gismo::expr Namespace Reference

This namespace contains expressions used for FE computations. More...

Classes
class	_expr< E, false >
	Base class for all expressions. More...
class	asdiag_expr
class	cartconinv_expr
class	cartcovinv_expr
class	constMat_expr
class	deriv2_expr
	Computes the second derivative of an expression. More...
class	deriv2dot_expr
	Expression that takes the second derivative of an expression and multiplies it with a row vector. More...
class	exp_expr
class	flat_expr
class	flatdot2_expr
	Computes the product of expressions E1 and E2 and multiplies with a vector E3 in voight notation. More...
class	flatdot_expr
	Computes the product of expressions E1 and E2 and multiplies with a vector E3 in voight notation. More...
class	gsFeSpace
class	gsFeVariable
class	idMat_expr
class	integral_expr
class	lapl_expr
class	matrix_by_space_expr
class	matrix_by_space_expr_tr
class	normal_expr
class	onormal_expr
class	ovar1_expr
	Expression for the first variation of the outer normal. More...
class	ovar2dot_expr
	Expression for the second variation of the outer normal times a vector. More...
class	pow_expr
class	ppart_expr
class	ppartval_expr
class	sign_expr
class	tangent_expr
class	tvar1_expr
	Expression for the first variation of the outer tangent. More...
class	unitVec_expr
	Simple expression for the unit vector of length dim and with value 1 on index. More...
class	var1_expr
	Expression for the first variation of the surface normal. More...
class	var2_expr
	Second variation of the normal. More...
class	var2deriv2dot_expr
	Second variation of the surface normal times the second derivative of the geometry map times a vector. More...
class	var2dot_expr
	Second variation of the surface normal times a vector. More...

