Namespace to perform operation on Eigen objects. More...

Functions
void	sortEigenvalues (Eigen::VectorXd &eigenvalues, Eigen::MatrixXd &eigenvectors)
	sort eigenvalues
Eigen::VectorXd	ExpSpaced (double first, double last, int n)
	Returns exponentially spaced vector.
template<typename T>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	vectorTensorProduct (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &g, const Eigen::Tensor< T, 3 > &c, const Eigen::Matrix< T, Eigen::Dynamic, 1 > &a)
	A function that computes the product of g.T c a, where c is a third dim tensor.
template Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	vectorTensorProduct (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &g, const Eigen::Tensor< double, 3 > &c, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &a)
template Eigen::Matrix< int, Eigen::Dynamic, Eigen::Dynamic >	vectorTensorProduct (const Eigen::Matrix< int, Eigen::Dynamic, 1 > &g, const Eigen::Tensor< int, 3 > &c, const Eigen::Matrix< int, Eigen::Dynamic, 1 > &a)
template Eigen::Matrix< float, Eigen::Dynamic, Eigen::Dynamic >	vectorTensorProduct (const Eigen::Matrix< float, Eigen::Dynamic, 1 > &g, const Eigen::Tensor< float, 3 > &c, const Eigen::Matrix< float, Eigen::Dynamic, 1 > &a)
Eigen::VectorXd	repeatElements (Eigen::VectorXd input, int n)
	Repeat each element n times after themselves.
Eigen::VectorXd	reorderVectorFromDim (Eigen::VectorXd input, int dim)
	Changes the order of the vector's elements given a dimension.
template<typename T>
Eigen::SparseMatrix< T >	vectorize (Eigen::SparseMatrix< T > &Matrix)
	Vectorize a Sparse Matrix.
template<typename T>
T	max (Eigen::SparseMatrix< T > &mat, label &ind_row, label &ind_col)
	Find the maximum of a sparse Matrix (Useful for DEIM).
template<typename T>
T	min (Eigen::SparseMatrix< T > &mat, label &ind_row, label &ind_col)
	Find the minimum of a sparse Matrix (Useful for DEIM).
template<typename T>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	innerProduct (List< Eigen::SparseMatrix< T > > &A, List< Eigen::SparseMatrix< T > > &B)
	Perform Frobenius inner Product between two list of sparse matrices A and B.
template<typename T>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	innerProduct (List< Eigen::SparseMatrix< T > > &A, Eigen::SparseMatrix< T > &B)
	Perform Frobenius inner Product between a list of sparse matrices A and a sparse matrix B.
template<typename T>
T	innerProduct (Eigen::SparseMatrix< T > &A, Eigen::SparseMatrix< T > &B)
	Perform Frobenius inner Product between two sparse matrices A and B.
template<typename T>
Eigen::SparseMatrix< T >	MVproduct (List< Eigen::SparseMatrix< T > > &A, Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &C)
	Sparse Matrix-Vector product between a list of sparse matrices and a vector of coefficients.
template<typename T>
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	MVproduct (const std::vector< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &A, Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &C)
	Dense Matrix-Vector product between a list of sparse matrices and a vector of coefficients.
template<typename T>
List< Eigen::SparseMatrix< T > >	MMproduct (List< Eigen::SparseMatrix< T > > &A, Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &C)
	Sparse Matrix - Dense Matrix product between a list of sparse matrices and a dense matrix.
template<typename T>
T	condNumber (Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &A)
	Conditioning number of a dense matrix.

Detailed Description

Namespace to perform operation on Eigen objects.

Function Documentation

◆ condNumber()

template<typename T>

T EigenFunctions::condNumber ( Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & A )

Conditioning number of a dense matrix.

Parameters

[in] A input Matrix

Template Parameters

T	type of object, i.e. double, float, ....

Returns: Conditioning number

Definition at line 451 of file EigenFunctions.H.

◆ ExpSpaced()

Eigen::VectorXd EigenFunctions::ExpSpaced	(	double	first,
		double	last,
		int	n )

Returns exponentially spaced vector.

