FEAT Math namespace. More...

Classes
class	Limits
	Math Limits class template. More...

Functions
template<typename T_ >
T_	abs (T_ x)
	Returns the absolute value. More...

template<typename T_ >
T_	acos (T_ x)
	Returns the arccosine of a value. More...

template<typename T_ >
T_	asin (T_ x)
	Returns the arcsine of a value. More...

template<typename T_ >
T_	atan (T_ x)
	Returns the arctangent of a value. More...

template<typename T_ >
T_	atan2 (T_ y, T_ x)
	Returns the arctangent of y/x. More...

template<typename T_ >
T_	binomial (T_ n, T_ k)
	Calculates the binomial coefficient. More...

template<typename DT_ >
DT_	calc_opening_angle (DT_ x1, DT_ x2, DT_ y1, DT_ y2)
	Calculates the opening angle of two 2D vectors. More...

template<typename DT_ >
DT_	calc_opening_angle_intern (DT_ cross_prod, DT_ dot_prod)
	Calculates the opening angle from the dot and cross product of two 2D vectors. More...

template<typename T_ >
T_	clamp (T_ x, T_ a, T_ b)
	Clamps a value to a range. More...

template<typename T_ >
T_	cos (T_ x)
	Returns the cosine of a value. More...

template<typename T_ >
T_	cosh (T_ x)
	Returns the hyperbolic cosine of a value. More...

template<typename T_ >
T_	cub (T_ x)
	Returns the cube of a value. More...

template<typename T_ >
T_	eps ()
	Returns the machine precision constant for a floating-point data type. More...

template<typename T_ >
T_	exp (T_ x)
	Returns the exponential of a value. More...

template<typename T_ >
T_	factorial (T_ n, T_ m=T_(0))
	Calculates the (partial) factorial. More...

template<typename T_ >
T_	huge ()
	Returns the maximum positive finite (full-precision) value for a data type. More...

template<typename T_ >
T_	ilog10 (T_ x)
	Computes the integral base-10 logarithm of an integer, i.e. its number of non-zero decimal digits. More...

template<typename DT_ , typename IT_ >
DT_	invert_matrix (const IT_ n, const IT_ stride, DT_ a[], IT_ p[])
	Inverts a matrix and returns its determinant. More...

template<typename T_ >
bool	isfinite (T_ x)
	Checks whether a value is finite. More...

template<typename T_ >
bool	isinf (T_ x)
	Checks whether a value is infinite. More...

template<typename T_ >
bool	isnan (T_ x)
	Checks whether a value is Not-A-Number. More...

template<typename T_ >
bool	isnormal (T_ x)
	Checks whether a value is normal. More...

template<typename T_ >
T_	log (T_ x)
	Returns the natural logarithm of a value. More...

template<typename T_ >
T_	log10 (T_ x)
	Returns the logarithm to the base 10 of a value. More...

template<typename T_ >
T_	max (T_ a, T_ b)
	Returns the maximum of two values. More...

template<typename T_ >
void	maxi (T_ &xmax, T_ x)
	Updates the maximum of a set of values. More...

template<typename T_ >
T_	min (T_ a, T_ b)
	Returns the minimum of two values. More...

template<typename T_ >
void	mini (T_ &xmin, T_ x)
	Updates the minimum of a set of values. More...

template<typename T_ >
void	minimax (T_ x, T_ &a, T_ &b)
	Updates the minimum and maximum. More...

template<typename T_ >
T_	nan ()
	Returns a quiet Not-A-Number (NaN) More...

template<typename T_ >
T_	pi ()
	Returns the mathematical constant pi = 3.1415... More...

template<typename T_ >
T_	pow (T_ x, T_ y)
	Returns x raised to the power of y. More...

template<typename T_ >
bool	signbit (T_ x)
	Returns the status of the sign bit. More...

template<typename T_ >
T_	signum (T_ x)
	Returns the sign of a value. More...

template<typename T_ >
T_	sin (T_ x)
	Returns the sine of a value. More...

template<typename T_ >
T_	sinh (T_ x)
	Returns the hyperbolic sine of a value. More...

template<typename T_ >
T_	sqr (T_ x)
	Returns the square of a value. More...

template<typename T_ >
T_	sqrt (T_ x)
	Returns the square-root of a value. More...

template<typename T_ >
T_	tan (T_ x)
	Returns the tangent of a value. More...

template<typename T_ >
T_	tanh (T_ x)
	Returns the hyperbolic tangent of a value. More...

template<typename T_ >
T_	tiny ()
	Returns the minimum positive finite (full-precision) value for a data type. More...

