A collecion of methematical routines. All functions are static. More...

#include "us_math2.h"

Classes
class	Peptide
	A structure used for calculating a peptide sequence. More...

class	SolutionData
	A structure used for holding solution data. More...

Static Public Member Functions
static double	box_muller (double, double)
	Normal random variate generator. More...

static double	ranf (void)
	Return a random floating point number. More...

static double	linefit (double , double , double , double , double , double , int)
	Given a line as a set of x and y coordinates, calculate the line's characteristics. More...

static int	nearest_curve_point (double , double , const int, bool, double &, double &, double , double , double , double )
	Given a set of curve points and a given outside point, return the curve point nearest the given point. Return either a point in the curve array or one interpolated based on distance. Optionally also return a value in a third dimension that corresponds to the nearest point. More...

static bool	intersect (double &, double &, double &, double &, double , double )
	Given the slopes and intercepts of two lines, return the intersection point of the two lines, if it exists. More...

static bool	intersect (double , double , int, double , double , int, double , double )
	Given arrays representing two curves, return the intersection point of two lines fitted to them, if it exists. More...

static void	calc_vbar (Peptide &, const QString &, double)
	A routine to calculate the vbar and MW of a peptide sequence. More...

static double	adjust_vbar20 (double vbar, double degC)

static double	adjust_vbar (double vbar, double degC)
	The inverse of adjust_vbar20. Returns vbar20. More...

static void	data_correction (double, SolutionData &)
	Correct buffer data for temperature. More...

static double	normal_distribution (double, double, double)
	A routine to calculate the value of a normally distributed value. More...

static double	time_correction (const QVector< US_DataIO::EditedData > &)
	Calculate the time correction in a run due to acceleration of the rotor. More...

static uint	randomize (void)
	Set the sysem random sequence. More...

static uint	randomize (uint)
	Set the sysem random sequence. More...

static int	nnls (double a, int a_dim1, int m, int n, double b, double x, double rnorm=NULL, double wp=NULL, double zzp=NULL, int *indexp=NULL)

static void	gaussian_smoothing (QVector< double > &, int)
	Remove high frequency noise from a signal. More...

static double	calcCommonVbar (US_Solution &, double)
	Calculate common vbar of a solution. More...

static double	erfc (double)
	An approximation of the Complimentary Gauss Error Fiunction, erfc(). Use for WIN32 only as Linux already has it implemented in <math.h> More...

static int	best_grid_reps (int &, int &)
	Compute best uniform grid repetitions for 2DSA and possibly modify grid point counts in each dimension. More...

Static Private Member Functions
static void	_nnls_g1 (double a, double b, double , double , double *)

static int	_nnls_h12 (int, int, int, int m, double , int, double , double *, int, int, int)

Detailed Description

A collecion of methematical routines. All functions are static.

Definition at line 25 of file us_math2.h.

Member Function Documentation

void US_Math2::_nnls_g1	(	double	a,
		double	b,
		double *	cterm,
		double *	sterm,
		double *	sig
	)

staticprivate

Definition at line 1058 of file us_math2.cpp.

int US_Math2::_nnls_h12	(	int	mode,
		int	lpivot,
		int	l1,
		int	m,
		double *	u,
		int	u_dim1,
		double *	up,
		double *	cm,
		int	ice,
		int	icv,
		int	ncv
	)

staticprivate

Definition at line 1102 of file us_math2.cpp.

static double US_Math2::adjust_vbar	(	double	vbar,
		double	degC
	)

inlinestatic

The inverse of adjust_vbar20. Returns vbar20.

Parameters

vbar	The vbar value at the specified temperature
degC	The temperature of the sample associated with vbar

Definition at line 177 of file us_math2.h.

static double US_Math2::adjust_vbar20	(	double	vbar,
		double	degC
	)

inlinestatic

Adjust the vbar for temperature. The values used in the unadjusted calculations are based on 20 degrees C. We use an observed linear adjustment of 0.000425 per degreee.

Parameters

vbar	The unadjusted vbar value
degC	The temperature used for the adjustment

Definition at line 170 of file us_math2.h.

int US_Math2::best_grid_reps	(	int &	ngrid_s,
		int &	ngrid_k
	)

static

Compute best uniform grid repetitions for 2DSA and possibly modify grid point counts in each dimension.

Parameters

ngrid_s	Reference to grid points in the s dimension, both input and possibly modified value
ngrid_k	Reference to grid points in the k dimension, both input and possibly modified value

Returns: Computed best number of grid repetitions

Definition at line 1364 of file us_math2.cpp.

double US_Math2::box_muller	(	double	m,
		double	s
	)

static

Normal random variate generator.

