template<typename Matrix >

Eigen::Map< const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor > > MathLib::toMatrix	(	std::vector< double > const &	data,
		Eigen::MatrixXd::Index	rows,
		Eigen::MatrixXd::Index	cols
	)

inline

Creates an Eigen mapped matrix from the given data vector.

Attention: The data vector must have the same storage order (row or column major) as the requested matrix type.

Creates an Eigen mapped matrix from the given data vector.

This is a convenience method which makes the specification of dynamically allocated Eigen matrices as return type easier.

Definition at line 72 of file EigenMapTools.h.

 {
     static_assert(Matrix::IsRowMajor || Matrix::IsVectorAtCompileTime,
                   "The default storage order in OGS is row major storage for "
                   "dense matrices.");
     assert(Matrix::RowsAtCompileTime == Eigen::Dynamic ||
            Matrix::RowsAtCompileTime == rows);
     assert(Matrix::ColsAtCompileTime == Eigen::Dynamic ||
            Matrix::ColsAtCompileTime == cols);
     assert(static_cast<Eigen::MatrixXd::Index>(data.size()) == rows * cols);
  
     return {data.data(), rows, cols};
 }

Referenced by ProcessLib::VectorMatrixAssembler::assemble(), ProcessLib::ComponentTransport::ComponentTransportLocalAssemblerInterface::assembleReactionEquation(), ProcessLib::CentralDifferencesJacobianAssembler::assembleWithJacobian(), ProcessLib::CompareJacobiansJacobianAssembler::assembleWithJacobian(), ProcessLib::VectorMatrixAssembler::assembleWithJacobian(), NumLib::LocalLinearLeastSquaresExtrapolator::calculateResidualElement(), ProcessLib::ComponentTransport::LocalAssemblerData< ShapeFunction, IntegrationMethod, GlobalDim >::computeSecondaryVariableConcrete(), NumLib::LocalLinearLeastSquaresExtrapolator::extrapolateElement(), ProcessLib::TES::TESLocalAssembler< ShapeFunction_, IntegrationMethod_, GlobalDim >::getIntPtDarcyVelocity(), and ProcessLib::transposeInPlace().

◆ toVector() [1/4]

Eigen::Map<Eigen::VectorXd> MathLib::toVector ( std::vector< double > & data )

inline

Creates an Eigen mapped vector from the given data vector.

This is a convenience method which makes the specification of dynamically allocated Eigen vectors as return type easier.

Definition at line 207 of file EigenMapTools.h.

 {
     return {data.data(), static_cast<Eigen::VectorXd::Index>(data.size())};
 }

◆ toVector() [2/4]

template<typename Vector >

Eigen::Map<Vector> MathLib::toVector	(	std::vector< double > &	data,
		Eigen::VectorXd::Index	size
	)

Creates an Eigen mapped vector from the given data vector.

Definition at line 180 of file EigenMapTools.h.

 {
     static_assert(Vector::IsVectorAtCompileTime, "A vector type is required.");
     assert(Vector::SizeAtCompileTime == Eigen::Dynamic ||
            Vector::SizeAtCompileTime == size);
     assert(static_cast<Eigen::VectorXd::Index>(data.size()) == size);
  
     return {data.data(), size};
 }

◆ toVector() [3/4]

Eigen::Map<const Eigen::VectorXd> MathLib::toVector ( std::vector< double > const & data )

inline

Creates an Eigen mapped vector from the given data vector.

This is a convenience method which makes the specification of dynamically allocated Eigen vectors as return type easier.

Definition at line 196 of file EigenMapTools.h.

 {
     return {data.data(), static_cast<Eigen::VectorXd::Index>(data.size())};
 }

◆ toVector() [4/4]

template<typename Vector >

Eigen::Map<const Vector> MathLib::toVector	(	std::vector< double > const &	data,
		Eigen::VectorXd::Index	size
	)

Creates an Eigen mapped vector from the given data vector.

Definition at line 167 of file EigenMapTools.h.

