least_square Class Reference

#include <least_square.h>

Public Member Functions
void	L2_nod2sp (FILE out, long nsp, double *spcoord, double nodvalue, double **spvalue, char typ_patch)
void	L2_sp2sp (FILE out, double spvalue, long nap, const long parentel, const double apcoord, double apvalue)
	least_square (long dim, long ncomp, gtopology *gt, long flag)
void	spr_default (FILE out, double spvalue, double nodvalue)
void	spr_optional (FILE out, long nsp, double spcoord, double spvalue, double *nodvalue, long cut_flag)
	~least_square (void)
Private Member Functions
void	adjap_assembling (long nap, const long parentel, const double apcoord, long nadjap, long **adjap)
void	apvalue_assembling (const vector &coef_normcoord, const vector a, long nadjap, const long adjap, const double apcoord, double apvalue)
void	compute_patches_nod2sp (char typ_patch)
void	compute_patches_sp2sp (long nap, const double *apcoord, const long nadjap, const long adjap, double apvalue)
void	compute_patches_spr (long cut_flag)
void	insidenod_assembling (void)
void	nodvalue_assembling_ae (const vector &coef_normcoord, const vector *a, long nid, ivector &magnitude)
void	normal_coordinates_ae (vector &coef_normcoord)
void	nsp_spcoord_maxcoord_assembling (char nsma_flag)
void	polynom (long ncoef, const double normcoord, double p)
void	polynom_coefficients_ae (const vector &coef_normcoord, vector *a)
void	polynom_coefficients_inv_ae (const vector &coef_normcoord, vector *a, char typ_patch)
void	sigma (long ncoef, long nid, const vector &coef_normcoord, const vector *a, ivector &magnitude)
void	spvalue_assembling_patch_ae (const vector &coef_normcoord, const vector a, long id, double *magnitude)
Private Attributes
long *	adjel
long	dim
	dimension (2 or 3)
long	flag
gtopology *	gt
	actual gtopology
long *	insidelem
	array indicating position of elements on domain, dimension (gt->ne ; ???)
long **	insidenod
	array indicating position of nodes on domain, dimension (gt->nn ; ???)
double **	maxcoord
	array of extreme element natural coordinates, dimension (gt->ne ; 4), maxcoord[i]==(max x; min x; max y; min y)
long	nadjel
long	ne
	number elements on domain
long	nn
	number nodes on domain
double *	nodvalue
long *	nsp
	number of coeficients of patch polynom
long	nvals
	number of smoothed ~ aproximated values
double **	spcoord
	array of natural coordinates of sampling points, dimension (gt->ne ; dim*nsp[i]), for 3D, nsp[i]==2 => spcoord[i]==(x1; y1; z1; x2; y2; z2)
double **	spvalue
	array of rough values in sampling points, dimension (gt->ne ; ncomp)

Detailed Description

Definition at line 10 of file least_square.h.

Constructor & Destructor Documentation

least_square	(	long	dim,
		long	ncomp,
		gtopology *	gt,
		long	flag
	)

Definition at line 26 of file least_square.cpp.

References adjel, dim, flag, gt, insidelem, insidenod, maxcoord, nadjel, gtopology::ne, ne, gtopology::nn, nn, nodvalue, nsp, nvals, spcoord, and spvalue.

~least_square ( void )

Definition at line 56 of file least_square.cpp.

References insidenod, maxcoord, ne, nn, nsp, and spcoord.

Member Function Documentation

void adjap_assembling	(	long	nap,
		const long *	parentel,
		const double **	apcoord,
		long *	nadjap,
		long **	adjap
	)			`[private]`

Definition at line 635 of file least_square.cpp.

References dim, dist(), gnode::distance2(), gtopology::gelements, gtopology::gnodes, gt, insidenod, memset(), nn, gelement::nne, and gelement::nodes.

Referenced by L2_sp2sp().

void apvalue_assembling	(	const vector &	coef_normcoord,
		const vector *	a,
		long	nadjap,
		const long *	adjap,
		const double **	apcoord,
		double **	apvalue
	)			`[private]`

Function computes values of `polynoms` in answer points (over all patch ?????).

Parameters:

	coef_normcoord	- array of coeficients for computing of normed coordinates
	a	- array of vector of coefficients of `polynoms`
	nadjap	-
	adjap	-
	@param

created 4.5.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 1081 of file least_square.cpp.

