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casacore::LSQFit Class Reference

Basic class for the least squares fitting. More...

#include <LSQFit.h>

Inheritance diagram for casacore::LSQFit:
casacore::LSQaips casacore::GenericL2Fit< T > casacore::GenericL2Fit< casacore::Float > casacore::GenericL2Fit< DComplex > casacore::GenericL2Fit< Double > casacore::GenericL2Fit< Float > casacore::LinearFit< T > casacore::NonLinearFit< T > casacore::LinearFit< casacore::Float > casacore::NonLinearFit< Double > casacore::LinearFit< Float > casacore::LinearFitSVD< T > casacore::NonLinearFitLM< T > casacore::LinearFitSVD< casacore::Float > casacore::NonLinearFitLM< Double > casacore::LinearFitSVD< Float >

Classes

struct  AsReal
 
struct  Complex
 
struct  Conjugate
 
struct  Real
 Simple classes to overload templated memberfunctions. More...
 
struct  Separable
 

Public Types

enum  ReadyCode {
  NONREADY,
  SOLINCREMENT,
  DERIVLEVEL,
  MAXITER,
  NOREDUCTION,
  SINGULAR,
  N_ReadyCode
}
 State of the non-linear solution. More...
 
enum  ErrorField {
  NC,
  SUMWEIGHT,
  SUMLL,
  CHI2,
  N_ErrorField
}
 Offset of fields in error_p data area. More...
 

Public Member Functions

 LSQFit (uInt nUnknowns, uInt nConstraints=0)
 Construct an object with the number of unknowns and constraints, using the default collinearity factor and the default Levenberg-Marquardt adjustment factor. More...
 
 LSQFit (uInt nUnknowns, const LSQReal &, uInt nConstraints=0)
 Allow explicit Real specification. More...
 
 LSQFit (uInt nUnknowns, const LSQComplex &, uInt nConstraints=0)
 Allow explicit Complex specification. More...
 
 LSQFit ()
 Default constructor (empty, only usable after a set(nUnknowns)) More...
 
 LSQFit (const LSQFit &other)
 Copy constructor (deep copy) More...
 
LSQFitoperator= (const LSQFit &other)
 Assignment (deep copy) More...
 
 ~LSQFit ()
 
Bool invert (uInt &nRank, Bool doSVD=False)
 Triangularize the normal equations and determine the rank nRank of the normal equations and, in the case of an SVD solution, the constraint equations. More...
 
template<class U >
void copy (const Double *beg, const Double *end, U &sol, LSQReal)
 Copy date from beg to end; converting if necessary to complex data. More...
 
template<class U >
void copy (const Double *beg, const Double *end, U &sol, LSQComplex)
 
template<class U >
void copy (const Double *beg, const Double *end, U *sol, LSQReal)
 
template<class U >
void copy (const Double *beg, const Double *end, U *sol, LSQComplex)
 
template<class U >
void uncopy (Double *beg, const Double *end, U &sol, LSQReal)
 
template<class U >
void uncopy (Double *beg, const Double *end, U &sol, LSQComplex)
 
template<class U >
void uncopy (Double *beg, const Double *end, U *sol, LSQReal)
 
template<class U >
void uncopy (Double *beg, const Double *end, U *sol, LSQComplex)
 
template<class U >
void copyDiagonal (U &errors, LSQReal)
 
template<class U >
void copyDiagonal (U &errors, LSQComplex)
 
template<class U >
void solve (U *sol)
 Solve normal equations. More...
 
template<class U >
void solve (std::complex< U > *sol)
 
template<class U >
void solve (U &sol)
 
template<class U >
Bool solveLoop (uInt &nRank, U *sol, Bool doSVD=False)
 Solve a loop in a non-linear set. More...
 
template<class U >
Bool solveLoop (uInt &nRank, std::complex< U > *sol, Bool doSVD=False)
 
template<class U >
Bool solveLoop (uInt &nRank, U &sol, Bool doSVD=False)
 
template<class U >
Bool solveLoop (Double &fit, uInt &nRank, U *sol, Bool doSVD=False)
 
template<class U >
Bool solveLoop (Double &fit, uInt &nRank, std::complex< U > *sol, Bool doSVD=False)
 
template<class U >
Bool solveLoop (Double &fit, uInt &nRank, U &sol, Bool doSVD=False)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)
 Make normal equations using the cEq condition equation (cArray) (with nUnknowns elements) and a weight weight, given the known observed value obs. More...
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const V &cEq2, const U &weight, const U &obs, const U &obs2, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNorm (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const U &obs, LSQFit::Real, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Complex, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Separable, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::AsReal, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V >
void makeNorm (const std::vector< std::pair< uInt, V > > &cEq, const U &weight, const std::complex< U > &obs, LSQFit::Conjugate, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNormSorted (uInt nIndex, const W &cEqIndex, const V &cEq, const U &weight, const U &obs, Bool doNorm=True, Bool doKnown=True)
 
template<class U , class V , class W >
void makeNormSorted (uInt nIndex, const W &cEqIndex, const V &cEq, const V &cEq2, const U &weight, const U &obs, const U &obs2, Bool doNorm=True, Bool doKnown=True)
 
template<class U >
Bool getConstraint (uInt n, U *cEq) const
 Get the n-th (from 0 to the rank deficiency, or missing rank, see e.g. More...
 
template<class U >
Bool getConstraint (uInt n, std::complex< U > *cEq) const
 
template<class U >
Bool getConstraint (uInt n, U &cEq) const
 
template<class U , class V >
Bool setConstraint (uInt n, const V &cEq, const U &obs)
 Add a new constraint equation (updating nConstraints); or set a numbered constraint equation (0..nConstraints-1). More...
 
template<class U , class V >
Bool setConstraint (uInt n, const V &cEq, const std::complex< U > &obs)
 
template<class U , class V , class W >
Bool setConstraint (uInt n, uInt nIndex, const W &cEqIndex, const V &cEq, const U &obs)
 
template<class U , class V , class W >
Bool setConstraint (uInt n, uInt nIndex, const W &cEqIndex, const V &cEq, const std::complex< U > &obs)
 
template<class U , class V >
Bool addConstraint (const V &cEq, const U &obs)
 
template<class U , class V >
Bool addConstraint (const V &cEq, const std::complex< U > &obs)
 
template<class U , class V , class W >
Bool addConstraint (uInt nIndex, const W &cEqIndex, const V &cEq, const U &obs)
 
template<class U , class V , class W >
Bool addConstraint (uInt nIndex, const W &cEqIndex, const V &cEq, const std::complex< U > &obs)
 
Bool merge (const LSQFit &other)
 Merge other LSQFit object (i.e. More...
 
