cern.colt.matrix.doublealgo

Class Statistic

java.lang.Object

cern.colt.matrix.doublealgo.Statistic

public class Statistic
extends Object

Basic statistics operations on matrices. Computation of covariance, correlation, distance matrix. Random sampling views. Conversion to histograms with and without OLAP cube operators. Conversion to bins with retrieval of statistical bin measures. Also see cern.jet.stat and hep.aida.bin, in particular hep.aida.bin.DynamicBin1D.

Examples:

A	covariance(A)	correlation(covariance(A))	distance(A,EUCLID)
4 x 3 matrix 1 2 3 2 4 6 3 6 9 4 -8 -10	3 x 3 matrix 1.25 -3.5 -4.5 -3.5 29 39 -4.5 39 52.5	3 x 3 matrix 1 -0.581318 -0.555492 -0.581318 1 0.999507 -0.555492 0.999507 1	3 x 3 matrix 0 12.569805 15.874508 12.569805 0 4.242641 15.874508 4.242641 0

Version:

1.0, 09/24/99

Author:

wolfgang.hoschek@cern.ch

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static interface	Statistic.VectorVectorFunction Interface that represents a function object: a function that takes two argument vectors and returns a single value.

Field Summary

Fields

Modifier and Type	Field and Description
static Statistic.VectorVectorFunction	BRAY_CURTIS Bray-Curtis distance function; Sum( abs(x[i]-y[i]) ) / Sum( x[i]+y[i] ).
static Statistic.VectorVectorFunction	CANBERRA Canberra distance function; Sum( abs(x[i]-y[i]) / abs(x[i]+y[i]) ).
static Statistic.VectorVectorFunction	EUCLID Euclidean distance function; Sqrt(Sum( (x[i]-y[i])^2 )).
static Statistic.VectorVectorFunction	MANHATTAN Manhattan distance function; Sum( abs(x[i]-y[i]) ).
static Statistic.VectorVectorFunction	MAXIMUM Maximum distance function; Max( abs(x[i]-y[i]) ).

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	Statistic() Makes this class non instantiable, but still let's others inherit from it.

Method Summary

Methods

Modifier and Type	Method and Description
static DoubleMatrix2D	correlation(DoubleMatrix2D covariance) Modifies the given covariance matrix to be a correlation matrix (in-place).
static DoubleMatrix2D	covariance(DoubleMatrix2D matrix) Constructs and returns the covariance matrix of the given matrix.
static void	demo1() Demonstrates usage of this class.
static void	demo2(int rows, int columns, boolean print) Demonstrates usage of this class.
static void	demo3(Statistic.VectorVectorFunction norm) Demonstrates usage of this class.
static DoubleMatrix2D	distance(DoubleMatrix2D matrix, Statistic.VectorVectorFunction distanceFunction) Constructs and returns the distance matrix of the given matrix.
static void	main(String[] args) Benchmarks covariance computation.
static DoubleMatrix1D	viewSample(DoubleMatrix1D matrix, double fraction, RandomEngine randomGenerator) Constructs and returns a sampling view with a size of round(matrix.size() * fraction).
static DoubleMatrix2D	viewSample(DoubleMatrix2D matrix, double rowFraction, double columnFraction, RandomEngine randomGenerator) Constructs and returns a sampling view with round(matrix.rows() * rowFraction) rows and round(matrix.columns() * columnFraction) columns.
static DoubleMatrix3D	viewSample(DoubleMatrix3D matrix, double sliceFraction, double rowFraction, double columnFraction, RandomEngine randomGenerator) Constructs and returns a sampling view with round(matrix.slices() * sliceFraction) slices and round(matrix.rows() * rowFraction) rows and round(matrix.columns() * columnFraction) columns.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

EUCLID

public static final Statistic.VectorVectorFunction EUCLID

Euclidean distance function; Sqrt(Sum( (x[i]-y[i])^2 )).

BRAY_CURTIS

public static final Statistic.VectorVectorFunction BRAY_CURTIS

Bray-Curtis distance function; Sum( abs(x[i]-y[i]) ) / Sum( x[i]+y[i] ).

CANBERRA

public static final Statistic.VectorVectorFunction CANBERRA

Canberra distance function; Sum( abs(x[i]-y[i]) / abs(x[i]+y[i]) ).

MAXIMUM

public static final Statistic.VectorVectorFunction MAXIMUM

Maximum distance function; Max( abs(x[i]-y[i]) ).

MANHATTAN

public static final Statistic.VectorVectorFunction MANHATTAN

Manhattan distance function; Sum( abs(x[i]-y[i]) ).

Constructor Detail

Statistic

protected Statistic()

Makes this class non instantiable, but still let's others inherit from it.

Method Detail

correlation

public static DoubleMatrix2D correlation(DoubleMatrix2D covariance)

Modifies the given covariance matrix to be a correlation matrix (in-place). The correlation matrix is a square, symmetric matrix consisting of nothing but correlation coefficients. The rows and the columns represent the variables, the cells represent correlation coefficients. The diagonal cells (i.e. the correlation between a variable and itself) will equal 1, for the simple reason that the correlation coefficient of a variable with itself equals 1. The correlation of two column vectors x and y is given by corr(x,y) = cov(x,y) / (stdDev(x)*stdDev(y)) (Pearson's correlation coefficient). A correlation coefficient varies between -1 (for a perfect negative relationship) to +1 (for a perfect positive relationship). See the math definition and another def. Compares two column vectors at a time. Use dice views to compare two row vectors at a time.