References vector::a, dim, vector::n, nvals, polynom(), and scprd().

Referenced by compute_patches_sp2sp().

void compute_patches_nod2sp ( char typ_patch ) [private]

Function creates element patch around every vertex node (typ_patch=='n') or inside element (typ_patch=='e') and from nodes on patch interpolates values to sampling points.

Parameters:

typ_patch

- flag for definition of type of patch

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 766 of file least_square.cpp.

References adjel, gtopology::adjelel, gtopology::adjelnod, destrm(), destrv(), dim, gt, insidelem, insidenod, memset(), nadjel, gtopology::nadjelel, gtopology::nadjelnod, ne, nn, normal_coordinates_ae(), nsp, nvals, polynom_coefficients_inv_ae(), spvalue, and spvalue_assembling_patch_ae().

Referenced by L2_nod2sp().

void compute_patches_sp2sp	(	long	nap,
		const double **	apcoord,
		const long *	nadjap,
		const long **	adjap,
		double **	apvalue
	)			`[private]`

Function creates element patch around every vertex node and from sampling points inside of patch interpolates values to answer points.

created 4.5.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 828 of file least_square.cpp.

References adjel, gtopology::adjelnod, allocv(), apvalue_assembling(), destrv(), dim, gt, insidenod, nadjel, gtopology::nadjelnod, nn, normal_coordinates_ae(), nvals, and polynom_coefficients_ae().

Referenced by L2_sp2sp().

void compute_patches_spr ( long cut_flag ) [private]

Function creates element patch around every vertex node and from sampling points inside of patch interpolates values to nodes.

Parameters:

cut_flag

- flag, whether to null values on the "null border" = border of region where known values are zero

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 694 of file least_square.cpp.

References adjel, gtopology::adjelnod, allocv(), gelement::auxinf, destrv(), dim, gtopology::gelements, gt, insidenod, nadjel, gtopology::nadjelnod, nn, nodvalue, nodvalue_assembling_ae(), normal_coordinates_ae(), nsp, nullv(), nvals, polynom_coefficients_ae(), and spvalue.

Referenced by spr_default(), and spr_optional().

void insidenod_assembling ( void ) [private]

loop 1 : assembles vector of node position in domain 2D: insidenod[i]== 1 -> inside node of domain insidenod[i]==-1 -> node on edge of domain insidenod[i]==-2 -> node at vertex of domain 3D: insidenod[i]== 1 -> inside node of domain insidenod[i]==-1 -> node on boundary area of domain insidenod[i]==-2 -> node on edge of domain insidenod[i]==-3 -> node at vertex of domain

loop 2 : for every "node at vertex of domain"=vn is found "oposite node"=on => => inside[on][inside[on][0]++ - 1] = nv where 'on' is "oposite node" already "inside[on][0]" times.

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 386 of file least_square.cpp.

References gtopology::adjelnod, gelement::auxinf, edge_position(), gtopology::gelements, gtopology::give_nne(), gt, if(), insidelem, insidenod, gtopology::nadjelnod, ne, gelement::nne, gelement::nodes, on, opposite_node(), and surface_position().

Referenced by L2_nod2sp(), L2_sp2sp(), spr_default(), and spr_optional().

void L2_nod2sp	(	FILE *	out,
		long *	nsp,
		double **	spcoord,
		double *	nodvalue,
		double **	spvalue,
		char	typ_patch
	)

ONLY FOR LINEAR TRIANGLE (312) !!!!!!!!!!

This is main function of class least_square. It aproximates values from nodes to 'sampling points'. Answer is array of aproximated values in 'sampling points'. Sampling points are defined by arrays nsp and spcoord.

Parameters:

	nsp	- number of sampling points on element, dimension is least_square::ne
	spcoord	- cartesian coorinates of sampling points, dimension is (least_square::ne x nsp[i]*least_squaredim)
	nodvalue	- known values in nodes, dimension is (least_square::nn * least_square::nvals)
	spvalue	- answer - smoothed 'values' in sampling points, dimension is (least_square::ne x nsp[i]*least_squarenvals)

created 3.2.2003, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 161 of file least_square.cpp.

References gtopology::adjacelem(), compute_patches_nod2sp(), gt, insidenod_assembling(), gtopology::nadjelnod, nodvalue, nsp, nsp_spcoord_maxcoord_assembling(), spcoord, and spvalue.

void L2_sp2sp	(	FILE *	out,
		double **	spvalue,
		long	nap,
		const long *	parentel,
		const double **	apcoord,
		double **	apvalue
	)

ONLY FOR LINEAR TRIANGLE (312) !!!!!!!!!!