Detailed Description

FEAT Math namespace.

This namespace encapsulates common mathematical functions used throughout the FEAT kernel. This namespace contains all math functions from the standard cmath header.

Function Documentation

◆ abs()

template<typename T_ >

T_ FEAT::Math::abs ( T_ x )

inline

Returns the absolute value.

Parameters

[in] x The value to get the absolute value from.

Returns: abs(x)

Definition at line 275 of file math.hpp.

◆ acos()

template<typename T_ >

T_ FEAT::Math::acos ( T_ x )

inline

Returns the arccosine of a value.

Parameters

[in] x The value to calculate the arccosine from.

Returns: acos(x)

Definition at line 967 of file math.hpp.

References asin().

Referenced by calc_opening_angle_intern().

◆ asin()

template<typename T_ >

T_ FEAT::Math::asin ( T_ x )

inline

Returns the arcsine of a value.

Parameters

[in] x The value to calculate the arcsine from.

Returns: asin(x)

Definition at line 949 of file math.hpp.

References atan(), signum(), and sqrt().

Referenced by acos(), and calc_opening_angle_intern().

◆ atan()

template<typename T_ >

T_ FEAT::Math::atan ( T_ x )

inline

Returns the arctangent of a value.

Parameters

[in] x The value to calculate the arctangent from.

Returns: atan(x)

Definition at line 662 of file math.hpp.

References abs(), and sqrt().

Referenced by asin(), and atan2().

◆ atan2()

template<typename T_ >

T_ FEAT::Math::atan2	(	T_	y,
		T_	x
	)

inline

Returns the arctangent of y/x.

Parameters

[in]	y	The nominator of the value to calculate the arctangent from.
[in]	x	The denominator of the value to calculate the arctangent from.

Returns: atan2(y,x) = atan(y/x)

Definition at line 708 of file math.hpp.

References atan(), and sqrt().

Referenced by FEAT::Geometry::Atlas::Extrude< Mesh_, SubChart_ >::write().

◆ binomial()

template<typename T_ >

T_ FEAT::Math::binomial	(	T_	n,
		T_	k
	)

inline

Calculates the binomial coefficient.

This function calculates the binomial coefficient

\[ {n \choose k} := \frac{n!}{k!(n-k)!} \]

Attention: This function works only for integral data types; it will give incorrect results for floating point data types!

Parameters

[in] n,k The parameters for the binomial coefficient.

Returns: The binomial coefficient n choose k.

Author: Peter Zajac

Definition at line 1196 of file math.hpp.

References min().

◆ calc_opening_angle()

template<typename DT_ >

DT_ FEAT::Math::calc_opening_angle	(	DT_	x1,
		DT_	x2,
		DT_	y1,
		DT_	y2
	)

Calculates the opening angle of two 2D vectors.

This function calculates the opening angle between two unit 2D vectors x and y in a right handed matter, i.e. the angle is returned required to transform x into y in an anti-clockwise rotation. The angle is calculated on the [0, 2\pi) domain.

Template Parameters

DT_ The data

Parameters

[in]	x1,x2	The first and second value of x.
[in]	y1,y2	The first and second value of y.

Definition at line 1450 of file math.hpp.

References calc_opening_angle_intern(), sqr(), and sqrt().

Referenced by FEAT::Analytic::PolarCoordinate< Function_, pos_range_ >::PolarCoordinate(), and FEAT::Tiny::calculate_opening_angle().

◆ calc_opening_angle_intern()

template<typename DT_ >

DT_ FEAT::Math::calc_opening_angle_intern	(	DT_	cross_prod,
		DT_	dot_prod
	)

Calculates the opening angle from the dot and cross product of two 2D vectors.

This function calculates the opening angle between two unit 2D vectors x and y in a right handed matter, i.e. the angle is returned required to transform x into y in an anti-clockwise rotation. The angle is calculated on the [0, 2\pi) domain.

Template Parameters

DT_ The data

Parameters

[in]	cross_prod	The cross product of vector x and y.
[in]	dot_pord	The dot product of vector x and y.

Attention: The implicit vectors x and y have to be normalized.

Definition at line 1414 of file math.hpp.

References abs(), acos(), and asin().

Referenced by calc_opening_angle().

