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java.lang.Objectcern.colt.matrix.tdouble.algo.DoubleStatistic
public class DoubleStatistic
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.tdouble.bin
, in particular
DynamicDoubleBin1D
.
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 |
Nested Class Summary | |
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static interface |
DoubleStatistic.VectorVectorFunction
Interface that represents a function object: a function that takes two argument vectors and returns a single value. |
Field Summary | |
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static DoubleStatistic.VectorVectorFunction |
BRAY_CURTIS
Bray-Curtis distance function; Sum( abs(x[i]-y[i]) ) / Sum( x[i]+y[i] ). |
static DoubleStatistic.VectorVectorFunction |
CANBERRA
Canberra distance function; Sum( abs(x[i]-y[i]) / abs(x[i]+y[i]) ). |
static DoubleStatistic.VectorVectorFunction |
EUCLID
Euclidean distance function; Sqrt(Sum( (x[i]-y[i])^2 )). |
static DoubleStatistic.VectorVectorFunction |
MANHATTAN
Manhattan distance function; Sum( abs(x[i]-y[i]) ). |
static DoubleStatistic.VectorVectorFunction |
MAXIMUM
Maximum distance function; Max( abs(x[i]-y[i]) ). |
Method Summary | |
---|---|
static DoubleMatrix2D |
aggregate(DoubleMatrix2D matrix,
DoubleBinFunction1D[] aggr,
DoubleMatrix2D result)
Applies the given aggregation functions to each column and stores the results in a the result matrix. |
static DynamicDoubleBin1D |
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 DoubleIHistogram2D |
cube(DoubleMatrix1D x,
DoubleMatrix1D y,
DoubleMatrix1D weights)
2-d OLAP cube operator; Fills all cells of the given vectors into the given histogram. |
static DoubleIHistogram3D |
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 |
demo3(DoubleStatistic.VectorVectorFunction norm)
Demonstrates usage of this class. |
static DoubleMatrix2D |
distance(DoubleMatrix2D matrix,
DoubleStatistic.VectorVectorFunction distanceFunction)
Constructs and returns the distance matrix of the given matrix. |
static DoubleIHistogram1D[][] |
histogram(DoubleIHistogram1D[][] histo,
DoubleMatrix2D matrix,
int m,
int n)
Splits the given matrix into m x n pieces and computes 1D histogram of each piece. |
static DoubleIHistogram1D |
histogram(DoubleIHistogram1D histo,
DoubleMatrix1D vector)
Fills all cells of the given vector into the given histogram. |
static DoubleIHistogram1D |
histogram(DoubleIHistogram1D histo,
DoubleMatrix2D matrix)
Fills all cells of the given matrix into the given histogram. |
static DoubleIHistogram2D |
histogram(DoubleIHistogram2D histo,
DoubleMatrix1D x,
DoubleMatrix1D y)
Fills all cells of the given vectors into the given histogram. |
static DoubleIHistogram2D |
histogram(DoubleIHistogram2D histo,
DoubleMatrix1D x,
DoubleMatrix1D y,
DoubleMatrix1D weights)
Fills all cells of the given vectors into the given histogram. |
static DoubleIHistogram3D |
histogram(DoubleIHistogram3D histo,
DoubleMatrix1D x,
DoubleMatrix1D y,
DoubleMatrix1D z,
DoubleMatrix1D weights)
Fills all cells of the given vectors into the given histogram. |
static void |
main(String[] args)
Benchmarks covariance computation. |
static DoubleMatrix1D |
viewSample(DoubleMatrix1D matrix,
double fraction,
DoubleRandomEngine randomGenerator)
Constructs and returns a sampling view with a size of round(matrix.size() * fraction). |
static DoubleMatrix2D |
viewSample(DoubleMatrix2D matrix,
double rowFraction,
double columnFraction,
DoubleRandomEngine 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,
DoubleRandomEngine 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 |
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equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
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public static final DoubleStatistic.VectorVectorFunction EUCLID
public static final DoubleStatistic.VectorVectorFunction BRAY_CURTIS
public static final DoubleStatistic.VectorVectorFunction CANBERRA
public static final DoubleStatistic.VectorVectorFunction MAXIMUM
public static final DoubleStatistic.VectorVectorFunction MANHATTAN
Method Detail |
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public static DoubleMatrix2D aggregate(DoubleMatrix2D matrix, DoubleBinFunction1D[] aggr, DoubleMatrix2D result)
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.
