Functions
int	tpltz_init (int n, int lambda, int nfft, int blocksize, fftw_complex *T_fft, double T, fftw_complex V_fft, double V_rfft, fftw_plan plan_f, fftw_plan plan_b, Flag flag_stgy)
	Sets a block size and initializes all fftw arrays and plans needed for the computation.
int	tpltz_cleanup (fftw_complex T_fft, fftw_complex V_fft, double *V_rfft, fftw_plan plan_f, fftw_plan *plan_b)
	Cleans fftw workspace used in the Toeplitz matrix matrix product's computation.
int	reset_gaps (double *V, int id0, int local_V_size, int m, int nrow, int m_rowwise, int64_t id0gap, int *lgap, int ngap)
	Set the data to zeros at the gaps location.
int	gap_masking (double *V, int l, int id0gap, int *lgap, int ngap)
	Reduce the vector and mask the defined gaps.
int	gap_filling (double *V, int l, int id0gap, int *lgap, int ngap)
	Extend the vector and add zeros on the gaps locations.
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.
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.

Detailed Description

These are shared-memory routines.

Function Documentation

int tpltz_init	(	int	n,
		int	lambda,
		int *	nfft,
		int *	blocksize,
		fftw_complex **	T_fft,
		double *	T,
		fftw_complex **	V_fft,
		double **	V_rfft,
		fftw_plan *	plan_f,
		fftw_plan *	plan_b,
		Flag	flag_stgy
	)

Sets a block size and initializes all fftw arrays and plans needed for the computation.

Initializes the fftw arrays and plans is necessary before any computation of the Toeplitz matrix matrix product. Use tpltz_cleanup afterwards.

See also:: tpltz_cleanup

Parameters:

n	row size of the matrix used for later product
lambda	Toeplitz band width
nfft	maximum number of FFTs you want to compute at the same time
blocksize	optimal block size used in the sliding window algorithm to compute an optimize value)
T_fft	complex array used for FFTs
T	Toeplitz matrix
V_fft	complex array used for FFTs
V_rfft	real array used for FFTs
plan_f	fftw plan forward (r2c)
plan_b	fftw plan backward (c2r)

Definition at line 257 of file toeplitz.c.

int tpltz_cleanup	(	fftw_complex **	T_fft,
		fftw_complex **	V_fft,
		double **	V_rfft,
		fftw_plan *	plan_f,
		fftw_plan *	plan_b
	)

Cleans fftw workspace used in the Toeplitz matrix matrix product's computation.

Destroy fftw plans, free memory and reset fftw workspace.

See also:: tpltz_init

Parameters:

T_fft	complex array used for FFTs
V_fft	complex array used for FFTs
V_rfft	real array used for FFTs
plan_f	fftw plan forward (r2c)
plan_b	fftw plan backward (c2r)

Definition at line 435 of file toeplitz.c.

int reset_gaps	(	double **	V,
		int	id0,
		int	local_V_size,
		int	m,
		int	nrow,
		int	m_rowwise,
		int64_t *	id0gap,
		int *	lgap,
		int	ngap
	)

Set the data to zeros at the gaps location.

The datas located on a gap are set to zeros. The gaps are defined in the time space, meaning their indexes are defined in the row dimension.

Definition at line 189 of file toeplitz_gappy.c.

int gap_masking	(	double **	V,
		int	l,
		int *	id0gap,
		int *	lgap,
		int	ngap
	)

Reduce the vector and mask the defined gaps.

Parameters:

V	input/output vector
l	length of the vector
id0gap	gap first index
lgap	gap length
ngap	number of gaps

Definition at line 255 of file toeplitz_gappy_seq.dev.c.

int gap_filling	(	double **	V,
		int	l,
		int *	id0gap,
		int *	lgap,
		int	ngap
	)

Extend the vector and add zeros on the gaps locations.

Parameters:

V	input/output vector
l	length of the extend vector
id0gap	gap first index
lgap	gap length
ngap	number of gaps

Definition at line 293 of file toeplitz_gappy_seq.dev.c.

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 72 of file toeplitz_seq.c.

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 170 of file toeplitz_seq.c.

Functions

Detailed Description

Function Documentation