Bool merge (const LSQFit &other, uInt nIndex, const uInt *nEqIndex)
 
Bool merge (const LSQFit &other, uInt nIndex, const std::vector< uInt > &nEqIndex)
 
template<class W >
Bool merge (const LSQFit &other, uInt nIndex, const W &nEqIndex)
 
void reset ()
 Reset status to empty. More...
 
void set (uInt nUnknowns, uInt nConstraints=0)
 Set new sizes (default is for Real) More...
 
void set (Int nUnknowns, Int nConstraints=0)
 
void set (uInt nUnknowns, const LSQReal &, uInt nConstraints=0)
 
void set (Int nUnknowns, const LSQReal &, Int nConstraints=0)
 
void set (uInt nUnknowns, const LSQComplex &, uInt nConstraints=0)
 
void set (Int nUnknowns, const LSQComplex &, Int nConstraints=0)
 
void set (Double factor=1e-6, Double LMFactor=1e-3)
 Set new factors (collinearity factor, and Levenberg-Marquardt LMFactor) More...
 
void setEpsValue (Double epsval=1e-8)
 Set new value solution test. More...
 
void setEpsDerivative (Double epsder=1e-8)
 Set new derivative test. More...
 
void setMaxIter (uInt maxiter=0)
 Set maximum number of iterations. More...
 
uInt nIterations () const
 Get number of iterations done. More...
 
void setBalanced (Bool balanced=False)
 Set the expected form of the normal equations. More...
 
LSQFit::ReadyCode isReady () const
 Ask the state of the non-linear solutions. More...
 
const std::string & readyText () const
 
template<class U >
Bool getCovariance (U *covar)
 Get the covariance matrix (of size nUnknowns * nUnknowns) More...
 
template<class U >
Bool getCovariance (std::complex< U > *covar)
 
template<class U >
Bool getErrors (U *errors)
 Get main diagonal of covariance function (of size nUnknowns) More...
 
template<class U >
Bool getErrors (std::complex< U > *errors)
 
template<class U >
Bool getErrors (U &errors)
 
uInt nUnknowns () const
 Get the number of unknowns. More...
 
uInt nConstraints () const
 Get the number of constraints. More...
 
uInt getDeficiency () const
 Get the rank deficiency
Warning: Note that the number is returned assuming real values; For complex values it has to be halved
More...
 
Double getChi () const
 Get chi^2 (both are identical); the standard deviation (per observation) and the standard deviation per weight unit. More...
 
Double getChi2 () const
 
Double getSD () const
 
Double getWeightedSD () const
 
void debugIt (uInt &nun, uInt &np, uInt &ncon, uInt &ner, uInt &rank, Double *&nEq, Double *&known, Double *&constr, Double *&er, uInt *&piv, Double *&sEq, Double *&sol, Double &prec, Double &nonlin) const
 Debug: More...
 
Bool fromRecord (String &error, const RecordInterface &in)
 Create an LSQFit object from a record. More...
 
Bool toRecord (String &error, RecordInterface &out) const
 Create a record from an LSQFit object. More...
 
const Stringident () const
 Get identification of record. More...
 
void toAipsIO (AipsIO &) const
 Save or restore using AipsIO. More...
 
void fromAipsIO (AipsIO &)
 

Static Public Attributes

static Real REAL
 And values to use. More...
 
static Complex COMPLEX
 
static Separable SEPARABLE
 
static AsReal ASREAL
 
static Conjugate CONJUGATE
 

Protected Types

enum  StateBit {
  INVERTED,
  TRIANGLE,
  NONLIN,
  N_StateBit
}
 Bits that can be set/referenced. More...
 

Protected Member Functions

Doublerowrt (uInt i) const
 Get pointer in rectangular array. More...
 
Doublerowru (uInt i) const
 
void init ()
 Initialise areas. More...
 
void clear ()
 Clear areas. More...
 
void deinit ()
 De-initialise area. More...
 
void solveIt ()
 Solve normal equations. More...
 
Bool solveItLoop (Double &fit, uInt &nRank, Bool doSVD=False)
 One non-linear LM loop. More...
 
void solveMR (uInt nin)
 Solve missing rank part. More...
 
Bool invertRect ()
 Invert rectangular matrix (i.e. More...
 
Double normSolution (const Double *sol) const
 Get the norm of the current solution vector. More...
 
Double normInfKnown (const Double *known) const
 Get the infinite norm of the known vector. More...
 
Bool mergeIt (const LSQFit &other, uInt nIndex, const uInt *nEqIndex)
 Merge sparse normal equations. More...
 
void save (Bool all=True)
 Save current status (or part) More...
 
void restore (Bool all=True)
 Restore current status. More...
 
void copy (const LSQFit &other, Bool all=True)
 Copy data. More...
 
void extendConstraints (uInt n)
 Extend the constraint equation area to the specify number of equations. More...
 
void createNCEQ ()
 Create the solution equation area nceq_p and fill it. More...
 
void getWorkSOL ()
 Get work areas for solutions, covariance. More...
 
void getWorkCOV ()
 

Static Protected Member Functions

static Double realMC (const std::complex< Double > &x, const std::complex< Double > &y)
 Calculate the real or imag part of x*conj(y) More...
 
static Double imagMC (const std::complex< Double > &x, const std::complex< Double > &y)
 
static Float realMC (const std::complex< Float > &x, const std::complex< Float > &y)
 
static Float imagMC (const std::complex< Float > &x, const std::complex< Float > &y)
 

Protected Attributes

uInt state_p
 Bits set to indicate state. More...
 
uInt nun_p
 Number of unknowns. More...
 
uInt ncon_p
 Number of constraints. More...
 
uInt n_p
 Matrix size (will be n_p = nun_p + ncon_p) More...
 
uInt r_p
 Rank of normal equations (normally n_p) More...
 