Functions
template<class E >
EIGEN_STRONG_INLINE abs_expr< E >	abs (const E &u)
	Absolute value.
template<class T >
EIGEN_STRONG_INLINE curl_expr< T >	curl (const gsFeVariable< T > &u)
	The curl of a finite element variable.
template<typename E >
EIGEN_STRONG_INLINE diag_expr< E > const	diagonal (E const &u)
	Get diagonal elements of matrix as a vector.
template<class T >
EIGEN_STRONG_INLINE dJacG_expr< T >	dJac (const gsGeometryMap< T > &G)
	The partial derivatives of the Jacobian matrix of a geometry map.
template<class E >
EIGEN_STRONG_INLINE dJacdc_expr< E >	dJacdc (const E &u, index_t c)
	The derivative of the jacobian of a geometry map with respect to a coordinate.
template<class T >
EIGEN_STRONG_INLINE fform2nd_expr< T >	fform2nd (const gsGeometryMap< T > &G)
	The second fundamental form of G.
template<typename E >
EIGEN_STRONG_INLINE flat_expr< E > const	flat (E const &u)
	Make a matrix 2x2 expression "flat".
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE frprod3_expr< E1, E2 > const	frprod3 (E1 const &u, E2 const &M)
	Frobenious product (also known as double dot product) operator for expressions.
	GISMO_EXPR_VECTOR_EXPRESSION (inv, cramerInverse, 0)
	Inverse of a matrix expression.
	GISMO_EXPR_VECTOR_EXPRESSION (norm, norm, 1)
	Eucledian Norm.
	GISMO_EXPR_VECTOR_EXPRESSION (normalized, normalized, 0)
	Normalization of a vector to unit measure.
	GISMO_EXPR_VECTOR_EXPRESSION (sqNorm, squaredNorm, 1)
	Squared Eucledian Norm.
template<class E >
EIGEN_STRONG_INLINE grad_expr< E >	grad (const E &u)
	The gradient of a variable.
template<class T >
EIGEN_STRONG_INLINE hess_expr< gsFeSolution< T > >	hess (const gsFeSolution< T > &u)
	The hessian of a solution variable.
template<class T >
EIGEN_STRONG_INLINE hess_expr< gsGeometryMap< T > >	hess (const gsGeometryMap< T > &u)
	The hessian of a geometry map.
EIGEN_STRONG_INLINE idMat_expr	id (const index_t dim)
	The identity matrix of dimension dim.
template<class T >
EIGEN_STRONG_INLINE grad_expr< gsFeSolution< T > >	jac (const gsFeSolution< T > &s)
	Jacobian matrix for a solution expression.
template<class T >
EIGEN_STRONG_INLINE jac_expr< gsGeometryMap< T > >	jac (const gsGeometryMap< T > &G)
	The Jacobian matrix of a geometry map.
template<class E >
EIGEN_STRONG_INLINE jac_expr< E >	jac (const symbol_expr< E > &u)
	The Jacobian matrix of a FE variable.
template<class E >
EIGEN_STRONG_INLINE jacScaledLx_expr< E >	jacScaledLx (const E &u, const gsGeometryMap< typename E::Scalar > &G)
	jacobian matrix of scaled Lx for PDE-based parameterization construction
template<class E >
EIGEN_STRONG_INLINE jacScaledLxDiag_expr< E >	jacScaledLxDiag (const E &u, const gsGeometryMap< typename E::Scalar > &G)
	diagonal part of jacobian matrix of scaled Lx for PDE-based parameterization construction
template<class E >
EIGEN_STRONG_INLINE jacScaledLxDiagBlock_expr< E >	jacScaledLxDiagBlock (const E &u, const gsGeometryMap< typename E::Scalar > &G)
	diagonal block part of jacobian matrix of scaled Lx for PDE-based parameterization construction
template<class E >
EIGEN_STRONG_INLINE jacScaledLxH1_expr< E >	jacScaledLxH1 (const E &u, const gsGeometryMap< typename E::Scalar > &G)
	jacobian matrix of scaled Lx (in H1 space) for PDE-based parameterization construction
template<class E >
EIGEN_STRONG_INLINE jacScaledLxH1DiagBlock_expr< E >	jacScaledLxH1DiagBlock (const E &u, const gsGeometryMap< typename E::Scalar > &G)
	jacobian matrix of scaled Lx (in H1 space) for PDE-based parameterization construction
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE matrix_by_space_expr< E1, E2 > const	matrix_by_space (E1 const &u, E2 const &v)
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE matrix_by_space_expr_tr< E1, E2 > const	matrix_by_space_tr (E1 const &u, E2 const &v)
template<class T >
EIGEN_STRONG_INLINE meas_expr< T >	meas (const gsGeometryMap< T > &G)
	The measure of a geometry map.
template<class T >
EIGEN_STRONG_INLINE nabla_expr< T >	nabla (const gsFeVariable< T > &u)
	The nabla ( \(\nabla\)) of a finite element variable.
template<class T >
nabla2_expr< T >	nabla2 (const gsFeVariable< T > &u)
	The nabla2 ( \(\nabla^2\)) of a finite element variable.
template<class T >
EIGEN_STRONG_INLINE onormal_expr< T >	nv (const gsGeometryMap< T > &u)
	The (outer pointing) boundary normal of a geometry map.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE frprod_expr< E1, E2 > const	operator% (_expr< E1 > const &u, _expr< E2 > const &v)
	Frobenious product (also known as double dot product) operator for expressions.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE mult_expr< E1, E2 > const	operator* (_expr< E1 > const &u, _expr< E2 > const &v)
	Multiplication operator for expressions.
template<typename E >
EIGEN_STRONG_INLINE add_expr< E, _expr< typename E::Scalar, true > >	operator+ (_expr< E > const &u, const typename E::Scalar v)
	Addition operator for expressions and numbers.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE add_expr< E1, E2 > const	operator+ (_expr< E1 > const &u, _expr< E2 > const &v)
	Addition operator for expressions.
template<typename E >
EIGEN_STRONG_INLINE add_expr< E, _expr< typename E::Scalar, true > >	operator+ (const typename E::Scalar v, _expr< E > const &u)
	Addition operator for expressions and numbers.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE sub_expr< E1, E2 > const	operator- (_expr< E1 > const &u, _expr< E2 > const &v)
	Subtraction operator for expressions.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE divide_expr< E1, E2 > const	operator/ (_expr< E1 > const &u, _expr< E2 > const &v)
	Scalar division operator for expressions.
template<typename E >
std::ostream &	operator<< (std::ostream &os, const _expr< E > &b)
	Stream operator for expressions.
template<typename E >
EIGEN_STRONG_INLINE replicate_expr< E > const	replicate (E const &u, index_t n, index_t m=1)
	Replicate an expression.
template<typename E >
EIGEN_STRONG_INLINE reshape_expr< E > const	reshape (E const &u, index_t n, index_t m)
	Reshape an expression.
template<typename E1 , typename E2 >
EIGEN_STRONG_INLINE summ_expr< E1, E2 > const	summ (E1 const &u, E2 const &M)
	Matrix-summation operator for expressions.
template<class E0 , class E1 , class E2 >
EIGEN_STRONG_INLINE ternary_expr< E0, E1, E2 >	ternary (const E0 &u, const E1 &v, const E2 &w)
	Ternary ternary_expr.
template<class T >
EIGEN_STRONG_INLINE tangent_expr< T >	tv (const gsGeometryMap< T > &u)
	The tangent boundary vector of a geometry map in 2D.

Detailed Description

This namespace contains expressions used for FE computations.

Function Documentation

matrix_by_space()

template<typename E1 , typename E2 >

EIGEN_STRONG_INLINE matrix_by_space_expr< E1, E2 > const matrix_by_space	(	E1 const &	u,
		E2 const &	v
	)

Matrix by space TODO: find better name and/or description? And is this the best place? [Jg Jg Jg] * Jb ..

matrix_by_space_tr()

template<typename E1 , typename E2 >

EIGEN_STRONG_INLINE matrix_by_space_expr_tr< E1, E2 > const matrix_by_space_tr	(	E1 const &	u,
		E2 const &	v
	)

Matrix by space TODO: find better name and/or description? And is this the best place? [Jg Jg Jg] * Jb ..