StandardKernel1dShape (Starlink-UK API)

java.lang.Object
- uk.ac.starlink.ttools.plot2.layer.StandardKernel1dShape

All Implemented Interfaces:

Kernel1dShape
```
@Equality
public abstract class StandardKernel1dShape
extends Object
implements Kernel1dShape
```
Implementation class for Kernel1dShapes based on evaluating symmetric functions over a limited extent.

Since:

12 Mar 2015

Author:

Mark Taylor

Field Summary

Fields
Modifier and Type	Field and Description
`static StandardKernel1dShape`	`COS` Cosine kernel shape.
`static StandardKernel1dShape`	`COS2` Cosine squared kernel shape.
`static Kernel1d`	`DELTA` Delta function kernel.
`static StandardKernel1dShape`	`EPANECHNIKOV` Epanechnikov (parabola) kernel shape.
`static StandardKernel1dShape`	`LINEAR` Linear (triangular) kernel shape.
`static StandardKernel1dShape`	`SQUARE` Rectangular kernel shape.

Constructor Summary

Constructors
Modifier	Constructor and Description
`protected`	`StandardKernel1dShape(String name, String description, double normExtent, boolean isSquare)` Constructor.

Method Summary

All Methods Static Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method and Description
`Kernel1d`	`createFixedWidthKernel(double width)` Creates a fixed width kernel with a given nominal width.
`Kernel1d`	`createKnnKernel(double k, boolean isSymmetric, int minWidth, int maxWidth)` Creates an adaptive kernel that uses a K-nearest-neighbours algorithm to determine local smoothing width, so that the width of the kernel is determined by the distance (number of 1-pixel bins) within which the given number `k` of samples is found.
`Kernel1d`	`createMeanKernel(double width)` Creates an averaging kernel with a given nominal fixed width.
`static Kernel1d`	`createSymmetricMeanKernel(double[] levels, boolean isSquare)` Creates a symmetric averabing kernel based on a fixed array of function values.
`static Kernel1d`	`createSymmetricNormalisedKernel(double[] levels, boolean isSquare)` Creates a symmetric normalised kernel based on a fixed array of function values.
`static StandardKernel1dShape`	`createTruncatedGaussian(double truncSigma)` Returns a kernel shape based on the Gaussian function with truncation at a given number of standard deviations.
`protected abstract double`	`evaluate(double x)` Returns the point value of the function defining this shape at a point a given absolute fraction of the nominal width from the center.
`String`	`getDescription()` Returns a short description for this shape.
`String`	`getName()` Returns a one-word name for this shape.
`double`	`getNormalisedExtent()` Returns the extent of a kernel with this shape of unit nominal width.
`static Kernel1dShape[]`	`getStandardOptions()` Returns an array of the generally recommended kernel shape options.
`boolean`	`isSquare()` Indicates whether this shape has features which are intentionally non-smooth and should be portrayed as such.
`String`	`toString()`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - SQUARE
```
public static final StandardKernel1dShape SQUARE
```
    Rectangular kernel shape.
  - LINEAR
```
public static final StandardKernel1dShape LINEAR
```
    Linear (triangular) kernel shape.
  - EPANECHNIKOV
```
public static final StandardKernel1dShape EPANECHNIKOV
```
    Epanechnikov (parabola) kernel shape.
  - COS
```
public static final StandardKernel1dShape COS
```
    Cosine kernel shape.
  - COS2
```
public static final StandardKernel1dShape COS2
```
    Cosine squared kernel shape.
  - DELTA
```
public static final Kernel1d DELTA
```
    Delta function kernel. Convolution of a function with this kernel leaves it unaffected.
- Constructor Detail
  - StandardKernel1dShape
```
protected StandardKernel1dShape(String name,
                                String description,
                                double normExtent,
                                boolean isSquare)
```
    Constructor.
    
    Parameters:
    
    name - kernel shape name
    
    description - short description
    
    normExtent - kernel extent for unit nominal width
    
    isSquare - true iff kernel is considered non-smooth
- Method Detail
  - evaluate
```
protected abstract double evaluate(double x)
```
    Returns the point value of the function defining this shape at a point a given absolute fraction of the nominal width from the center. Calling this method for values of x out of the range 0<=x<=getNormalisedExtent() has an undefined effect; the function value is assumed symmetric and zero for larger absolute values.
    
    Parameters:
    
    x - normalised absolute distance in range 0..normExtent
    
    Returns:
    
    function value at x
  - getNormalisedExtent
```
public double getNormalisedExtent()
```
    Returns the extent of a kernel with this shape of unit nominal width. The value of the evaluate(x) method for x greater than the value returned from this method is taken to be zero.
  - isSquare
```
public boolean isSquare()
```
    Indicates whether this shape has features which are intentionally non-smooth and should be portrayed as such. This non-smoothness applies either within the extent or at its edge.
    
