MathUtils.h File Reference

Various mathematical functions. More...

#include "arcane/utils/Math.h"
#include "arcane/utils/ArrayView.h"
#include "arcane/utils/NumericTypes.h"
#include "arcane/utils/Real2x2.h"
#include "arcane/utils/Real3.h"
#include "arcane/utils/Real2.h"
#include "arcane/core/Algorithm.h"

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Namespaces
namespace	Arcane
	-- tab-width: 2; indent-tabs-mode: nil; coding: utf-8-with-signature --
namespace	Arcane::math
	Namespace for mathematical functions.

Functions
__host__ __device__ Real3	Arcane::math::vecMul (Real3 u, Real3 v)
	Vector cross product of u by v in \(R^3\).
__host__ __device__ Real	Arcane::math::vecMul2D (Real3 u, Real3 v)
	Vector cross product of u by v in \(R^2\).
__host__ __device__ Real	Arcane::math::cross2D (Real3 u, Real3 v)
	Vector cross product of u by v in \(R^2\).
__host__ __device__ Real	Arcane::math::dot (Real2 u, Real2 v)
	Dot product of u by v in \(R^2\).
__host__ __device__ Real	Arcane::math::scaMul (Real2 u, Real2 v)
	Dot product of u by v in \(R^2\).
__host__ __device__ Real	Arcane::math::dot (Real3 u, Real3 v)
	Dot product of u by v.
__host__ __device__ Real	Arcane::math::scaMul (Real3 u, Real3 v)
	Dot product of u by v.
__host__ __device__ Real	Arcane::math::mixteMul (Real3 u, Real3 v, Real3 w)
	Mixed product of u, v and w.
__host__ __device__ Real	Arcane::math::matDet (Real3 u, Real3 v, Real3 w)
	Determinant of the matrix u,v,w.
Real3x3	Arcane::math::prodTens (Real3 u, Real3 v)
	Tensor product of two Real3 vectors.
__host__ __device__ Real3	Arcane::math::prodTensVec (Real3x3 t, Real3 v)
	Matrix-vector product between a tensor and a vector.
__host__ __device__ Real2	Arcane::math::prodTensVec (Real2x2 t, Real2 v)
__host__ __device__ Real3	Arcane::math::prodVecTens (Real3 v, Real3x3 t)
	Transposed(vector) matrix product between the transpose of a vector and a matrix.
__host__ __device__ Real3x3	Arcane::math::matrixProduct (const Real3x3 &t, const Real3x3 &v)
	Matrix-matrix product between two tensors.
__host__ __device__ Real3x3	Arcane::math::transpose (const Real3x3 &t)
	Transpose the matrix.
__host__ __device__ Real3x3	Arcane::math::matrixTranspose (const Real3x3 &t)
	Transpose the matrix.
__host__ __device__ Real	Arcane::math::doubleContraction (const Real3x3 &u, const Real3x3 &v)
__host__ __device__ Real	Arcane::math::doubleContraction (const Real2x2 &u, const Real2x2 &v)
__host__ __device__ Real2	Arcane::math::min (Real2 a, Real2 b)
	Returns the minimum of two Real2.
__host__ __device__ Real3	Arcane::math::min (Real3 a, Real3 b)
	Returns the minimum of two Real3s.
__host__ __device__ Real2x2	Arcane::math::min (const Real2x2 &a, const Real2x2 &b)
	Returns the minimum of two Real2x2s.
__host__ __device__ Real3x3	Arcane::math::min (const Real3x3 &a, const Real3x3 &b)
	Returns the minimum of two Real3x3s.
template<class T>
T	Arcane::math::min (const T &a, const T &b, const T &c)
	Returns the minimum of three elements.
template<class T>
T	Arcane::math::max (const T &a, const T &b, const T &c)
	Returns the maximum of three elements.
__host__ __device__ Real2	Arcane::math::max (Real2 a, Real2 b)
	Returns the maximum of two Real2s.
__host__ __device__ Real3	Arcane::math::max (Real3 a, Real3 b)
	Returns the maximum of two Real3s.
__host__ __device__ Real2x2	Arcane::math::max (const Real2x2 &a, const Real2x2 &b)
	Returns the maximum of two Real2x2s.
__host__ __device__ Real3x3	Arcane::math::max (const Real3x3 &a, const Real3x3 &b)
	Returns the maximum of two Real3x3s.
__host__ __device__ Real	Arcane::math::min4Real (Real a, Real b, Real c, Real d)
	Returns the minimum of four Reals.
__host__ __device__ Real	Arcane::math::max4Real (Real a, Real b, Real c, Real d)
	Returns the maximum of four Reals.
__host__ __device__ Real	Arcane::math::min8Real (const Real a[8])
	Returns the minimum of eight Reals.
