gkpclib.cpp File Reference

#include "math.h"
#include "tools.h"
#include "gkplib.h"

Macros
#define	MAX(a, b)

Functions
void	getCC (int n, int *nq, double **x, double **w)
	retrieve pointers to 1D Clenshaw-Curtis rules
void	getGKPunif (int n, int *nq, double **x, double **w)
	retrieve pointers to 1D Gauss-Kronrod-Patterson rules for uniform pdf based on the quadrature level
void	getGKPnorm (int n, int *nq, double **x, double **w)
	retrieve pointers to 1D Kronrod-Patterson rules for normal pdf based on the quadrature level
int	getOrderCC (int lev)
	get order of Clenshaw-Curtis rules based on level
int	getOrderGKPunif (int lev)
	get order of uniform Gauss-Kronrod-Patterson rules based on level
int	getOrderGKPnorm (int lev)
	get order of normal Gauss-Kronrod-Patterson rules based on level
void	getCompNintoDim (int n, int dim, int *nelem, int **plist)
	List of decompositions of 'n' into 'dim' parts. The implementation is based on Algorithm 5 of Combinatorial Algorithms by Albert Nijenhuis, Herbert Wilf.
int	getSpgSize (int getOrder(int), int dim, int lev)
	Initial estimate for sparse grid size.
void	getSpgQW (void get1DQW(int, int *, double **, double **), int getOrder(int), int dim, int lev, int *nqpts, double **qpts, double **w)
	Main function that connects the user setup for pdftype, dimensionality, and quadrature level and various pieces of the sparse quadrature algorithm employing Gauss-Kronrod-Patterson rules.
void	getSpgAnisQW (void get1DQW(int, int *, double **, double **), int getOrder(int), int dim, int *levList, int *nqpts, double **qpts, double **w)
void	sortSpg (int dim, int spgSize, double *qpts, double *w)
	Sort sparse grid in lexicographical order.
void	getTensorProd (int dim, double *qpts, double *w, int *spgSize, int *n1D, double **x1D, double **w1D, double qfac)
	compute dim-dimensional tensor grid based a series of 1D rules

Variables
static double	x1 [] = {0.0000000}
static double	w1 [] = {2.0000000}
static double	x3 [] = {-0.77459666924148337704,0.0, 0.77459666924148337704 }
static double	w3 [] = {0.555555555555555555556,0.888888888888888888889,0.555555555555555555556}
static double	x7 []
static double	w7 []
static double	x15 []
static double	w15 []
static double	x31 []
static double	w31 []
static double	x63 []
static double	w63 []
static double	xn1 [] = {0.0000000000000000}
static double	wn1 [] = {1.0000000000000000}
static double	xn3 [] = {-1.73205080756887719, 0.000000000000000000, 1.73205080756887719}
static double	wn3 [] = {0.166666666666666657, 0.66666666666666663, 0.166666666666666657}
static double	xn9 []
static double	wn9 []
static double	xn19 []
static double	wn19 []
static double	xn35 []
static double	wn35 []

Macro Definition Documentation

MAX

#define MAX	(		a,
			b )

Value:

(((a) > (b)) ? (a) : (b))

Function Documentation

getCC()

void getCC	(	int	n,
		int *	nq,
		double **	x,
		double **	w )

retrieve pointers to 1D Clenshaw-Curtis rules

getCompNintoDim()

void getCompNintoDim	(	int	n,
		int	dim,
		int *	nelem,
		int **	plist )

List of decompositions of 'n' into 'dim' parts. The implementation is based on Algorithm 5 of Combinatorial Algorithms by Albert Nijenhuis, Herbert Wilf.

getGKPnorm()

void getGKPnorm	(	int	n,
		int *	nq,
		double **	x,
		double **	w )

retrieve pointers to 1D Kronrod-Patterson rules for normal pdf based on the quadrature level

getGKPunif()

void getGKPunif	(	int	n,
		int *	nq,
		double **	x,
		double **	w )

retrieve pointers to 1D Gauss-Kronrod-Patterson rules for uniform pdf based on the quadrature level

getOrderCC()

int getOrderCC

(

int

lev

)

get order of Clenshaw-Curtis rules based on level

getOrderGKPnorm()

int getOrderGKPnorm

(

int

lev

)

get order of normal Gauss-Kronrod-Patterson rules based on level

getOrderGKPunif()

int getOrderGKPunif

(

int

lev

)

get order of uniform Gauss-Kronrod-Patterson rules based on level

getSpgAnisQW()

void getSpgAnisQW	(	void	get1DQWint, int *, double **, double **,
		int	getOrderint,
		int	dim,
		int *	levList,
		int *	nqpts,
		double **	qpts,
		double **	w )

getSpgQW()

void getSpgQW	(	void	get1DQWint, int *, double **, double **,
		int	getOrderint,
		int	dim,
		int	lev,
		int *	nqpts,
		double **	qpts,
		double **	w )