 {
     static_assert(Vector::IsVectorAtCompileTime, "A vector type is required.");
     assert(Vector::SizeAtCompileTime == Eigen::Dynamic ||
            Vector::SizeAtCompileTime == size);
     assert(static_cast<Eigen::VectorXd::Index>(data.size()) == size);
  
     return {data.data(), size};
 }

Referenced by ProcessLib::PythonBoundaryConditionLocalAssembler< ShapeFunction, IntegrationMethod, GlobalDim >::assemble(), ProcessLib::VectorMatrixAssembler::assemble(), ProcessLib::SourceTerms::Python::PythonSourceTermLocalAssembler< ShapeFunction, IntegrationMethod, GlobalDim >::assemble(), ProcessLib::ComponentTransport::ComponentTransportLocalAssemblerInterface::assembleReactionEquation(), ProcessLib::CompareJacobiansJacobianAssembler::assembleWithJacobian(), ProcessLib::VectorMatrixAssembler::assembleWithJacobian(), ProcessLib::LocalAssemblerInterface::computeSecondaryVariable(), ProcessLib::ComponentTransport::createComponentTransportProcess(), ProcessLib::HT::createHTProcess(), ProcessLib::LiquidFlow::createLiquidFlowProcess(), ProcessLib::RichardsComponentTransport::createRichardsComponentTransportProcess(), ProcessLib::RichardsFlow::createRichardsFlowProcess(), ProcessLib::ThermalTwoPhaseFlowWithPP::createThermalTwoPhaseFlowWithPPProcess(), ProcessLib::TwoPhaseFlowWithPP::createTwoPhaseFlowWithPPProcess(), ProcessLib::TwoPhaseFlowWithPrho::createTwoPhaseFlowWithPrhoProcess(), NumLib::LocalLinearLeastSquaresExtrapolator::extrapolateElement(), ProcessLib::ComponentTransport::ComponentTransportLocalAssemblerInterface::initializeChemicalSystem(), ProcessLib::LocalAssemblerInterface::postTimestep(), ProcessLib::ComponentTransport::ComponentTransportLocalAssemblerInterface::setChemicalSystem(), and ProcessLib::Deformation::solidMaterialInternalToSecondaryVariables().

Variable Documentation

◆ ORIGIN

MATHLIB_EXPORT const Point3d MathLib::ORIGIN {{{0.0, 0.0, 0.0}}}

extern

Definition at line 26 of file Point3d.h.

Referenced by MeshLib::getBulkElementPoint(), and getOrigin().

◆ p

const double MathLib::p = 0.1126879257180162 / 6.

static

Definition at line 62 of file GaussLegendreTet.cpp.

Referenced by ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::assembleWithJacobian(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::assembleWithJacobianForDeformationEquations(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::assembleWithJacobianForPressureEquations(), barycentricPointInTriangle(), calcProjPntToLineAndDists(), ModelTest::checkChildren(), MaterialLib::Fluid::FluidPropertiesWithDensityDependentModels::compute_df_drho_drho_dp(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::computeSecondaryVariableConcrete(), VtkImageDataToPointCloudFilter::createPoints(), VtkImageDataToSurfacePointsFilter::createPointSurface(), VtkColorLookupTable::expInterpolation(), getClosestPointElevation(), MeshLib::PropertyVector< T * >::getComponent(), MaterialLib::Fluid::FluidPropertiesWithDensityDependentModels::getdValue(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::getIntPtDarcyVelocity(), DiagramList::getPath(), DiagramList::getPoint(), MeshLib::PropertyVector< T * >::initPropertyValue(), VtkImageDataToPointCloudFilter::interpolate(), isPointInTetrahedron(), isPointInTriangle(), isPointInTriangleXY(), MathLib::PiecewiseLinearMonotonicCurve::isStrongMonotonic(), ModelTest::layoutChanged(), VtkColorLookupTable::linInterpolation(), main(), MeshGeoToolsLib::mapPointOnSurfaceElement(), MeshGeoToolsLib::mapPolylineOnSurfaceMesh(), mark_used(), operator*(), operator<<(), operator>>(), orientation3d(), ProjectData::parseParameters(), ProjectData::parseProcesses(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::postNonLinearSolverConcrete(), VtkColorByHeightFilter::RequestData(), VtkImageDataToLinePolyDataFilter::RequestData(), VtkImageDataToPointCloudFilter::RequestData(), VtkImageDataToSurfacePointsFilter::RequestData(), rotateGeometryToXY(), ProcessLib::HydroMechanics::HydroMechanicsLocalAssembler< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, DisplacementDim >::setInitialConditionsConcrete(), DiagramList::setList(), ElementTreeModel::setMesh(), VtkCompositeNodeSelectionFilter::setSelectionArray(), VisualizationWidget::showAll(), MeshGeoToolsLib::snapPointToElementNode(), and testTriangleIntersectingAABB().