Real	Arcane::math::max8Real (const Real a[8])
	Returns the maximum of eight Reals.
__host__ __device__ Real	Arcane::math::minMod (Real a, Real b, Real c, Real d)
	Returns the Min mod of four Reals.
__host__ __device__ Real	Arcane::math::minMod2 (Real a, Real b)
	Returns the Min mod of two Reals.
__host__ __device__ Real	Arcane::math::maxMod2 (Real a, Real b)
	Returns the Max mod of two Reals.
Real	Arcane::math::relativeError (Real a, Real b)
	Returns the relative error between two scalars a and b.
Real	Arcane::math::relativeError (const Real3x3 &T1, const Real3x3 &T2)
	Returns the relative error between two tensors T1 and T2.
Real	Arcane::math::relativeError2 (Real a, Real b)
	Returns the relative error between two scalars a and b relative to b.
Real	Arcane::math::relativeError1 (Real a, Real b)
	Returns the relative error between two scalars a and b relative to a.
bool	Arcane::math::searchExtrema (ConstArrayView< Real2 > array, Real &xmin, Real &xmax, Real &ymin, Real &ymax, bool need_init)
	Searches for the extreme values of an array of pairs (x,y).
__host__ __device__ Real	Arcane::math::matrixDeterminant (Real3x3 m)
	Calculates the determinant of a 3x3 matrix.
Real	Arcane::math::normeR3 (Real3 v1)
	Norm of a vector.
__host__ __device__ Real3x3	Arcane::math::matrix3x3Id ()
	Identity matrix.
__host__ __device__ Real3x3	Arcane::math::inverseMatrix (const Real3x3 &m, Real d)
	Calculates the inverse of a matrix m assuming its determinant d is known.
__host__ __device__ Real3x3	Arcane::math::inverseMatrix (const Real3x3 &m)
	Calculates the inverse of a matrix m.
Real3	Arcane::math::crossProduct3 (Real3 v1, Real3 v2)
	Cross product of two 3-component vectors.
__host__ __device__ Real3	Arcane::math::cross (Real3 v1, Real3 v2)
	Cross product of two 3-component vectors.
__host__ __device__ Real3	Arcane::math::normalizeReal3 (Real3 v)
	Normalization of a Real3.
Real3	Arcane::math::normalizedCrossProduct3 (Real3 v1, Real3 v2)
	Normalized cross product.
Real3x3	Arcane::math::matrix3x3Transp (Real3x3 m)
Real3x3	Arcane::math::matrix3x3Prod (Real3x3 m1, Real3x3 m2)
	Multiplication of 2 3x3 matrices.
__host__ __device__ Real3	Arcane::math::multiply (const Real3x3 &m, Real3 v)
	3x3 matrix multiplied by a vector.
bool	Arcane::math::isNearlyId (Real3x3 m, Real epsilon=1.e-10)
	Checks if a matrix is the identity matrix.
Real3	Arcane::math::planarSymmetric (Real3 u, Real3 n)
	Symmetry of a vector u with respect to a normal plane n.
Real3	Arcane::math::axisSymmetric (Real3 u, Real3 a)
	Symmetry of a vector u with respect to an axis defined by direction vector a.
template<typename T>
void	Arcane::math::add (ArrayView< T > lhs, ConstArrayView< T > copy_array)
	Adds the array copy_array to the instance.
template<typename T>
void	Arcane::math::add (ArrayView< T > lhs, ArrayView< T > copy_array)
	Adds the array copy_array to the instance.
template<typename T>
void	Arcane::math::sub (ArrayView< T > lhs, ConstArrayView< T > copy_array)
	Subtracts the array copy_array from the instance.
template<typename T>
void	Arcane::math::sub (ArrayView< T > lhs, ArrayView< T > copy_array)
	Subtracts the array copy_array from the instance.
template<typename T>
void	Arcane::math::mult (ArrayView< T > lhs, ConstArrayView< T > copy_array)
	Multiplies the elements of the instance term-by-term by the elements of the array copy_array.
template<typename T>
void	Arcane::math::mult (ArrayView< T > lhs, ArrayView< T > copy_array)
	Multiplies the elements of the instance term-by-term by the elements of the array copy_array.
template<typename T>
void	Arcane::math::mult (ArrayView< T > lhs, T o)
	Multiplies all elements of the array by the real number o.
template<typename T>
void	Arcane::math::power (ArrayView< T > lhs, T o)
	Raises all elements of the array to the power o.

Detailed Description

Various mathematical functions.

Definition in file MathUtils.h.