distributed memory (MPI) routines

Functions
int	mpi_stmm (double **V, int n, int m, int id0, int l, double *T, int lambda, Flag flag_stgy, MPI_Comm comm)
	Performs the product of a Toeplitz matrix by a general matrix using MPI. We assume that the matrix has already been scattered. (a USER routine)
int	mpi_gstbmm (double **V, int nrow, int m, int m_rowwise, Block *tpltzblocks, int nb_blocks_local, int nb_blocks_all, int id0p, int local_V_size, int64_t *id0gap, int *lgap, int ngap, Flag flag_stgy, 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.
int	stbmm (double **V, int nrow, int m_cw, int m_rw, Block *tpltzblocks, int nb_blocks, int64_t idp, int local_V_size, Flag flag_stgy)
	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.

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Detailed Description

These are distributed-memory routines.

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Function Documentation

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

Performs the product of a Toeplitz matrix by a general matrix using MPI. We assume that the matrix has already been scattered. (a USER routine)

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.
flag_stgy	flag strategy for the product computation
comm	communicator (usually MPI_COMM_WORLD)

Definition at line 980 of file toeplitz.c.

int mpi_gstbmm	(	double **	V,
		int	nrow,
		int	m,
		int	m_rowwise,
		Block *	tpltzblocks,
		int	nb_blocks_local,
		int	nb_blocks_all,
		int	id0p,
		int	local_V_size,
		int64_t *	id0gap,
		int *	lgap,
		int	ngap,
		Flag	flag_stgy,
		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
nrow	number of rows of the global data matrix V
m	number of columns for the data matrix V in the global rowwise order
m_rowwise	number of columns for the data matrix V in the rowwise order per processor
tpltzblocks	list of the toeplitz blocks struture with its own parameters (idv, n, T_block, lambda) : idv is the global row index defining for each Toeplitz block as stored in the vector T ; n size of each Toeplitz block T_block location of each Toeplitz matrix data composed of the non-zero entries of the first row ; lambda size of each Toeplitz block data T_block. The bandwith size is then equal to lambda*2-1
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
idp	global index of the first element of the local part of V
local_V_size	a 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
flag_stgy	flag strategy for the product computation
comm	MPI communicator

Definition at line 88 of file toeplitz_gappy.c.

int stbmm	(	double **	V,
		int	nrow,
		int	m_cw,
		int	m_rw,
		Block *	tpltzblocks,
		int	nb_blocks,
		int64_t	idp,
		int	local_V_size,
		Flag	flag_stgy
	)

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
nrow	number of rows of the global data matrix V
m	number of columns for the data matrix V in the global rowwise order
m_rowwise	number of columns for the data matrix V in the rowwise order per processor
tpltzblocks	list of the toeplitz blocks struture with its own parameters (idv, n, T_block, lambda) :
nb_blocks	number of Toeplitz blocks as stored in T
idp	global index of the first element of the local part of V
local_V_size	a number of all elements in local V
flag_stgy	flag strategy for the product computation

Definition at line 121 of file toeplitz_seq.c.