This is main function of class least_square. It aproximates values from known 'sampling points' to another 'sampling points' = 'answer points'. Answer is array of aproximated values in another 'sampling points' = 'answer points'. ???????? Sampling and answer points ARE IDENTICAL to main integration points on elements, ???????? they are defined by arrays nsp, spcoord ... .

Parameters:

	nsp	- number of sampling points on element, dimension is least_square::ne
	spcoord	- cartesian coorinates of sampling points, dimension is (least_square::ne x nsp[i]*least_squaredim)
	spvalue	- answer - smoothed 'values' in sampling points, dimension is (least_square::ne x nsp[i]*least_squarenvals)
	nodvalue	- known values in nodes, dimension is (least_square::nn * least_square::nvals)

created 4.5.2003, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 204 of file least_square.cpp.

References gtopology::adjacelem(), adjap_assembling(), compute_patches_sp2sp(), gt, insidenod_assembling(), gtopology::nadjelnod, ne, nn, nsp, nsp_spcoord_maxcoord_assembling(), spcoord, and spvalue.

void nodvalue_assembling_ae	(	const vector &	coef_normcoord,
		const vector *	a,
		long	nid,
		ivector &	magnitude
	)			`[private]`

Function computes values of `polynoms` in nodes over all patch.

Parameters:

	coef_normcoord	- array of coeficients for computing of normed coordinates
	a	- array of vector of coefficients of `polynoms`
	id	- id of middle node
	magnitude	- 2D array of sums of magnitudes of values in sampling points

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 1007 of file least_square.cpp.

References adjel, gtopology::gelements, gtopology::give_nne(), gt, insidenod, vector::n, nadjel, nn, gelement::nodes, nodes, and sigma().

Referenced by compute_patches_spr().

void normal_coordinates_ae ( vector & coef_normcoord ) [private]

Function computes coeficients for computing of normed coordinates in patch. This function is called for every patch.

Parameters:

coef_normcoord

- answer = array of coeficients for computing of normed coordinates

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 869 of file least_square.cpp.

References adjel, dim, fillv(), maxcoord, and nadjel.

Referenced by compute_patches_nod2sp(), compute_patches_sp2sp(), and compute_patches_spr().

void nsp_spcoord_maxcoord_assembling ( char nsma_flag ) [private]

Function fills up arrays: 'nsp' (number of sampling points) by default values, 'spcoord' by natural coordinates of default sampling points, 'maxcoord' by extreme element coordinates.

Parameters:

nsma_flag

- determines which array will be actually filled: 'a' = all arrays, 'm' = only array maxcoord

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 249 of file least_square.cpp.

References vector::a, allocv(), gelement::auxinf, bf_quad_3_2d(), bf_quad_4_2d(), destrv(), dim, gtopology::gelements, gtopology::give_node_coord2d(), gtopology::give_node_coord3d(), gt, maxcoord, maxmin_3(), maxmin_4(), ne, gelement::nne, nsp, scprd(), and spcoord.

Referenced by L2_nod2sp(), L2_sp2sp(), spr_default(), and spr_optional().

void polynom	(	long	ncoef,
		const double *	normcoord,
		double *	p
	)			`[private]`

Function computes

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 1128 of file least_square.cpp.

References dim.

Referenced by apvalue_assembling(), polynom_coefficients_ae(), polynom_coefficients_inv_ae(), sigma(), and spvalue_assembling_patch_ae().

void polynom_coefficients_ae	(	const vector &	coef_normcoord,
		vector *	a
	)			`[private]`

Function computes

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 894 of file least_square.cpp.

References addm(), addv(), adjel, cmulv(), dim, fillv(), gause(), vector::n, nadjel, nsp, nvals, polynom(), spcoord, spvalue, and vxv().

Referenced by compute_patches_sp2sp(), and compute_patches_spr().

void polynom_coefficients_inv_ae	(	const vector &	coef_normcoord,
		vector *	a,
		char	typ_patch
	)			`[private]`

Function computes

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 934 of file least_square.cpp.

References addm(), addv(), adjel, allocv(), cmulv(), destrv(), dim, gause(), gtopology::gelements, gtopology::gnodes, gt, nadjel, nn, gelement::nne, gelement::nodes, nodes, nodvalue, nullv(), nvals, polynom(), vxv(), gnode::x, gnode::y, and gnode::z.