Double prec_p
 Collinearity precision. More...
 
Double startnon_p
 Levenberg start factor. More...
 
Double nonlin_p
 Levenberg current factor. More...
 
Double stepfactor_p
 Levenberg step factor. More...
 
Double epsval_p
 Test value for [incremental] solution in non-linear loop. More...
 
Double epsder_p
 Test value for known vector in non-linear loop. More...
 
Bool balanced_p
 Indicator for a well balanced normal equation. More...
 
uInt maxiter_p
 Maximum number of iterations for non-linear solution. More...
 
uInt niter_p
 Iteration count for non-linear solution. More...
 
ReadyCode ready_p
 Indicate the non-linear state. More...
 
uIntpiv_p
 Pivot table (n_p) More...
 
LSQMatrixnorm_p
 Normal equations (triangular nun_p * nun_p) More...
 
uInt nnc_p
 Current length nceq_p. More...
 
LSQMatrixnceq_p
 Normal combined with constraint equations for solutions (triangular nnc_p*nnc_p) More...
 
Doubleknown_p
 Known part equations (n_p) More...
 
Doubleerror_p
 Counts for errors (N_ErrorField) More...
 
Doubleconstr_p
 Constraint equation area (nun_p*ncon_p)) More...
 
Doublesol_p
 Solution area (n_p) More...
 
LSQFitnar_p
 Save area for non-linear case (size determined internally) More...
 
Doublelar_p
 Save area for non-symmetric (i.e. More...
 
Doublewsol_p
 Work areas for interim solutions and covariance. More...
 
Doublewcov_p
 

Static Protected Attributes

static const String recid
 Record field names. More...
 
static const String state
 
static const String nun
 
static const String ncon
 
static const String prec
 
static const String startnon
 
static const String nonlin
 
static const String rank
 
static const String nnc
 
static const String piv
 
static const String constr
 
static const String known
 
static const String errors
 
static const String sol
 
static const String lar
 
static const String wsol
 
static const String wcov
 
static const String nceq
 
static const String nar
 

Detailed Description

Basic class for the least squares fitting.

Review Status

Reviewed By:
Neil Killeen
Date Reviewed:
2000/06/01
Test programs:
tLSQFit

Prerequisite

Etymology

From Least SQuares and Fitting

Synopsis

The LSQFit class contains the basic functions to do all the fitting described in the Note about fitting. It handles real, and complex equations;
linear and non-linear (Levenberg-Marquardt) solutions;
regular (with optional constraints) or Singular Value Decomposition (SVD).
In essence they are a set of routines to generate normal equations (makeNorm()) in triangular form from a set of condition equations;
to do a Cholesky-type decomposition of the normal equations (either regular or SVD) and test its rank (invert());
to do a quasi inversion of the decomposed equations (solve()) to obtain the solution and/or the errors.

All calculations are done in place. Methods to obtain additional information about the fitting process are available.

This class can be used as a stand-alone class outside of the Casacore environment. In that case the aips.h include file can be replaced if necessary by appropriate typedefs for Double, Float and uInt.
The interface to the methods have standard data or standard STL iterator arguments only. They can be used with any container having an STL random-access iterator interface. Especially they can be used with carrays (necessary templates provided), Casacore Vectors (necessary templates provided in LSQaips), standard random access STL containers (like std::vector).

The normal operation of the class consists of the following steps:

An LSQFit object can be re-used by issuing the reset() command, or set() of new values. If an unknown has not been used in the condition equations at all, the doDiagonal() will make sure a proper solution is obtained, with missing unknowns zeroed.

Most of the calculations are done in place; however, enough data is saved that it is possible to continue with the same (partial) normal equations after e.g. an interim solution.

If the normal equations are produced in separate partial sets (e.g. in a multi-processor environment) a merge() method can combine them.
Tip: It is suggested to add any possible constraint equations after the merge;

A debugIt() method provides read access to all internal information.

The member definitions are split over three files. The second one contains the templated member function definitions, to bypass the problem of duplicate definitions of non-templated members when pre-compiling them. The third contains methods for saving objects as Records or through AipsIO.


Warning: No boundary checks on input and output containers is done for faster execution; In general these tests should be done at the higher level routines, like the LinearFit and NonLinearFit classes which should be checked for usage of LSQFit;

The contents can be saved in a record (toRecord), and an object can be created from a record (fromRecord). The record identifier is 'lfit'.
The object can also be saved or restored using AipsIO.

Example

See the tLSQFit.cc and tLSQaips.cc program for extensive examples.

