org.apache.commons.math3.geometry.partitioning.utilities

## Class OrderedTuple

- java.lang.Object
- - org.apache.commons.math3.geometry.partitioning.utilities.OrderedTuple

All Implemented Interfaces:
  java.lang.Comparable<OrderedTuple>

    public class OrderedTuple
    extends java.lang.Object
    implements java.lang.Comparable<OrderedTuple>

This class implements an ordering operation for T-uples.

Ordering is done by encoding all components of the T-uple into a single scalar value and using this value as the sorting key. Encoding is performed using the method invented by Georg Cantor in 1877 when he proved it was possible to establish a bijection between a line and a plane. The binary representations of the components of the T-uple are mixed together to form a single scalar. This means that the 2k bit of component 0 is followed by the 2k bit of component 1, then by the 2k bit of component 2 up to the 2k bit of component `t`, which is followed by the 2k-1 bit of component 0, followed by the 2k-1 bit of component 1 ... The binary representations are extended as needed to handle numbers with different scales and a suitable 2p offset is added to the components in order to avoid negative numbers (this offset is adjusted as needed during the comparison operations).

The more interesting property of the encoding method for our purpose is that it allows to select all the points that are in a given range. This is depicted in dimension 2 by the following picture:

This picture shows a set of 100000 random 2-D pairs having their first component between -50 and +150 and their second component between -350 and +50. We wanted to extract all pairs having their first component between +30 and +70 and their second component between -120 and -30. We built the lower left point at coordinates (30, -120) and the upper right point at coordinates (70, -30). All points smaller than the lower left point are drawn in red and all points larger than the upper right point are drawn in blue. The green points are between the two limits. This picture shows that all the desired points are selected, along with spurious points. In this case, we get 15790 points, 4420 of which really belonging to the desired rectangle. It is possible to extract very small subsets. As an example extracting from the same 100000 points set the points having their first component between +30 and +31 and their second component between -91 and -90, we get a subset of 11 points, 2 of which really belonging to the desired rectangle.

the previous selection technique can be applied in all dimensions, still using two points to define the interval. The first point will have all its components set to their lower bounds while the second point will have all its components set to their upper bounds.

T-uples with negative infinite or positive infinite components are sorted logically.

Since the specification of the `Comparator` interface allows only `ClassCastException` errors, some arbitrary choices have been made to handle specific cases. The rationale for these choices is to keep regular and consistent T-uples together.

- instances with different dimensions are sorted according to their dimension regardless of their components values
- instances with `Double.NaN` components are sorted after all other ones (even after instances with positive infinite components
- instances with both positive and negative infinite components are considered as if they had `Double.NaN` components

Since:
  3.0
Version:
  $Id: OrderedTuple.java 1416643 2012-12-03 19:37:14Z tn $

### Field Summary

Fields
`private double[]` `components` Double components of the T-uple.
`private long[]` `encoding` Ordering encoding of the double components.
`private static long` `EXPONENT_MASK` Exponent bits mask.
`private static long` `IMPLICIT_ONE` Implicit MSB for normalized numbers.
`private int` `lsb` Least Significant Bit scale.
`private static long` `MANTISSA_MASK` Mantissa bits mask.
`private boolean` `nan` Not A Number marker.
`private boolean` `negInf` Negative infinity marker.
`private int` `offset` Offset scale.
`private boolean` `posInf` Positive infinity marker.
`private static long` `SIGN_MASK` Sign bit mask.

### Constructor Summary

Constructors
Constructor and Description
`OrderedTuple(double... components)` Build an ordered T-uple from its components.

### Method Summary

Methods
`int` `compareTo(OrderedTuple ot)` Compares this ordered T-uple with the specified object.
`private static int` `computeLSB(long l)` Compute the least significant bit of a long.
`private static int` `computeMSB(long l)` Compute the most significant bit of a long.
`private void` `encode(int minOffset)` Encode the T-uple with a given offset.
`boolean` `equals(java.lang.Object other)`
`private static int` `exponent(long bits)` Extract the exponent from the bits of a double.
`private int` `getBit(int i, int k)` Get a bit from the mantissa of a double.
`double[]` `getComponents()` Get the components array.
`int` `hashCode()`
`private static long` `mantissa(long bits)` Extract the mantissa from the bits of a double.
`private static long` `sign(long bits)` Extract the sign from the bits of a double.

