SymmetricTensor.h File Reference

Basic algebra for symmetric 2nd order tensors. More...

#include "math/AffineMatrix.h"
#include "objects/containers/StaticArray.h"

Go to the source code of this file.

Classes
class	SymmetricTensor
	Symmetric tensor of 2nd order. More...
struct	Eigen
struct	Svd

Functions
INLINE SymmetricTensor	transform (const SymmetricTensor &t, const AffineMatrix &transform)
template<typename T1 , typename T2 >
T1	convert (const T2 &matrix)
template<>
INLINE SymmetricTensor	convert (const AffineMatrix &matrix)
template<>
INLINE AffineMatrix	convert (const SymmetricTensor &t)
INLINE bool	almostEqual (const SymmetricTensor &t1, const SymmetricTensor &t2, const Float eps=EPS)
	Tensor utils. More...
template<>
INLINE Float	norm (const SymmetricTensor &t)
template<>
INLINE Float	normSqr (const SymmetricTensor &t)
	Arbitrary squared norm of the tensor. More...
template<>
INLINE auto	abs (const SymmetricTensor &t)
	Returns the tensor of absolute values. More...
template<>
INLINE Float	minElement (const SymmetricTensor &t)
	Returns the minimal element of the tensor. More...
template<>
INLINE Float	maxElement (const SymmetricTensor &t)
	Returns the maximal element of the tensor. More...
template<>
INLINE SymmetricTensor	min (const SymmetricTensor &t1, const SymmetricTensor &t2)
	Component-wise minimum of two tensors. More...
template<>
INLINE SymmetricTensor	max (const SymmetricTensor &t1, const SymmetricTensor &t2)
	Component-wise maximum of two tensors. More...
template<>
INLINE SymmetricTensor	clamp (const SymmetricTensor &t, const Interval &range)
	Clamping all components by range. More...
template<>
INLINE bool	isReal (const SymmetricTensor &t)
template<>
INLINE auto	less (const SymmetricTensor &t1, const SymmetricTensor &t2)
template<>
INLINE StaticArray< Float, 6 >	getComponents (const SymmetricTensor &t)
INLINE Float	ddot (const SymmetricTensor &t1, const SymmetricTensor &t2)
	Double-dot product t1 : t2 = sum_ij t1_ij t2_ij. More...
INLINE SymmetricTensor	symmetricOuter (const Vector &v1, const Vector &v2)
	SYMMETRIZED outer product of two vectors. More...
INLINE StaticArray< Float, 3 >	findEigenvalues (const SymmetricTensor &t)
	Returns three eigenvalue of symmetric matrix. More...
Eigen	eigenDecomposition (const SymmetricTensor &t)
	Computes eigenvectors and corresponding eigenvalues of symmetric matrix. More...
Svd	singularValueDecomposition (const SymmetricTensor &t)
	Computes the singular value decomposition of symmetric matrix. More...

Detailed Description

Basic algebra for symmetric 2nd order tensors.

Author

Pavel Sevecek (sevecek at sirrah.troja.mff.cuni.cz)

Date

2016-2021

Definition in file SymmetricTensor.h.

Function Documentation

abs()

template<>

INLINE auto abs

(

const SymmetricTensor &

t

)

Returns the tensor of absolute values.

Definition at line 304 of file SymmetricTensor.h.

almostEqual()

INLINE bool almostEqual	(	const SymmetricTensor &	t1,
		const SymmetricTensor &	t2,
		const Float	eps = EPS
	)

Tensor utils.

Checks if two tensors are equal to some given accuracy.

Definition at line 279 of file SymmetricTensor.h.

clamp()

template<>

INLINE SymmetricTensor clamp	(	const SymmetricTensor &	t,
		const Interval &	range
	)

Clamping all components by range.

Definition at line 334 of file SymmetricTensor.h.

convert() [1/3]

template<>

INLINE SymmetricTensor convert

(

const AffineMatrix &

matrix

)

Definition at line 257 of file SymmetricTensor.h.

convert() [2/3]

template<>

INLINE AffineMatrix convert

(

const SymmetricTensor &

t

)

Definition at line 266 of file SymmetricTensor.h.

convert() [3/3]

template<typename T1 , typename T2 >

T1 convert

(

const T2 &

matrix

)

ddot()

INLINE Float ddot	(	const SymmetricTensor &	t1,
		const SymmetricTensor &	t2
	)

Double-dot product t1 : t2 = sum_ij t1_ij t2_ij.

Definition at line 354 of file SymmetricTensor.h.

eigenDecomposition()

Eigen eigenDecomposition

(

const SymmetricTensor &

t

)

Computes eigenvectors and corresponding eigenvalues of symmetric matrix.

Definition at line 249 of file SymmetricTensor.cpp.

findEigenvalues()

INLINE StaticArray<Float, 3> findEigenvalues

(

const SymmetricTensor &

t

)

Returns three eigenvalue of symmetric matrix.

Definition at line 370 of file SymmetricTensor.h.

getComponents()

template<>

INLINE StaticArray<Float, 6> getComponents

(

const SymmetricTensor &

t

)

Definition at line 349 of file SymmetricTensor.h.

isReal()

template<>

INLINE bool isReal

(

const SymmetricTensor &

t

)

Definition at line 339 of file SymmetricTensor.h.

less()

template<>

INLINE auto less	(	const SymmetricTensor &	t1,
		const SymmetricTensor &	t2
	)

Definition at line 344 of file SymmetricTensor.h.

max()

template<>

INLINE SymmetricTensor max	(	const SymmetricTensor &	t1,
		const SymmetricTensor &	t2
	)

Component-wise maximum of two tensors.

Definition at line 328 of file SymmetricTensor.h.

maxElement()

template<>

INLINE Float maxElement

(

const SymmetricTensor &

t

)

Returns the maximal element of the tensor.

Definition at line 316 of file SymmetricTensor.h.

min()

template<>

INLINE SymmetricTensor min	(	const SymmetricTensor &	t1,
		const SymmetricTensor &	t2
	)

Component-wise minimum of two tensors.

Definition at line 322 of file SymmetricTensor.h.

minElement()

template<>

INLINE Float minElement

(

const SymmetricTensor &

t

)

Returns the minimal element of the tensor.

Definition at line 310 of file SymmetricTensor.h.

norm()

template<>

INLINE Float norm

(

const SymmetricTensor &

t

)

Arbitrary norm of the tensor.

Note

This norm is NOT an invariant.

Todo:

Use some well-defined norm instead? (spectral norm, L1 or L2 norm, ...)

Definition at line 289 of file SymmetricTensor.h.

normSqr()

template<>

INLINE Float normSqr

(

const SymmetricTensor &

t

)

Arbitrary squared norm of the tensor.

Definition at line 297 of file SymmetricTensor.h.

singularValueDecomposition()

Svd singularValueDecomposition

(

const SymmetricTensor &

t

)

Computes the singular value decomposition of symmetric matrix.

Definition at line 526 of file SymmetricTensor.cpp.

symmetricOuter()

INLINE SymmetricTensor symmetricOuter	(	const Vector &	v1,
		const Vector &	v2
	)

SYMMETRIZED outer product of two vectors.

Note that simple outer product is not necessarily symmetric matrix.

Todo:

optimize

Definition at line 361 of file SymmetricTensor.h.

transform()

INLINE SymmetricTensor transform	(	const SymmetricTensor &	t,
		const AffineMatrix &	transform
	)

Transforms given symmetric tensor by matrix.

Todo:

optimize

Definition at line 244 of file SymmetricTensor.h.