The following example will first create 2 condition equations for 3 unknowns (the third is degenerate). It will first create normal equations for a 2 unknown solution and solve; then it will create normal equations for a 3 unknown solution, and solve (note that the degenerate will be set to 0. The last one will use SVD and one condition equation.r

#include <iostream>
int main() {
// Condition equations for x+y=2; x-y=4;
Double ce[2][3] = {{1, 1, 0}, {1, -1, 0}};
Double m[2] = {2, 4};
// Solution and error area
Double sol[3];
Double sd, mu;
Bool ok;
// LSQ object
LSQFit fit(2);
// Make normal equation
for (uInt i=0; i<2; i++) fit.makeNorm(ce[i], 1.0, m[i]);
// Invert(decompose) and show
ok = fit.invert(rank);
cout << "ok? " << ok << "; rank: " << rank << endl;
// Solve and show
if (ok) {
fit.solve(sol, &sd, &mu);
for (uInt i=0; i<2; i++) cout << "Sol" << i << ": " << sol[i] << endl;
cout << "sd: "<< sd << "; mu: " << mu << endl;
};
cout << "----------" << endl;
// Retry with 3 unknowns: note auto fill of unmentioned one
fit.set(uInt(3));
for (uInt i=0; i<2; i++) fit.makeNorm(ce[i], 1.0, m[i]);
ok = fit.invert(rank);
cout << "ok? " << ok << "; rank: " << rank << endl;
if (ok) {
fit.solve(sol, &sd, &mu);
for (uInt i=0; i<3; i++) cout << "Sol" << i << ": " << sol[i] << endl;
cout << "sd: "<< sd << "; mu: " << mu << endl;
};
cout << "----------" << endl;
// Retry with 3 unknowns; but 1 condition equation and use SVD
fit.reset();
for (uInt i=0; i<1; i++) fit.makeNorm(ce[i], 1.0, m[i]);
ok = fit.invert(rank, True);
cout << "ok? " << ok << "; rank: " << rank << endl;
if (ok) {
fit.solve(sol, &sd, &mu);
for (uInt i=0; i<3; i++) cout << "Sol" << i << ": " << sol[i] << endl;
cout << "sd: "<< sd << "; mu: " << mu << endl;
};
cout << "----------" << endl;
// Without SVD it would be:
fit.reset();
for (uInt i=0; i<1; i++) fit.makeNorm(ce[i], 1.0, m[i]);
ok = fit.invert(rank);
cout << "ok? " << ok << "; rank: " << rank << endl;
if (ok) {
fit.solve(sol, &sd, &mu);
for (uInt i=0; i<3; i++) cout << "Sol" << i << ": " << sol[i] << endl;
cout << "sd: "<< sd << "; mu: " << mu << endl;
};
cout << "----------" << endl;
exit(0);
}

Which will produce the output:

ok? 1; rank: 2
Sol0: 3
Sol1: -1
sd: 0; mu: 0
----------
ok? 1; rank: 3
Sol0: 3
Sol1: -1
Sol2: 0
sd: 0; mu: 0
----------
ok? 1; rank: 2
Sol0: 1
Sol1: 1
Sol2: 0
sd: 0; mu: 0
----------
ok? 0; rank: 2
----------

Motivation

The class was written to be able to do complex, real standard and SVD solutions in a simple and fast way.

To Do

Definition at line 330 of file LSQFit.h.

Member Enumeration Documentation

Offset of fields in error_p data area.

Enumerator
NC 

Number of condition equations.

SUMWEIGHT 

Sum weights of condition equations.

SUMLL 

Sum known terms squared.

CHI2 

Calculated chi^2.

N_ErrorField 

Number of error fields.

Definition at line 357 of file LSQFit.h.

State of the non-linear solution.

Enumerator
NONREADY 
SOLINCREMENT 
DERIVLEVEL 
MAXITER 
NOREDUCTION 
SINGULAR 
N_ReadyCode 

Definition at line 347 of file LSQFit.h.

Bits that can be set/referenced.

Enumerator
INVERTED 

Inverted matrix present.

TRIANGLE 

Triangularised.

NONLIN 

Non-linear solution.

N_StateBit 

Filler for cxx2html.

Definition at line 831 of file LSQFit.h.

Constructor & Destructor Documentation

casacore::LSQFit::LSQFit ( uInt  nUnknowns,
uInt  nConstraints = 0 
)
explicit

Construct an object with the number of unknowns and constraints, using the default collinearity factor and the default Levenberg-Marquardt adjustment factor.

Assume real

casacore::LSQFit::LSQFit ( uInt  nUnknowns,
const LSQReal ,
uInt  nConstraints = 0 
)

Allow explicit Real specification.

casacore::LSQFit::LSQFit ( uInt  nUnknowns,
const LSQComplex ,
uInt  nConstraints = 0 
)

Allow explicit Complex specification.

casacore::LSQFit::LSQFit ( )

Default constructor (empty, only usable after a set(nUnknowns))

casacore::LSQFit::LSQFit ( const LSQFit other)

Copy constructor (deep copy)

casacore::LSQFit::~LSQFit ( )

Member Function Documentation

template<class U , class V >
Bool casacore::LSQFit::addConstraint ( const V &  cEq,
const U &  obs 
)
template<class U , class V >
Bool casacore::LSQFit::addConstraint ( const V &  cEq,
const std::complex< U > &  obs 
)
template<class U , class V , class W >
Bool casacore::LSQFit::addConstraint ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  obs 
)
template<class U , class V , class W >
Bool casacore::LSQFit::addConstraint ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const std::complex< U > &  obs 
)
void casacore::LSQFit::clear ( )
protected

Clear areas.

template<class U >
void casacore::LSQFit::copy ( const Double beg,
const Double end,
U &  sol,
LSQReal   
)

Copy date from beg to end; converting if necessary to complex data.

template<class U >
void casacore::LSQFit::copy ( const Double beg,
const Double end,
U &  sol,
LSQComplex   
)
template<class U >
void casacore::LSQFit::copy ( const Double beg,
const Double end,
U *  sol,
LSQReal   
)
template<class U >
void casacore::LSQFit::copy ( const Double beg,
const Double end,
U *  sol,
LSQComplex   
)
void casacore::LSQFit::copy ( const LSQFit other,
Bool  all = True 
)
protected

Copy data.