◆ clamp()

template<typename T_ >

T_ FEAT::Math::clamp	(	T_	x,
		T_	a,
		T_	b
	)

inline

Clamps a value to a range.

Parameters

[in]	x	The value to be clamped.
[in]	a,b	The clamp boundaries.

Returns: max(a, min(x, b))

Definition at line 216 of file math.hpp.

References max(), and min().

Referenced by FEAT::Geometry::Atlas::Bezier< Mesh_ >::project_on_segment().

◆ cos()

template<typename T_ >

T_ FEAT::Math::cos ( T_ x )

inline

Returns the cosine of a value.

Parameters

[in] x The value to calculate the cosine from.

Returns: cos(x)

Definition at line 386 of file math.hpp.

◆ cosh()

template<typename T_ >

T_ FEAT::Math::cosh ( T_ x )

inline

Returns the hyperbolic cosine of a value.

Parameters

[in] x The value to calculate the hyperbolic cosine from.

Returns: cosh(x)

Definition at line 489 of file math.hpp.

Referenced by tanh().

◆ cub()

template<typename T_ >

T_ FEAT::Math::cub ( T_ x )

inline

Returns the cube of a value.

Parameters

[in] x The value to be cubed.

Returns x*x*x

Definition at line 109 of file math.hpp.

Referenced by FEAT::Geometry::VoxelMap::get_bounding_box_volume().

◆ eps()

template<typename T_ >

T_ FEAT::Math::eps ( )

inline

Returns the machine precision constant for a floating-point data type.

Definition at line 787 of file math.hpp.

◆ exp()

template<typename T_ >

T_ FEAT::Math::exp ( T_ x )

inline

Returns the exponential of a value.

Parameters

[in] x The value to calculate the exponential from.

Returns: exp(x)

Definition at line 550 of file math.hpp.

Referenced by FEAT::Analytic::Common::ExpBubbleScalarStatic< DataType_ >::der_x(), FEAT::Analytic::Common::ExpBubbleScalarStatic< DataType_ >::der_xx(), FEAT::Analytic::Common::ExpBubbleScalarStatic< DataType_ >::eval(), log(), and pow().

◆ factorial()

template<typename T_ >

T_ FEAT::Math::factorial	(	T_	n,
		T_	m = `T_(0)`
	)

inline

Calculates the (partial) factorial.

This function calculates the coefficient

\[ f(n,m) := \prod_{k=m}^n k \]

The factorial n! is given by f(n,0).

Attention

Please keep in mind that the factorial becomes very huge very fast, i.e. for integral data types, one should honor the following boundaries to avoid overflow:

8-bit: n <= 5
16-bit: n <= 7 (signed); n <= 8 (unsigned)
32-bit: n <= 12
64-bit: n <= 20

Parameters

[in] n,m The coefficients for the (partial) factorial.

Returns: The partial factorial from m to n.

Author: Peter Zajac

Definition at line 1164 of file math.hpp.

References max().

◆ huge()

template<typename T_ >

T_ FEAT::Math::huge ( )

inline

Returns the maximum positive finite (full-precision) value for a data type.

The return value of this function coincides with std::numeric_limits<T_>::max().

Definition at line 842 of file math.hpp.

◆ ilog10()

template<typename T_ >

T_ FEAT::Math::ilog10 ( T_ x )

inline

Computes the integral base-10 logarithm of an integer, i.e. its number of non-zero decimal digits.

Parameters

[in] x The number whose digit count is to be computed.

Returns: The number of non-zero decimal digits of x.

Definition at line 231 of file math.hpp.

Referenced by FEAT::Solver::NLCG< Functional_, Filter_ >::NLCG(), FEAT::Solver::NLSD< Functional_, Filter_ >::NLSD(), FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Dist::Comm::allprint(), FEAT::Solver::IterativeSolver< Vector_ >::set_max_iter(), FEAT::Geometry::ExportVTK< Mesh_, cell_dim_ >::write(), and FEAT::Geometry::ExportVTK< Mesh_, cell_dim_ >::write_pvtu().

◆ invert_matrix()

template<typename DT_ , typename IT_ >

DT_ FEAT::Math::invert_matrix	(	const IT_	n,
		const IT_	stride,
		DT_	a[],
		IT_	p[]
	)

Inverts a matrix and returns its determinant.

This function inverts a dense n x n matrix by means of partially pivoted Gaussian elimination and returns its determinant.

