Package cern.colt.matrix.doublealgo
Class Statistic
java.lang.Object
cern.colt.matrix.doublealgo.Statistic
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 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
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Nested Class Summary
Nested ClassesModifier and TypeClassDescriptionstatic interface
Interface that represents a function object: a function that takes two argument vectors and returns a single value. -
Field Summary
FieldsModifier and TypeFieldDescriptionstatic final Statistic.VectorVectorFunction
Bray-Curtis distance function; Sum( abs(x[i]-y[i]) ) / Sum( x[i]+y[i] ).static final Statistic.VectorVectorFunction
Canberra distance function; Sum( abs(x[i]-y[i]) / abs(x[i]+y[i]) ).static final Statistic.VectorVectorFunction
Euclidean distance function; Sqrt(Sum( (x[i]-y[i])^2 )).private static final Functions
static final Statistic.VectorVectorFunction
Manhattan distance function; Sum( abs(x[i]-y[i]) ).static final Statistic.VectorVectorFunction
Maximum distance function; Max( abs(x[i]-y[i]) ). -
Constructor Summary
ConstructorsModifierConstructorDescriptionprotected
Makes this class non instantiable, but still let's others inherit from it. -
Method Summary
Modifier and TypeMethodDescriptionstatic DoubleMatrix2D
aggregate
(DoubleMatrix2D matrix, BinFunction1D[] aggr, DoubleMatrix2D result) Applies the given aggregation functions to each column and stores the results in a the result matrix.static DynamicBin1D
bin
(DoubleMatrix1D vector) Fills all cell values of the given vector into a bin from which statistics measures can be retrieved efficiently.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 IHistogram2D
cube
(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D weights) 2-d OLAP cube operator; Fills all cells of the given vectors into the given histogram.static IHistogram3D
cube
(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights) 3-d OLAP cube operator; Fills all cells of the given vectors into the given histogram.static void
demo1()
Demonstrates usage of this class.static void
demo2
(int rows, int columns, boolean print) Demonstrates usage of this class.static void
Demonstrates usage of this class.static DoubleMatrix2D
distance
(DoubleMatrix2D matrix, Statistic.VectorVectorFunction distanceFunction) Constructs and returns the distance matrix of the given matrix.static IHistogram1D
histogram
(IHistogram1D histo, DoubleMatrix1D vector) Fills all cells of the given vector into the given histogram.static IHistogram2D
histogram
(IHistogram2D histo, DoubleMatrix1D x, DoubleMatrix1D y) Fills all cells of the given vectors into the given histogram.static IHistogram2D
histogram
(IHistogram2D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D weights) Fills all cells of the given vectors into the given histogram.static IHistogram3D
histogram
(IHistogram3D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights) Fills all cells of the given vectors into the given histogram.static void
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.private static DoubleMatrix2D
xdistanceOld
(DoubleMatrix2D matrix, int norm) Constructs and returns the distance matrix of the given matrix.private static DoubleMatrix2D
xdistanceOld2
(DoubleMatrix2D matrix, int norm) Constructs and returns the distance matrix of the given matrix.
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Field Details
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F
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EUCLID
Euclidean distance function; Sqrt(Sum( (x[i]-y[i])^2 )). -
BRAY_CURTIS
Bray-Curtis distance function; Sum( abs(x[i]-y[i]) ) / Sum( x[i]+y[i] ). -
CANBERRA
Canberra distance function; Sum( abs(x[i]-y[i]) / abs(x[i]+y[i]) ). -
MAXIMUM
Maximum distance function; Max( abs(x[i]-y[i]) ). -
MANHATTAN
Manhattan distance function; Sum( abs(x[i]-y[i]) ).
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Constructor Details
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Statistic
protected Statistic()Makes this class non instantiable, but still let's others inherit from it.
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Method Details
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aggregate
public static DoubleMatrix2D aggregate(DoubleMatrix2D matrix, BinFunction1D[] aggr, DoubleMatrix2D result) Applies the given aggregation functions to each column and stores the results in a the result matrix. If matrix has shape m x n, then result must have shape aggr.length x n. Tip: To do aggregations on rows use dice views (transpositions), as in aggregate(matrix.viewDice(),aggr,result.viewDice()).- Parameters:
matrix
- any matrix; a column holds the values of a given variable.aggr
- the aggregation functions to be applied to each column.result
- the matrix to hold the aggregation results.- Returns:
- result (for convenience only).
- See Also:
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bin
Fills all cell values of the given vector into a bin from which statistics measures can be retrieved efficiently. Cells values are copied.
Tip: Use System.out.println(bin(vector)) to print most measures computed by the bin. Example:Size: 20000 Sum: 299858.02350278624 SumOfSquares: 5399184.154095971 Min: 0.8639113139711261 Max: 59.75331890541892 Mean: 14.992901175139313 RMS: 16.43043540825375 Variance: 45.17438077634358 Standard deviation: 6.721188940681818 Standard error: 0.04752598277592142 Geometric mean: 13.516615397064466 Product: Infinity Harmonic mean: 11.995174297952191 Sum of inversions: 1667.337172700724 Skew: 0.8922838940067878 Kurtosis: 1.1915828121825598 Sum of powers(3): 1.1345828465808412E8 Sum of powers(4): 2.7251055344494686E9 Sum of powers(5): 7.367125643433887E10 Sum of powers(6): 2.215370909100143E12 Moment(0,0): 1.0 Moment(1,0): 14.992901175139313 Moment(2,0): 269.95920770479853 Moment(3,0): 5672.914232904206 Moment(4,0): 136255.27672247344 Moment(5,0): 3683562.8217169433 Moment(6,0): 1.1076854545500715E8 Moment(0,mean()): 1.0 Moment(1,mean()): -2.0806734113421045E-14 Moment(2,mean()): 45.172122057305664 Moment(3,mean()): 270.92018671421 Moment(4,mean()): 8553.8664869067 Moment(5,mean()): 153357.41712233616 Moment(6,mean()): 4273757.570142922 25%, 50% and 75% Quantiles: 10.030074811938091, 13.977982089912224, 18.86124362967137 quantileInverse(mean): 0.559163335012079 Distinct elements invalid input: '&' frequencies not printed (too many).
