casacore
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Class for linear least-squares fit. More...
#include <LinearFit.h>
Public Member Functions | |
LinearFit () | |
Create a fitter: the normal way to generate a fitter object. More... | |
LinearFit (const LinearFit &other) | |
Copy constructor (deep copy) More... | |
LinearFit & | operator= (const LinearFit &other) |
Assignment (deep copy) More... | |
virtual | ~LinearFit () |
Destructor. More... | |
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GenericL2Fit () | |
Create a fitter: the normal way to generate a fitter object. More... | |
GenericL2Fit (const GenericL2Fit &other) | |
Copy constructor (deep copy) More... | |
GenericL2Fit & | operator= (const GenericL2Fit &other) |
Assignment (deep copy) More... | |
virtual | ~GenericL2Fit () |
Destructor. More... | |
template<class U > | |
void | setFunction (const Function< U, U > &function) |
Sets the function to be fitted. More... | |
template<class U > | |
Bool | setConstraint (const uInt n, const Function< U, U > &function, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
Set the possible constraint functions. More... | |
Bool | setConstraint (const uInt n, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
Bool | setConstraint (const uInt n, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
Bool | addConstraint (const Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > &function, const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
Bool | addConstraint (const Vector< typename FunctionTraits< T >::BaseType > &x, const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
Bool | addConstraint (const typename FunctionTraits< T >::BaseType y=typename FunctionTraits< T >::BaseType(0)) |
void | setCollinearity (const Double cln) |
Set the collinearity factor as the square of the sine of the minimum angle allowed between input vectors (default zero for non-SVD, 1e-8 for SVD) More... | |
void | asWeight (const Bool aswgt) |
Set sigma values to be interpreted as weight (i.e. More... | |
void | asSVD (const Bool svd) |
Set the use of SVD or not (default). More... | |
Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * | fittedFunction () |
Return a pointer to the function being fitted. More... | |
const Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * | fittedFunction () const |
uInt | fittedNumber () const |
Return the number of fitted parameters. More... | |
uInt | NConstraints () |
Return the number of constraints, and pointers to constraint functions. More... | |
Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * | getConstraint (const uInt n) |
Vector< typename LSQTraits< typename FunctionTraits< T >::BaseType >::base > | getSVDConstraint (uInt n) |
Return the nth constraint equation derived from SVD Note that the number present will be given by getDeficiency() More... | |
void | setParameterValues (const Vector< typename FunctionTraits< T >::BaseType > &parms) |
Set the parameter values. More... | |
void | setMaskedParameterValues (const Vector< typename FunctionTraits< T >::BaseType > &parms) |
Vector< typename FunctionTraits< T >::BaseType > | fit (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
Fit the function to the data. More... | |
Vector< typename FunctionTraits< T >::BaseType > | fit (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
Vector< typename FunctionTraits< T >::BaseType > | fit (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0) |
Vector< typename FunctionTraits< T >::BaseType > | fit (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0) |
Vector< typename FunctionTraits< T >::BaseType > | fit (const Vector< Bool > *const mask=0) |
Bool | fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
Bool | fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
Bool | fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const typename FunctionTraits< T >::BaseType &sigma, const Vector< Bool > *const mask=0) |
Bool | fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const typename FunctionTraits< T >::BaseType &sigma, const Vector< Bool > *const mask=0) |
Bool | fit (Vector< typename FunctionTraits< T >::BaseType > &sol, const Vector< Bool > *const mask=0) |
Double | chiSquare () const |
Obtain the chi squared. More... | |
const Vector< typename FunctionTraits< T >::BaseType > & | errors () const |
Get the errors on the solved values. More... | |
Bool | errors (Vector< typename FunctionTraits< T >::BaseType > &err) const |
Matrix< Double > | compuCovariance () |
Get covariance matrix. More... | |
void | compuCovariance (Matrix< Double > &cov) |
void | buildNormalMatrix (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
Generate the normal equations by one or more calls to the buildNormalMatrix(), before calling a fit() without arguments. More... | |
void | buildNormalMatrix (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > &sigma, const Vector< Bool > *const mask=0) |
void | buildNormalMatrix (const Vector< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0) |
void | buildNormalMatrix (const Matrix< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< Bool > *const mask=0) |
Bool | residual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &sol, const Bool model=False) |
Return the residual after a fit in y. More... | |
Bool | residual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Bool model=False) |
uInt | getRank () const |
Get the rank of the solution (or zero of no fit() done yet). More... | |
Protected Member Functions | |
virtual Bool | fitIt (Vector< typename FunctionTraits< T >::BaseType > &sol, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > *const sigma, const Vector< Bool > *const mask=0) |
Generalised fitter. More... | |
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void | buildMatrix (const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > *const sigma, const Vector< Bool > *const mask=0) |
Build the normal matrix. More... | |
void | buildConstraint () |
Build the constraint equations. More... | |
void | fillSVDConstraints () |
Get the SVD constraints. More... | |
Bool | buildResidual (Vector< typename FunctionTraits< T >::BaseType > &y, const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > *const sol, const Bool model=False) |
Calculate residuals. More... | |
FunctionTraits< T >::BaseType | getVal_p (const Array< typename FunctionTraits< T >::BaseType > &x, uInt j, uInt i) const |
Function to get evaluated functional value. More... | |
void | initfit_p (uInt parcnt) |
Initialise the fitter with number of solvable parameters. More... | |