Attention: This function does not check whether the input matrix is regular, therefore one should always check whether the determinant returned by this function is normal by using the Math::isnormal() function. If the returned determinant is not normal, i.e. if Math::isnormal returns false, then the matrix inversion most failed and the output matrix a most probably contains garbage!

Note: This function returns zero if any of the input parameters are invalid.

Parameters

[in]	n	The dimension of the matrix to be inverted. Must be > 0.
[in]	stride	The stride of the matrix. Must be >= n.
[in]	a	On entry, the matrix to be inverted. On exit, the inverse matrix. Must not be `nullptr`.
[in]	p	A temporary pivot array of length at least n. Must not be `nullptr`.

Returns: The determinant of the input matrix a.

Implementational Details:
This functions implements the 'classical' column-pivoted Gauss-Jordan elimination algorithm, which computes the inverse of a matrix by transforming the system

       \f[ [~A~|~I~] \rightarrow [~I~|~A^{-1}~] \f]

There are three major modifications in contrast to the original widely known algorithm:

First, this algorithm works in-situ, i.e. it successively replaces columns of the left-hand-side input matrix by the corresponding columns of the right-hand-side identity matrix during the column elimination process.

Second, this algorithm eliminates whole columns of the left-hand-side matrix, whereas the original algorithm only eliminates all entries below the pivot element. Due to this fact, no backward substitution is necessary after the primary elimination process.

Third, this algorithm does not physically swap rows during the pivoting step, but simply remembers the pivoted positions in a temporary pivot array p, which is initialized to identity. So in the k-th iteration of the primary elimination loop:

p[k] contains the index of the row which is currently being used for elimination of column k
p[j] for j < k contains the indices of all columns which have already been eliminated, i.e. the corresponding columns already contain the entries of the right-hand-side matrix
p[j] for j > k contains the indices of all columns which have not yet been eliminated, i.e. the corresponding columns still hold the entries of the left-hand-side matrix and are therefore candidates for future pivoting steps.

Author: Peter Zajac

Definition at line 1292 of file math.hpp.

References abs().

Referenced by FEAT::Solver::Vanka< LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >, Filter_ >::_factor_diag(), FEAT::Solver::Vanka< LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >, Filter_ >::_factor_full(), FEAT::Assembly::GridTransfer::assemble_intermesh_transfer(), FEAT::Assembly::GridTransfer::assemble_prolongation(), FEAT::Assembly::SpaceTransfer::assemble_transfer(), FEAT::Assembly::GridTransfer::assemble_truncation(), FEAT::Solver::AmaVanka< Matrix_, Filter_ >::init_numeric(), FEAT::LAFEM::DenseMatrix< DT_, IT_ >::invert(), FEAT::Assembly::RewProjector::project(), FEAT::Assembly::GridTransfer::prolongate_vector(), FEAT::Assembly::GridTransfer::transfer_intermesh_vector(), and FEAT::Assembly::SpaceTransfer::transfer_vector().

◆ isfinite()

template<typename T_ >

bool FEAT::Math::isfinite ( T_ x )

inline

Checks whether a value is finite.

A value is finite if it is neither NaN nor inifinity.

Note: There exists no generic implementation for this function.

Parameters

[in] x The value to be checked for finiteness.

Returns: true if x is finite, otherwise false.

Referenced by FEAT::Solver::IterativeSolver< Vector_ >::_analyze_defect(), FEAT::Solver::RBiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::BiCGStab< Matrix_, Filter_ >::_apply_intern(), FEAT::Solver::QPenalty< Functional_ >::_apply_intern(), FEAT::Solver::Linesearch< Functional_, Filter_ >::_check_convergence(), FEAT::Solver::QPenalty< Functional_ >::_set_initial_defect(), FEAT::Solver::IterativeSolver< Vector_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_initial_defect(), FEAT::Solver::NLOptLS< Functional_, Filter_ >::_set_new_defect(), and FEAT::Solver::Linesearch< Functional_, Filter_ >::_startup().

◆ isinf()

template<typename T_ >

bool FEAT::Math::isinf ( T_ x )

inline

Checks whether a value is infinite.

Note: There exists no generic implementation for this function.

Parameters

[in] x The value to be checked for infinity.

Returns: true if x is +/-infinity, otherwise false.

◆ isnan()

template<typename T_ >

bool FEAT::Math::isnan ( T_ x )

inline

Checks whether a value is Not-A-Number.

Note: There exists no generic implementation for this function.

Parameters

[in] x The value to be checked for NaN.

Returns: true if x is NaN, otherwise false.