◆ q

const double MathLib::q = 0.0734930431163619 / 6.

static

Definition at line 63 of file GaussLegendreTet.cpp.

Referenced by GeoLib::MinimalBoundingSphere::MinimalBoundingSphere(), ProcessLib::LIE::HydroMechanics::HydroMechanicsLocalAssemblerMatrix< ShapeFunctionDisplacement, ShapeFunctionPressure, IntegrationMethod, GlobalDim >::assembleBlockMatricesWithJacobian(), GeoLib::Triangle::containsPoint(), gaussPointInTriangle(), ProcessLib::ComponentTransport::LocalAssemblerData< ShapeFunction, IntegrationMethod, GlobalDim >::getFlux(), ProcessLib::HT::HTFEM< ShapeFunction, IntegrationMethod, GlobalDim >::getFlux(), GeoLib::lineSegmentIntersect2d(), MeshGeoToolsLib::mapPointOnSurfaceElement(), BaseLib::GradualSubdivisionFixedNum::operator()(), and GeoLib::triangleLineIntersection().

◆ r

const double MathLib::r = 0.0425460207770812 / 6.

static

Definition at line 64 of file GaussLegendreTet.cpp.

Detailed Description

Namespaces

Classes

Typedefs

Enumerations

Functions

Variables

Typedef Documentation

◆ Point3d

◆ SparsityPattern

◆ WeightedPoint1D

◆ WeightedPoint2D

◆ WeightedPoint3D

Enumeration Type Documentation

◆ TriangleTest

◆ VecNormType

Function Documentation

◆ addToMatrix()

◆ applyKnownSolution() [1/2]

◆ applyKnownSolution() [2/2]

◆ barycentricPointInTriangle()

◆ calcProjPntToLineAndDists()

◆ calcTetrahedronVolume()

◆ calcTriangleArea()

◆ checkLisError()

◆ convertStringToVecNormType()

◆ convertVecNormTypeToString()

◆ createPiecewiseLinearCurve()

◆ createZeroedMatrix()

◆ createZeroedVector()

◆ dividedByPlane()

◆ finalizeMatrixAssembly() [1/3]

◆ finalizeMatrixAssembly() [2/3]

◆ finalizeMatrixAssembly() [3/3]

◆ finalizeVectorAssembly() [1/2]

◆ finalizeVectorAssembly() [2/2]

◆ gaussPointInTriangle()

◆ getAngle()

◆ ignoreOtherLinearSolvers()

◆ initGLTet3X()

◆ isCoplanar()

◆ isPointInTetrahedron()

◆ isPointInTriangle()

◆ isPointInTriangleXY()

◆ lessEq()

◆ operator*()

◆ operator<()

◆ operator<<()

◆ operator==()

◆ operator>>()

◆ orientation3d()

◆ setMatrix() [1/2]

◆ setMatrix() [2/2]

◆ setMatrixSparsity()

◆ setVector() [1/2]

◆ setVector() [2/2]

◆ SPECIALIZE_MATRIX_VECTOR_TRAITS() [1/2]

◆ SPECIALIZE_MATRIX_VECTOR_TRAITS() [2/2]

◆ sqrDist()

◆ sqrDist2d()

◆ toMatrix() [1/2]

◆ toMatrix() [2/2]

◆ toVector() [1/4]

◆ toVector() [2/4]

◆ toVector() [3/4]

◆ toVector() [4/4]

Variable Documentation

◆ ORIGIN

◆ p

◆ q

◆ r