    Returns:
    
    true iff there are non-smooth features that should be visible
  - getName
```
public String getName()
```
    Returns a one-word name for this shape.
    
    Specified by:
    
    getName in interface Kernel1dShape
    
    Returns:
    
    name
  - getDescription
```
public String getDescription()
```
    Returns a short description for this shape.
    
    Specified by:
    
    getDescription in interface Kernel1dShape
    
    Returns:
    
    description
  - createFixedWidthKernel
```
public Kernel1d createFixedWidthKernel(double width)
```
    Description copied from interface: Kernel1dShape
    
    Creates a fixed width kernel with a given nominal width. The width is some kind of characteristic half-width in one direction of the smoothing function. It is in units of grid points (array element spacing). It would generally be less than or equal to the kernel's extent.
    
    Specified by:
    
    createFixedWidthKernel in interface Kernel1dShape
    
    Parameters:
    
    width - half-width
    
    Returns:
    
    new kernel
  - createMeanKernel
```
public Kernel1d createMeanKernel(double width)
```
    Description copied from interface: Kernel1dShape
    
    Creates an averaging kernel with a given nominal fixed width. The 'convolution' it performs is not really a convolution, instead it's a sort of weighted moving average. This is a smoothing that's suitable for intensive quantities. Using proper convolution for intensive quantities like the mean or median is problematic if there may be blank values in the input array, since the smoothed value has to keep track of how many non-blank values it has encountered.
    
    Specified by:
    
    createMeanKernel in interface Kernel1dShape
    
    Parameters:
    
    width - half-width
    
    Returns:
    
    new kernel
  - createKnnKernel
```
public Kernel1d createKnnKernel(double k,
                                boolean isSymmetric,
                                int minWidth,
                                int maxWidth)
```
    Description copied from interface: Kernel1dShape
    
    Creates an adaptive kernel that uses a K-nearest-neighbours algorithm to determine local smoothing width, so that the width of the kernel is determined by the distance (number of 1-pixel bins) within which the given number k of samples is found.
    The nearest neighbour search may be symmetric or asymmetric. In the asymmetric case, the kernel width is determined separately for the positive and negative directions along the axis.
    Minimum and maximum smoothing widths are also supplied as bounds on the smoothing width for the case that the samples are very dense or very spread out (the latter case covers the edge of the data region as well). If minWidth==maxWidth, the result is a fixed-width kernel.
    
    Specified by:
    
    createKnnKernel in interface Kernel1dShape
    
    Parameters:
    
    k - number of nearest neighbours included in the distance that characterises the smoothing
    
    isSymmetric - true for bidirectional KNN search, false for unidirectional
    
    minWidth - minimum smoothing width
    
    maxWidth - maximum smoothing width
    
    Returns:
    
    new kernel
  - toString
```
public String toString()
```
    Overrides:
    
    toString in class Object
  - getStandardOptions
```
public static Kernel1dShape[] getStandardOptions()
```
    Returns an array of the generally recommended kernel shape options.
    
    Returns:
    
    kernel shape options
  - createTruncatedGaussian
```
public static StandardKernel1dShape createTruncatedGaussian(double truncSigma)
```
    Returns a kernel shape based on the Gaussian function with truncation at a given number of standard deviations.
    
    Parameters:
    
    truncSigma - number of sigma at which to truncate the kernel
    
    Returns:
    
    new kernel shape
  - createSymmetricNormalisedKernel
```
public static Kernel1d createSymmetricNormalisedKernel(double[] levels,
                                                       boolean isSquare)
```
    Creates a symmetric normalised kernel based on a fixed array of function values. The levels array gives a list of the values at x=0, 1 (and -1), 2 (and -2), ....
    
    Parameters:
    
    levels - kernel function values on 1d grid starting from 0
    
    isSquare - true iff the kernel is considered non-smooth
    
    Returns:
    
    new kernel
  - createSymmetricMeanKernel
```
public static Kernel1d createSymmetricMeanKernel(double[] levels,
                                                 boolean isSquare)
```
    Creates a symmetric averabing kernel based on a fixed array of function values. The levels array gives a list of the values at x=0, 1 (and -1), 2 (and -2), ....
    
    Parameters:
    
    levels - kernel function values on 1d grid starting from 0
    
    isSquare - true iff the kernel is considered non-smooth
    
    Returns:
    
    new kernel

Class StandardKernel1dShape

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

SQUARE

LINEAR

EPANECHNIKOV

COS

COS2

DELTA

Constructor Detail

StandardKernel1dShape

Method Detail

evaluate

getNormalisedExtent

isSquare

getName

getDescription

createFixedWidthKernel

createMeanKernel

createKnnKernel

toString

getStandardOptions

createTruncatedGaussian

createSymmetricNormalisedKernel

createSymmetricMeanKernel