◆ isnormal()

template<typename T_ >

bool FEAT::Math::isnormal ( T_ x )

inline

Checks whether a value is normal.

A value is normal if it is neither infinity, NaN, zero or subnormal.

Note: There exists no generic implementation for this function.

Parameters

[in] x The value to be checked for normalty.

Returns: true if x is normal, otherwise false.

Referenced by FEAT::Solver::Vanka< LAFEM::SaddlePointMatrix< MatrixA_, MatrixB_, MatrixD_ >, Filter_ >::_factor_diag(), FEAT::Assembly::GridTransfer::assemble_intermesh_transfer(), FEAT::Assembly::GridTransfer::assemble_prolongation(), FEAT::Assembly::SpaceTransfer::assemble_transfer(), FEAT::Assembly::GridTransfer::assemble_truncation(), FEAT::Assembly::GridTransfer::prolongate_vector(), FEAT::Assembly::GridTransfer::transfer_intermesh_vector(), and FEAT::Assembly::SpaceTransfer::transfer_vector().

◆ log()

template<typename T_ >

T_ FEAT::Math::log ( T_ x )

inline

Returns the natural logarithm of a value.

Parameters

[in] x The value to calculate the natural logarithm from.

Returns: log(x)

Definition at line 580 of file math.hpp.

References exp().

Referenced by log10(), pow(), and FEAT::Trafo::Isoparam::Evaluator< Trafo_, EvalPolicy_, degree_, Shape::Hypercube< 1 > >::volume().

◆ log10()

template<typename T_ >

T_ FEAT::Math::log10 ( T_ x )

inline

Returns the logarithm to the base 10 of a value.

Parameters

[in] x The value to calculate the 10-logarithm from.

Returns: log10(x)

Definition at line 623 of file math.hpp.

References log().

◆ max()

template<typename T_ >

T_ FEAT::Math::max	(	T_	a,
		T_	b
	)

inline

Returns the maximum of two values.

Parameters

[in] a,b The two values whose maximum is to be returned.

Returns: The maximum of a and b.

Definition at line 137 of file math.hpp.

◆ maxi()

template<typename T_ >

void FEAT::Math::maxi	(	T_ &	xmax,
		T_	x
	)

inline

Updates the maximum of a set of values.

This functions performs: xmax := max(xmax, x)

Parameters

[in,out]	xmax	The maximum that is to be updated.
[in]	x	The new value for the maximum update.

Definition at line 172 of file math.hpp.

Referenced by FEAT::Geometry::UmbrellaSmoother< MeshType_ >::smooth().

◆ min()

template<typename T_ >

T_ FEAT::Math::min	(	T_	a,
		T_	b
	)

inline

Returns the minimum of two values.

Parameters

[in] a,b The two values whose minimum is to be returned.

Returns: The minimum of a and b.

Definition at line 123 of file math.hpp.