Main function that connects the user setup for pdftype, dimensionality, and quadrature level and various pieces of the sparse quadrature algorithm employing Gauss-Kronrod-Patterson rules.

getSpgSize()

int getSpgSize	(	int	getOrderint,
		int	dim,
		int	lev )

Initial estimate for sparse grid size.

getTensorProd()

void getTensorProd	(	int	dim,
		double *	qpts,
		double *	w,
		int *	spgSize,
		int *	n1D,
		double **	x1D,
		double **	w1D,
		double	qfac )

compute dim-dimensional tensor grid based a series of 1D rules

sortSpg()

void sortSpg	(	int	dim,
		int	spgSize,
		double *	qpts,
		double *	w )

Sort sparse grid in lexicographical order.

Variable Documentation

w1

double w1[] = {2.0000000}

static

w15

double w15[]

static

Initial value:

= {0.0170017196299402603390,0.0516032829970797396969,0.0929271953151245376859,
                       0.134415255243784220360, 0.171511909136391380787, 0.200628529376989021034,
                       0.219156858401587496404, 0.225510499798206687386, 0.219156858401587496404,
                       0.200628529376989021034, 0.171511909136391380787, 0.134415255243784220360,
                       0.0929271953151245376859,0.0516032829970797396969, 0.0170017196299402603390}

w3

double w3[] = {0.555555555555555555556,0.888888888888888888889,0.555555555555555555556}

static

w31

double w31[]

static

Initial value:

= {0.00254478079156187441540,0.00843456573932110624631,0.0164460498543878109338,
                       0.0258075980961766535646, 0.0359571033071293220968, 0.0464628932617579865414,
                       0.0569795094941233574122, 0.0672077542959907035404, 0.0768796204990035310427,
                       0.0857559200499903511542, 0.0936271099812644736167, 0.100314278611795578771,
                       0.105669893580234809744,  0.109578421055924638237,  0.111956873020953456880,
                       0.112755256720768691607,
                       0.111956873020953456880,  0.109578421055924638237,  0.105669893580234809744,
                       0.100314278611795578771,  0.0936271099812644736167, 0.0857559200499903511542,
                       0.0768796204990035310427, 0.0672077542959907035404, 0.0569795094941233574122,
                       0.0464628932617579865414, 0.0359571033071293220968, 0.0258075980961766535646,
                       0.0164460498543878109338, 0.00843456573932110624631,0.00254478079156187441540 }

w63

double w63[]

static

Initial value:

= {0.000363221481845530659694,0.00126515655623006801137,0.00257904979468568827243,
                       0.00421763044155885483908, 0.00611550682211724633968,0.00822300795723592966926,
                       0.0104982469096213218983,  0.0129038001003512656260, 0.0154067504665594978021,
                       0.0179785515681282703329,  0.0205942339159127111492, 0.0232314466399102694433,
                       0.0258696793272147469108,  0.0284897547458335486125, 0.0310735511116879648799,
                       0.0336038771482077305417,  0.0360644327807825726401, 0.0384398102494555320386,
                       0.0407155101169443189339,  0.0428779600250077344929, 0.0449145316536321974143,
                       0.0468135549906280124026,  0.0485643304066731987159, 0.0501571393058995374137,
                       0.0515832539520484587768,  0.0528349467901165198621, 0.0539054993352660639269,
                       0.0547892105279628650322,  0.0554814043565593639878, 0.0559784365104763194076,
                       0.0562776998312543012726,  0.0563776283603847173877, 0.0562776998312543012726,  
                       0.0559784365104763194076,  0.0554814043565593639878, 0.0547892105279628650322,
                       0.0539054993352660639269,  0.0528349467901165198621, 0.0515832539520484587768,
                       0.0501571393058995374137,  0.0485643304066731987159, 0.0468135549906280124026,
                       0.0449145316536321974143,  0.0428779600250077344929, 0.0407155101169443189339,
                       0.0384398102494555320386,  0.0360644327807825726401, 0.0336038771482077305417,
                       0.0310735511116879648799,  0.0284897547458335486125, 0.0258696793272147469108,
                       0.0232314466399102694433,  0.0205942339159127111492, 0.0179785515681282703329,
                       0.0154067504665594978021,  0.0129038001003512656260, 0.0104982469096213218983,
                       0.00822300795723592966926, 0.00611550682211724633968,0.00421763044155885483908,
                       0.00257904979468568827243, 0.00126515655623006801137,0.000363221481845530659694 }

w7

double w7[]

static

Initial value:

