Abstract base class for all nonsingular polymorphic matrices that can be used to compute matrix-vector products and solve for linear systems efficiently. More...

#include <AbstractLinAlgPack_MatrixOpNonsing.hpp>

Inheritance diagram for AbstractLinAlgPack::MatrixOpNonsing:

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Public Member Functions
MatrixOpNonsing &	operator= (const MatrixOpNonsing &M)
	Calls operator=(MatrixOp&) More...

Public Member Functions inherited from AbstractLinAlgPack::MatrixOp
virtual void	zero_out ()
	M_lhs = 0 : Zero out the matrix. More...

virtual void	Mt_S (value_type alpha)
	M_lhs *= alpha : Multiply a matrix by a scalar. More...

virtual MatrixOp &	operator= (const MatrixOp &mwo_rhs)
	M_lhs = mwo_rhs : Virtual assignment operator. More...

virtual std::ostream &	output (std::ostream &out) const
	Virtual output function. More...

const MatNorm	calc_norm (EMatNormType requested_norm_type=MAT_NORM_1, bool allow_replacement=false) const
	Compute a norm of this matrix. More...

virtual mat_ptr_t	sub_view (const Range1D &row_rng, const Range1D &col_rng) const
	Create a transient constant sub-matrix view of this matrix (if supported). More...

mat_ptr_t	sub_view (const index_type &rl, const index_type &ru, const index_type &cl, const index_type &cu) const
	Inlined implementation calls `this->sub_view(Range1D(rl,ru),Range1D(cl,cu))`. More...

virtual mat_ptr_t	perm_view (const Permutation P_row, const index_type row_part[], int num_row_part, const Permutation P_col, const index_type col_part[], int num_col_part) const
	Create a permuted view: `M_perm = P_row' * M * P_col`. More...

virtual mat_ptr_t	perm_view_update (const Permutation P_row, const index_type row_part[], int num_row_part, const Permutation P_col, const index_type col_part[], int num_col_part, const mat_ptr_t &perm_view) const
	Reinitialize a permuted view: `M_perm = P_row' * M * P_col`. More...

Public Member Functions inherited from AbstractLinAlgPack::MatrixBase
virtual	~MatrixBase ()
	Virtual destructor. More...

virtual const VectorSpace &	space_cols () const =0
	Vector space for vectors that are compatible with the columns of the matrix. More...

virtual const VectorSpace &	space_rows () const =0
	Vector space for vectors that are compatible with the rows of the matrix. More...

virtual size_type	rows () const
	Return the number of rows in the matrix. More...

virtual size_type	cols () const
	Return the number of columns in the matrix. More...

virtual size_type	nz () const
	Return the number of nonzero elements in the matrix. More...

Public Member Functions inherited from AbstractLinAlgPack::MatrixNonsing
virtual void	V_InvMtV (VectorMutable *v_lhs, BLAS_Cpp::Transp trans_rhs1, const Vector &v_rhs2) const =0
	v_lhs = inv(op(M_rhs1)) * vs_rhs2 More...

virtual void	V_InvMtV (VectorMutable *v_lhs, BLAS_Cpp::Transp trans_rhs1, const SpVectorSlice &sv_rhs2) const
	v_lhs = inv(op(M_rhs1)) * sv_rhs2 More...

virtual value_type	transVtInvMtV (const Vector &v_rhs1, BLAS_Cpp::Transp trans_rhs2, const Vector &v_rhs3) const
	result = vs_rhs1' * inv(op(M_rhs2)) * vs_rhs3 More...

virtual value_type	transVtInvMtV (const SpVectorSlice &sv_rhs1, BLAS_Cpp::Transp trans_rhs2, const SpVectorSlice &sv_rhs3) const
	result = sv_rhs1' * inv(op(M_rhs2)) * sv_rhs3 More...

virtual void	M_StInvMtM (MatrixOp *m_lhs, value_type alpha, BLAS_Cpp::Transp trans_rhs1, const MatrixOp &mwo_rhs2, BLAS_Cpp::Transp trans_rhs2) const
	m_lhs = alpha * inv(op(M_rhs1)) * op(mwo_rhs2) (right). More...

virtual void	M_StMtInvM (MatrixOp *m_lhs, value_type alpha, const MatrixOp &mwo_rhs1, BLAS_Cpp::Transp trans_rhs1, BLAS_Cpp::Transp trans_rhs2) const
	m_lhs = alpha * op(mwo_rhs1) * inv(op(M_rhs2)) (left). More...