Parameters

[in]	first	First element of the vector
[in]	last	Last element of the vector
[in]	n	Number of elements

Template Parameters

T	type of object, i.e. double, float, ....

Returns: Exponentially spaced vector

Definition at line 72 of file EigenFunctions.C.

◆ innerProduct() [1/3]

template<typename T>

T EigenFunctions::innerProduct	(	Eigen::SparseMatrix< T > &	A,
		Eigen::SparseMatrix< T > &	B )

Perform Frobenius inner Product between two sparse matrices A and B.

\[out = tr(\mathbf{A}^T \mathbf{B} ) \]

Parameters

[in]	A	Sparse Matrix A
[in]	B	Sparse Matrix B

Template Parameters

T	type of object, i.e. double, float, ....

Returns: out Value of the inner products between the two matrices

Definition at line 385 of file EigenFunctions.H.

◆ innerProduct() [2/3]

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > EigenFunctions::innerProduct	(	List< Eigen::SparseMatrix< T > > &	A,
		Eigen::SparseMatrix< T > &	B )

Perform Frobenius inner Product between a list of sparse matrices A and a sparse matrix B.

\[\mathbf{A} = [\mathbf{A_1}, \dots, \mathbf{A_N}] , out_i = tr(\mathbf{A_i}^T \mathbf{B} ) \]

Parameters

[in]	A	List of Matrices A
[in]	B	Sparse Matrix B

Template Parameters

T	type of object, i.e. double, float, ....

Returns: out Vector containing the inner products between the matrix lists

Definition at line 368 of file EigenFunctions.H.

◆ innerProduct() [3/3]

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > EigenFunctions::innerProduct	(	List< Eigen::SparseMatrix< T > > &	A,
		List< Eigen::SparseMatrix< T > > &	B )

Perform Frobenius inner Product between two list of sparse matrices A and B.

\[ \mathbf{A} = [\mathbf{A_1}, \dots, \mathbf{A_N}] , \mathbf{B} = [\mathbf{B_1}, \dots, \mathbf{B_M}] , out_{ij} = tr(\mathbf{A_i}^T \mathbf{B_j} ) \]

Parameters

[in]	A	List of Matrices A
[in]	B	List of Matrices B

Template Parameters

T	type of object, i.e. double, float, ....

Returns: out Matrix containing the inner products between the matrix lists

Definition at line 348 of file EigenFunctions.H.

◆ max()

template<typename T>

T EigenFunctions::max	(	Eigen::SparseMatrix< T > &	mat,
		label &	ind_row,
		label &	ind_col )

Find the maximum of a sparse Matrix (Useful for DEIM).

Parameters

[out]	mat	The matrix
[out]	ind_row	The ind row
[out]	ind_col	The ind col

Template Parameters

T	type of object, i.e. double, float, ....

Returns: the maximum

Definition at line 300 of file EigenFunctions.H.

◆ min()

template<typename T>

T EigenFunctions::min	(	Eigen::SparseMatrix< T > &	mat,
		label &	ind_row,
		label &	ind_col )

Find the minimum of a sparse Matrix (Useful for DEIM).

Parameters

[out]	mat	The matrix
[out]	ind_row	The index for the row
[out]	ind_col	The ind col

Template Parameters

T	type of object, i.e. double, float, ....

Returns: the minimum

Definition at line 324 of file EigenFunctions.H.

◆ MMproduct()

template<typename T>

List< Eigen::SparseMatrix< T > > EigenFunctions::MMproduct	(	List< Eigen::SparseMatrix< T > > &	A,
		Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &	C )

Sparse Matrix - Dense Matrix product between a list of sparse matrices and a dense matrix.

\[ \mathbf{A} = [\mathbf{A_1}, \dots, \mathbf{A_N}] , \mathbf{C} = [\mathbf{c_{\bullet 1}}, ...., \mathbf{c_{\bullet N}}], \mathbf{out} = [\mathbf{O_1},\dots,\mathbf{O_N}] \]

\[ \mathbf{O_i} = \sum_{k=1}^N \mathbf{A_k} c_{ki} \]

Parameters

[in]	A	List of sparse Matrices
[in]	C	Dense Matrix

Template Parameters

T	type of object, i.e. double, float, ....

