densemat.hpp File Reference

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Classes
class	DenseMatrix
	Data type dense matrix. More...
class	DenseMatrixInverse
class	DenseMatrixEigensystem
class	DenseMatrixSVD
class	DenseTensor
	Rank 3 tensor (array of matrices) More...
Functions
void	Add (const DenseMatrix &A, const DenseMatrix &B, double alpha, DenseMatrix &C)
	C = A + alpha*B.
void	Mult (const DenseMatrix &b, const DenseMatrix &c, DenseMatrix &a)
	Matrix matrix multiplication. A = B * C.
void	CalcAdjugate (const DenseMatrix &a, DenseMatrix &adja)
	Calculate the adjugate of a matrix (for 2x2 or 3x3 matrices)
void	CalcAdjugateTranspose (const DenseMatrix &a, DenseMatrix &adjat)
	Calculate the transposed adjugate of a matrix (for 2x2 or 3x3 matrices)
void	CalcInverse (const DenseMatrix &a, DenseMatrix &inva)
void	CalcInverseTranspose (const DenseMatrix &a, DenseMatrix &inva)
	Calculate the inverse transpose of a matrix (for 2x2 or 3x3 matrices)
void	MultAAt (const DenseMatrix &a, DenseMatrix &aat)
	Calculate the matrix A.At.
void	MultADAt (const DenseMatrix &A, const Vector &D, DenseMatrix &ADAt)
	ADAt = A D A^t, where D is diagonal.
void	AddMultADAt (const DenseMatrix &A, const Vector &D, DenseMatrix &ADAt)
	ADAt += A D A^t, where D is diagonal.
void	MultABt (const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
	Multiply a matrix A with the transpose of a matrix B: A*Bt.
void	AddMultABt (const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &ABt)
	ABt += A * B^t.
void	MultAtB (const DenseMatrix &A, const DenseMatrix &B, DenseMatrix &AtB)
	Multiply the transpose of a matrix A with a matrix B: At*B.
void	AddMult_a_AAt (double a, const DenseMatrix &A, DenseMatrix &AAt)
	AAt += a * A * A^t.
void	Mult_a_AAt (double a, const DenseMatrix &A, DenseMatrix &AAt)
	AAt = a * A * A^t.
void	MultVVt (const Vector &v, DenseMatrix &vvt)
	Make a matrix from a vector V.Vt.
void	MultVWt (const Vector &v, const Vector &w, DenseMatrix &VWt)
void	AddMultVWt (const Vector &v, const Vector &w, DenseMatrix &VWt)
	VWt += v w^t.
void	AddMult_a_VVt (const double a, const Vector &v, DenseMatrix &VVt)
	VVt += a * v v^t.

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Function Documentation

void Add	(	const DenseMatrix &	A,
		const DenseMatrix &	B,
		double	alpha,
		DenseMatrix &	C
	)

C = A + alpha*B.

Definition at line 1795 of file densemat.cpp.

References DenseMatrix::Height(), and Operator::Size().

Referenced by aGMRES(), and GMRES().

void AddMult_a_AAt	(	double	a,
		const DenseMatrix &	A,
		DenseMatrix &	AAt
	)

AAt += a * A * A^t.

Definition at line 2226 of file densemat.cpp.

References DenseMatrix::Height(), and DenseMatrix::Width().

Referenced by VectorFEMassIntegrator::AssembleElementMatrix(), CurlCurlIntegrator::AssembleElementMatrix(), and DiffusionIntegrator::AssembleElementMatrix().

void AddMult_a_VVt	(	const double	a,
		const Vector &	v,
		DenseMatrix &	VVt
	)

VVt += a * v v^t.

Definition at line 2303 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), Vector::Size(), and DenseMatrix::Width().

Referenced by ElasticityIntegrator::AssembleElementMatrix(), DivDivIntegrator::AssembleElementMatrix(), and MassIntegrator::AssembleElementMatrix().

void AddMultABt	(	const DenseMatrix &	A,
		const DenseMatrix &	B,
		DenseMatrix &	ABt
	)

ABt += A * B^t.

Definition at line 2154 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), and DenseMatrix::Width().

Referenced by DiffusionIntegrator::AssembleElementMatrix(), and VectorFECurlIntegrator::AssembleElementMatrix2().

void AddMultADAt	(	const DenseMatrix &	A,
		const Vector &	D,
		DenseMatrix &	ADAt
	)

ADAt += A D A^t, where D is diagonal.

Definition at line 2032 of file densemat.cpp.

References DenseMatrix::Height(), and DenseMatrix::Width().

Referenced by VectorFEMassIntegrator::AssembleElementMatrix().

void AddMultVWt	(	const Vector &	v,
		const Vector &	w,
		DenseMatrix &	VWt
	)

VWt += v w^t.

Definition at line 2286 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), Vector::Size(), and DenseMatrix::Width().

Referenced by ConvectionIntegrator::AssembleElementMatrix(), VectorDivergenceIntegrator::AssembleElementMatrix2(), DerivativeIntegrator::AssembleElementMatrix2(), VectorFEDivergenceIntegrator::AssembleElementMatrix2(), and MassIntegrator::AssembleElementMatrix2().

void CalcAdjugate	(	const DenseMatrix &	a,
		DenseMatrix &	adja
	)

Calculate the adjugate of a matrix (for 2x2 or 3x3 matrices)

Definition at line 1838 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), and Operator::Size().