= { 0.104656226026467265194,0.268488089868333440729,0.401397414775962222905,
                       0.450916538658474142345,
                       0.401397414775962222905,0.268488089868333440729,0.104656226026467265194}

wn1

double wn1[] = {1.0000000000000000}

static

wn19

double wn19[]

static

Initial value:

= { 8.62968460222986318E-10, 6.09480873146898402E-07, 6.01233694598479965E-05, 
                         0.00288488043650675591, -0.00633722479337375712,  0.0180852342547984622,  
                         0.0640960546868076103,   0.0611517301252477163,   0.208324991649608771,  
                         0.303467199854206227,    
                         0.208324991649608771,    0.0611517301252477163,  0.0640960546868076103, 
                         0.0180852342547984622,  -0.00633722479337375712, 0.00288488043650675591,  
                         6.01233694598479965E-05, 6.09480873146898402E-07,8.62968460222986318E-10 }

wn3

double wn3[] = {0.166666666666666657, 0.66666666666666663, 0.166666666666666657}

static

wn35

double wn35[]

static

Initial value:

= { 1.05413265823340136E-18, 5.45004126506381281E-15, 3.09722235760629949E-12, 
                         4.60117603486559168E-10, 2.13941944795610622E-08, 2.46764213457981401E-07, 
                         2.73422068011878881E-06, 3.57293481989753322E-05, 0.000275242141167851312, 
                         0.000818953927502267349, 0.00231134524035220713,  0.00315544626918755127, 
                         0.015673473751851151,    0.0452736854651503914,   0.0923647267169863534, 
                         0.148070831155215854,    0.191760115888044341,    
                         0.000514894508069213769, 
                         0.191760115888044341,    0.148070831155215854,    
                         0.0923647267169863534,   0.0452736854651503914,   0.015673473751851151,    
                         0.00315544626918755127,  0.00231134524035220713,  0.000818953927502267349,
                         0.000275242141167851312, 3.57293481989753322E-05, 2.73422068011878881E-06,     
                         2.46764213457981401E-07, 2.13941944795610622E-08, 4.60117603486559168E-10,     
                         3.09722235760629949E-12, 5.45004126506381281E-15, 1.05413265823340136E-18 }

wn9

double wn9[]

static

Initial value:

= { 9.42694575565174701E-05, 0.00799632547089352934, 0.0948509485094851251,  
                        0.270074329577937755, 0.253968253968254065, 0.270074329577937755,  
                        0.0948509485094851251,0.00799632547089352934,9.42694575565174701E-05 }

x1

double x1[] = {0.0000000}

static

x15

double x15[]

static

Initial value:

= {-0.99383196321275502221,-0.96049126870802028342,-0.88845923287225699889,
                       -0.77459666924148337704,-0.62110294673722640294,-0.43424374934680255800,
                       -0.22338668642896688163, 0.0,                    0.22338668642896688163,
                        0.43424374934680255800, 0.62110294673722640294, 0.77459666924148337704,
                        0.88845923287225699889, 0.96049126870802028342, 0.99383196321275502221 }

x3

double x3[] = {-0.77459666924148337704,0.0, 0.77459666924148337704 }

static

x31

double x31[]

static

Initial value:

= {-0.99909812496766759766,-0.99383196321275502221,-0.98153114955374010687,
                       -0.96049126870802028342,-0.92965485742974005667,-0.88845923287225699889,
                       -0.83672593816886873550,-0.77459666924148337704,-0.70249620649152707861,
                       -0.62110294673722640294,-0.53131974364437562397,-0.43424374934680255800,
                       -0.33113539325797683309,-0.22338668642896688163,-0.11248894313318662575,
                        0.0,
                        0.11248894313318662575, 0.22338668642896688163, 0.33113539325797683309,
                        0.43424374934680255800, 0.53131974364437562397, 0.62110294673722640294,
                        0.70249620649152707861, 0.77459666924148337704, 0.83672593816886873550,
                        0.88845923287225699889, 0.92965485742974005667, 0.96049126870802028342,
                        0.98153114955374010687, 0.99383196321275502221, 0.99909812496766759766 }

x63

double x63[]

static

Initial value:

= {-0.99987288812035761194,-0.99909812496766759766,-0.99720625937222195908,
                       -0.99383196321275502221,-0.98868475754742947994,-0.98153114955374010687,
                       -0.97218287474858179658,-0.96049126870802028342,-0.94634285837340290515,
                       -0.92965485742974005667,-0.91037115695700429250,-0.88845923287225699889,
                       -0.86390793819369047715,-0.83672593816886873550,-0.80694053195021761186,
                       -0.77459666924148337704,-0.73975604435269475868,-0.70249620649152707861,
                       -0.66290966002478059546,-0.62110294673722640294,-0.57719571005204581484,
                       -0.53131974364437562397,-0.48361802694584102756,-0.43424374934680255800,
                       -0.38335932419873034692,-0.33113539325797683309,-0.27774982202182431507,
                       -0.22338668642896688163,-0.16823525155220746498,-0.11248894313318662575,
                       -0.056344313046592789972,0.0,                    0.056344313046592789972,
                        0.11248894313318662575, 0.16823525155220746498, 0.22338668642896688163,
                        0.27774982202182431507, 0.33113539325797683309, 0.38335932419873034692,
                        0.43424374934680255800, 0.48361802694584102756, 0.53131974364437562397,
                        0.57719571005204581484, 0.62110294673722640294, 0.66290966002478059546,
                        0.70249620649152707861, 0.73975604435269475868, 0.77459666924148337704,
                        0.80694053195021761186, 0.83672593816886873550, 0.86390793819369047715,
                        0.88845923287225699889, 0.91037115695700429250, 0.92965485742974005667,
                        0.94634285837340290515, 0.96049126870802028342, 0.97218287474858179658,
                        0.98153114955374010687, 0.98868475754742947994, 0.99383196321275502221,
                        0.99720625937222195908, 0.99909812496766759766, 0.99987288812035761194 }

x7

double x7[]

static

Initial value:

= {-0.96049126870802028342,-0.77459666924148337704,-0.43424374934680255800,
                       0.0,
                       0.43424374934680255800, 0.77459666924148337704, 0.96049126870802028342}

xn1

double xn1[] = {0.0000000000000000}

static

xn19

double xn19[]

static

Initial value:

= {-6.36339449433636961,  -5.18701603991365623, -4.18495601767273229,  
                        -3.20533379449919442,  -2.86127957605705818, -2.59608311504920231,  
                        -1.73205080756887719,  -1.23042363402730603, -0.741095349994540853,  
                         0.0000000000000000,      
                         0.741095349994540853,  1.23042363402730603,  1.73205080756887719,     
                         2.59608311504920231,    2.86127957605705818,  3.20533379449919442,     
                         4.18495601767273229,    5.18701603991365623,  6.36339449433636961 }

xn3

double xn3[] = {-1.73205080756887719, 0.000000000000000000, 1.73205080756887719}

static

xn35

double xn35[]

static

Initial value:

= {-9.0169397898903032,   -7.98077179859056063,  -7.12210670080461661, 
                        -6.36339449433636961,  -5.69817776848810986,  -5.18701603991365623, 
                        -4.73643308595229673,  -4.18495601767273229,  -3.63531851903727832, 
                        -3.20533379449919442,  -2.86127957605705818,  -2.59608311504920231, 
                        -2.23362606167694189,  -1.73205080756887719,  -1.23042363402730603, 
                        -0.741095349994540853, -0.248992297579960609,  
                         0.00000000000000000, 
                         0.248992297579960609,  0.741095349994540853,  
                         1.23042363402730603,   1.73205080756887719,   2.23362606167694189, 
                         2.59608311504920231,   2.86127957605705818,   3.20533379449919442,    
                         3.63531851903727832,   4.18495601767273229,   4.73643308595229673,    
                         5.18701603991365623,   5.69817776848810986,   6.36339449433636961,     
                         7.12210670080461661,   7.98077179859056063,   9.0169397898903032 }

xn9

double xn9[]

static

Initial value:

= {-4.18495601767273229, -2.86127957605705818, -1.73205080756887719, 
                       -0.741095349994540853, 0.00000000000000000,  0.741095349994540853, 
                        1.73205080756887719,  2.86127957605705818,  4.18495601767273229 }