#include <Interpolate1D.h>

Public Types
enum	Method { nearestNeighbour , linear , cubic , spline }
	The different interpolation methods are enumerated here. More...

Public Types inherited from casacore::Function1D< Domain, Range >
typedef const Domain *	FunctionArg

Public Types inherited from casacore::Function< T, U >
typedef FunctionTraits< T >::ArgType	ArgType

typedef const ArgType *	FunctionArg

Public Member Functions
	Interpolate1D ()
	The default constructor generates a useless object until the setData function has been called. More...

	Interpolate1D (const SampledFunctional< Domain > &x, const SampledFunctional< Range > &y, const Bool sorted=False, const Bool uniq=False)
	Construct an object with the specified data. More...

void	setData (const SampledFunctional< Domain > &x, const SampledFunctional< Range > &y, const Bool sorted=False, const Bool uniq=False)
	Define a new data set for the class to operate on. More...

	Interpolate1D (const Interpolate1D< Domain, Range > &other)
	The standard copy constructor, assignment operator and destructor. More...

Interpolate1D< Domain, Range > &	operator= (const Interpolate1D< Domain, Range > &other)

	~Interpolate1D ()

virtual const String &	name () const
	Name of function. More...

virtual Range	eval (typename Function1D< Domain, Range >::FunctionArg x) const
	Interpolation is done using the () operator (see example above). More...

uInt	getMethod () const
	inquire/set the current interpolation method. More...

void	setMethod (uInt method)

Vector< Domain >	getX () const
	Access the data set that interpolation is done over. More...

Vector< Range >	getY () const

virtual Function< Domain, Range > *	clone () const
	A function to copy the Interpolate1D object. More...

Public Member Functions inherited from casacore::Function1D< Domain, Range >
	Function1D ()
	Constructors. More...

	Function1D (const uInt n)

	Function1D (const Vector< Domain > &in)

	Function1D (const FunctionParam< Domain > &other)

	Function1D (const Function1D< W, X > &other)

virtual	~Function1D ()
	Destructor. More...

virtual uInt	ndim () const
	Returns the number of dimensions of function. More...

Public Member Functions inherited from casacore::Function< T, U >
	Function ()
	Constructors. More...

	Function (const uInt n)

	Function (const Vector< T > &in)

	Function (const FunctionParam< T > &other)

template<class W , class X >
	Function (const Function< W, X > &other)

virtual	~Function ()
	Destructor. More...

uInt	nparameters () const
	Returns the number of parameters. More...

virtual U	eval (FunctionArg x) const =0
	Evaluate the function object. More...

T &	operator[] (const uInt n)
	Manipulate the nth parameter (0-based) with no index check. More...

const T &	operator[] (const uInt n) const

virtual U	operator() () const
	Evaluate this function object at `x`or at `x, y`. More...

virtual U	operator() (const ArgType &x) const

virtual U	operator() (const Vector< ArgType > &x) const

virtual U	operator() (FunctionArg x) const

virtual U	operator() (const ArgType &x, const ArgType &y) const

virtual U	operator() (const ArgType &x, const ArgType &y, const ArgType &z) const

Bool &	mask (const uInt n)
	Manipulate the mask associated with the nth parameter (e.g. More...

const Bool &	mask (const uInt n) const

const FunctionParam< T > &	parameters () const
	Return the parameter interface. More...

FunctionParam< T > &	parameters ()

const Vector< ArgType > &	argp () const
	Get `arg_p` and `parset_p`. More...

Bool	parsetp () const

void	lockParam ()
	Compiler cannot always find the correct 'const' version of parameter access. More...

void	unlockParam ()

virtual void	setMode (const RecordInterface &mode)
	get/set the function mode. More...

virtual void	getMode (RecordInterface &mode) const

virtual Bool	hasMode () const
	return True if the implementing function supports a mode. More...

ostream &	print (ostream &os) const
	Print the function (i.e. More...

virtual Function< typename FunctionTraits< T >::DiffType > *	cloneAD () const

virtual Function< typename FunctionTraits< T >::BaseType > *	cloneNonAD () const

Public Member Functions inherited from casacore::Functional< FunctionTraits< T >::ArgType, T >
virtual	~Functional ()
	Destructor. More...

virtual T	operator() (const FunctionTraits< T >::ArgType &x) const=0
	Map a Domain `x` into a Range `y` value. More...

Public Member Functions inherited from casacore::Functional< Vector< FunctionTraits< T >::ArgType >, T >
virtual	~Functional ()
	Destructor. More...

virtual T	operator() (const Vector< FunctionTraits< T >::ArgType > &x) const=0
	Map a Domain `x` into a Range `y` value. More...

Private Member Functions
Range	polynomialInterpolation (const Domain x, uInt n, uInt offset) const
	A private function for doing polynomial interpolation. More...

