/usr/include/casacore/scimath/Mathematics/VanVleck.h is in casacore-dev 2.2.0-2.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 | //# VanVleck.h: Class of static functions to aid with vanVleck corrections.
//# Copyright (C) 2002
//# Associated Universities, Inc. Washington DC, USA.
//#
//# This library is free software; you can redistribute it and/or modify it
//# under the terms of the GNU Library General Public License as published by
//# the Free Software Foundation; either version 2 of the License, or (at your
//# option) any later version.
//#
//# This library is distributed in the hope that it will be useful, but WITHOUT
//# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
//# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public
//# License for more details.
//#
//# You should have received a copy of the GNU Library General Public License
//# along with this library; if not, write to the Free Software Foundation,
//# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA.
//#
//# Correspondence concerning AIPS++ should be addressed as follows:
//# Internet email: aips2-request@nrao.edu.
//# Postal address: AIPS++ Project Office
//# National Radio Astronomy Observatory
//# 520 Edgemont Road
//# Charlottesville, VA 22903-2475 USA
//#
//# $Id$
#ifndef SCIMATH_VANVLECK_H
#define SCIMATH_VANVLECK_H
//#! Includes go here
#include <casacore/casa/aips.h>
#include <casacore/casa/Arrays/Matrix.h>
#include <casacore/scimath/Functionals/Interpolate1D.h>
#include <casacore/casa/BasicSL/Constants.h>
#include <casacore/casa/OS/Mutex.h>
namespace casacore { //# NAMESPACE CASACORE - BEGIN
//# Forward Declarations
// <summary>
// A class of static functions to aid with vanVleck corrections of lag data.
// </summary>
// <use visibility=export>
// <reviewed reviewer="" date="yyyy/mm/dd" tests="" demos="">
// </reviewed>
// <prerequisite>
// <li> Familiarity with the issues involved in turning digitally
// sampled lag data from a correlator into spectral data.
// </prerequisite>
//
// <etymology>
// This provides the functions necessary to determine the van Vleck correction
// for a general n-level by m-level correlator.
// </etymology>
//
// <synopsis>
// This provides the functions necessary to determine the van Vleck correction
// for a general n-level by m-level correlator.
// </synopsis>
//
// <example>
// </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.
// </motivation>
//
// <thrown>
// <li>
// <li>
// </thrown>
//
// <todo asof="2002/07/19">
// <li> The inverse error functions may be more generally useful.
// It exists here only as a private member function to be
// used internally.
// </todo>
class VanVleck
{
public:
// Set the interpolation table size.
// Should be an odd number. The default size is 65.
static void size(uInt npts);
// get the current size.
static uInt getsize();
// 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 setQuantization(const Matrix<Double> &qx,
const Matrix<Double> &qy);
// 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 Bool setEquiSpaced(Double xlev, Double ylev,
Double xmean, Double ymean,
Int n);
// Get the data used in setting up the interpolation
static void getTable(Vector<Double> &rs, Vector<Double> &rhos);
// Given a rho return the corresponding corrected r
// Returns 0.0 if no quantization has been set yet.
static Double r(const Double rho);
// 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.
static Double thresh(Int n, Double zerolag)
{ return ( (n>3) ? threshNgt3(n,zerolag) : threshN3(zerolag) ); }
// 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.
static Double predict(Int n, Double threshhold)
{ return ( (n>3) ? predictNgt3(n,threshhold) : predictN3(threshhold));}
// 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 dcoff(Double &dcoffset, Double &threshold,
Int n, Double zerolag, Double bias);
private:
// the number of points to use in setting up the interpolator
static uInt itsSize, itsNx, itsNy;
static Bool itsEquiSpaced;
static Double itsXlev, itsYlev, itsXmean, itsYmean;
// The interpolator
static Interpolate1D<Double, Double> *itsInterp;
// the quantization functions
static Vector<Double> itsQx0, itsQx1, itsQy0, itsQy1;
// 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()).
static Vector<Double> itsQx0Qx0, itsQy0Qy0;
// This is Qx0[i]*Qy0[j]
static Matrix<Double> itsQx0Qy0;
// This is (Qx1[i+1]-Qx1[i])*(Qy1[j+1]*Qy1[j])
static Matrix<Double> itsQx1Qy1diffs;
// The mutex to make the functions thread-safe.
static Mutex theirMutex;
// 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 Double drbydrho(Double *rho);
// 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 Double rinc(Double &rhoi, Double &rhof);
// initialize the interpolator
static void initInterpolator();
// compute first threshhold for a given zerolag for n>3
static Double threshNgt3(Int n, Double zerolag);
// compute first threshhold for a given zerolag for n==3
static Double threshN3(Double zerolag)
{ return sqrt(2.0)*invErfc(zerolag);}
// inverse err fn - used by invErfc
static Double invErf(Double x);
// inverse complementary err fn - used by threshN3
static Double invErfc(Double x);
// Predict a zero-lag value given the indicated first threshold level
// for n>3.
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)
{ return ::erfc(threshhold/sqrt(2.0));}
// implementation of dcoff for the 3-level case
static Bool dcoff3(Double &dcoffset, Double &threshold,
Double zerolag, Double bias);
};
} //# NAMESPACE CASACORE - END
#endif
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