A group of static mathematical functions to support finite element calculations. More...

#include "us_astfem_math.h"

Classes
class	AstFemParameters
	Parameters for finite element solution. More...

class	ComponentRole
	Component Role. More...

class	MfemData
	A data set comprised of scans from one sample taken at constant speed. More...

class	MfemInitial
	Initial concentration conditions. More...

class	MfemScan
	A scan entry. More...

class	ReactionGroup
	Reaction Group. More...

Static Public Member Functions
static void	interpolate_C0 (MfemInitial &, MfemInitial &)
	Interpolate first onto second. More...

static void	interpolate_C0 (MfemInitial &, double *, QVector< double > &)
	Interpolate starting concentration QVector MfemInitial onto C0. More...

static void	zero_2d (int, int, double **)
	Initialize a 2d matrix in memory to all zeros. More...

static void	initialize_2d (int, int, double ***)
	Create a 2d matrix in memory and initilize to all zeros. More...

static void	clear_2d (int, double **)
	Delete a 2d matrix in memory. More...

static double	maxval (const QVector< double > &)
	Find the maximum value in a vector. More...

static double	minval (const QVector< double > &)
	Find the minimum value in a vector. More...

static double	maxval (const QVector< US_Model::SimulationComponent > &)
	Find the maximum s in a vector of SimulationComponent entries. More...

static double	minval (const QVector< US_Model::SimulationComponent > &)
	Find the minimum s in a vector of SimulationComponent entries. More...

static void	initialize_3d (int, int, int, double ****)
	Create a 3d matrix in memory and initilize to all zeros. More...

static void	clear_3d (int, int, double ***)
	Delete a 3d matrix in memory. More...

static void	tridiag (double , double , double , double , double *, int)
	Solve a Ax = b where A is tridiagonal. More...

static double	cube_root (double, double, double)
	Find the positive cubic-root of a cubic polynomial with a0 <= 0 and a1, a2 >= 0. More...

static int	GaussElim (int, double *, double )
	Solve Ax = b using Gaussian Elimination. More...

static double	find_C1_mono_Nmer (int, double, double)
	Solve f(x) = x + K * x^n - C using Newton's method. This function needs to be renamed! More...

static int	interpolate (MfemData &, MfemData &, bool)
	Interpolate one dataset onto another using time or omega^2t. More...

static int	interpolate (MfemData &, MfemData &, bool, int, int)
	Interpolate one dataset onto another using time or omega^2t. More...

static void	QuadSolver (double , double , double , double , double , double , int)
	Solve Quad-diagonal system. More...

static void	IntQT1 (double , double, double, double *, double)
	Integration on test function seperately on left Q, right T. More...

static void	IntQTm (double , double, double, double *, double)
	Integration on test function. More...

static void	IntQTn2 (double , double, double, double *, double)
	Integration on test function. More...

static void	IntQTn1 (double , double, double, double *, double)
	Integration on test function. More...

static void	DefineFkp (int, double **)
	Define Lamm equation values. More...

static double	AreaT (double , double )
	Compute the area of a triangle (v1, v2, v3) More...

static void	BasisTS (double, double, double , double , double *)
	Computer basis on standard element (TS) More...

static void	BasisQS (double, double, double , double , double *)
	Computer basis on standard element (QS) More...

static void	BasisTR (double , double , double, double, double , double , double *)
	Computer basis on real element T at given(xs,ts) point. More...

static void	BasisQR (double , double, double, double , double , double , double)
	Computer basis on real element Q at given(xs,ts) point. More...

static double	Integrand (double, double, double, double, double, double, double, double)
	Integrand for Lamm equation. More...

static void	DefineGaussian (int, double **)
	Define Gaussian. More...

static void	initSimData (US_DataIO::RawData &, US_DataIO::EditedData &, double)
	Initialize simulation data from experimental. More...

static double	variance (US_DataIO::RawData &, US_DataIO::EditedData &)
	Calculate variance for Simulation-Experimental difference. More...

static double	variance (US_DataIO::RawData &, US_DataIO::EditedData &, QList< int >)
	Calculate variance for Simulation-Experimental difference. More...

static double	calc_bottom (double, double, double *)
	Calculate bottom radius from channel bottom and rotor coefficients. More...

Detailed Description

A group of static mathematical functions to support finite element calculations.