Private Attributes
uInt	curMethod

uInt	nElements

Block< Domain >	xValues

Block< Range >	yValues

Block< Range >	y2Values

Additional Inherited Members
Protected Attributes inherited from casacore::Function< T, U >
FunctionParam< T >	param_p
	The parameters and masks. More...

Vector< ArgType >	arg_p
	Aid for non-contiguous argument storage. More...

Bool	parset_p
	Indicate parameter written. More...

Bool	locked_p
	Indicate that parameters are expected to be locked from changing. More...

Detailed Description

template<class Domain, class Range>
class casacore::Interpolate1D< Domain, Range >

Interpolate in one dimension

Intended use:

Public interface

Review Status

Reviewed By:: wyoung
Date Reviewed:: 1996/10/18
Test programs:: tInterpolate1D
Demo programs:: dInterpolate1D

Prerequisite

Etymology

The Interpolate1D class does interpolation in one dimension only.

Synopsis

This class will, given the abscissa and ordinates of a set of one dimensional data, interpolate on this data set giving the value at any specified ordinate. It will extrapolate if necessary, but this is will usually give a poor result. There is no requirement for the ordinates to be regularly spaced, or even sorted in any numerical order. However each abscissa should have a unique value.

Interpolation can be done using the following methods:

Nearest Neighbour (default if there is one data point)
Linear (default unless there is only one data point)
Cubic Polynomial
Natural Cubic Spline

The restriction that each abcissus has a unique value can be lifted by setting the uniq=True option in the appropriate functions. This imposes the following additional restrictions on interpolation.

You cannot use cubic spline interpolation.
You cannot cannot interpolate within two data points of a repeated x-value when using cubic interpolation.
You cannot interpolate within one data point of a repeated x-value when using linear or nearest neighbour interpolation.

The abscissa must be a SampledFunctional that returns a scalar value that can be ordered. ie. an uInt, Int, Float or Double (not Complex). The ordinate can be any data type that has addition, and subtraction defined as well as multiplication by a scalar. So the ordinate can be complex numbers, where the interpolation is done separately on the real and imaginary components, or an array, where the interpolation is done separately on an element by element basis.

This class will curently make an internal copy of the data supplied to it, and sort the data if it is not told it is already sorted, by using the sorted=True flag.

Example

This code fragment sets the interpolation method to cubic before interpolating on the supplied (x,y) vectors.

Vector<Float> x(4); indgen(x); 
Vector<Double> y(4); indgen(y); y = y*y*y;
ScalarSampledFunctional<Float> fx(x)
ScalarSampledFunctional<Double> fy(y);
Interpolate1D<Float, Double> gain(fx, fy);
gain.setMethod(Interpolate1D<Float,Double>::cubic);
for (Float xs = -1; xs < 5; xs += 0.1)
cout << "gain(" << xs << "):" << gain(xs) << endl;

Motivation

This class is motivated by the need to interpolate over the gain solutions obtained from calibrator observations, in order to get the gain at arbitrary times.

Template Type Argument Requirements (Domain)

The Domain class must be a type that can be ordered in a mathematical sense. This includes uInt, Int, Float, Double, but not Complex.

Template Type Argument Requirements (Range)

The Range class must have addition and subtraction of Range objects with each other as well as multiplication by a scalar defined. Besides the scalar types listed above this includes Complex, DComplex, and Arrays of any of these types.

Thrown Exceptions

AipsError

To Do

avoid an internal copy of the data and have an index array as the only private data (plus the interpolation method and pointers to the actual data).
Review the use of copy semantics in the copy constructor & assignment operator after making the above change.

Definition at line 140 of file Interpolate1D.h.

Member Enumeration Documentation

◆ Method

template<class Domain , class Range >

enum casacore::Interpolate1D::Method

The different interpolation methods are enumerated here.

Enumerator
nearestNeighbour	Crude but sometimes useful.
linear	The most common method and the Default.
cubic	Fits a third order polynomial to 4 pts
spline	Natural Cubic Splines.

Definition at line 144 of file Interpolate1D.h.

Constructor & Destructor Documentation

◆ Interpolate1D() [1/3]

template<class Domain , class Range >

casacore::Interpolate1D< Domain, Range >::Interpolate1D ( )

The default constructor generates a useless object until the setData function has been called.

◆ Interpolate1D() [2/3]

template<class Domain , class Range >

casacore::Interpolate1D< Domain, Range >::Interpolate1D	(	const SampledFunctional< Domain > &	x,
		const SampledFunctional< Range > &	y,
		const Bool	sorted = `False`,
		const Bool	uniq = `False`
	)

Construct an object with the specified data.

◆ Interpolate1D() [3/3]

template<class Domain , class Range >

casacore::Interpolate1D< Domain, Range >::Interpolate1D ( const Interpolate1D< Domain, Range > & other )

The standard copy constructor, assignment operator and destructor.

