A class of static functions to aid with vanVleck corrections of lag data. More...

#include <VanVleck.h>

Static Public Member Functions
static void	size (uInt npts)
	Set the interpolation table size.
static uInt	getsize ()
	get the current size.
static void	setQuantization (const Matrix< Double > &qx, const Matrix< Double > &qy)
	Set the x and y quantization functions.
static Bool	setEquiSpaced (Double xlev, Double ylev, Double xmean, Double ymean, Int n)
	Set the x and y quantization levels for the case of equi-spaced levels with a possible non-zero offset.
static void	getTable (Vector< Double > &rs, Vector< Double > &rhos)
	Get the data used in setting up the interpolation.
static Double	r (const Double rho)
	Given a rho return the corresponding corrected r Returns 0.0 if no quantization has been set yet.
static Double	thresh (Int n, Double zerolag)
	Given a measured zero-lag autocorrelation and number of levels (n>=3) return the first positive quantizer input threshold level.
static Double	predict (Int n, Double threshhold)
	Predict a given zero-lag given n and a threshold.
static Bool	dcoff (Double &dcoffset, Double &threshold, Int n, Double zerolag, Double bias)
	Compute an approximation to the mean signal level (DC offset) and quantizer threshold setting (both in terms of the r.m.s.
Static Private Member Functions
static Double	drbydrho (Double *rho)
	The fortran numerical integration function will call this.
static Double	rinc (Double &rhoi, Double &rhof)
	For a given rhoi, rhof, this produces a high-accuracy numerical approximation to the integral of drbydrho over the range rhoi to rhof.
static void	initInterpolator ()
	initialize the interpolator
static Double	threshNgt3 (Int n, Double zerolag)
	compute first threshhold for a given zerolag for n>3
static Double	threshN3 (Double zerolag)
	compute first threshhold for a given zerolag for n==3
static Double	invErf (Double x)
	inverse err fn - used by invErfc
static Double	invErfc (Double x)
	inverse complementary err fn - used by threshN3
static Double	predictNgt3 (Int n, Double threshhold)
	Predict a zero-lag value given the indicated first threshold level for n>3.
static Double	predictN3 (Double threshhold)
	Predict a zero-lag value given the indicated first threshold level for n=3.
static Bool	dcoff3 (Double &dcoffset, Double &threshold, Double zerolag, Double bias)
	implementation of dcoff for the 3-level case
Static Private Attributes
static uInt	itsSize
	the number of points to use in setting up the interpolator
static uInt	itsNx
static uInt	itsNy
static Bool	itsEquiSpaced
static Double	itsXlev
static Double	itsYlev
static Double	itsXmean
static Double	itsYmean
static Interpolate1D< Double, Double > *	itsInterp
	The interpolator.
static Vector< Double >	itsQx0
	the quantization functions
static Vector< Double >	itsQx1
static Vector< Double >	itsQy0
static Vector< Double >	itsQy1
static Vector< Double >	itsQx0Qx0
	Useful combinations of the above - to speed up drbydrho these are -1/2(Qx0Qx0) and -1/2(Qy0Qy0) These are only used for i up to (itsQx0.nelements() and for j up to (itsQy0.nelements()).
static Vector< Double >	itsQy0Qy0
static Matrix< Double >	itsQx0Qy0
	This is Qx0[i]*Qy0[j].
static Matrix< Double >	itsQx1Qy1diffs
	This is (Qx1[i+1]-Qx1[i])(Qy1[j+1]Qy1[j])
static Mutex	theirMutex
	The mutex to make the functions thread-safe.

Detailed Description

A class of static functions to aid with vanVleck corrections of lag data.

Intended use:

Public interface

Review Status

Date Reviewed:: yyyy/mm/dd

Prerequisite

Familiarity with the issues involved in turning digitally sampled lag data from a correlator into spectral data.

Etymology

This provides the functions necessary to determine the van Vleck correction for a general n-level by m-level correlator.

Synopsis

This provides the functions necessary to determine the van Vleck correction for a general n-level by m-level correlator.

Example

Motivation

The GBT spectrometer provides the measured auto-correlation and cross-correlation lags. The gbt MeasurementSet filler (gbtmsfiller) needs to convert those lags to the spectral domain. These functions allow the filler to calculate the van Vleck correction appropriate for each measured set of lags. They are of general and hence are not specific to the GBT spectrometer.

The functions here are static because of the nature of the underlying numerical quadrature fortran code used to integrate the drbyrho function.

Thrown Exceptions

To Do

The inverse error functions may be more generally useful. It exists here only as a private member function to be used internally.

Definition at line 94 of file VanVleck.h.

Member Function Documentation

static Bool casa::VanVleck::dcoff	(	Double &	dcoffset,
		Double &	threshold,
		Int	n,
		Double	zerolag,
		Double	bias
	)		`[static]`

Compute an approximation to the mean signal level (DC offset) and quantizer threshold setting (both in terms of the r.m.s.

signal input level) given the observed positive bias (the asymptotic limit of the measured autocorrelation at large lags) and the zero-lag autocorrelation. dcoffset is the mean signal level, threshold is the quantizer setting, n is the number of levels, zerolag is the zero-lag value and bias is the asymptotic bias. Currently, this is only available for the n==3 level case, all other cases set the returned dcoffset to 0 and use thresh() to set the returned value of threshold. A return value of F indicates that the zerolag and bias values are inconsistent and the dcoffset can not be determined. In that case, the returned dcoffset is 0 and thresh() is used to set the threshold level.

static Bool casa::VanVleck::dcoff3	(	Double &	dcoffset,
		Double &	threshold,
		Double	zerolag,
		Double	bias
	)		`[static, private]`

implementation of dcoff for the 3-level case

static Double casa::VanVleck::drbydrho ( Double * rho ) [static, private]

The fortran numerical integration function will call this.

