Norms and Invariants

Scalar measures of tensors: norms, determinant, trace, principal invariants, and argmax queries. More...

Functions
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::norm (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::norm_1 (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::norm_infinity (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION Tensor< T, N >	minitensor::subtensor (Tensor< T, N > const &A, Index const i, Index const j)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::det (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::trace (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::I1 (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::I2 (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::I3 (Tensor< T, N > const &A)
template<typename T , Index N>
KOKKOS_INLINE_FUNCTION T	minitensor::norm_off_diagonal (Tensor< T, N > const &A)
template<typename T , Index N>
std::pair< Index, Index >	minitensor::arg_max_abs (Tensor< T, N > const &A)
template<typename T , Index N>
std::pair< Index, Index >	minitensor::arg_max_off_diagonal (Tensor< T, N > const &A)

Detailed Description

Scalar measures of tensors: norms, determinant, trace, principal invariants, and argmax queries.

Function Documentation

norm()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::norm

(

Tensor< T, N > const &

A

)

Tensor Frobenius norm

Returns

\( \sqrt{A:A} \)

Definition at line 138 of file MiniTensor_Norms.h.

norm_1()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::norm_1

(

Tensor< T, N > const &

A

)

Tensor 1-norm

Returns

\( \max_{j \in {0,1,2}}\Sigma_{i=0}^2 |A_{ij}| \)

Definition at line 181 of file MiniTensor_Norms.h.

norm_infinity()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::norm_infinity

(

Tensor< T, N > const &

A

)

Tensor infinity-norm

Returns

\( \max_{i \in {0,1,2}}\Sigma_{j=0}^2 |A_{ij}| \)

Definition at line 239 of file MiniTensor_Norms.h.

subtensor()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION Tensor< T, N > minitensor::subtensor	(	Tensor< T, N > const &	A,
		Index const	i,
		Index const	j
	)

Subtensor

Parameters

A	tensor
i	index
j	index

Returns

Subtensor with i-row and j-col deleted.

Definition at line 504 of file MiniTensor_Norms.h.

det()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::det

(

Tensor< T, N > const &

A

)

Determinant

Returns

\( \det A \)

Definition at line 300 of file MiniTensor_Norms.h.

trace()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::trace

(

Tensor< T, N > const &

A

)

Trace

Returns

\( A:I \)

Definition at line 355 of file MiniTensor_Norms.h.

I1()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::I1

(

Tensor< T, N > const &

A

)

First invariant, trace

Returns

\( I_A = A:I \)

Definition at line 395 of file MiniTensor_Norms.h.

I2()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::I2

(

Tensor< T, N > const &

A

)

Second invariant

Returns

\( II_A = \frac{1}{2}((I_A)^2-I_{A^2}) \)

Definition at line 408 of file MiniTensor_Norms.h.

I3()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::I3

(

Tensor< T, N > const &

A

)

Third invariant

Returns

\( III_A = \det A \)

Definition at line 457 of file MiniTensor_Norms.h.

norm_off_diagonal()

template<typename T , Index N>

KOKKOS_INLINE_FUNCTION T minitensor::norm_off_diagonal

(

Tensor< T, N > const &

A

)

Off-diagonal norm. Useful for SVD and other algorithms that rely on Jacobi-type procedures.

Returns

\( \sqrt(\sum_i \sum_{j, j\neq i} a_{ij}^2) \)

Definition at line 539 of file MiniTensor_Norms.h.

arg_max_abs()

template<typename T , Index N>

std::pair< Index, Index > minitensor::arg_max_abs

(

Tensor< T, N > const &

A

)

Arg max abs. Useful for inverse and other algorithms that rely on Jacobi-type procedures.

Returns

\( (p,q) = arg max_{i,j} |a_{ij}| \)

Definition at line 581 of file MiniTensor_Norms.h.

arg_max_off_diagonal()

template<typename T , Index N>

std::pair< Index, Index > minitensor::arg_max_off_diagonal

(

Tensor< T, N > const &

A

)

Arg max off-diagonal. Useful for SVD and other algorithms that rely on Jacobi-type procedures.

Returns

\( (p,q) = arg max_{i \neq j} |a_{ij}| \)

Definition at line 612 of file MiniTensor_Norms.h.