If all False, only the relevant data for non-linear solution are copied (normal equations, knows and errors).

template<class U >
void casacore::LSQFit::copyDiagonal ( U &  errors,
LSQReal   
)
template<class U >
void casacore::LSQFit::copyDiagonal ( U &  errors,
LSQComplex   
)
void casacore::LSQFit::createNCEQ ( )
protected

Create the solution equation area nceq_p and fill it.

void casacore::LSQFit::debugIt ( uInt nun,
uInt np,
uInt ncon,
uInt ner,
uInt rank,
Double *&  nEq,
Double *&  known,
Double *&  constr,
Double *&  er,
uInt *&  piv,
Double *&  sEq,
Double *&  sol,
Double prec,
Double nonlin 
) const

Debug:

  • nun = number of unknowns
  • np = total number of solved unknowns (nun+ncon)
  • ncon = number of constraint equations
  • ner = number of elements in chi2 vector
  • rank = rank)
  • nEq = normal equation (nun*nun as triangular matrix)
  • known = known vector (np)
  • constr = constraint matrix (ncon*nun)
  • er = error info vector (ner)
  • piv = pivot vector (np)
  • sEq = normal solution equation (np*np triangular)
  • sol = internal solution vector (np)
  • prec = collinearity precision
  • nonlin = current Levenberg factor-1

Note that all pointers may be 0.

void casacore::LSQFit::deinit ( )
protected

De-initialise area.

void casacore::LSQFit::extendConstraints ( uInt  n)
protected

Extend the constraint equation area to the specify number of equations.

void casacore::LSQFit::fromAipsIO ( AipsIO )
Bool casacore::LSQFit::fromRecord ( String error,
const RecordInterface in 
)

Create an LSQFit object from a record.

An error message is generated, and False returned if an invalid record is given. A valid record will return True. Error messages are postfixed to error.

Double casacore::LSQFit::getChi ( ) const

Get chi^2 (both are identical); the standard deviation (per observation) and the standard deviation per weight unit.

Referenced by casacore::GenericL2Fit< DComplex >::chiSquare(), and getChi2().

Double casacore::LSQFit::getChi2 ( ) const
inline

Definition at line 780 of file LSQFit.h.

References getChi().

template<class U >
Bool casacore::LSQFit::getConstraint ( uInt  n,
U *  cEq 
) const

Get the n-th (from 0 to the rank deficiency, or missing rank, see e.g.

getDeficiency()) constraint equation as determined by invert() in SVD-mode in cEq[nUnknown]. False returned for illegal n. Note that nMissing will be equal to the number of unknowns (nUnknowns, or double that for the complex case) minus the rank as returned from the invert() method.

template<class U >
Bool casacore::LSQFit::getConstraint ( uInt  n,
std::complex< U > *  cEq 
) const
template<class U >
Bool casacore::LSQFit::getConstraint ( uInt  n,
U &  cEq 
) const
template<class U >
Bool casacore::LSQFit::getCovariance ( U *  covar)

Get the covariance matrix (of size nUnknowns * nUnknowns)

Referenced by casacore::LSQaips::getCovariance().

template<class U >
Bool casacore::LSQFit::getCovariance ( std::complex< U > *  covar)
uInt casacore::LSQFit::getDeficiency ( ) const
inline

Get the rank deficiency
Warning: Note that the number is returned assuming real values; For complex values it has to be halved

Definition at line 775 of file LSQFit.h.

References n_p, and r_p.

Referenced by casacore::GenericL2Fit< DComplex >::getRank().

template<class U >
Bool casacore::LSQFit::getErrors ( U *  errors)

Get main diagonal of covariance function (of size nUnknowns)

Referenced by casacore::LSQaips::getErrors().

template<class U >
Bool casacore::LSQFit::getErrors ( std::complex< U > *  errors)
template<class U >
Bool casacore::LSQFit::getErrors ( U &  errors)
Double casacore::LSQFit::getSD ( ) const
Double casacore::LSQFit::getWeightedSD ( ) const
void casacore::LSQFit::getWorkCOV ( )
protected
void casacore::LSQFit::getWorkSOL ( )
protected

Get work areas for solutions, covariance.

const String& casacore::LSQFit::ident ( ) const

Get identification of record.

static Double casacore::LSQFit::imagMC ( const std::complex< Double > &  x,
const std::complex< Double > &  y 
)
inlinestaticprotected

Definition at line 941 of file LSQFit.h.

static Float casacore::LSQFit::imagMC ( const std::complex< Float > &  x,
const std::complex< Float > &  y 
)
inlinestaticprotected

Definition at line 947 of file LSQFit.h.

void casacore::LSQFit::init ( )
protected

Initialise areas.

Bool casacore::LSQFit::invert ( uInt nRank,
Bool  doSVD = False 
)

Triangularize the normal equations and determine the rank nRank of the normal equations and, in the case of an SVD solution, the constraint equations.

The collinearity factor is used to determine if the system can be solved (in essence it is the square of the sine of the angle between a column in the normal equations and the plane suspended by the other columns: if too parallel, the equations are degenerate). If doSVD is given as False, False is returned if rank not maximal, else an SVD solution is done.

Bool casacore::LSQFit::invertRect ( )
protected

Invert rectangular matrix (i.e.

when constraints present)

LSQFit::ReadyCode casacore::LSQFit::isReady ( ) const
inline

Ask the state of the non-linear solutions.

Definition at line 749 of file LSQFit.h.

References ready_p.

template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const U &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)

Make normal equations using the cEq condition equation (cArray) (with nUnknowns elements) and a weight weight, given the known observed value obs.

doNorm and doKnown can be used to e.g. re-use existing normal equations, i.e. the condition equations, but make a new known side (i.e. new observations).

The versions with cEqIndex[] indicate which of the nUnknowns are actually present in the condition equation (starting indexing at 0); the other terms are supposed to be zero. E.g. if a 12-telescope array has an equation only using telescopes 2 and 4, the lengths of cEqIndex and cEq will be both 2, and the index will contain 1 and 3 (when telescope numbering starts at 1) or 2 and 4 (when telescope numbering starts at 0. The index is given as an iterator (and hence can be a raw pointer)

The complex versions can have different interpretation of the inputs, where the complex number can be seen either as a complex number; as two real numbers, or as coefficients of equations with complex conjugates. See Note 224) for the details.