For a given rho and quantization functions, this computes, via Price's theorem, the value dr/drho of the derivative, with respect to rho, of the expected value of the correlator output.

static uInt casa::VanVleck::getsize ( ) [static]

get the current size.

static void casa::VanVleck::getTable	(	Vector< Double > &	rs,
		Vector< Double > &	rhos
	)		`[static]`

Get the data used in setting up the interpolation.

static void casa::VanVleck::initInterpolator ( ) [static, private]

initialize the interpolator

static Double casa::VanVleck::invErf ( Double x ) [static, private]

inverse err fn - used by invErfc

static Double casa::VanVleck::invErfc ( Double x ) [static, private]

inverse complementary err fn - used by threshN3

Referenced by threshN3().

static Double casa::VanVleck::predict	(	Int	n,
		Double	threshhold
	)		`[inline, static]`

Predict a given zero-lag given n and a threshold.

This is included here to be used as a check against the output of thresh.

Definition at line 145 of file VanVleck.h.

References predictN3(), and predictNgt3().

static Double casa::VanVleck::predictN3 ( Double threshhold ) [inline, static, private]

Predict a zero-lag value given the indicated first threshold level for n=3.

Definition at line 229 of file VanVleck.h.

References casa::sqrt().

Referenced by predict().

static Double casa::VanVleck::predictNgt3	(	Int	n,
		Double	threshhold
	)		`[static, private]`

Predict a zero-lag value given the indicated first threshold level for n>3.

Referenced by predict().

static Double casa::VanVleck::r ( const Double rho ) [static]

Given a rho return the corresponding corrected r Returns 0.0 if no quantization has been set yet.

static Double casa::VanVleck::rinc	(	Double &	rhoi,
		Double &	rhof
	)		`[static, private]`

For a given rhoi, rhof, this produces a high-accuracy numerical approximation to the integral of drbydrho over the range rhoi to rhof.

It calls the standard QUADPACK adaptive Gaussian quadrature procedure, dqags, to do the numerical integration.

static Bool casa::VanVleck::setEquiSpaced	(	Double	xlev,
		Double	ylev,
		Double	xmean,
		Double	ymean,
		Int	n
	)		`[static]`

Set the x and y quantization levels for the case of equi-spaced levels with a possible non-zero offset.

The total number of levels is given by n, which must be 3 or 9. If n is not 3 or 9, False will be returned and no quantization will have been set. For the 3- and 9- level cases a bivarate normal integral calculation will be used. That is much faster than the more general numerical integration used by setQuantization.

static void casa::VanVleck::setQuantization	(	const Matrix< Double > &	qx,
		const Matrix< Double > &	qy
	)		`[static]`

Set the x and y quantization functions.

Each matrix should have dimensions (2,n) where n is the number of levels. The first row (0,...) is the (n-1) threshold levels and the second row is the n quantizations based on those thresholds. The thresholds may include a DC offset. The (0,(n-1)) element is never used and need not be set.

static void casa::VanVleck::size ( uInt npts ) [static]

Set the interpolation table size.

Should be an odd number. The default size is 65.

static Double casa::VanVleck::thresh	(	Int	n,
		Double	zerolag
	)		`[inline, static]`

Given a measured zero-lag autocorrelation and number of levels (n>=3) return the first positive quantizer input threshold level.

This can be used to set the up the matrix arguments used in setQuantization.

Definition at line 139 of file VanVleck.h.

References threshN3(), and threshNgt3().

static Double casa::VanVleck::threshN3 ( Double zerolag ) [inline, static, private]

compute first threshhold for a given zerolag for n==3

Definition at line 214 of file VanVleck.h.

References invErfc(), and casa::sqrt().

Referenced by thresh().

static Double casa::VanVleck::threshNgt3	(	Int	n,
		Double	zerolag
	)		`[static, private]`

compute first threshhold for a given zerolag for n>3

Referenced by thresh().

Member Data Documentation

Bool casa::VanVleck::itsEquiSpaced [static, private]

Definition at line 171 of file VanVleck.h.

Interpolate1D<Double, Double>* casa::VanVleck::itsInterp [static, private]

The interpolator.

Definition at line 176 of file VanVleck.h.

uInt casa::VanVleck::itsNx [static, private]

Definition at line 169 of file VanVleck.h.

uInt casa::VanVleck::itsNy [static, private]

Definition at line 169 of file VanVleck.h.

Vector<Double> casa::VanVleck::itsQx0 [static, private]

the quantization functions

Definition at line 179 of file VanVleck.h.

Vector<Double> casa::VanVleck::itsQx0Qx0 [static, private]

Useful combinations of the above - to speed up drbydrho these are -1/2*(Qx0*Qx0) and -1/2*(Qy0*Qy0) These are only used for i up to (itsQx0.nelements() and for j up to (itsQy0.nelements()).

Definition at line 185 of file VanVleck.h.

Matrix<Double> casa::VanVleck::itsQx0Qy0 [static, private]

This is Qx0[i]*Qy0[j].

Definition at line 187 of file VanVleck.h.

Vector<Double> casa::VanVleck::itsQx1 [static, private]

Definition at line 179 of file VanVleck.h.

Matrix<Double> casa::VanVleck::itsQx1Qy1diffs [static, private]

This is (Qx1[i+1]-Qx1[i])*(Qy1[j+1]*Qy1[j])

Definition at line 189 of file VanVleck.h.

Vector<Double> casa::VanVleck::itsQy0 [static, private]

Definition at line 179 of file VanVleck.h.

Vector<Double> casa::VanVleck::itsQy0Qy0 [static, private]