Definition at line 13 of file us_astfem_math.h.

Member Function Documentation

double US_AstfemMath::AreaT	(	double *	xv,
		double *	yv
	)

static

Compute the area of a triangle (v1, v2, v3)

Parameters

xv	The XV vector
yv	The YV vector

Definition at line 1684 of file us_astfem_math.cpp.

void US_AstfemMath::BasisQR	(	double *	vx,
		double	xs,
		double	ts,
		double *	phi,
		double *	phix,
		double *	phiy,
		double	dt
	)

static

Computer basis on real element Q at given(xs,ts) point.

Parameters

vx	The VX vector
xs	The start X coordinate
ts	The start Y coordinate
phi	The Phi vector to fill
phix	The PhiX vector to fill
phiy	The PhiY vector to fill
dt	The d-t constant

Definition at line 1790 of file us_astfem_math.cpp.

void US_AstfemMath::BasisQS	(	double	xi,
		double	et,
		double *	phi,
		double *	phi1,
		double *	phi2
	)

static

Computer basis on standard element (QS)

Parameters

xi	The XI constant
et	The ET constant
phi	The Phi vector to fill
phi1	The Phi1 vector to fill
phi2	The Phi2 vector to fill

Definition at line 1712 of file us_astfem_math.cpp.

void US_AstfemMath::BasisTR	(	double *	vx,
		double *	vy,
		double	xs,
		double	ys,
		double *	phi,
		double *	phix,
		double *	phiy
	)

static

Computer basis on real element T at given(xs,ts) point.

Parameters

vx	The Vx vector
vy	The Vy vector
xs	The start X coordinate
ys	The start Y coordinate
phi	The Phi vector to fill
phix	The PhiX vector to fill
phiy	The PhiY vector to fill

Definition at line 1737 of file us_astfem_math.cpp.

void US_AstfemMath::BasisTS	(	double	xi,
		double	et,
		double *	phi,
		double *	phi1,
		double *	phi2
	)

static

Computer basis on standard element (TS)

Parameters

xi	The XI constant
et	The ET constant
phi	The Phi vector to fill
phi1	The Phi1 vector to fill
phi2	The Phi2 vector to fill

Definition at line 1692 of file us_astfem_math.cpp.

double US_AstfemMath::calc_bottom	(	double	rpm,
		double	bottom_chan,
		double *	rotorcoefs
	)

static

Calculate bottom radius from channel bottom and rotor coefficients.

Parameters

rpm	Rotor revolutions per minute.
bottom_chan	Initial bottom for centerpiece channel
rotorcoefs	Array of 2 rotor coefficients

Returns: The calculated bottom radius value.

Definition at line 2015 of file us_astfem_math.cpp.

void US_AstfemMath::clear_2d	(	int	val1,
		double **	matrix
	)

static

Delete a 2d matrix in memory.

Parameters

val1	First dimension
matrix	val1 x n matrix to be deleted

Definition at line 109 of file us_astfem_math.cpp.

void US_AstfemMath::clear_3d	(	int	val1,
		int	val2,
		double ***	matrix
	)

static

Delete a 3d matrix in memory.

Parameters

val1	First dimension
val2	Second dimension
matrix	Deleted val1 x val2 x n matrix

Definition at line 179 of file us_astfem_math.cpp.

double US_AstfemMath::cube_root	(	double	a0,
		double	a1,
		double	a2
	)

static

Find the positive cubic-root of a cubic polynomial
with a0 <= 0 and
a1, a2 >= 0.

Parameters

a0	The a0 value
a1	The a0 value
a2	The a0 value

Returns: Cube root

Definition at line 240 of file us_astfem_math.cpp.

void US_AstfemMath::DefineFkp	(	int	npts,
		double **	Lam
	)

static

Define Lamm equation values.

Parameters

npts	Order of the equation
Lam	Matrix of Lamm values to fill

Definition at line 1407 of file us_astfem_math.cpp.

void US_AstfemMath::DefineGaussian	(	int	nGauss,
		double **	Gs2
	)

static

Define Gaussian.

Parameters

nGauss	Order of the matrix
Gs2	Matrix to be filled

Definition at line 1840 of file us_astfem_math.cpp.

double US_AstfemMath::find_C1_mono_Nmer	(	int	n,
		double	K,
		double	CT
	)

static

Solve f(x) = x + K * x^n - C using Newton's method.
This function needs to be renamed!