Versions with pair assume that the pairs are created by the SparseDiff automatic differentiation class. The pair is an index and a value. The indices are assumed to be sorted.

Special (makeNormSorted) indexed versions exist which assume that the given indices are sorted (which is the case for the LOFAR BBS environment).

Some versions exist with two sets of equations (cEq2, obs2). If two simultaneous equations are created they will be faster.

Note that the use of const U & is due to a Float->Double conversion problem on Solaris. Linux was ok.

template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const U &  obs,
LSQFit::Real  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Complex  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Separable  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::AsReal  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Conjugate  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const U &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const V &  cEq2,
const U &  weight,
const U &  obs,
const U &  obs2,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const U &  obs,
LSQFit::Real  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Complex  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Separable  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::AsReal  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNorm ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Conjugate  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const U &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const U &  obs,
LSQFit::Real  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const std::complex< U > &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Complex  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Separable  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::AsReal  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V >
void casacore::LSQFit::makeNorm ( const std::vector< std::pair< uInt, V > > &  cEq,
const U &  weight,
const std::complex< U > &  obs,
LSQFit::Conjugate  ,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNormSorted ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  weight,
const U &  obs,
Bool  doNorm = True,
Bool  doKnown = True 
)
template<class U , class V , class W >
void casacore::LSQFit::makeNormSorted ( uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const V &  cEq2,
const U &  weight,
const U &  obs,
const U &  obs2,
Bool  doNorm = True,
Bool  doKnown = True 
)
Bool casacore::LSQFit::merge ( const LSQFit other)

Merge other LSQFit object (i.e.

the normal equation and related information) into this. Both objects must have the same number of unknowns, and be pure normal equations (i.e. no invert(), solve(), solveLoop() or statistics calls should have been made). If merging cannot be done, False is returned. The index case (the index is an iterator) assumes that the normal equations to be merged are a sparse subset of the complete matrix. The index 'vector' specifies which unknowns are present. An index outside the scope of the final equations will be skipped.
Tip: For highest numerical precision in the case of a larger number of partial normal equations to be merged, it is best to merge them in pairs (and repeat);

Bool casacore::LSQFit::merge ( const LSQFit other,
uInt  nIndex,
const uInt nEqIndex 
)
inline

Definition at line 703 of file LSQFit.h.

References mergeIt().

Bool casacore::LSQFit::merge ( const LSQFit other,
uInt  nIndex,
const std::vector< uInt > &  nEqIndex 
)
inline

Definition at line 705 of file LSQFit.h.

References mergeIt().

template<class W >
Bool casacore::LSQFit::merge ( const LSQFit other,
uInt  nIndex,
const W &  nEqIndex 
)
inline

Definition at line 709 of file LSQFit.h.

References mergeIt().

Bool casacore::LSQFit::mergeIt ( const LSQFit other,
uInt  nIndex,
const uInt nEqIndex 
)
protected

Merge sparse normal equations.

Referenced by merge().

uInt casacore::LSQFit::nConstraints ( ) const
inline

Get the number of constraints.

Definition at line 771 of file LSQFit.h.

References ncon_p.

Referenced by set().

uInt casacore::LSQFit::nIterations ( ) const
inline

Get number of iterations done.

Definition at line 744 of file LSQFit.h.

References maxiter_p, and niter_p.

Double casacore::LSQFit::normInfKnown ( const Double known) const
protected

Get the infinite norm of the known vector.

Double casacore::LSQFit::normSolution ( const Double sol) const
protected

Get the norm of the current solution vector.

uInt casacore::LSQFit::nUnknowns ( ) const
inline

Get the number of unknowns.

Definition at line 769 of file LSQFit.h.

References nun_p.

Referenced by casacore::LSQaips::getErrors(), casacore::GenericL2Fit< DComplex >::getRank(), and casacore::LSQaips::solve().

LSQFit& casacore::LSQFit::operator= ( const LSQFit other)

Assignment (deep copy)

Referenced by casacore::LSQaips::operator=().

const std::string& casacore::LSQFit::readyText ( ) const
static Double casacore::LSQFit::realMC ( const std::complex< Double > &  x,
const std::complex< Double > &  y 
)
inlinestaticprotected

Calculate the real or imag part of x*conj(y)

Definition at line 938 of file LSQFit.h.

static Float casacore::LSQFit::realMC ( const std::complex< Float > &  x,
const std::complex< Float > &  y 
)
inlinestaticprotected

Definition at line 944 of file LSQFit.h.

void casacore::LSQFit::reset ( )

Reset status to empty.

void casacore::LSQFit::restore ( Bool  all = True)
protected

Restore current status.

Double* casacore::LSQFit::rowrt ( uInt  i) const
inlineprotected

Get pointer in rectangular array.

Definition at line 933 of file LSQFit.h.

References lar_p, and n_p.

Double* casacore::LSQFit::rowru ( uInt  i) const
inlineprotected

Definition at line 934 of file LSQFit.h.

References lar_p, and nun_p.

void casacore::LSQFit::save ( Bool  all = True)
protected

Save current status (or part)

void casacore::LSQFit::set ( uInt  nUnknowns,
uInt  nConstraints = 0 
)

Set new sizes (default is for Real)

Referenced by set().

void casacore::LSQFit::set ( Int  nUnknowns,
Int  nConstraints = 0 
)
inline

Definition at line 719 of file LSQFit.h.

References nConstraints(), and set().

void casacore::LSQFit::set ( uInt  nUnknowns,
const LSQReal ,
uInt  nConstraints = 0 
)
inline

Definition at line 722 of file LSQFit.h.

References nConstraints(), and set().

void casacore::LSQFit::set ( Int  nUnknowns,
const LSQReal ,
Int  nConstraints = 0 
)
inline

Definition at line 725 of file LSQFit.h.