Clone
virtual mat_mwons_mut_ptr_t	clone_mwons ()
	Clone the non-const matrix object (if supported). More...

virtual mat_mwons_ptr_t	clone_mwons () const
	Clone the const matrix object (if supported). More...

Condition number estimation
const MatNorm	calc_cond_num (EMatNormType requested_norm_type=MAT_NORM_1, bool allow_replacement=false) const
	Compute an estimate of the condition number of this matrix. More...

Overridden from MatrixOp
mat_mut_ptr_t	clone ()
	Returns `this->clone_mwons()`. More...

mat_ptr_t	clone () const
	Returns `this->clone_mwons()`. More...

Overridden from MatrixNonsing
mat_mns_mut_ptr_t	clone_mns ()
	Returns `this->clone_mwons()`. More...

mat_mns_ptr_t	clone_mns () const
	Returns `this->clone_mwons()`. More...

Detailed Description

Abstract base class for all nonsingular polymorphic matrices that can be used to compute matrix-vector products and solve for linear systems efficiently.

Definition at line 54 of file AbstractLinAlgPack_MatrixOpNonsing.hpp.

Member Function Documentation

MatrixOpNonsing::mat_mwons_mut_ptr_t AbstractLinAlgPack::MatrixOpNonsing::clone_mwons ( )

virtual

Clone the non-const matrix object (if supported).

The default implementation returns NULL which is perfectly acceptable. A matrix object is not required to return a non-NULL value but almost every good matrix implementation will.

Reimplemented in AbstractLinAlgPack::MatrixSymOpNonsing.

Definition at line 52 of file AbstractLinAlgPack_MatrixOpNonsing.cpp.

MatrixOpNonsing::mat_mwons_ptr_t AbstractLinAlgPack::MatrixOpNonsing::clone_mwons ( ) const

virtual

Clone the const matrix object (if supported).

The behavior of this method is the same as for the non-const version above except it returns a smart pointer to a const matrix object.

Reimplemented in AbstractLinAlgPack::MatrixSymOpNonsing.

Definition at line 58 of file AbstractLinAlgPack_MatrixOpNonsing.cpp.

const MatrixOp::MatNorm AbstractLinAlgPack::MatrixOpNonsing::calc_cond_num	(	EMatNormType	requested_norm_type = `MAT_NORM_1`,
		bool	allow_replacement = `false`
	)		const

Compute an estimate of the condition number of this matrix.

Parameters

requested_norm_type	[in] Determines the requested type of norm for the condition number.
allow_replacement	[in] Determines if the requested norm in specified in `norm_type` can be replaced with another norm that can be computde by the matrix.

Returns: If a condition number is computed, then return.value gives the value of the condition number in the norm of type return.type.

Postconditions:

If allow_replacement==true, the matrix object must return a computed condition number who's type is given in return.type.
If allow_replacement==false and the underlying matrix object can not compute condition number for the norm requested in norm_type, then a MethodNotImplemented exception will be thrown. If the matrix object can an estimate of the condition number for this norm, then return.type will be equal to requested_norm_type.

The default implementation of this method uses Algorithm 2.5 in "Applied Numerical Linear Algebra" by James Demmel (1997) to estimate ||inv(M)||1 or ||inv(M)||inf. The algorithm uses some of the refinements in the referenced algorithm by Highman. This algorithm only requires solves and transposed solves so every nonsingular matrix object can implement this method. The default arguments for this function will compute an estimate of the condition number and will not thrown an exception. The default implementation will throw an exception for any other norm type than requested_norm_type = MAT_NORM_1 or requested_norm_type = MAT_NORM_INF.

Definition at line 64 of file AbstractLinAlgPack_MatrixOpNonsing.cpp.

MatrixOpNonsing::mat_mut_ptr_t AbstractLinAlgPack::MatrixOpNonsing::clone ( )

virtual

Returns this->clone_mwons().

Reimplemented from AbstractLinAlgPack::MatrixOp.

Reimplemented in AbstractLinAlgPack::MatrixSymOpNonsing.

Definition at line 121 of file AbstractLinAlgPack_MatrixOpNonsing.cpp.

MatrixOpNonsing::mat_ptr_t AbstractLinAlgPack::MatrixOpNonsing::clone ( ) const

virtual

Returns this->clone_mwons().

Reimplemented from AbstractLinAlgPack::MatrixOp.

Reimplemented in AbstractLinAlgPack::MatrixSymOpNonsing.