Parameters

n	The power exponent
K	The scalar constant
CT	The test C value

Definition at line 285 of file us_astfem_math.cpp.

int US_AstfemMath::GaussElim	(	int	n,
		double **	a,
		double *	b
	)

static

Solve Ax = b using Gaussian Elimination.

Parameters

n	The order of the square matrix
a	The n x n matrix
b	The b vector

Returns: Success flag: -1 -> singular, no solution; 1 -> success

Definition at line 326 of file us_astfem_math.cpp.

void US_AstfemMath::initialize_2d	(	int	val1,
		int	val2,
		double ***	matrix
	)

static

Create a 2d matrix in memory and initilize to all zeros.

Parameters

val1	First dimension
val2	Second dimension
matrix	Initialized val1 x val2 matrix

Definition at line 95 of file us_astfem_math.cpp.

void US_AstfemMath::initialize_3d	(	int	val1,
		int	val2,
		int	val3,
		double ****	matrix
	)

static

Create a 3d matrix in memory and initilize to all zeros.

Parameters

val1	First dimension
val2	Second dimension
val3	Third dimension
matrix	Initialized val1 x val2 x val3 matrix

Definition at line 158 of file us_astfem_math.cpp.

void US_AstfemMath::initSimData	(	US_DataIO::RawData &	simdata,
		US_DataIO::EditedData &	editdata,
		double	concval1 = `0.0`
	)

static

Initialize simulation data from experimental.

Parameters

simdata	Reference to simulation Raw Data to initialize.
editdata	Reference to experimental Edited Data to mirror.
concval1	Optional constant concentration value for first scan.

Definition at line 1913 of file us_astfem_math.cpp.

double US_AstfemMath::Integrand	(	double	x_gauss,
		double	D,
		double	sw2,
		double	u,
		double	ux,
		double	ut,
		double	v,
		double	vx
	)

static

Integrand for Lamm equation.

Parameters

x_gauss	The X-gaussian constant
D	The D constant
sw2	The SW2 constant
u	The U constant
ux	The Ux constant
ut	The Ut constant
v	The V constant
vx	The Vx constant

Definition at line 1831 of file us_astfem_math.cpp.

int US_AstfemMath::interpolate	(	MfemData &	expdata,
		MfemData &	simdata,
		bool	use_time
	)

static

Interpolate one dataset onto another using time or omega^2t.

Parameters

expdata	Experimental data to create, sized on input
simdata	Simulation from which to create modeled experiment
use_time	Flag of whether to use time interpolation

Returns: Success flag: 0 -> success

Definition at line 390 of file us_astfem_math.cpp.

int US_AstfemMath::interpolate	(	MfemData &	expdata,
		MfemData &	simdata,
		bool	use_time,
		int	fscan,
		int	lscan
	)

static

Interpolate one dataset onto another using time or omega^2t.

Parameters

expdata	Experimental data to create, sized on input
simdata	Simulation from which to create modeled experiment
use_time	Flag of whether to use time correction
fscan	First update expdata scan index
lscan	Last update expdata scan index plus one

Returns: Success flag: 0 -> success

Definition at line 466 of file us_astfem_math.cpp.

void US_AstfemMath::interpolate_C0	(	MfemInitial &	C0,
		MfemInitial &	C1
	)

static

Interpolate first onto second.

Parameters

C0	Input MfemInitial
C1	MfemInitial with interpolated concentrations

Definition at line 48 of file us_astfem_math.cpp.

void US_AstfemMath::interpolate_C0	(	MfemInitial &	C0,
		double *	C1,
		QVector< double > &	xvec
	)

static

Interpolate starting concentration QVector MfemInitial onto C0.

Parameters

C0	Input MfemInitial
C1	First scan with interpolated concentrations
xvec	Start x (radius) values for each scan

Definition at line 6 of file us_astfem_math.cpp.

void US_AstfemMath::IntQT1	(	double *	vx,
		double	D,
		double	sw2,
		double **	Stif,
		double	dt
	)

static

Integration on test function seperately on left Q, right T.

Parameters

vx	The vx vector
D	The D value
sw2	The sw2 value
Stif	The Stif matrix
dt	The dt value

Definition at line 846 of file us_astfem_math.cpp.

void US_AstfemMath::IntQTm	(	double *	vx,
		double	D,
		double	sw2,
		double **	Stif,
		double	dt
	)

static

Integration on test function.