Returns: List of Sparse Matrices containing the sum of all the matrices multiplied by the matrix coefficients by columns

Definition at line 433 of file EigenFunctions.H.

◆ MVproduct() [1/2]

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > EigenFunctions::MVproduct	(	const std::vector< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &	A,
		Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &	C )

Dense Matrix-Vector product between a list of sparse matrices and a vector of coefficients.

\[ \mathbf{A} = [\mathbf{A_1}, \dots, \mathbf{A_N}] , \mathbf{c} = [c_1, ...., c_N] \]

\[ \mathbf{out} = \sum_{k=1}^N \mathbf{A_k} c_k \]

Parameters

[in]	A	Dense Matrix A
[in]	C	Dense Vector C

Template Parameters

T	type of object, i.e. double, float, ....

Returns: Dense Matrix containing the sum of all the matrices multiplied by the vector coefficients

Definition at line 415 of file EigenFunctions.H.

◆ MVproduct() [2/2]

template<typename T>

Eigen::SparseMatrix< T > EigenFunctions::MVproduct	(	List< Eigen::SparseMatrix< T > > &	A,
		Eigen::DenseBase< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > > &	C )

Sparse Matrix-Vector product between a list of sparse matrices and a vector of coefficients.

\[ \mathbf{A} = [\mathbf{A_1}, \dots, \mathbf{A_N}] , \mathbf{c} = [c_1, ...., c_N] \]

\[ \mathbf{out} = \sum_{k=1}^N \mathbf{A_k} c_k \]

Parameters

[in]	A	Sparse Matrix A
[in]	C	Dense Vector C

Template Parameters

T	type of object, i.e. double, float, ....

Returns: out Sparse Matrix containing the sum of all the matrices multiplied by the vector coefficients

Definition at line 399 of file EigenFunctions.H.

◆ reorderVectorFromDim()

Eigen::VectorXd EigenFunctions::reorderVectorFromDim	(	Eigen::VectorXd	input,
		int	dim )

Changes the order of the vector's elements given a dimension.

Example: input = (a_1, b_1, a_2, b_2, a_3, b_3); dim = 3 output = (a_1, a_2, a_3, b_1, b_2, b_3) Typically switch from a component then coordinate order to the opposite as did the change in the Foam2Eigen mapping

Parameters

input	Eigen::VectorXd
dim	int

Definition at line 146 of file EigenFunctions.C.

◆ repeatElements()

Eigen::VectorXd EigenFunctions::repeatElements	(	Eigen::VectorXd	input,
		int	n )

Repeat each element n times after themselves.

Example: input = (a, b); n = 3 output = (a, a, a, b, b, b)

Parameters

input	Eigen::VectorXd
n	int

Definition at line 125 of file EigenFunctions.C.

◆ sortEigenvalues()

void EigenFunctions::sortEigenvalues	(	Eigen::VectorXd &	eigenvalues,
		Eigen::MatrixXd &	eigenvectors )

sort eigenvalues

Parameters

[in,out]	eigenvalues	The eigenvalues
[in,out]	eigenvectors	The eigenvectors

Definition at line 39 of file EigenFunctions.C.

◆ vectorize()

template<typename T>

Eigen::SparseMatrix< T > EigenFunctions::vectorize ( Eigen::SparseMatrix< T > & Matrix )

Vectorize a Sparse Matrix.

Parameters

[in] Matrix The matrix

Template Parameters

T	type of object, i.e. double, float, ....

Returns: The Sparse Vector

Definition at line 278 of file EigenFunctions.H.

◆ vectorTensorProduct()

template<typename T>

Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > EigenFunctions::vectorTensorProduct	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	g,
		const Eigen::Tensor< T, 3 > &	c,
		const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	a )

A function that computes the product of g.T c a, where c is a third dim tensor.

Parameters

[in]	g	The first vector
[in]	c	The three dim tensor
[in]	a	The second vector

Returns: The vector which corresponds to the product g.T c a

Definition at line 89 of file EigenFunctions.C.