EigenFunctions Namespace Reference

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)
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 427 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 362 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 345 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 325 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 277 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 301 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 410 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 392 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

Examples

09DEIM_ROM.C.

Definition at line 376 of file EigenFunctions.H.

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 255 of file EigenFunctions.H.

vectorTensorProduct() [1/4]

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

vectorTensorProduct() [2/4]

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

vectorTensorProduct() [3/4]

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

vectorTensorProduct() [4/4]

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.