References nConstraints(), and set().

void casacore::LSQFit::set ( uInt  nUnknowns,
const LSQComplex ,
uInt  nConstraints = 0 
)
void casacore::LSQFit::set ( Int  nUnknowns,
const LSQComplex ,
Int  nConstraints = 0 
)
inline

Definition at line 729 of file LSQFit.h.

References nConstraints(), and set().

void casacore::LSQFit::set ( Double  factor = 1e-6,
Double  LMFactor = 1e-3 
)

Set new factors (collinearity factor, and Levenberg-Marquardt LMFactor)

void casacore::LSQFit::setBalanced ( Bool  balanced = False)
inline

Set the expected form of the normal equations.

Definition at line 746 of file LSQFit.h.

References balanced_p.

template<class U , class V >
Bool casacore::LSQFit::setConstraint ( uInt  n,
const V &  cEq,
const U &  obs 
)

Add a new constraint equation (updating nConstraints); or set a numbered constraint equation (0..nConstraints-1).

False if illegal number n. The constraints are equations with nUnknowns terms, and a constant value. E.g. measuring three angles of a triangle could lead to equation [1,1,1] with obs as 3.1415. Note that each complex constraint will be converted into two real constraints (see Note 224).

template<class U , class V >
Bool casacore::LSQFit::setConstraint ( uInt  n,
const V &  cEq,
const std::complex< U > &  obs 
)
template<class U , class V , class W >
Bool casacore::LSQFit::setConstraint ( uInt  n,
uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const U &  obs 
)
template<class U , class V , class W >
Bool casacore::LSQFit::setConstraint ( uInt  n,
uInt  nIndex,
const W &  cEqIndex,
const V &  cEq,
const std::complex< U > &  obs 
)
void casacore::LSQFit::setEpsDerivative ( Double  epsder = 1e-8)
inline

Set new derivative test.

Definition at line 740 of file LSQFit.h.

References epsder_p.

void casacore::LSQFit::setEpsValue ( Double  epsval = 1e-8)
inline

Set new value solution test.

Definition at line 738 of file LSQFit.h.

References epsval_p.

void casacore::LSQFit::setMaxIter ( uInt  maxiter = 0)
inline

Set maximum number of iterations.

Definition at line 742 of file LSQFit.h.

References maxiter_p.

template<class U >
void casacore::LSQFit::solve ( U *  sol)

Solve normal equations.

The solution will be given in sol.

Referenced by casacore::LSQaips::solve().

template<class U >
void casacore::LSQFit::solve ( std::complex< U > *  sol)
template<class U >
void casacore::LSQFit::solve ( U &  sol)
void casacore::LSQFit::solveIt ( )
protected

Solve normal equations.

Bool casacore::LSQFit::solveItLoop ( Double fit,
uInt nRank,
Bool  doSVD = False 
)
protected

One non-linear LM loop.

template<class U >
Bool casacore::LSQFit::solveLoop ( uInt nRank,
U *  sol,
Bool  doSVD = False 
)

Solve a loop in a non-linear set.

The methods with the fit argument are deprecated. Use the combination without the 'fit' parameter, and the isReady() call. The 'fit' parameter returns for each loop a goodness of fit indicator. If it is >0; more loops are necessary. If it is negative, and has an absolute value of say less than.001, it is probably ok, and the iterations can be stopped. Other arguments are as for solve() and invert(). The sol is used for both input (parameter guess) and output.

Referenced by casacore::LSQaips::solveLoop().

template<class U >
Bool casacore::LSQFit::solveLoop ( uInt nRank,
std::complex< U > *  sol,
Bool  doSVD = False 
)
template<class U >
Bool casacore::LSQFit::solveLoop ( uInt nRank,
U &  sol,
Bool  doSVD = False 
)
template<class U >
Bool casacore::LSQFit::solveLoop ( Double fit,
uInt nRank,
U *  sol,
Bool  doSVD = False 
)
template<class U >
Bool casacore::LSQFit::solveLoop ( Double fit,
uInt nRank,
std::complex< U > *  sol,
Bool  doSVD = False 
)
template<class U >
Bool casacore::LSQFit::solveLoop ( Double fit,
uInt nRank,
U &  sol,
Bool  doSVD = False 
)
void casacore::LSQFit::solveMR ( uInt  nin)
protected

Solve missing rank part.

void casacore::LSQFit::toAipsIO ( AipsIO ) const

Save or restore using AipsIO.

Bool casacore::LSQFit::toRecord ( String error,
RecordInterface out 
) const

Create a record from an LSQFit object.

The return will be False and an error message generated only if the object does not contain a valid object. Error messages are postfixed to error.

template<class U >
void casacore::LSQFit::uncopy ( Double beg,
const Double end,
U &  sol,
LSQReal   
)
template<class U >
void casacore::LSQFit::uncopy ( Double beg,
const Double end,
U &  sol,
LSQComplex   
)
template<class U >
void casacore::LSQFit::uncopy ( Double beg,
const Double end,
U *  sol,
LSQReal   
)
template<class U >
void casacore::LSQFit::uncopy ( Double beg,
const Double end,
U *  sol,
LSQComplex   
)

Member Data Documentation

AsReal casacore::LSQFit::ASREAL
static

Definition at line 342 of file LSQFit.h.

Bool casacore::LSQFit::balanced_p
protected

Indicator for a well balanced normal equation.

A balanced equation is one with similar values in the main diagonal.

Definition at line 892 of file LSQFit.h.

Referenced by setBalanced().

Complex casacore::LSQFit::COMPLEX
static

Definition at line 340 of file LSQFit.h.

Conjugate casacore::LSQFit::CONJUGATE
static

Definition at line 343 of file LSQFit.h.

const String casacore::LSQFit::constr
staticprotected

Definition at line 854 of file LSQFit.h.

Double* casacore::LSQFit::constr_p
protected

Constraint equation area (nun_p*ncon_p))

Definition at line 917 of file LSQFit.h.

Double casacore::LSQFit::epsder_p
protected

Test value for known vector in non-linear loop.

||known||inf is tested

Definition at line 889 of file LSQFit.h.