Referenced by FEAT::Solver::ALGLIBMinLBFGS< Functional_, Filter_ >::ALGLIBMinLBFGS(), FEAT::Control::Time::NvsBdfQ< DT_ >::NvsBdfQ(), FEAT::LAFEM::SparseMatrixBanded< DT_, IT_ >::SparseMatrixBanded(), FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >::_apply_cycle_f(), FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >::_apply_cycle_w(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_apply_intern(), FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >::_apply_prol(), FEAT::Solver::MultiGrid< SystemMatrix_, SystemFilter_, TransferOperator_ >::_apply_rest(), FEAT::Assembly::DomainAssembler< Trafo_ >::_build_colors(), FEAT::Assembly::DomainAssembler< Trafo_ >::_build_thread_layers(), FEAT::Geometry::MeshDistortion< MeshType_ >::_calc_shortest_edge(), FEAT::Geometry::DistributedMeshDistortion< MeshType_ >::_calc_shortest_edge(), FEAT::Geometry::DistributedMeshDistortion< MeshType_ >::_calc_vertex_owners(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_clamp_step(), FEAT::Geometry::VoxelMap::_compute_voxel_map(), FEAT::LAFEM::SparseMatrixBanded< DT_, IT_ >::_end_offset(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_polynomial_fit(), FEAT::Control::Domain::VoxelDomainControl< DomainLevel_ >::_precreate_voxel_map(), binomial(), clamp(), FEAT::Meshopt::DuDvFunctional< DT_, IT_, TrafoType_, MatrixType_ >::compute_cell_size_defect_post_sync(), FEAT::Meshopt::HyperelasticityFunctional< DT_, IT_, Trafo_, CellFunctionalType_, RefCellTrafo_ >::compute_cell_size_defect_post_sync(), FEAT::Meshopt::DuDvFunctional< DT_, IT_, TrafoType_, MatrixType_ >::compute_cell_size_defect_pre_sync(), FEAT::Meshopt::HyperelasticityFunctional< DT_, IT_, Trafo_, CellFunctionalType_, RefCellTrafo_ >::compute_cell_size_defect_pre_sync(), FEAT::LAFEM::SparseMatrixCSR< DT_, IT_ >::convert(), FEAT::Solver::NLCG< Functional_, Filter_ >::dy_hs_hybrid(), FEAT::Solver::NLCG< Functional_, Filter_ >::hager_zhang(), FEAT::LAFEM::PowerVector< SubType_, count_ >::min_abs_element(), FEAT::LAFEM::TupleVector< First_, Rest_ >::min_abs_element(), FEAT::LAFEM::PowerVector< SubType_, count_ >::min_element(), FEAT::LAFEM::TupleVector< First_, Rest_ >::min_element(), FEAT::Geometry::Atlas::Bezier< Mesh_ >::project_on_segment(), FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::project_point(), FEAT::LAFEM::SparseMatrixCSR< DT_, IT_ >::radius_row(), FEAT::Geometry::VoxelMap::read(), sqrt(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::trace(), FEAT::Geometry::AdaptiveMeshLayer< AdaptiveMeshType_ >::validate_element_layering(), FEAT::Geometry::ConformalMesh< Shape_, num_coords_, Coord_ >::validate_element_layering(), FEAT::Geometry::ExportEPS::write(), FEAT::Geometry::ExportSVG::write(), and FEAT::Geometry::VoxelMap::write().

◆ mini()

template<typename T_ >

void FEAT::Math::mini	(	T_ &	xmin,
		T_	x
	)

inline

Updates the minimum of a set of values.

This functions performs: xmin := min(xmin, x)

Parameters

[in,out]	xmin	The minimum that is to be updated.
[in]	x	The new value for the minimum update.

Definition at line 154 of file math.hpp.

◆ minimax()

template<typename T_ >

void FEAT::Math::minimax	(	T_	x,
		T_ &	a,
		T_ &	b
	)

inline

Updates the minimum and maximum.

This functions performs:

a := min(x, a)
b := max(x, b)

Parameters

[in]	x	The new value for the minimum/maximum update.
[in,out]	a	The minimum that is to be updated.
[in,out]	b	The maximum that is to be updated.

Definition at line 195 of file math.hpp.

Referenced by FEAT::Control::Domain::VoxelDomainControl< DomainLevel_ >::_gather_element_weights(), FEAT::Control::Domain::VoxelDomainControl< DomainLevel_ >::_gather_masked_elements(), FEAT::Trafo::InverseMapping< Trafo_, DataType_ >::init_bounding_boxes(), FEAT::Geometry::ExportEPS::write(), and FEAT::Geometry::ExportSVG::write().

◆ nan()

template<typename T_ >

T_ FEAT::Math::nan ( )

inline

Returns a quiet Not-A-Number (NaN)

Note: The generic implementation simply returns 0/0, which should result in a NaN for any IEEE-754 conforming implementation.

Returns: NaN

Definition at line 897 of file math.hpp.

◆ pi()

template<typename T_ >

T_ FEAT::Math::pi ( )

inline

Returns the mathematical constant pi = 3.1415...

Definition at line 724 of file math.hpp.

◆ pow()

template<typename T_ >

T_ FEAT::Math::pow	(	T_	x,
		T_	y
	)

inline

Returns x raised to the power of y.

Parameters

[in]	x	The base value. Must be positive.
[in]	y	The exponent value.

Returns: x^y

Definition at line 643 of file math.hpp.

References exp(), and log().