DoubleFormatter
,
DoubleBinFunction1D
,
DoubleBinFunctions1D
public static DynamicDoubleBin1D bin(DoubleMatrix1D vector)
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 & frequencies not printed (too many). |
vector
- the vector to analyze.
public static DoubleMatrix2D correlation(DoubleMatrix2D covariance)
covariance
- a covariance matrix, as, for example, returned by method
covariance(DoubleMatrix2D)
.
public static DoubleMatrix2D covariance(DoubleMatrix2D matrix)
matrix
- any matrix; a column holds the values of a given variable.
public static DoubleIHistogram2D cube(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D weights)
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 | |
IllegalArgumentException
- if
x.size() != y.size() || y.size() != weights.size().public static DoubleIHistogram3D cube(DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights)
Computes the distinct values of x and y and z, yielding histogram axes that capture one distinct value per bin. Then fills the histogram.
IllegalArgumentException
- if
x.size() != y.size() || x.size() != z.size() || x.size() != weights.size()
.public static void demo1()
public static void demo2(int rows, int columns, boolean print)
public static void demo3(DoubleStatistic.VectorVectorFunction norm)
public static DoubleMatrix2D distance(DoubleMatrix2D matrix, DoubleStatistic.VectorVectorFunction distanceFunction)
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).
public static DoubleIHistogram1D histogram(DoubleIHistogram1D histo, DoubleMatrix1D vector)
public static DoubleIHistogram1D histogram(DoubleIHistogram1D histo, DoubleMatrix2D matrix)
public static DoubleIHistogram1D[][] histogram(DoubleIHistogram1D[][] histo, DoubleMatrix2D matrix, int m, int n)
public static DoubleIHistogram2D histogram(DoubleIHistogram2D histo, DoubleMatrix1D x, DoubleMatrix1D y)
IllegalArgumentException
- if x.size() != y.size().public static DoubleIHistogram2D histogram(DoubleIHistogram2D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D weights)
IllegalArgumentException
- if
x.size() != y.size() || y.size() != weights.size().public static DoubleIHistogram3D histogram(DoubleIHistogram3D histo, DoubleMatrix1D x, DoubleMatrix1D y, DoubleMatrix1D z, DoubleMatrix1D weights)
IllegalArgumentException
- if
x.size() != y.size() || x.size() != z.size() || x.size() != weights.size()
.public static void main(String[] args)
public static DoubleMatrix1D viewSample(DoubleMatrix1D matrix, double fraction, DoubleRandomEngine randomGenerator)
matrix
- any matrix.fraction
- the percentage 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.
IllegalArgumentException
- if
! (0 <= rowFraction <= 1 && 0 <= columnFraction <= 1)
.DoubleRandomSampler
public static DoubleMatrix2D viewSample(DoubleMatrix2D matrix, double rowFraction, double columnFraction, DoubleRandomEngine randomGenerator)
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 |
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.
IllegalArgumentException
- if
! (0 <= rowFraction <= 1 && 0 <= columnFraction <= 1)
.DoubleRandomSampler
public static DoubleMatrix3D viewSample(DoubleMatrix3D matrix, double sliceFraction, double rowFraction, double columnFraction, DoubleRandomEngine randomGenerator)
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.
IllegalArgumentException
- if
! (0 <= sliceFraction <= 1 && 0 <= rowFraction <= 1 && 0 <= columnFraction <= 1)
.DoubleRandomSampler
|
Parallel Colt 0.9.4 | |||||||||
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