Internal data is copied in both cases (copy semantics)

◆ ~Interpolate1D()

template<class Domain , class Range >

casacore::Interpolate1D< Domain, Range >::~Interpolate1D ( )

Member Function Documentation

◆ clone()

template<class Domain , class Range >

virtual Function<Domain, Range>* casacore::Interpolate1D< Domain, Range >::clone ( ) const

virtual

A function to copy the Interpolate1D object.

Implements casacore::Function< T, U >.

◆ eval()

template<class Domain , class Range >

virtual Range casacore::Interpolate1D< Domain, Range >::eval ( typename Function1D< Domain, Range >::FunctionArg x ) const

virtual

Interpolation is done using the () operator (see example above).

Actual use is through the virtual eval() function.

◆ getMethod()

template<class Domain , class Range >

uInt casacore::Interpolate1D< Domain, Range >::getMethod ( ) const

inline

inquire/set the current interpolation method.

uInts are used as arguments instead of the Interpolate1D::Method enumerator due to compiler limitations. See the example above (or the demo code) for the recommended way to call these functions.

Definition at line 195 of file Interpolate1D.h.

References casacore::Interpolate1D< Domain, Range >::curMethod.

◆ getX()

template<class Domain , class Range >

Vector<Domain> casacore::Interpolate1D< Domain, Range >::getX ( ) const

Access the data set that interpolation is done over.

This will usually be sorted.

◆ getY()

template<class Domain , class Range >

Vector<Range> casacore::Interpolate1D< Domain, Range >::getY ( ) const

◆ name()

template<class Domain , class Range >

virtual const String& casacore::Interpolate1D< Domain, Range >::name ( ) const

inlinevirtual

Name of function.

Reimplemented from casacore::Function< T, U >.

Definition at line 182 of file Interpolate1D.h.

◆ operator=()

template<class Domain , class Range >

Interpolate1D<Domain, Range>& casacore::Interpolate1D< Domain, Range >::operator= ( const Interpolate1D< Domain, Range > & other )

◆ polynomialInterpolation()

template<class Domain , class Range >

Range casacore::Interpolate1D< Domain, Range >::polynomialInterpolation	(	const Domain	x,
		uInt	n,
		uInt	offset
	)		const

private

A private function for doing polynomial interpolation.

◆ setData()

template<class Domain , class Range >

void casacore::Interpolate1D< Domain, Range >::setData	(	const SampledFunctional< Domain > &	x,
		const SampledFunctional< Range > &	y,
		const Bool	sorted = `False`,
		const Bool	uniq = `False`
	)

Define a new data set for the class to operate on.

Equivalent in many aspects to creating a new object.

◆ setMethod()

template<class Domain , class Range >

void casacore::Interpolate1D< Domain, Range >::setMethod ( uInt method )

Member Data Documentation

◆ curMethod

template<class Domain , class Range >

uInt casacore::Interpolate1D< Domain, Range >::curMethod

private

Definition at line 215 of file Interpolate1D.h.

Referenced by casacore::Interpolate1D< Domain, Range >::getMethod().

◆ nElements

template<class Domain , class Range >

uInt casacore::Interpolate1D< Domain, Range >::nElements

private

Definition at line 216 of file Interpolate1D.h.

◆ xValues

template<class Domain , class Range >

Block<Domain> casacore::Interpolate1D< Domain, Range >::xValues

private

Definition at line 217 of file Interpolate1D.h.

◆ y2Values

template<class Domain , class Range >

Block<Range> casacore::Interpolate1D< Domain, Range >::y2Values

private

Definition at line 219 of file Interpolate1D.h.

◆ yValues

template<class Domain , class Range >

Block<Range> casacore::Interpolate1D< Domain, Range >::yValues

private

Definition at line 218 of file Interpolate1D.h.

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

coordinates/Coordinates/TabularCoordinate.h
scimath/Functionals/Interpolate1D.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<class Domain, class Range> class casacore::Interpolate1D< Domain, Range >

Intended use:

Review Status

Prerequisite

Etymology

Synopsis

Example

Motivation

Template Type Argument Requirements (Domain)

Template Type Argument Requirements (Range)

Thrown Exceptions

To Do

Member Enumeration Documentation

◆ Method

Constructor & Destructor Documentation

◆ Interpolate1D() [1/3]

◆ Interpolate1D() [2/3]

◆ Interpolate1D() [3/3]

◆ ~Interpolate1D()

Member Function Documentation

◆ clone()

◆ eval()

◆ getMethod()

◆ getX()

◆ getY()

◆ name()

◆ operator=()

◆ polynomialInterpolation()

◆ setData()

◆ setMethod()

Member Data Documentation

◆ curMethod

◆ nElements

◆ xValues

◆ y2Values

◆ yValues

template<class Domain, class Range>
class casacore::Interpolate1D< Domain, Range >