- Parameters:
vector
- the vector to analyze.- Returns:
- a bin holding the statistics measures of the vector.
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correlation
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 methodcovariance(DoubleMatrix2D)
.- Returns:
- the modified covariance, now correlation matrix (for convenience only).
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covariance
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).
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cube
2-d OLAP cube operator; Fills all cells of the given vectors into the given histogram. If you use hep.aida.ref.Converter.toString(histo) on the result, the OLAP cube of x-"column" vs. y-"column" , summing the weights "column" will be printed. For example, aggregate sales by product by region.Computes the distinct values of x and y, yielding histogram axes that capture one distinct value per bin. Then fills the histogram.
Example output:
Cube: Entries=5000, ExtraEntries=0 MeanX=4.9838, RmsX=NaN MeanY=2.5304, RmsY=NaN xAxis: Min=0, Max=10, Bins=11 yAxis: Min=0, Max=5, Bins=6 Heights: | X | 0 1 2 3 4 5 6 7 8 9 10 | Sum ---------------------------------------------------------- Y 5 | 30 53 51 52 57 39 65 61 55 49 22 | 534 4 | 43 106 112 96 92 94 107 98 98 110 47 | 1003 3 | 39 134 87 93 102 103 110 90 114 98 51 | 1021 2 | 44 81 113 96 101 86 109 83 111 93 42 | 959 1 | 54 94 103 99 115 92 98 97 103 90 44 | 989 0 | 24 54 52 44 42 56 46 47 56 53 20 | 494 ---------------------------------------------------------- Sum | 234 522 518 480 509 470 535 476 537 493 226 |
- Returns:
- the histogram containing the cube.
- Throws:
IllegalArgumentException
- if x.size() != y.size() || y.size() != weights.size().
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cube
public static IHistogram3D cube(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights) 3-d OLAP cube operator; Fills all cells of the given vectors into the given histogram. If you use hep.aida.ref.Converter.toString(histo) on the result, the OLAP cube of x-"column" vs. y-"column" vs. z-"column", summing the weights "column" will be printed. For example, aggregate sales by product by region by time.Computes the distinct values of x and y and z, yielding histogram axes that capture one distinct value per bin. Then fills the histogram.
- Returns:
- the histogram containing the cube.
- Throws:
IllegalArgumentException
- if x.size() != y.size() || x.size() != z.size() || x.size() != weights.size().
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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
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).
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histogram
Fills all cells of the given vector into the given histogram.- Returns:
- histo (for convenience only).
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histogram
Fills all cells of the given vectors into the given histogram.- Returns:
- histo (for convenience only).
- Throws:
IllegalArgumentException
- if x.size() != y.size().
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histogram
public static IHistogram2D histogram(IHistogram2D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D weights) Fills all cells of the given vectors into the given histogram.- Returns:
- histo (for convenience only).
- Throws:
IllegalArgumentException
- if x.size() != y.size() || y.size() != weights.size().
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histogram
public static IHistogram3D histogram(IHistogram3D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights) Fills all cells of the given vectors into the given histogram.- Returns:
- histo (for convenience only).
- Throws:
IllegalArgumentException
- if x.size() != y.size() || x.size() != z.size() || x.size() != weights.size().
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main
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.randomGenerator
- a uniform random number generator; set this parameter to null to use a default generator seeded with the current time.rowFraction
- the percentage of rows to be included in the view.columnFraction
- the percentage of columns to be included in the view.- Returns:
- the sampling view.
- Throws:
IllegalArgumentException
- if ! (0 invalid input: '<'= rowFraction invalid input: '<'= 1 invalid input: '&'invalid input: '&' 0 invalid input: '<'= columnFraction invalid input: '<'= 1).- See Also:
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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:matrixrowFraction=0.2
columnFraction=0.2rowFraction=0.2
columnFraction=1.0rowFraction=1.0
columnFraction=0.210 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 1002 x 2 matrix
43 50
53 602 x 10 matrix
41 42 43 44 45 46 47 48 49 50
91 92 93 94 95 96 97 98 99 10010 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 invalid input: '<'= rowFraction invalid input: '<'= 1 invalid input: '&'invalid input: '&' 0 invalid input: '<'= columnFraction invalid input: '<'= 1).- See Also:
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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 invalid input: '<'= sliceFraction invalid input: '<'= 1 invalid input: '&'invalid input: '&' 0 invalid input: '<'= rowFraction invalid input: '<'= 1 invalid input: '&'invalid input: '&' 0 invalid input: '<'= columnFraction invalid input: '<'= 1).- See Also:
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xdistanceOld
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).norm
- the kind of norm to be used (EUCLID, CANBERRA, ...).- Returns:
- the distance matrix (n x n, n=matrix.columns).
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xdistanceOld2
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).norm
- the kind of norm to be used (EUCLID, CANBERRA, ...).- Returns:
- the distance matrix (n x n, n=matrix.columns).
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