dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix > Class Template Reference

Compute the inverse of a general tridiagonal matrix. More...

Public Types
using	value_type = dg::get_value_type< ContainerType >

Public Member Functions
	TridiagInvD ()
	Allocate nothing, Call construct method before usage. More...
	TridiagInvD (const ContainerType &copyable)
	Construct from vector. More...
	TridiagInvD (unsigned size)
	Construct from size of vector. More...
void	resize (unsigned new_size)
	Resize inverse tridiagonal matrix and helper vectors. More...
void	operator() (const DiaMatrix &T, CooMatrix &Tinv)
	Compute the inverse of a tridiagonal matrix T. More...
CooMatrix	operator() (const DiaMatrix &T)
	Compute the inverse of a tridiagonal matrix T. More...
template<class ContainerType0 , class ContainerType1 , class ContainerType2 >
void	operator() (const ContainerType0 &a, const ContainerType1 &b, const ContainerType2 &c, CooMatrix &Tinv)
	Compute the inverse of a tridiagonal matrix with diagonal vectors a,b,c. More...

Detailed Description

template<class ContainerType, class DiaMatrix, class CooMatrix>
class dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >

Compute the inverse of a general tridiagonal matrix.

Attention

If roughly the matrix size m>150 the algorithm is unstable. However, it performs extremely fast if it stays below this value. This is the algorihm of "Inversion of a Tridiagonal Jacobi Matrix" by Riaz A. Usmani

Template Parameters

ContainerType	thrust::host_vector<value_type> or similar shared memory host vector
CooMatrix	cusp::coo_matrix<int, value_type, cusp::host_memory>;
DiaMatrix	cusp::dia_matrix<int, value_type, cusp::host_memory>;

Member Typedef Documentation

value_type

template<class ContainerType , class DiaMatrix , class CooMatrix >

using dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::value_type = dg::get_value_type<ContainerType>

value type of the ContainerType class

Constructor & Destructor Documentation

TridiagInvD() [1/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::TridiagInvD ( )

inline

Allocate nothing, Call construct method before usage.

TridiagInvD() [2/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::TridiagInvD ( const ContainerType &  copyable )

inline

Construct from vector.

Parameters

copyable

vector

TridiagInvD() [3/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::TridiagInvD ( unsigned  size )

inline

Construct from size of vector.

Parameters

size	size of vector

Member Function Documentation

operator()() [1/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

template<class ContainerType0 , class ContainerType1 , class ContainerType2 >

void dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::operator() ( const ContainerType0 &  a, const ContainerType1 &  b, const ContainerType2 &  c, CooMatrix &  Tinv  )

inline

Compute the inverse of a tridiagonal matrix with diagonal vectors a,b,c.

The diagonal vectors are given as in the cusp dia_matrix format

Parameters

a	"0" diagonal vector (index 0 is on row 0)
b	"+1" diagonal vector (index 0 is on row 0, last index outside)
c	"-1" diagonal vector (index 0 is on row 0, outside of matrix)
Tinv	the inverse of the tridiagonal matrix (coordinate format) gets resized if necessary

operator()() [2/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

CooMatrix dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::operator() ( const DiaMatrix &  T )

inline

Compute the inverse of a tridiagonal matrix T.

Parameters

T	tridiagonal matrix

Returns

the inverse of the tridiagonal matrix (coordinate format)

operator()() [3/3]

template<class ContainerType , class DiaMatrix , class CooMatrix >

void dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::operator() ( const DiaMatrix &  T, CooMatrix &  Tinv  )

inline

Compute the inverse of a tridiagonal matrix T.

Parameters

T	tridiagonal matrix
Tinv	the inverse of the tridiagonal matrix (coordinate format) gets resized if necessary

resize()

template<class ContainerType , class DiaMatrix , class CooMatrix >

void dg::mat::TridiagInvD< ContainerType, DiaMatrix, CooMatrix >::resize ( unsigned  new_size )

inline

Resize inverse tridiagonal matrix and helper vectors.

Parameters

new_size

new size of square matrix

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The documentation for this class was generated from the following file:

• tridiaginv.h