Parameters:

covariance - a covariance matrix, as, for example, returned by method covariance(DoubleMatrix2D).

Returns:

the modified covariance, now correlation matrix (for convenience only).

covariance

public static DoubleMatrix2D covariance(DoubleMatrix2D matrix)

Constructs and returns the covariance matrix of the given matrix. The covariance matrix is a square, symmetric matrix consisting of nothing but covariance coefficients. The rows and the columns represent the variables, the cells represent covariance coefficients. The diagonal cells (i.e. the covariance between a variable and itself) will equal the variances. The covariance of two column vectors x and y is given by cov(x,y) = (1/n) * Sum((x[i]-mean(x)) * (y[i]-mean(y))). See the math definition. Compares two column vectors at a time. Use dice views to compare two row vectors at a time.

Parameters:

matrix - any matrix; a column holds the values of a given variable.

Returns:

the covariance matrix (n x n, n=matrix.columns).

demo1

public static void demo1()

Demonstrates usage of this class.

demo2

public static void demo2(int rows,
         int columns,
         boolean print)

Demonstrates usage of this class.

demo3

public static void demo3(Statistic.VectorVectorFunction norm)

Demonstrates usage of this class.

distance

public static DoubleMatrix2D distance(DoubleMatrix2D matrix,
                      Statistic.VectorVectorFunction distanceFunction)

Constructs and returns the distance matrix of the given matrix. The distance matrix is a square, symmetric matrix consisting of nothing but distance coefficients. The rows and the columns represent the variables, the cells represent distance coefficients. The diagonal cells (i.e. the distance between a variable and itself) will be zero. Compares two column vectors at a time. Use dice views to compare two row vectors at a time.

Parameters:

matrix - any matrix; a column holds the values of a given variable (vector).

distanceFunction - (EUCLID, CANBERRA, ..., or any user defined distance function operating on two vectors).

Returns:

the distance matrix (n x n, n=matrix.columns).

main

public static void main(String[] args)

Benchmarks covariance computation.

viewSample

public static DoubleMatrix1D viewSample(DoubleMatrix1D matrix,
                        double fraction,
                        RandomEngine randomGenerator)

Constructs and returns a sampling view with a size of round(matrix.size() * fraction). Samples "without replacement" from the uniform distribution.

Parameters:

matrix - any matrix.

rowFraction - the percentage of rows to be included in the view.

columnFraction - the percentage of columns to be included in the view.

randomGenerator - a uniform random number generator; set this parameter to null to use a default generator seeded with the current time.

Returns:

the sampling view.

Throws:

IllegalArgumentException - if ! (0 <= rowFraction <= 1 && 0 <= columnFraction <= 1).

See Also:

RandomSampler

viewSample

public static DoubleMatrix2D viewSample(DoubleMatrix2D matrix,
                        double rowFraction,
                        double columnFraction,
                        RandomEngine randomGenerator)

Constructs and returns a sampling view with round(matrix.rows() * rowFraction) rows and round(matrix.columns() * columnFraction) columns. Samples "without replacement". Rows and columns are randomly chosen from the uniform distribution. Examples:

matrix	rowFraction=0.2 columnFraction=0.2	rowFraction=0.2 columnFraction=1.0	rowFraction=1.0 columnFraction=0.2
10 x 10 matrix 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100	2 x 2 matrix 43 50 53 60	2 x 10 matrix 41 42 43 44 45 46 47 48 49 50 91 92 93 94 95 96 97 98 99 100	10 x 2 matrix 4 8 14 18 24 28 34 38 44 48 54 58 64 68 74 78 84 88 94 98

Parameters:

matrix - any matrix.

rowFraction - the percentage of rows to be included in the view.

columnFraction - the percentage of columns to be included in the view.

randomGenerator - a uniform random number generator; set this parameter to null to use a default generator seeded with the current time.

Returns:

the sampling view.

Throws:

IllegalArgumentException - if ! (0 <= rowFraction <= 1 && 0 <= columnFraction <= 1).

See Also:

RandomSampler

viewSample

public static DoubleMatrix3D viewSample(DoubleMatrix3D matrix,
                        double sliceFraction,
                        double rowFraction,
                        double columnFraction,
                        RandomEngine randomGenerator)

Constructs and returns a sampling view with round(matrix.slices() * sliceFraction) slices and round(matrix.rows() * rowFraction) rows and round(matrix.columns() * columnFraction) columns. Samples "without replacement". Slices, rows and columns are randomly chosen from the uniform distribution.

Parameters:

matrix - any matrix.

sliceFraction - the percentage of slices to be included in the view.

rowFraction - the percentage of rows to be included in the view.

columnFraction - the percentage of columns to be included in the view.

randomGenerator - a uniform random number generator; set this parameter to null to use a default generator seeded with the current time.

Returns:

the sampling view.

Throws:

IllegalArgumentException - if ! (0 <= sliceFraction <= 1 && 0 <= rowFraction <= 1 && 0 <= columnFraction <= 1).

See Also:

RandomSampler