Computing and applying rational filters. More...

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <complex.h>
#include <math.h>
#include "def.h"
#include "blaslapack.h"
#include "struct.h"
#include "internal_proto.h"

Functions
void	contQuad (int method, int n, complex double *zk)
	Compute the locations of the poles. More...

void	ratf2p2 (int n, int mulp, complex double zk, complex double alp, int m, double z, double *xx)
	Compute the function value of the multiple pole rational filter at real locations. More...

void	pfe2 (complex double s1, complex double s2, int k1, int k2, complex double alp, complex double bet)
	Get the fraction expansion of 1/[(z-s1)^k1 (z-s2)^k2]. More...

complex double	integg2 (complex double s1, complex double s2, complex double alp, int k1, complex double bet, int k2, double a, double b)
	Integration of 1/[(z-s1)^k1 (z-s2)^k2] from a to b. More...

void	weights (int n, complex double zk, int mulp, double lambda, complex double *omega)
	Compute the LS weight for each multiple pole. More...

int	scaleweigthts (int n, double a, double b, complex double zk, int mulp, complex double *omegaM)
	Compute the weights and pole locations on [a, b]. More...

void	set_ratf_def (ratparams *rat)
	Sets default values for ratparams struct. More...

int	find_ratf (double intv, ratparams rat)

void	free_rat (ratparams *rat)

void	RatFiltApply (int n, ratparams rat, double b, double x, double w6)
	Apply rational filter R to a vetor b. More...

Detailed Description

Computing and applying rational filters.

Definition in file ratfilter.c.

Function Documentation

void contQuad	(	int	method,
		int	n,
		complex double *	zk
	)

Compute the locations of the poles.

----------------------— Cauchy integration-based filter -----------—

Parameters

	method	0 for Guass Legendre; 1 for midpoint
	n	Number of poles in the upper half plane
[out]	zk	Vector of pole locations

Definition at line 23 of file ratfilter.c.

References DSTEV(), M_PI, and Malloc.

Referenced by find_ratf().

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int find_ratf	(	double *	intv,
		ratparams *	rat
	)

Parameters

intv	= an array of length 4 [intv[0], intv[1]] is the interval of desired eigenvalues [intv[2], intv[3]] is the global interval of all eigenvalues it must contain all eigenvalues of A

OUT:

Parameters

[out]

rat

these are set in rat struct:
omega : expansion coefficients of rational filter
zk : location of the poles used
aa : adjusted left endpoint
bb : adjusted right endpoint
dd : half-width and..
cc : ..center of interval

Definition at line 375 of file ratfilter.c.

References _ratparams::aa, _ratparams::ASIGBsol, _ratparams::bb, _ratparams::beta, contQuad(), Malloc, max, _ratparams::method, min, _ratparams::mulp, _ratparams::num, _ratparams::omega, _ratparams::pow, _ratparams::pw, scaleweigthts(), weights(), and _ratparams::zk.

Referenced by evsl_find_rat(), and main().

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void free_rat ( ratparams * rat )

Definition at line 424 of file ratfilter.c.

References _ratparams::ASIGBsol, _ratparams::mulp, _ratparams::omega, and _ratparams::zk.

Referenced by evsl_free_rat(), and main().

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complex double integg2	(	complex double	s1,
		complex double	s2,
		complex double *	alp,
		int	k1,
		complex double *	bet,
		int	k2,
		double	a,
		double	b
	)

Integration of 1/[(z-s1)^k1 (z-s2)^k2] from a to b.

Definition at line 129 of file ratfilter.c.

Referenced by weights().

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void pfe2	(	complex double	s1,
		complex double	s2,
		int	k1,
		int	k2,
		complex double *	alp,
		complex double *	bet
	)

Get the fraction expansion of 1/[(z-s1)^k1 (z-s2)^k2].

Definition at line 95 of file ratfilter.c.

Referenced by weights().

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void ratf2p2	(	int	n,
		int *	mulp,
		complex double *	zk,
		complex double *	alp,
		int	m,
		double *	z,
		double *	xx
	)

Compute the function value of the multiple pole rational filter at real locations.

---------------—Multiple pole rational filter evaluation -----------—

Parameters

	n	number of the pole
	mulp	multiplicity of the pole
	zk	array containing the poles.
	alp	fractional expansion coefficients
	m	number of locations to be evaluated
	z	real locations to be evaluated
[out]	xx	: function values at real locations z

Definition at line 69 of file ratfilter.c.

Referenced by scaleweigthts(), and weights().

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void RatFiltApply	(	int	n,
		ratparams *	rat,
		double *	b,
		double *	x,
		double *	w6
	)

Apply rational filter R to a vetor b.

For generalized e.v problem x = L' * (A-SB) \ L*b [w:=work] x = L * b w = (A-sB) \ x x = L' * w

Parameters

[in]	rat	ratparams struct
[in]	n	Length of array
[in]	b	x = L * b
	w6	Work array of size 4n for standard ev problem, size 6n for generalized ev problem
[out]	x	Becomes R(A)b

Definition at line 448 of file ratfilter.c.

References _ratparams::ASIGBsol, DAXPY(), DSCAL(), evsl_timer(), evsldata, evslstat, _evsldata::ifGenEv, _ratparams::mulp, _evslstat::n_ratAv, _ratparams::num, _ratparams::omega, and _evslstat::t_ratAv.

Referenced by RatLanNr(), and RatLanTr().

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int scaleweigthts	(	int	n,
		double	a,
		double	b,
		complex double *	zk,
		int *	mulp,
		complex double *	omegaM
	)

Compute the weights and pole locations on [a, b].

---------------—Transform poles and weights computed on [-1, 1] to [a, b] -------—

Parameters

	n	number of poles used in the upper half plane
	a,b	[a, b] is the interval of desired eigenvalues
	zk	location of the poles
	mulp	multiplicity of the poles
[out]	omegaM	multiple LS weights

Definition at line 313 of file ratfilter.c.

References ratf2p2().

Referenced by find_ratf().

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void set_ratf_def ( ratparams * rat )

Sets default values for ratparams struct.

Definition at line 345 of file ratfilter.c.

References _ratparams::aa, _ratparams::bar, _ratparams::bb, _ratparams::beta, _ratparams::method, _ratparams::num, and _ratparams::pw.

Referenced by evsl_find_rat(), and main().

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void weights	(	int	n,
		complex double *	zk,
		int *	mulp,
		double	lambda,
		complex double *	omega
	)

Compute the LS weight for each multiple pole.

---------------—multiple pole LS rational filter weights-----------—

Parameters

	n	number of poles in the upper half plane
	zk	pole locations
	mulp	multiplicity of each pole
	lambda	LS integration weight for [-1, 1]
[out]	omega	LS weight for each pole

Definition at line 169 of file ratfilter.c.

References integg2(), Malloc, pfe2(), ratf2p2(), and ZGESV().

Referenced by find_ratf().

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Functions

Detailed Description

Function Documentation