Tensor Operators


Functions
void	Tensors::Dot (Tensor2 const &A, Tensor1 const &u, Tensor1 &v)
REAL	Tensors::Dot (Tensor2 const &x, Tensor2 const &y)
	$sc\gets\{x\}\bullet\{y\} \quad\equiv\quad sc\gets\TeSe{x}:\TeSe{y}$
void	Tensors::Dot (Tensor2 const &x, Tensor4 const &A, Tensor2 &y)
	$\{y\}\gets\{x\}\bullet[A] \quad\equiv\quad \TeSe{y}\gets\TeSe{x}:\TeFo{A}$
void	Tensors::Dot (Tensor4 const &A, Tensor2 const &x, Tensor2 &y)
	$\{y\}\gets[A]\bullet\{x\} \quad\equiv\quad \TeSe{y}\gets\TeFo{A}:\TeSe{x}$
void	Tensors::Dot (Tensor4 const &A, Tensor4 const &B, Tensor4 &C)
	$[C]\gets[A]\bullet[B] \quad\equiv\quad \TeFo{C}\gets\TeFo{A}:\TeFo{B}$
void	Tensors::Dyad (Tensor2 const &x, Tensor2 const &y, Tensor4 &A)
	$[A]=\{x\}\otimes\{y\} \quad\equiv\quad \TeFo{A}\gets\TeSe{x}\otimes\TeSe{y}$
void	Tensors::AddScaled (REAL const &a, Tensor4 const &X, REAL const &b, Tensor4 const &Y, Tensor4 &Z)
	Add scaled tensors: $[Z] \gets a[X]+b[Y] \quad\equiv\quad \TeFo{Z}\gets a\TeFo{X}+b\TeFo{Y}$ .
void	Tensors::Ger (REAL const &a, Tensor2 const &x, Tensor2 const &y, Tensor4 &A)
	$[A]=\alpha\{x\}\otimes\{y\}+[A] \quad\equiv\quad \TeFo{A}\gets\alpha\TeSe{x}\otimes\TeSe{y}+\TeFo{A}$
void	Tensors::GerX (REAL const &a, Tensor4 const &A, Tensor2 const &x, Tensor2 const &y, Tensor4 const &B, Tensor4 const &C, Tensor4 &D)
	$[D]=\alpha([A]\bullet\{x\})\otimes(\{y\}\bullet[B])+[C] \quad\equiv\quad \TeFo{D}\gets\alpha(\TeFo{A}:\TeSe{x})\otimes(\TeSe{y}:\TeFo{B})+\TeFo{C}$
void	Tensors::Scale (REAL const &a, Tensor4 &B)
	$[B]=\alpha([B]) \quad\equiv\quad \TeFo{B}\gets\alpha\TeFo{B}$
void	Tensors::CopyScale (REAL const &a, Tensor4 const &A, Tensor4 &B)
	$[B]=\alpha([A]) \quad\equiv\quad \TeFo{B}\gets\alpha\TeFo{A}$
REAL	Tensors::Reduce (Tensor2 const &x, Tensor4 const &A, Tensor2 const &y)
	$s=\{x\}^T[A]\{y\} \quad\equiv\quad s=\Dc{\Dc{\TeSe{x}}{\TeFo{A}}}{\TeSe{y}}$

Generated on Wed Jan 24 15:56:28 2007 for MechSys by

1.4.7

Tensor Operators

Functions