dg::mat::TridiagInvDF< real_type > Class Template Reference

USE THIS ONE Compute the inverse of a general tridiagonal matrix. The algorithm does not rely on the determinant. More...

Public Types
using	value_type = real_type

Public Member Functions
	TridiagInvDF ()
	Allocate nothing, Call construct method before usage.
	TridiagInvDF (const thrust::host_vector< real_type > &copyable)
	Construct from vector.
	TridiagInvDF (unsigned size)
	Construct from size of vector.
void	resize (unsigned new_size)
	Resize inverse tridiagonal matrix and helper vectors.
void	operator() (const dg::TriDiagonal< thrust::host_vector< real_type > > &T, dg::SquareMatrix< real_type > &Tinv)
	Compute the inverse of a tridiagonal matrix T.
dg::SquareMatrix< real_type >	operator() (const dg::TriDiagonal< thrust::host_vector< real_type > > &T)
	Compute the inverse of a tridiagonal matrix T.
template<class ContainerType0 , class ContainerType1 , class ContainerType2 >
void	operator() (const ContainerType0 &a, const ContainerType1 &b, const ContainerType2 &c, dg::SquareMatrix< real_type > &Tinv)
	Compute the inverse of a tridiagonal matrix with diagonal vectors a,b,c.

Detailed Description

template<class real_type>
class dg::mat::TridiagInvDF< real_type >

USE THIS ONE Compute the inverse of a general tridiagonal matrix. The algorithm does not rely on the determinant.

Note

For some special cases division by zero occurs (can be fixed if necessary cf. 2nd paper) This is the algorihm of "On the inverses of general tridiagonal matrices" by Hou-Biao Li, Ting-Zhu Huang, Xing-Ping Liu, Hong Li Appears to be the same as the algorithm in "ON AN INVERSE FORMULA OF A TRIDIAGONAL MATRIX" by Tomoyuki Sugimoto

Template Parameters

real_type

float or double

Member Typedef Documentation

value_type

template<class real_type >

using dg::mat::TridiagInvDF< real_type >::value_type = real_type

value type of the ContainerType class

Constructor & Destructor Documentation

TridiagInvDF() [1/3]

template<class real_type >

dg::mat::TridiagInvDF< real_type >::TridiagInvDF ( )

inline

Allocate nothing, Call construct method before usage.

TridiagInvDF() [2/3]

template<class real_type >

dg::mat::TridiagInvDF< real_type >::TridiagInvDF ( const thrust::host_vector< real_type > & copyable )

inline

Construct from vector.

Parameters

copyable

vector

TridiagInvDF() [3/3]

template<class real_type >

dg::mat::TridiagInvDF< real_type >::TridiagInvDF ( unsigned size )

inline

Construct from size of vector.

Parameters

size	size of vector

Member Function Documentation

operator()() [1/3]

template<class real_type >

template<class ContainerType0 , class ContainerType1 , class ContainerType2 >

void dg::mat::TridiagInvDF< real_type >::operator() ( const ContainerType0 & a, const ContainerType1 & b, const ContainerType2 & c, dg::SquareMatrix< real_type > & Tinv )

inline

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

The diagonal vectors are given as in the dg::TriDiagonal matrix format

Parameters

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

operator()() [2/3]

template<class real_type >

dg::SquareMatrix< real_type > dg::mat::TridiagInvDF< real_type >::operator() ( const dg::TriDiagonal< thrust::host_vector< real_type > > & 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 real_type >

void dg::mat::TridiagInvDF< real_type >::operator() ( const dg::TriDiagonal< thrust::host_vector< real_type > > & T, dg::SquareMatrix< real_type > & 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 real_type >

void dg::mat::TridiagInvDF< real_type >::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