Referenced by setEpsDerivative().

Double casacore::LSQFit::epsval_p
protected

Test value for [incremental] solution in non-linear loop.

The ||sol increment||/||sol|| is tested

Definition at line 886 of file LSQFit.h.

Referenced by setEpsValue().

Double* casacore::LSQFit::error_p
protected

Counts for errors (N_ErrorField)

Definition at line 915 of file LSQFit.h.

const String casacore::LSQFit::errors
staticprotected

Definition at line 856 of file LSQFit.h.

const String casacore::LSQFit::known
staticprotected

Definition at line 855 of file LSQFit.h.

Double* casacore::LSQFit::known_p
protected

Known part equations (n_p)

Definition at line 913 of file LSQFit.h.

const String casacore::LSQFit::lar
staticprotected

Definition at line 858 of file LSQFit.h.

Double* casacore::LSQFit::lar_p
protected

Save area for non-symmetric (i.e.

with constraints) (n_p * n_p)

Definition at line 923 of file LSQFit.h.

Referenced by rowrt(), and rowru().

uInt casacore::LSQFit::maxiter_p
protected

Maximum number of iterations for non-linear solution.

If a non-zero maximum number of iterations is set, the value is tested in non-linear loops

Definition at line 896 of file LSQFit.h.

Referenced by nIterations(), and setMaxIter().

uInt casacore::LSQFit::n_p
protected

Matrix size (will be n_p = nun_p + ncon_p)

Definition at line 873 of file LSQFit.h.

Referenced by getDeficiency(), and rowrt().

const String casacore::LSQFit::nar
staticprotected

Definition at line 862 of file LSQFit.h.

LSQFit* casacore::LSQFit::nar_p
protected

Save area for non-linear case (size determined internally)

Definition at line 921 of file LSQFit.h.

const String casacore::LSQFit::nceq
staticprotected

Definition at line 861 of file LSQFit.h.

LSQMatrix* casacore::LSQFit::nceq_p
protected

Normal combined with constraint equations for solutions (triangular nnc_p*nnc_p)

Definition at line 911 of file LSQFit.h.

const String casacore::LSQFit::ncon
staticprotected

Definition at line 847 of file LSQFit.h.

uInt casacore::LSQFit::ncon_p
protected

Number of constraints.

Definition at line 871 of file LSQFit.h.

Referenced by nConstraints().

uInt casacore::LSQFit::niter_p
protected

Iteration count for non-linear solution.

Definition at line 898 of file LSQFit.h.

Referenced by nIterations().

const String casacore::LSQFit::nnc
staticprotected

Definition at line 852 of file LSQFit.h.

uInt casacore::LSQFit::nnc_p
protected

Current length nceq_p.

Definition at line 908 of file LSQFit.h.

const String casacore::LSQFit::nonlin
staticprotected

Definition at line 850 of file LSQFit.h.

Double casacore::LSQFit::nonlin_p
protected

Levenberg current factor.

Definition at line 881 of file LSQFit.h.

LSQMatrix* casacore::LSQFit::norm_p
protected

Normal equations (triangular nun_p * nun_p)

Definition at line 906 of file LSQFit.h.

const String casacore::LSQFit::nun
staticprotected

Definition at line 846 of file LSQFit.h.

uInt casacore::LSQFit::nun_p
protected

Number of unknowns.

Definition at line 869 of file LSQFit.h.

Referenced by nUnknowns(), and rowru().

const String casacore::LSQFit::piv
staticprotected

Definition at line 853 of file LSQFit.h.

uInt* casacore::LSQFit::piv_p
protected

Pivot table (n_p)

Definition at line 904 of file LSQFit.h.

const String casacore::LSQFit::prec
staticprotected

Definition at line 848 of file LSQFit.h.

Double casacore::LSQFit::prec_p
protected

Collinearity precision.

Definition at line 877 of file LSQFit.h.

uInt casacore::LSQFit::r_p
protected

Rank of normal equations (normally n_p)

Definition at line 875 of file LSQFit.h.

Referenced by getDeficiency().

const String casacore::LSQFit::rank
staticprotected

Definition at line 851 of file LSQFit.h.

ReadyCode casacore::LSQFit::ready_p
protected

Indicate the non-linear state.

A non-zero code indicates that non-linear looping is ready.

Definition at line 901 of file LSQFit.h.

Referenced by isReady().

Real casacore::LSQFit::REAL
static

And values to use.

Definition at line 339 of file LSQFit.h.

const String casacore::LSQFit::recid
staticprotected

Record field names.

Definition at line 844 of file LSQFit.h.

Separable casacore::LSQFit::SEPARABLE
static

Definition at line 341 of file LSQFit.h.

const String casacore::LSQFit::sol
staticprotected

Definition at line 857 of file LSQFit.h.

Double* casacore::LSQFit::sol_p
protected

Solution area (n_p)

Definition at line 919 of file LSQFit.h.

const String casacore::LSQFit::startnon
staticprotected

Definition at line 849 of file LSQFit.h.

Double casacore::LSQFit::startnon_p
protected

Levenberg start factor.

Definition at line 879 of file LSQFit.h.

const String casacore::LSQFit::state
staticprotected

Definition at line 845 of file LSQFit.h.

uInt casacore::LSQFit::state_p
protected

Bits set to indicate state.

Definition at line 867 of file LSQFit.h.

Double casacore::LSQFit::stepfactor_p
protected

Levenberg step factor.

Definition at line 883 of file LSQFit.h.

const String casacore::LSQFit::wcov
staticprotected

Definition at line 860 of file LSQFit.h.

Double* casacore::LSQFit::wcov_p
protected

Definition at line 927 of file LSQFit.h.

const String casacore::LSQFit::wsol
staticprotected

Definition at line 859 of file LSQFit.h.

Double* casacore::LSQFit::wsol_p
protected

Work areas for interim solutions and covariance.

Definition at line 926 of file LSQFit.h.


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