toeplitz_seq.c File Reference

Contains sequential/openMP routines for Toeplitz algebra. More...

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Functions
int	stmm (double **V, int n, int m, double *T, int lambda, Flag flag_stgy)
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)
int	gstbmm (double **V, int nrow, int m_cw, int m_rw, Block *tpltzblocks, int nb_blocks, int64_t idp, int local_V_size, int64_t *id0gap, int *lgap, int ngap, Flag flag_stgy)
int	gstbmm0 (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)

Detailed Description

Contains sequential/openMP routines for Toeplitz algebra.

version 1.1b, July 2012

Author

Frederic Dauvergne

Project: Midapack library, ANR MIDAS'09 - Toeplitz Algebra module Purpose: Provide Toeplitz algebra tools suitable for Cosmic Microwave Background (CMB) data analysis.

Note

Copyright (c) 2010-2012 APC CNRS Université Paris Diderot

This program is free software; you can redistribute it and/or modify it under the terms

of the GNU Lesser General Public License as published by the Free Software Foundation;

either version 3 of the License, or (at your option) any later version. This program is

distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even

the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with this

program; if not, see http://www.gnu.org/licenses/lgpl.html

For more information about ANR MIDAS'09 project see :

http://www.apc.univ-paris7.fr/APC_CS/Recherche/Adamis/MIDAS09/index.html

ACKNOWLEDGMENT: This work has been supported in part by the French National Research

Agency (ANR) through COSINUS program (project MIDAS no. ANR-09-COSI-009).

Log: toeplitz*.c

Revision 1.0b 2012/05/07 Frederic Dauvergne (APC) Official release 1.0beta. The first installement of the library is the Toeplitz algebra module.

Revision 1.1b 2012/07/- Frederic Dauvergne (APC)

• mpi_stbmm allows now rowi-wise order per process datas and no-blocking communications.
• OMP improvment for optimal cpu time.
• bug fixed for OMP in the stmm_basic routine.
• distcorrmin is used to communicate only lambda-1 datas when it is needed.
• new reshaping routines using transformation functions in stmm. Thus, only one copy at most is needed.
• tpltz_init improvement using define_nfft and define_blocksize routines.
• add Block struture to define each Toeplitz block.
• add Flag structure and preprocessing parameters to define the computational strategy. All the flag parameters are then available directly from the API.

Definition in file toeplitz_seq.c.

Function Documentation

stmm()

int stmm	(	double **	V,
		int	n,
		int	m,
		double *	T,
		int	lambda,
		Flag	flag_stgy
	)

Perform the product of a Toeplitz matrix by a general matrix using the sliding window algorithm.

This is a simplifed call of the sequential product including initialization and cleaning. This use the flag parameters to set the comutational options.

Parameters

V	[input] 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
m	number of columns of V
T	Toeplitz matrix data composed of the non-zero entries of his first row
lambda	number of non-zero in the first row of the Toeplitz and size of T
flag_stgy	flag strategy for the product computation

Definition at line 85 of file toeplitz_seq.c.

stbmm()

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 136 of file toeplitz_seq.c.

gstbmm()

int gstbmm	(	double **	V,
		int	nrow,
		int	m_cw,
		int	m_rw,
		Block *	tpltzblocks,
		int	nb_blocks,
		int64_t	idp,
		int	local_V_size,
		int64_t *	id0gap,
		int *	lgap,
		int	ngap,
		Flag	flag_stgy
	)

Performs the multiplication of a symmetric, Toeplitz block-diagonal matrix with gaps, T, by an arbitrary matrix, V, distributed over processes.

We first rebuild the Toeplitz block matrix structure to reduce the computation cost and skip the computations of the values on the defined gaps.

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

Definition at line 189 of file toeplitz_seq.c.

gstbmm0()

int gstbmm0	(	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
	)

Definition at line 206 of file toeplitz_seq.c.