### Methods inherited from class java.lang.Object

`clone, finalize, getClass, notify, notifyAll, toString, wait, wait, wait`

### Field Detail

#### SIGN_MASK

    private static final long SIGN_MASK

Sign bit mask.

See Also:
  Constant Field Values

#### EXPONENT_MASK

    private static final long EXPONENT_MASK

Exponent bits mask.

See Also:
  Constant Field Values

#### MANTISSA_MASK

    private static final long MANTISSA_MASK

Mantissa bits mask.

See Also:
  Constant Field Values

#### IMPLICIT_ONE

    private static final long IMPLICIT_ONE

Implicit MSB for normalized numbers.

See Also:
  Constant Field Values

#### components

    private double[] components

Double components of the T-uple.

#### offset

    private int offset

Offset scale.

#### lsb

    private int lsb

Least Significant Bit scale.

#### encoding

    private long[] encoding

Ordering encoding of the double components.

#### posInf

    private boolean posInf

Positive infinity marker.

#### negInf

    private boolean negInf

Negative infinity marker.

#### nan

    private boolean nan

Not A Number marker.

### Constructor Detail

#### OrderedTuple

    public OrderedTuple(double... components)

Build an ordered T-uple from its components.

Parameters:
  `components` - double components of the T-uple

### Method Detail

#### encode

    private void encode(int minOffset)

Encode the T-uple with a given offset.

Parameters:
  `minOffset` - minimal scale of the offset to add to all components (must be greater than the MSBs of all components)

#### compareTo

    public int compareTo(OrderedTuple ot)

Compares this ordered T-uple with the specified object.

The ordering method is detailed in the general description of the class. Its main property is to be consistent with distance: geometrically close T-uples stay close to each other when stored in a sorted collection using this comparison method.

T-uples with negative infinite, positive infinite are sorted logically.

Some arbitrary choices have been made to handle specific cases. The rationale for these choices is to keep normal and consistent T-uples together.

- instances with different dimensions are sorted according to their dimension regardless of their components values
- instances with `Double.NaN` components are sorted after all other ones (evan after instances with positive infinite components
- instances with both positive and negative infinite components are considered as if they had `Double.NaN` components

Specified by:
  `compareTo` in interface `java.lang.Comparable<OrderedTuple>`
Parameters:
  `ot` - T-uple to compare instance with
Returns:
  a negative integer if the instance is less than the object, zero if they are equal, or a positive integer if the instance is greater than the object

#### equals

    public boolean equals(java.lang.Object other)

Overrides:
  `equals` in class `java.lang.Object`

#### hashCode

    public int hashCode()

Overrides:
  `hashCode` in class `java.lang.Object`

#### getComponents

    public double[] getComponents()

Get the components array.

Returns:
  array containing the T-uple components

#### sign

    private static long sign(long bits)

Extract the sign from the bits of a double.

Parameters:
  `bits` - binary representation of the double
Returns:
  sign bit (zero if positive, non zero if negative)

#### exponent

    private static int exponent(long bits)

Extract the exponent from the bits of a double.

Parameters:
  `bits` - binary representation of the double
Returns:
  exponent

#### mantissa

    private static long mantissa(long bits)

Extract the mantissa from the bits of a double.

Parameters:
  `bits` - binary representation of the double
Returns:
  mantissa

#### computeMSB

    private static int computeMSB(long l)

Compute the most significant bit of a long.

Parameters:
  `l` - long from which the most significant bit is requested
Returns:
  scale of the most significant bit of `l`, or 0 if `l` is zero
See Also:
  `computeLSB(long)`

#### computeLSB

    private static int computeLSB(long l)

Compute the least significant bit of a long.

Parameters:
  `l` - long from which the least significant bit is requested
Returns:
  scale of the least significant bit of `l`, or 63 if `l` is zero
See Also:
  `computeMSB(long)`

#### getBit

    private int getBit(int i,
             int k)

Get a bit from the mantissa of a double.

Parameters:
  `i` - index of the component
  `k` - scale of the requested bit
Returns:
  the specified bit (either 0 or 1), after the offset has been added to the double