FloatStatistic
cern.colt.matrix.tfloat.algo

Class FloatStatistic



  • public class FloatStatisticextends 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.tfloat.bin, in particular DynamicFloatBin1D.

    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       
         
    • Method Detail

      • aggregate

        public static FloatMatrix2D aggregate(FloatMatrix2D matrix,                      FloatBinFunction1D[] aggr,                      FloatMatrix2D 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:
        FloatFormatter, FloatBinFunction1D, FloatBinFunctions1D
      • bin

        public static DynamicFloatBin1D bin(FloatMatrix1D vector)
        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 & frequencies not printed (too many).  
        Parameters:
        vector - the vector to analyze.
        Returns:
        a bin holding the statistics measures of the vector.
      • correlation

        public static FloatMatrix2D correlation(FloatMatrix2D 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(FloatMatrix2D).
        Returns:
        the modified covariance, now correlation matrix (for convenience only).
      • covariance

        public static FloatMatrix2D covariance(FloatMatrix2D 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).
      • cube

        public static FloatIHistogram2D cube(FloatMatrix1D x,                     FloatMatrix1D y,                     FloatMatrix1D weights)
        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().
      • cube

        public static FloatIHistogram3D cube(FloatMatrix1D x,                     FloatMatrix1D y,                     FloatMatrix1D z,                     FloatMatrix1D 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() .
      • 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.
      • distance

        public static FloatMatrix2D distance(FloatMatrix2D matrix,                     FloatStatistic.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).
      • histogram

        public static FloatIHistogram1D[][] histogram(FloatIHistogram1D[][] histo,                              FloatMatrix2D matrix,                              int m,                              int n)
        Splits the given matrix into m x n pieces and computes 1D histogram of each piece.
        Returns:
        histo (for convenience only).
      • main

        public static void main(String[] args)
        Benchmarks covariance computation.
      • viewSample

        public static FloatMatrix1D viewSample(FloatMatrix1D matrix,                       float fraction,                       FloatRandomEngine 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.
        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.
        Returns:
        the sampling view.
        Throws:
        IllegalArgumentException - if ! (0 <= rowFraction <= 1 && 0 <= columnFraction <= 1) .
        See Also:
        FloatRandomSampler
      • viewSample

        public static FloatMatrix2D viewSample(FloatMatrix2D matrix,                       float rowFraction,                       float columnFraction,                       FloatRandomEngine 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:
        FloatRandomSampler
      • viewSample

        public static FloatMatrix3D viewSample(FloatMatrix3D matrix,                       float sliceFraction,                       float rowFraction,                       float columnFraction,                       FloatRandomEngine 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:
        FloatRandomSampler

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