Referenced by FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_apply_intern(), FEAT::Assembly::BurgersCarreauBlockedAssemblyTaskBase< Job_, DataType_, block_size_ >::assemble_burgers_point(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_matrix(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), FEAT::Solver::IterativeSolver< Vector_ >::calc_convergence_rate(), FEAT::Meshopt::MeshConcentrationFunction< ElementalFunction_, Trafo_, RefCellTrafo_ >::compute_grad_h(), FEAT::Meshopt::ConcentrationFunctionPowOfDist< DT_ >::conc_der(), FEAT::Meshopt::ConcentrationFunctionPowOfDist< DT_ >::conc_val(), FEAT::Tiny::Vector< T_, n_, s_ >::normalized(), FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point(), FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::project_meshpart(), FEAT::Meshopt::HyperelasticityFunctional< DT_, IT_, Trafo_, CellFunctionalType_, RefCellTrafo_ >::set_penalty_param(), FEAT::VoxelAssembly::VoxelBurgersVeloMaterialAssembler< Q2StandardHyperCube< dim_ >, DT_, IT_ >::wrap_material_params(), and FEAT::Geometry::Atlas::Extrude< Mesh_, SubChart_ >::write().

◆ signbit()

template<typename T_ >

bool FEAT::Math::signbit ( T_ x )

inline

Returns the status of the sign bit.

Parameters

[in] x The value whose signbit status is to be returned.

Definition at line 262 of file math.hpp.

◆ signum()

template<typename T_ >

T_ FEAT::Math::signum ( T_ x )

inline

Returns the sign of a value.

Parameters

[in] x The value whose sign is to be returned.

Definition at line 250 of file math.hpp.

Referenced by FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_argmin_cubic(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_argmin_cubic_case_3(), asin(), FEAT::Geometry::Atlas::Bezier< Mesh_ >::compute_signed_dist(), FEAT::Geometry::Atlas::Circle< Mesh_ >::compute_signed_dist(), FEAT::Geometry::Atlas::Sphere< Mesh_ >::compute_signed_dist(), FEAT::Meshopt::ConcentrationFunctionPowOfDist< DT_ >::conc_der(), and FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::project_point().

◆ sin()

template<typename T_ >

T_ FEAT::Math::sin ( T_ x )

inline

Returns the sine of a value.

Parameters

[in] x The value to calculate the sine from.

Returns: sin(x)

Definition at line 344 of file math.hpp.

◆ sinh()

template<typename T_ >

T_ FEAT::Math::sinh ( T_ x )

inline

Returns the hyperbolic sine of a value.

Parameters

[in] x The value to calculate the hyperbolic sine from.

Returns: sinh(x)

Definition at line 447 of file math.hpp.

Referenced by tanh().

◆ sqr()

template<typename T_ >

T_ FEAT::Math::sqr ( T_ x )

inline

Returns the square of a value.

Parameters

[in] x The value to be squared.

Returns x*x

Definition at line 95 of file math.hpp.

◆ sqrt()

template<typename T_ >

T_ FEAT::Math::sqrt ( T_ x )

inline

Returns the square-root of a value.

Parameters

[in] x The value to calculate the square-root from.

Returns: sqrt(x)

Compiler Hack:: disable "warning C4723: potential divide by 0" for MSVC compiler

Definition at line 300 of file math.hpp.

References min().