Parameters

m	- mean
s	- standard deviation

Definition at line 22 of file us_math2.cpp.

void US_Math2::calc_vbar	(	Peptide &	pep,
		const QString &	sequence,
		double	temperature
	)

static

A routine to calculate the vbar and MW of a peptide sequence.

Parameters

pep	The structure to be populated
sequence	The secuence used for the calculations
temperature	The temperature to use for calculations

Definition at line 311 of file us_math2.cpp.

double US_Math2::calcCommonVbar	(	US_Solution &	solution,
		double	temperature
	)

static

Calculate common vbar of a solution.

Parameters

solution	Solution for which to calculate common vbar
temperature	Average temperature of associated experiment

Returns: The common temperature-corrected vbar

Definition at line 1336 of file us_math2.cpp.

void US_Math2::data_correction	(	double	t,
		SolutionData &	d
	)

static

Correct buffer data for temperature.

Parameters

t	Temperature of solution
d	Data to be corrected

The density of water. An empirical equation derived from density vs temperature data. See Krell, J. Chem. & Eng. Data 1975, 20.

$\rho_t = \xi_{max}{{c_0 + c_1 * t + c_2 * t^2 + c_3 * t^3 + c_4 * t^4 + c_5 * t^5} \over{ 1 + bt }}$

where:
$\xi_{max} = 1.000028 \times 10^{-3}$
$ c_0 = 999.83952 $
$ c_1 = 16.945176 $
$c_2 = -7.9870401 \times 10^{-3}$
$c_3 = -46.170461 \times 10^{-6}$
$c_4 = 105.56302 \times 10^{-9}$
$c_5 = -280.54253 \times 10^{-12}$
$b = 16.879850 \times 10^{-3}$

Viscosity of water.
Implements an empirical equation taken from CRC Handbook of Chemistry and Physics, 55th Edition.

For temperature 0 to 20 degress C:

$\log_{10} \eta_t ={ c_0 \over{ c_1 + c_2 ( t-20 ) + c_3 ( t - 20 )^2 }} - c_4$

where:
$\eta$ = viscosity in centipoise ( gm / sec-cm / 100 )
$ t $ = temperature ( Celcius )
$ c_0 = 1301$
$ c_1 = 998.333$
$ c_2 = 8.1855$
$ c_3 = 0.00585$
$ c_4 = 3.30233$

For temperature 20 to 100 degrees C:

$\log_{10}{\eta_t\over\eta_{20}} = { {c_1(20 - t) -c_2(t-20)^2}\over {t+c_3}}$

where:
$\eta$ = viscosity in centipoise ( gm / sec-cm / 100 )
$ t $ = temperature ( Celcius )
$ c_1 = 1.3272$
$c_2 = 1.053 \times 10^{-3}$
$ c_3 = 105$

Definition at line 487 of file us_math2.cpp.

double US_Math2::erfc ( double x )

static

An approximation of the Complimentary Gauss Error Fiunction, erfc(). Use for WIN32 only as Linux already has it implemented in <math.h>

Parameters

x	The input value

Returns: Approximation of erfc(x)

Definition at line 688 of file us_math2.cpp.

void US_Math2::gaussian_smoothing	(	QVector< double > &	array,
		int	smooth
	)

static

Remove high frequency noise from a signal.

Parameters

array	Data to be smoothed. This array will be modified.
smooth	Number of values to smooth to be considered when smoothing

Definition at line 1215 of file us_math2.cpp.

bool US_Math2::intersect	(	double &	slope1,
		double &	intcp1,
		double &	slope2,
		double &	intcp2,
		double *	xisec,
		double *	yisec
	)

static

Given the slopes and intercepts of two lines, return the intersection point of the two lines, if it exists.

Parameters

slope1	The slope of the first line
intcp1	The intercept of the first line
slope2	The slope of the second line
intcp2	The intercept of the second line
xisec	Pointer for return of x of the intersection point
yisec	Pointer for return of y of the intersection point

Returns: Boolean flag if intersection exists (false->parallel)

Definition at line 272 of file us_math2.cpp.

bool US_Math2::intersect	(	double *	x1s,
		double *	y1s,
		int	npoint1,
		double *	x2s,
		double *	y2s,
		int	npoint2,
		double *	xisec,
		double *	yisec
	)

static

Given arrays representing two curves, return the intersection point of two lines fitted to them, if it exists.