uInt | testInput_p (const Array< typename FunctionTraits< T >::BaseType > &x, const Vector< typename FunctionTraits< T >::BaseType > &y, const Vector< typename FunctionTraits< T >::BaseType > *const sigma) |
Return number of condition equations and check sizes x, y, sigma. More... | |
void | resetFunction () |
Reset all the input. More... | |
Additional Inherited Members | |
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const Double | COLLINEARITY |
Default collinearity test for SVD. More... | |
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uInt | aCount_ai |
Adjustable. More... | |
Bool | svd_p |
SVD indicator. More... | |
Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * | ptr_derive_p |
Function to use in evaluating condition equation. More... | |
PtrBlock< Function< typename FunctionTraits< T >::DiffType, typename FunctionTraits< T >::DiffType > * > | constrFun_p |
List of functions describing the possible constraint equations e.g. More... | |
PtrBlock< Vector< typename FunctionTraits< T >::BaseType > * > | constrArg_p |
List of vectors describing the constraint equations' arguments. More... | |
PtrBlock< typename FunctionTraits< T >::BaseType * > | constrVal_p |
List of values describing the constraint equations' value. More... | |
uInt | pCount_p |
Number of available parameters. More... | |
uInt | ndim_p |
Number of dimensions of input data. More... | |
Bool | needInit_p |
No normal equations yet. More... | |
Bool | solved_p |
Have solution. More... | |
Bool | errors_p |
Have errors. More... | |
Bool | ferrors_p |
Bool | asweight_p |
Interpret as weights rather than as sigma the given values. More... | |
uInt | nr_p |
The rank of the solution. More... | |
Vector< typename FunctionTraits< T >::BaseType > | condEq_p |
Condition equation parameters (for number of adjustable parameters) More... | |
Vector< typename FunctionTraits< T >::BaseType > | fullEq_p |
Equation for all available parameters. More... | |
Vector< typename FunctionTraits< T >::ArgType > | arg_p |
Contiguous argument areas. More... | |
Vector< typename FunctionTraits< T >::ArgType > | carg_p |
Vector< typename FunctionTraits< T >::BaseType > | sol_p |
Local solution area. More... | |
Vector< typename FunctionTraits< T >::BaseType > | fsol_p |
Vector< typename FunctionTraits< T >::BaseType > | err_p |
Local error area. More... | |
Vector< typename FunctionTraits< T >::BaseType > | ferr_p |
FunctionTraits< T >::DiffType | valder_p |
Local value and derivatives. More... | |
Vector< Vector< typename LSQTraits< typename FunctionTraits< T >::BaseType >::base > > | consvd_p |
Local SVD constraints. More... | |
Class for linear least-squares fit.
A set of data point is fit with some functional equation. The equations solved are linear equations. The functions themselves however can be wildly nonlinear.
NOTE: Constraints added. Documentation out of date at moment, check the tLinearFitSVD and tNonLinearFirLM programs for examples.
The following is a brief summary of the linear least-squares fit problem. See module header, Fitting, for a more complete description.
Given a set of N data points (measurements), (x(i), y(i)) i = 0,...,N-1, along with a set of standard deviations, sigma(i), for the data points, and M specified functions, f(j)(x) j = 0,...,M-1, we form a linear combination of the functions:
where a(j) j = 0,...,M-1 are a set of parameters to be determined. The linear least-squares fit tries to minimize
by adjusting {a(j)} in the equation.
For complex numbers, [(y(i)-z(i))/sigma(i)]^2
in chi-square is replaced by [(y(i)-z(i))/sigma(i)]*conjugate([(y(i)-z(i))/sigma(i)])
For multidimensional functions, x(i) is a vector, and
Normally, it is necessary that N > M for the solutions to be valid, since there must be more data points than model parameters to be solved.
If the measurement errors (standard deviation sigma) are not known at all, they can all be set to one initially. In this case, we assume all measurements have the same standard deviation, after minimizing chi-square, we recompute
A statistic weight can also be assigned to each measurement if the standard deviation is not available. sigma can be calculated from
Alternatively a 'weight' switch can be set with asWeight()
. For best arithmetic performance, weight should be normalized to a maximum value of one. Having a large weight value can sometimes lead to overflow problems.
The function to be fitted to the data can be given as an instance of the Function class. One can also form a sum of functions using the CompoundFunction.
For small datasets the usage of the calls is:
Note that the fitter is reusable. An example is given in the following.
The solution of a fit always produces the total number of parameters given to the fitter. I.e. including any parameters that were fixed. In the latter case the solution returned will be the fixed value.
If there are a large number of unknowns or a large number of data points machine memory limits (or timing reasons) may not allow a complete in-core fitting to be performed. In this case one can incrementally build the normal equation (see buildNormalMatrix()).
The normal operation of the class tests for real inversion problems only. If tests are needed for almost collinear columns in the solution matrix, the collinearity can be set as the square of the sine of the minimum angle allowed.
Singular Value Decomposition is supported by the LinearFitSVD class, which has a behaviour completely identical to this class (apart from a default collinearity of 1e-8).
Other information (see a.o. LSQFit) can be set and obtained as well.
The creation of this class was driven by the need to write code to perform baseline fitting or continuum subtraction.
In the following a polynomial is fitted through the first 20 prime numbers. The data is given in the x vector (1 to 20) and in the primesTable (2, 3,..., 71) (see tLinearFitSVD test program). In the following all four methods to calculate a polynomial through the data is used
In the test program examples are given on how to get the other information, and other examples.
Definition at line 207 of file LinearFit.h.
casacore::LinearFit< T >::LinearFit | ( | ) |
Create a fitter: the normal way to generate a fitter object.
Necessary data will be deduced from the Functional provided with setFunction()
casacore::LinearFit< T >::LinearFit | ( | const LinearFit< T > & | other | ) |
Copy constructor (deep copy)
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virtual |
Destructor.
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protectedvirtual |
Generalised fitter.
Implements casacore::GenericL2Fit< T >.
LinearFit& casacore::LinearFit< T >::operator= | ( | const LinearFit< T > & | other | ) |
Assignment (deep copy)