Referenced by FEAT::Solver::SecantLinesearch< Functional_, Filter_ >::_apply_intern(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_argmin_cubic(), FEAT::Solver::MQCLinesearch< Functional_, Filter_ >::_argmin_cubic_case_3(), FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_build_coeff_matrix(), FEAT::Space::CroRavRanTur::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_build_coeff_matrix(), FEAT::Space::Q1TBNP::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Quadrilateral >::_build_coeff_matrix(), FEAT::Space::Q1TBNP::Evaluator< Space_, TrafoEvaluator_, SpaceEvalTraits_, Shape::Hexahedron >::_build_coeff_matrix(), asin(), FEAT::Assembly::BurgersAssembler< DataType_, IndexType_, dim_ >::assemble_matrix(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_matrix(), FEAT::Assembly::BurgersAssembler< DataType_, IndexType_, dim_ >::assemble_scalar_matrix(), FEAT::Assembly::BurgersAssemblerCarreau< DataType_, IndexType_, dim_ >::assemble_vector(), atan(), atan2(), FEAT::VoxelAssembly::Kernel::burgers_velo_material_defect_assembly_kernel(), FEAT::VoxelAssembly::Kernel::burgers_velo_material_mat_assembly_kernel(), calc_opening_angle(), FEAT::Assembly::VelocityAnalyser::compute(), FEAT::Assembly::ScalarErrorComputer< max_norm_, sub_dimensional_ >::compute(), FEAT::Assembly::VectorErrorComputer< max_norm_ >::compute(), FEAT::Geometry::Atlas::Bezier< Mesh_ >::compute_signed_dist(), FEAT::Geometry::Atlas::SurfaceMesh< Mesh_ >::determine_success(), FEAT::Cubature::HammerStroudD5Driver< Shape::Simplex< 3 > >::fill(), FEAT::Cubature::HammerStroudD2Driver< Shape::Simplex< dim_ > >::fill(), FEAT::Cubature::Scalar::GaussLobattoDriver::fill(), FEAT::Solver::NLCG< Functional_, Filter_ >::hager_zhang(), FEAT::Global::Vector< LocalVector_, Mirror_ >::norm2(), FEAT::LAFEM::PowerVector< SubType_, count_ >::norm2(), FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid(), FEAT::Tiny::Vector< T_, n_, s_ >::norm_euclid_n(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_frobenius(), FEAT::Tiny::Matrix< T_, m_, n_, sm_, sn_ >::norm_sub_id_frobenius(), FEAT::Assembly::BurgersCarreauAssemblyTaskBase< Job_, DataType_ >::prepare_point(), FEAT::Geometry::Atlas::Bezier< Mesh_ >::project_point(), FEAT::Geometry::UmbrellaSmoother< MeshType_ >::smooth(), FEAT::Assembly::ScalarErrorInfo< DataType_ >::synchronize(), FEAT::Assembly::VectorErrorInfo< DataType_, dim_ >::synchronize(), FEAT::Assembly::VelocityInfo< DataType_, dim_ >::synchronize(), FEAT::Trafo::Isoparam::Evaluator< Trafo_, EvalPolicy_, degree_, Shape::Hypercube< 1 > >::volume(), FEAT::Trafo::Standard::EvalHelper< DataType_, DomPointType_, ImgPointType_, JacMatType_, JacMatInvType_, JacDetType_, HessType_, HessInvType_, Shape::Simplex< 1 >, img_dim >::volume(), FEAT::Trafo::Standard::EvalHelper< DataType_, DomPointType_, ImgPointType_, JacMatType_, JacMatInvType_, JacDetType_, HessType_, HessInvType_, Shape::Hypercube< 1 >, img_dim >::volume(), FEAT::Global::SynchScalarTicket< DT_ >::wait(), FEAT::Trafo::Standard::EvalHelper< DataType_, DomPointType_, ImgPointType_, JacMatType_, JacMatInvType_, JacDetType_, HessType_, HessInvType_, Shape::Simplex< 2 >, img_dim >::width_directed(), FEAT::Trafo::Standard::EvalHelper< DataType_, DomPointType_, ImgPointType_, JacMatType_, JacMatInvType_, JacDetType_, HessType_, HessInvType_, Shape::Simplex< 3 >, img_dim >::width_directed(), and FEAT::Geometry::Atlas::Extrude< Mesh_, SubChart_ >::write().

◆ tan()

template<typename T_ >

T_ FEAT::Math::tan ( T_ x )

inline

Returns the tangent of a value.

Parameters

[in] x The value to calculate the tangent from.

Returns: tan(x)

Definition at line 428 of file math.hpp.

References cos(), and sin().

◆ tanh()

template<typename T_ >

T_ FEAT::Math::tanh ( T_ x )

inline

Returns the hyperbolic tangent of a value.

Parameters

[in] x The value to calculate the hyperbolic tangent from.

Returns: tanh(x)

Definition at line 531 of file math.hpp.

References cosh(), and sinh().

◆ tiny()

template<typename T_ >

T_ FEAT::Math::tiny ( )

inline

Returns the minimum positive finite (full-precision) value for a data type.

The return value of this function coincides with std::numeric_limits<T_>::min().

Definition at line 853 of file math.hpp.

Classes

Functions

Detailed Description

Function Documentation

◆ abs()

◆ acos()

◆ asin()

◆ atan()

◆ atan2()

◆ binomial()

◆ calc_opening_angle()

◆ calc_opening_angle_intern()

◆ clamp()

◆ cos()

◆ cosh()

◆ cub()

◆ eps()

◆ exp()

◆ factorial()

◆ huge()

◆ ilog10()

◆ invert_matrix()

◆ isfinite()

◆ isinf()

◆ isnan()

◆ isnormal()

◆ log()

◆ log10()

◆ max()

◆ maxi()

◆ min()

◆ mini()

◆ minimax()

◆ nan()

◆ pi()

◆ pow()

◆ signbit()

◆ signum()

◆ sin()

◆ sinh()

◆ sqr()

◆ sqrt()

◆ tan()

◆ tanh()

◆ tiny()