Parameters

vx	The vx vector
D	The D value
sw2	The sw2 value
Stif	The Stif matrix
dt	The dt value

Definition at line 990 of file us_astfem_math.cpp.

void US_AstfemMath::IntQTn1	(	double *	vx,
		double	D,
		double	sw2,
		double **	Stif,
		double	dt
	)

static

Integration on test function.

Parameters

vx	The vx vector
D	The D value
sw2	The sw2 value
Stif	The Stif matrix
dt	The dt value

Definition at line 1332 of file us_astfem_math.cpp.

void US_AstfemMath::IntQTn2	(	double *	vx,
		double	D,
		double	sw2,
		double **	Stif,
		double	dt
	)

static

Integration on test function.

Parameters

vx	The vx vector
D	The D value
sw2	The sw2 value
Stif	The Stif matrix
dt	The dt value

Definition at line 1161 of file us_astfem_math.cpp.

double US_AstfemMath::maxval ( const QVector< double > & value )

static

Find the maximum value in a vector.

Parameters

value Vector whose maximum is found

Returns: Vector maximum value

Definition at line 137 of file us_astfem_math.cpp.

double US_AstfemMath::maxval ( const QVector< US_Model::SimulationComponent > & value )

static

Find the maximum s in a vector of SimulationComponent entries.

Parameters

value Vector of components whose maximum s value is found

Returns: Vector maximum value

Definition at line 148 of file us_astfem_math.cpp.

double US_AstfemMath::minval ( const QVector< double > & value )

static

Find the minimum value in a vector.

Parameters

value Vector whose minimum is found

Returns: Vector minimum value

Definition at line 116 of file us_astfem_math.cpp.

double US_AstfemMath::minval ( const QVector< US_Model::SimulationComponent > & value )

static

Find the minimum s in a vector of SimulationComponent entries.

Parameters

value Vector of components whose minimum s value is found

Returns: Vector minimum value

Definition at line 127 of file us_astfem_math.cpp.

void US_AstfemMath::QuadSolver	(	double *	ai,
		double *	bi,
		double *	ci,
		double *	di,
		double *	cr,
		double *	solu,
		int	N
	)

static

Solve Quad-diagonal system.

Parameters

ai	The initial a vector
bi	The initial b vector
ci	The initial c vector
di	The initial d vector
cr	The Cr vector
solu	The calculated solution vector
N	The length of vectors

Definition at line 780 of file us_astfem_math.cpp.

void US_AstfemMath::tridiag	(	double *	a,
		double *	b,
		double *	c,
		double *	r,
		double *	u,
		int	N
	)

static

Solve a Ax = b where A is tridiagonal.

Parameters

a	Array of a values
b	Array of b values
c	Array of c values
r	Array of r values
u	Array of u values
N	Length of vectors

Definition at line 194 of file us_astfem_math.cpp.

double US_AstfemMath::variance	(	US_DataIO::RawData &	simdata,
		US_DataIO::EditedData &	editdata
	)

static

Calculate variance for Simulation-Experimental difference.

Parameters

simdata	Reference to simulation Raw Data.
editdata	Reference to experimental Edited Data.

Returns: The variance (average of differences squared) between the simulated and experimental readings values.

Definition at line 1962 of file us_astfem_math.cpp.

double US_AstfemMath::variance	(	US_DataIO::RawData &	simdata,
		US_DataIO::EditedData &	editdata,
		QList< int >	exclScans
	)

static

Calculate variance for Simulation-Experimental difference.

Parameters

simdata	Reference to simulation Raw Data.
editdata	Reference to experimental Edited Data.
exclScans	List of excluded scans.

Returns: The variance (average of differences squared) between the simulated and experimental readings values.

Definition at line 1972 of file us_astfem_math.cpp.

void US_AstfemMath::zero_2d	(	int	val1,
		int	val2,
		double **	matrix
	)

static

Initialize a 2d matrix in memory to all zeros.

Parameters

val1	First dimension
val2	Second dimension
matrix	Initialized val1 x val2 matrix

Definition at line 88 of file us_astfem_math.cpp.

The documentation for this class was generated from the following files:

Classes

Static Public Member Functions

Detailed Description

Member Function Documentation