Referenced by compute_patches_nod2sp().

void sigma	(	long	ncoef,
		long	nid,
		const vector &	coef_normcoord,
		const vector *	a,
		ivector &	magnitude
	)			`[private]`

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 1101 of file least_square.cpp.

References vector::a, dim, gtopology::gnodes, gt, nn, nodvalue, nvals, polynom(), scprd(), gnode::x, gnode::y, and gnode::z.

Referenced by nodvalue_assembling_ae().

void spr_default	(	FILE *	out,
		double **	spvalue,
		double *	nodvalue
	)

SPR Superconvergent patch recovery This is main function of class least_square. It smooths discontinuous 'values' which are known in 'sampling points'. Answer is array of smoothed values in nodes. Sampling points ARE IDENTICAL to main integration points in first block on elements.

Parameters:

	spvalue	- 2D array of rough values in sampling points, dimension is (gt->ne) x (nip*tncomp)
	nodvalue	- answer, 1D array, size is (least_square::nn * least_square::nvals)

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 82 of file least_square.cpp.

References gtopology::adjacelem(), compute_patches_spr(), gt, insidenod_assembling(), gtopology::nadjelnod, ne, nodvalue, nsp, nsp_spcoord_maxcoord_assembling(), spcoord, and spvalue.

void spr_optional	(	FILE *	out,
		long *	nsp,
		double **	spcoord,
		double **	spvalue,
		double *	nodvalue,
		long	cut_flag
	)

SPR Superconvergent patch recovery This is main function of class least_square. It smooths discontinuous 'values' which are known in 'sampling points'. Answer is array of smoothed values in nodes. Sampling points DO NOT HAVE TO BE IDENTICAL to main integration points in first block on elements, they are defined by arrays nsp,spcoord and spvalue.

Parameters:

	nsp	- number of sampling points on element, dimension is least_square::ne
	spcoord	- cartesian coorinates of sampling points, dimension is (least_square::ne x nsp[i]*least_squaredim)
	spvalue	- 'values' in sampling points, dimension is (least_square::ne x nsp[i]*least_squarenvals)
	nodvalue	- answer, dimension id is (least_square::nn * least_square::nvals)

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 121 of file least_square.cpp.

References gtopology::adjacelem(), compute_patches_spr(), gt, insidenod_assembling(), gtopology::nadjelnod, nodvalue, nsp, nsp_spcoord_maxcoord_assembling(), spcoord, and spvalue.

void spvalue_assembling_patch_ae	(	const vector &	coef_normcoord,
		const vector *	a,
		long	id,
		double **	magnitude
	)			`[private]`

Function computes values of `polynoms` in sampling points over all patch.

Parameters:

	coef_normcoord	- array of coeficients for computing of normed coordinates
	a	- array of vector of coefficients of `polynoms`
	id	- id of middle element; if patch is round node, id == -1
	magnitude	- 2D array of sums of magnitudes of values in sampling points

created 3.3.2002, Ladislav Svoboda, termit@cml.fsv.cvut.cz

Definition at line 1040 of file least_square.cpp.

References vector::a, adjel, dim, nadjel, nsp, nvals, polynom(), scprd(), spcoord, and spvalue.

Referenced by compute_patches_nod2sp().

Member Data Documentation

long* adjel [private]

Definition at line 78 of file least_square.h.

Referenced by compute_patches_nod2sp(), compute_patches_sp2sp(), compute_patches_spr(), least_square(), nodvalue_assembling_ae(), normal_coordinates_ae(), polynom_coefficients_ae(), polynom_coefficients_inv_ae(), and spvalue_assembling_patch_ae().

long dim [private]

dimension (2 or 3)

FOLLOWING CHARACTERISTICS MUST BE IDENTICAL FOR EVERY ELEMENT ALL OVER THE DOMAIN dim,ncomp(ncompother),deg(polynom degree of base functions),material

Definition at line 49 of file least_square.h.

Referenced by adjap_assembling(), apvalue_assembling(), compute_patches_nod2sp(), compute_patches_sp2sp(), compute_patches_spr(), least_square(), normal_coordinates_ae(), nsp_spcoord_maxcoord_assembling(), polynom(), polynom_coefficients_ae(), polynom_coefficients_inv_ae(), sigma(), and spvalue_assembling_patch_ae().