Parameters

x1s	An array of x values of the first curve
y1s	An array of y values of the first curve
npoint1	The number of points for the first curve
x2s	An array of x values of the second curve
y2s	An array of y values of the second curve
npoint2	The number of points for the second curve
xisec	Pointer for return of x of the intersection point
yisec	Pointer for return of y of the intersection point

Returns: Boolean flag if intersection exists (false=>parallel)

Definition at line 289 of file us_math2.cpp.

double US_Math2::linefit	(	double **	x,
		double **	y,
		double *	slope,
		double *	intercept,
		double *	sigma,
		double *	correlation,
		int	arraysize
	)

static

Given a line as a set of x and y coordinates, calculate the line's characteristics.

Parameters

x	Pointer to an array of x values
y	Pointer to an array of y values
slope	Pointer to location to return the line's slope
intercept	Pointer to location to return the line's y intercept
sigma	Pointer to location to return the standard deviation
correlation	Pointer to location to return the correlation
arraysize	Input array size

Definition at line 63 of file us_math2.cpp.

int US_Math2::nearest_curve_point	(	double *	xs,
		double *	ys,
		const int	npoints,
		bool	interp,
		double &	xgiven,
		double &	ygiven,
		double *	xnear,
		double *	ynear,
		double *	zs,
		double *	znear
	)

static

Given a set of curve points and a given outside point, return the curve point nearest the given point. Return either a point in the curve array or one interpolated based on distance. Optionally also return a value in a third dimension that corresponds to the nearest point.

Parameters

xs	An array of x values of the curve
ys	An array of y values of the curve
npoints	The number of curve points
interp	Flag to interpolate curve point (false->exact point)
xgiven	The x value of the given point
ygiven	The y value of the given point
xnear	Pointer for return of x of the nearest curve point
ynear	Pointer for return of y of the nearest curve point
zs	Optional third dimension values array (if non-NULL)
znear	Optional pointer for return of z for nearest point

Returns: Index in arrays of nearest curve point

Definition at line 151 of file us_math2.cpp.

int US_Math2::nnls	(	double *	a,
		int	a_dim1,
		int	m,
		int	n,
		double *	b,
		double *	x,
		double *	rnorm = `NULL`,
		double *	wp = `NULL`,
		double *	zzp = `NULL`,
		int *	indexp = `NULL`
	)

static

Algorithm NNLS (Non-negative least-squares)

Given an m by n matrix A, and an m-vector B, computes an n-vector X, that solves the least squares problem A * X = B , subject to X>=0 The A matrix is formatted such that the columns are placed into a vector end-to-end, and the parameter a_dim1 contains the length of each column

Function returns 0 if succesful, 1, if iteration count exceeded 3*N, or 2 in case of invalid problem dimensions or memory allocation error.

Instead of pointers for working space, NULL can be given to let this function to allocate and free the required memory.

Parameters

a	The m by n matrix A. On exit, a[] contains the product matrix Q*A, where Q is an m by n orthogonal matrix generated implicitly by this function. The matrix is column major.
a_dim1	Since matrix A is processed as a set of vectors, a_dim1 is needed to specify the storage increment between vectors in a[]
m	Columns
n	Rows
b	On entry, b[] must contain the m-vector B. On exit, b[] contains Q*B
x	On exit, x[] will contain the solution vector.
rnorm	On exit, rnorm contains the Euclidean norm of the residual vector. It may be set to NULL if the returned value is not needed.
wp	An n-array of working space, w[]. On exit, w[] will contain the dual solution vector. w[i]=0.0 for all i in set p and w[ i ] <= 0.0 for all i in set z.
zzp	An m-array of working space, zz[].
indexp	An n-array of working space, index[].

Definition at line 720 of file us_math2.cpp.

double US_Math2::normal_distribution	(	double	sigma,
		double	mean,
		double	x
	)

static

A routine to calculate the value of a normally distributed value.

Parameters

sigma	Standard deviation of the distribution
mean	Mean value of the distribution
x	Point where to compute desired value

Definition at line 621 of file us_math2.cpp.

uint US_Math2::randomize ( void )

static

Set the sysem random sequence.

Returns: The seed used to set the system time

Definition at line 661 of file us_math2.cpp.

uint US_Math2::randomize ( uint seed )

static

Set the sysem random sequence.

Parameters

seed	A predetermined seed

Returns: The seed used to set the system time

Definition at line 678 of file us_math2.cpp.

double US_Math2::ranf ( void )

static

Return a random floating point number.

Definition at line 57 of file us_math2.cpp.

double US_Math2::time_correction ( const QVector< US_DataIO::EditedData > & dataList )

static

Calculate the time correction in a run due to acceleration of the rotor.

Parameters

dataList The list of editedData for the run

Definition at line 627 of file us_math2.cpp.

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

Classes

Static Public Member Functions

Static Private Member Functions

Detailed Description

Member Function Documentation