Interpolate in one dimension. More...

#include <InterpolateArray1D.h>

Public Types
enum	InterpolationMethod { nearestNeighbour, linear, cubic, spline }
	Interpolation methods. More...

Static Public Member Functions
static void	interpolate (Array< Range > &yout, const Vector< Domain > &xout, const Vector< Domain > &xin, const Array< Range > &yin, Int method)
	Interpolate in the last dimension of array yin whose x coordinates along this dimension are given by xin. More...

static void	interpolate (Array< Range > &yout, const Block< Domain > &xout, const Block< Domain > &xin, const Array< Range > &yin, Int method)
	deprecated version of previous function using Blocks - no longer needed now that Vector has a fast index operator []. More...

static void	interpolate (Array< Range > &yout, Array< Bool > &youtFlags, const Vector< Domain > &xout, const Vector< Domain > &xin, const Array< Range > &yin, const Array< Bool > &yinFlags, Int method, Bool goodIsTrue=False, Bool extrapolate=False)
	Interpolate in the last dimension of array yin whose x coordinates along this dimension are given by xin. More...

static void	interpolate (Array< Range > &yout, Array< Bool > &youtFlags, const Block< Domain > &xout, const Block< Domain > &xin, const Array< Range > &yin, const Array< Bool > &yinFlags, Int method, Bool goodIsTrue=False, Bool extrapolate=False)
	deprecated version of previous function using Blocks - no longer needed now that Vector has a fast index operator []. More...

static void	interpolatey (Cube< Range > &yout, const Vector< Domain > &xout, const Vector< Domain > &xin, const Cube< Range > &yin, Int method)
	Interpolate in the middle axis in 3D array (yin) whose x coordinates along the this dimension are given by xin. More...

static void	interpolatey (Cube< Range > &yout, Cube< Bool > &youtFlags, const Vector< Domain > &xout, const Vector< Domain > &xin, const Cube< Range > &yin, const Cube< Bool > &yinFlags, Int method, Bool goodIsTrue=False, Bool extrapolate=False)
	Interpolate in the middle dimension of 3D array yin whose x coordinates along this dimension are given by xin. More...

Static Private Member Functions
static void	interpolatePtr (PtrBlock< Range * > &yout, Int ny, const Vector< Domain > &xout, const Vector< Domain > &xin, const PtrBlock< const Range * > &yin, Int method)
	Interpolate the y-vectors of length ny from x values xin to xout. More...

static void	interpolatePtr (PtrBlock< Range * > &yout, PtrBlock< Bool * > &youtFlags, Int ny, const Vector< Domain > &xout, const Vector< Domain > &xin, const PtrBlock< const Range * > &yin, const PtrBlock< const Bool * > &yinFlags, Int method, Bool goodIsTrue, Bool extrapolate)
	Interpolate the y-vectors of length ny from x values xin to xout. More...

static void	interpolateyPtr (PtrBlock< Range * > &yout, Int na, Int nb, Int nc, const Vector< Domain > &xout, const Vector< Domain > &xin, const PtrBlock< const Range * > &yin, Int method)
	Interpolate along yaxis. More...

static void	interpolateyPtr (PtrBlock< Range * > &yout, PtrBlock< Bool * > &youtFlags, Int na, Int nb, Int nc, const Vector< Domain > &xout, const Vector< Domain > &xin, const PtrBlock< const Range * > &yin, const PtrBlock< const Bool * > &yinFlags, Int method, Bool goodIsTrue, Bool extrapolate)
	Take flagging into account. More...

static void	polynomialInterpolation (PtrBlock< Range * > &yout, Int ny, const Vector< Domain > &xout, const Vector< Domain > &xin, const PtrBlock< const Range * > &yin, Int order)
	Interpolate the y-vectors of length ny from x values xin to xout using polynomial interpolation with specified order. More...

Detailed Description

template<class Domain, class Range>
class casacore::InterpolateArray1D< Domain, Range >

Interpolate in one dimension.

Intended use:

Public interface

Prerequisite

Array
Vector

Etymology

The InterpolateArray1D class does interpolation in one dimension of an Array 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, however they do need to be sorted and each abscissa should have a unique value.

Interpolation can be done using the following methods:

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

The abscissa must be a simple type (scalar value) that can be ordered. ie. an uInt, Int, Float or Double (not Complex). The ordinate can be an Array of any data type that has addition, and subtraction defined as well as multiplication by a scalar of the abcissa type. So the ordinate can be complex numbers, where the interpolation is done separately on the real and imaginary components. Use of Arrays as the the Range type is discouraged, operations will be very slow, it would be better to construct a single higher dimensional array that contains all the data.

Note: this class (and these docs) are heavily based on the Interpolate1D class in aips/Functionals. That class proved to be too slow for interpolation of large data volumes (i.e. spectral line visibility datasets) mainly due to the interface which forced the creation of large numbers of temporary Vectors and Arrays. This class is 5-10 times faster than Interpolate1D in cases where large amounts of data are to be interpolated.

Example

This code fragment does cubic interpolation on (xin,yin) pairs to produce (xout,yout) pairs.

Vector<Float> xin(4); indgen(xin); 
Vector<Double> yin(4); indgen(yin); yin = yin*yin*yin;
Vector<Float> xout(20); 
for (Int i=0; i<20; i++) xout(i) = 1 + i*0.1;
Vector<Double> yout;
InterpolateArray1D<Float, Double>::interpolate(yout, xout, xin, yin, 
InterpolateArray1D<Float,Double>::cubic);

Motivation

This class was motivated by the need to interpolate visibilities in frequency to allow selection and gridding in velocity space with on-the-fly doppler correction.

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. Use of Arrays is discouraged however.

Thrown Exceptions

AipsError