Referenced by VectorDivergenceIntegrator::AssembleElementMatrix2(), and VectorFiniteElement::Project_RT().

void CalcAdjugateTranspose	(	const DenseMatrix &	a,
		DenseMatrix &	adjat
	)

Calculate the transposed adjugate of a matrix (for 2x2 or 3x3 matrices)

Definition at line 1868 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), and Operator::Size().

Referenced by RT0TetFiniteElement::GetLocalInterpolation(), RT1HexFiniteElement::GetLocalInterpolation(), RT0HexFiniteElement::GetLocalInterpolation(), RT2QuadFiniteElement::GetLocalInterpolation(), RT1QuadFiniteElement::GetLocalInterpolation(), RT1TriangleFiniteElement::GetLocalInterpolation(), RT0QuadFiniteElement::GetLocalInterpolation(), RT0TriangleFiniteElement::GetLocalInterpolation(), VectorFiniteElement::LocalInterpolation_RT(), RT0TetFiniteElement::Project(), RT1HexFiniteElement::Project(), RT0HexFiniteElement::Project(), RT2QuadFiniteElement::Project(), RT1QuadFiniteElement::Project(), RT1TriangleFiniteElement::Project(), RT0QuadFiniteElement::Project(), RT0TriangleFiniteElement::Project(), and VectorFiniteElement::Project_RT().

void CalcInverse	(	const DenseMatrix &	a,
		DenseMatrix &	inva
	)

Calculate the inverse of a matrix (for 2x2 or 3x3 matrices) or the left inverse (A^t.A)^{-1}.A^t (for 2x1, 3x1, or 3x2 matrices)

Definition at line 1898 of file densemat.cpp.

References DenseMatrix::Data(), DenseMatrix::Det(), DenseMatrix::FNorm(), DenseMatrix::Height(), mfem_error(), and DenseMatrix::Width().

Referenced by ElasticityIntegrator::AssembleElementMatrix(), VectorDiffusionIntegrator::AssembleElementMatrix(), ConvectionIntegrator::AssembleElementMatrix(), DiffusionIntegrator::AssembleElementMatrix(), DerivativeIntegrator::AssembleElementMatrix2(), VectorFiniteElement::CalcVShape_ND(), DiffusionIntegrator::ComputeElementFlux(), GridFunction::ComputeH1Error(), GridFunction::ComputeW11Error(), Geometry::Geometry(), GridFunction::GetDerivative(), GridFunction::GetDivergence(), GridFunction::GetGradients(), GridFunction::GetVectorGradient(), and NodalFiniteElement::ProjectGrad().

void CalcInverseTranspose	(	const DenseMatrix &	a,
		DenseMatrix &	inva
	)

Calculate the inverse transpose of a matrix (for 2x2 or 3x3 matrices)

Definition at line 1983 of file densemat.cpp.

References DenseMatrix::Det(), DenseMatrix::Height(), mfem_error(), and Operator::Size().

void Mult	(	const DenseMatrix &	b,
		const DenseMatrix &	c,
		DenseMatrix &	a
	)

Matrix matrix multiplication. A = B * C.

Definition at line 1804 of file densemat.cpp.

References DenseMatrix::data, DenseMatrix::height, mfem_error(), and Operator::size.

void Mult_a_AAt	(	double	a,
		const DenseMatrix &	A,
		DenseMatrix &	AAt
	)

AAt = a * A * A^t.

Definition at line 2247 of file densemat.cpp.

References DenseMatrix::Height(), and DenseMatrix::Width().

void MultAAt	(	const DenseMatrix &	a,
		DenseMatrix &	aat
	)

Calculate the matrix A.At.

Definition at line 2020 of file densemat.cpp.

References DenseMatrix::Height(), and Operator::Size().

Referenced by ElasticityIntegrator::AssembleElementMatrix(), and VectorDiffusionIntegrator::AssembleElementMatrix().

void MultABt	(	const DenseMatrix &	A,
		const DenseMatrix &	B,
		DenseMatrix &	ABt
	)

Multiply a matrix A with the transpose of a matrix B: A*Bt.

Definition at line 2076 of file densemat.cpp.

References DenseMatrix::Data(), DenseMatrix::Height(), mfem_error(), and DenseMatrix::Width().

Referenced by CurlCurlIntegrator::AssembleElementMatrix(), DiffusionIntegrator::AssembleElementMatrix(), VectorFECurlIntegrator::AssembleElementMatrix2(), and VectorFiniteElement::CalcVShape_RT().

void MultADAt	(	const DenseMatrix &	A,
		const Vector &	D,
		DenseMatrix &	ADAt
	)

ADAt = A D A^t, where D is diagonal.

Definition at line 2056 of file densemat.cpp.

References DenseMatrix::Height(), and DenseMatrix::Width().

void MultAtB	(	const DenseMatrix &	A,
		const DenseMatrix &	B,
		DenseMatrix &	AtB
	)

Multiply the transpose of a matrix A with a matrix B: At*B.

Definition at line 2174 of file densemat.cpp.

References DenseMatrix::Data(), DenseMatrix::Height(), mfem_error(), Operator::Size(), and DenseMatrix::Width().

void MultVVt	(	const Vector &	v,
		DenseMatrix &	vvt
	)

Make a matrix from a vector V.Vt.

Definition at line 2259 of file densemat.cpp.

References Vector::Size().

Referenced by VectorMassIntegrator::AssembleElementMatrix().

void MultVWt	(	const Vector &	v,
		const Vector &	w,
		DenseMatrix &	VWt
	)

Definition at line 2268 of file densemat.cpp.

References DenseMatrix::Height(), mfem_error(), Operator::Size(), and Vector::Size().