Functions
int	mpi_stmm (double *V, int n, int m, int id0, int l, double T, int lambda, MPI_Comm comm)
	Perform the multiplication of a Toeplitz matrix by a matrix with MPI. We assume that the matrix has already been scattered.
int	mpi_stbmm (double *V, int n, int m, int nrow, double T, int nb_blocks_local, int nb_blocks_all, int lambda, int *idv, int idp, int local_V_size, MPI_Comm comm)
	Performs the multiplication of a symmetric, Toeplitz block-diagonal matrix, T, by an arbitrary matrix, V, distributed over processes in the generalized column-wise way.
int	mpi_gstbmm (double *V, int n, int m, int nrow, double T, int nb_blocks_local, int nb_blocks_all, int lambda, int idv, int id0p, int local_V_size, int id0gap, int *lgap, int ngap, MPI_Comm comm)
	Performs the multiplication of a symmetric, Toeplitz block-diagonal matrix, T, by an arbitrary matrix, V, distributed over processes in the generalized column-wise way. This matrix V contains defined gaps which represents the useless data for the comutation. The gaps indexes are defined in the global time space as the generized toeplitz matrix, meaning the row dimension. Each of his diagonal blocks is a symmetric, band-diagonal Toeplitz matrix, which can be different for each block.

Detailed Description

These are distributed-memory routines.

Function Documentation

int mpi_gstbmm	(	double **	V,
		int *	n,
		int	m,
		int	nrow,
		double *	T,
		int	nb_blocks_local,
		int	nb_blocks_all,
		int *	lambda,
		int *	idv,
		int	id0p,
		int	local_V_size,
		int *	id0gap,
		int *	lgap,
		int	ngap,
		MPI_Comm	comm
	)

Performs the multiplication of a symmetric, Toeplitz block-diagonal matrix, T, by an arbitrary matrix, V, distributed over processes in the generalized column-wise way. This matrix V contains defined gaps which represents the useless data for the comutation. The gaps indexes are defined in the global time space as the generized toeplitz matrix, meaning the row dimension. Each of his diagonal blocks is a symmetric, band-diagonal Toeplitz matrix, which can be different for each block.

We first rebuild the Toeplitz block matrix structure to reduce the computation cost and skip the computations of the values on the defined gaps. then, each process performs the multiplication sequentially for each of the gappy block and based on the sliding window algorithm. Prior to that MPI calls are used to exchange data between neighboring process. The parameters are :

Parameters:

V	[input] distributed data matrix (with the convention V(i,j)=V[i+j*n]) ; [out] result of the product TV
n	number of rows for each Toeplitz block as stored in T
m	number of columns of the global data matrix V
nrow	number of rows of the global data matrix V
T	Toeplitz matrix composed of the non-zero entries of the first row of each Toeplitz block and concatenated together have to be arranged in the increasing order of n without repetitions and overlaps.
nb_blocks_all	number of all Toeplitz block on the diagonal of the full Toeplitz matrix
nb_blocks_local	number of Toeplitz blocks as stored in T
lambda	half bandwith size for each Toeplitz block stroed in T
idv	global row index defining for each Toeplitz block as stored in the vector T first element of the interval to which given Toeplitz matrix is to be applied.
id0p	global index of the first element of the local part of V
local_V_size	number of all elements in local V
id0gap	index of the first element of each defined gap
lgap	length of each defined gaps
ngap	number of defined gaps
comm	MPI communicator

Definition at line 1576 of file toeplitz.c.

int mpi_stbmm	(	double **	V,
		int *	n,
		int	m,
		int	nrow,
		double *	T,
		int	nb_blocks_local,
		int	nb_blocks_all,
		int *	lambda,
		int *	idv,
		int	idp,
		int	local_V_size,
		MPI_Comm	comm
	)

Performs the multiplication of a symmetric, Toeplitz block-diagonal matrix, T, by an arbitrary matrix, V, distributed over processes in the generalized column-wise way.

Each process performs the multiplication sequentially for each diagonal block and based on the sliding window algorithm. Prior to that MPI calls are used to exchange data between neighboring process. Each of the diagonal blocks is a symmetric, band-diagonal Toeplitz matrix, which can be different for each block. The parameters are :

Parameters:

V	[input] distributed data matrix (with the convention V(i,j)=V[i+j*n]) ; [out] result of the product TV
n	number of rows for each Toeplitz block as stored in T
m	number of columns of the global data matrix V
nrow	number of rows of the global data matrix V
T	Toeplitz matrix composed of the non-zero entries of the first row of each Toeplitz block and concatenated together have to be arranged in the increasing order of n without repetitions and overlaps.
nb_blocks_all	number of all Toeplitz block on the diagonal of the full Toeplitz matrix
nb_blocks_local	number of Toeplitz blocks as stored in T
lambda	half bandwith size for each Toeplitz block stroed in T
idv	global row index defining for each Toeplitz block as stored in the vector T first element of the interval to which given Toeplitz matrix is to be applied.
idp	global index of the first element of the local part of V
local_V_size	a number of all elements in local V
comm	MPI communicator

Definition at line 1090 of file toeplitz.c.

int mpi_stmm	(	double **	V,
		int	n,
		int	m,
		int	id0,
		int	l,
		double *	T,
		int	lambda,
		MPI_Comm	comm
	)

Perform the multiplication of a Toeplitz matrix by a matrix with MPI. We assume that the matrix has already been scattered.

The multiplication is performed using FFT applied to circulant matrix in order to diagonalized it. The parameters are :

Parameters:

V	[input] distributed data matrix (with the convention V(i,j)=V[i+j*n]); [out] result of the product TV
n	number of rows of V
m	number of columns of V
id0	first index of scattered V
l	length of the scattered V
T	Toeplitz matrix.
lambda	Toeplitz band width.
comm	communicator (usually MPI_COMM_WORLD)

Definition at line 946 of file toeplitz.c.

Functions

Detailed Description

Function Documentation