Value Members

1.  def abs(x: MatrixExpression): AbsMatrix
2.  def abs(x: VectorExpression): AbsVector
3.  def acos(x: MatrixExpression): AcosMatrix
4.  def acos(x: VectorExpression): AcosVector
5.  implicit def array2VectorExpression(x: Array[Double]): VectorLift
6.  def asin(x: MatrixExpression): AsinMatrix
7.  def asin(x: VectorExpression): AsinVector
8.  def atan(x: MatrixExpression): AtanMatrix
9.  def atan(x: VectorExpression): AtanVector
10.  def beta(x: Double, y: Double): Double

    The beta function, also called the Euler integral of the first kind.

    The beta function, also called the Euler integral of the first kind.

    B(x, y) = ∫₀¹ t^x-1 (1-t)^y-1dt

    for x, y > 0 and the integration is over [0,1].The beta function is symmetric, i.e. B(x,y) = B(y,x).

11.  def cbrt(x: MatrixExpression): CbrtMatrix
12.  def cbrt(x: VectorExpression): CbrtVector
13.  def ceil(x: MatrixExpression): CeilMatrix
14.  def ceil(x: VectorExpression): CeilVector
15.  def chisqtest(table: Array[Array[Int]]): ChiSqTest

    Given a two-dimensional contingency table in the form of an array of integers, returns Chi-square test for independence.

    Given a two-dimensional contingency table in the form of an array of integers, returns Chi-square test for independence. The rows of contingency table are labels by the values of one nominal variable, the columns are labels by the values of the other nominal variable, and whose entries are non-negative integers giving the number of observed events for each combination of row and column. Continuity correction will be applied when computing the test statistic for 2x2 tables: one half is subtracted from all |O-E| differences. The correlation coefficient is calculated as Cramer's V.

16.  def chisqtest(x: Array[Int], prob: Array[Double], constraints: Int = 1): ChiSqTest

    One-sample chisq test.

    One-sample chisq test. Given the array x containing the observed numbers of events, and an array prob containing the expected probabilities of events, and given the number of constraints (normally one), a small value of p-value indicates a significant difference between the distributions.

17.  def chisqtest2(x: Array[Int], y: Array[Int], constraints: Int = 1): ChiSqTest

    Two-sample chisq test.

    Two-sample chisq test. Given the arrays x and y, containing two sets of binned data, and given one constraint, a small value of p-value indicates a significant difference between two distributions.

18.  def cholesky(A: MatrixExpression): Cholesky

    Cholesky decomposition.

19.  def cholesky(A: DenseMatrix): Cholesky

    Cholesky decomposition.

20.  def cholesky(A: Array[Array[Double]]): Cholesky

    Cholesky decomposition.

21.  def det(A: MatrixExpression): Double

    Returns the determinant of matrix.

22.  def det(A: DenseMatrix): Double

    Returns the determinant of matrix.

23.  def diag(A: Matrix): Array[Double]

    Returns the diagonal elements of matrix.

24.  def digamma(x: Double): Double

    The digamma function is defined as the logarithmic derivative of the gamma function.

25.  def eig(A: MatrixExpression): Array[Double]

    Returns eigen values.

26.  def eig(A: DenseMatrix): Array[Double]

    Returns eigen values.

27.  def eig(A: Array[Array[Double]]): Array[Double]

    Returns eigen values.

28.  def eigen(A: DenseMatrix, k: Int, kappa: Double = 1E-8, maxIter: Int = -1): EVD

    Eigen decomposition.

29.  def eigen(A: MatrixExpression): EVD

    Eigen decomposition.

30.  def eigen(A: DenseMatrix): EVD

    Eigen decomposition.

31.  def eigen(A: Array[Array[Double]]): EVD

    Eigen decomposition.

32.  def erf(x: Double): Double

    The error function (also called the Gauss error function) is a special function of sigmoid shape which occurs in probability, statistics, materials science, and partial differential equations.

    The error function (also called the Gauss error function) is a special function of sigmoid shape which occurs in probability, statistics, materials science, and partial differential equations. It is defined as:

    erf(x) = ∫₀^x e^-t2dt

    The complementary error function, denoted erfc, is defined as erfc(x) = 1 - erf(x). The error function and complementary error function are special cases of the incomplete gamma function.

33.  def erfc(x: Double): Double

    The complementary error function.

34.  def erfcc(x: Double): Double

    The complementary error function with fractional error everywhere less than 1.2 × 10^-7.

    The complementary error function with fractional error everywhere less than 1.2 × 10^-7. This concise routine is faster than erfc.

35.  def exp(x: MatrixExpression): ExpMatrix
36.  def exp(x: VectorExpression): ExpVector
37.  def expm1(x: MatrixExpression): Expm1Matrix
38.  def expm1(x: VectorExpression): Expm1Vector
39.  def eye(m: Int, n: Int): DenseMatrix

    Returns an m-by-n identity matrix.

40.  def eye(n: Int): DenseMatrix

    Returns an n-by-n identity matrix.

41.  def floor(x: MatrixExpression): FloorMatrix
42.  def floor(x: VectorExpression): FloorVector
43.  def ftest(x: Array[Double], y: Array[Double]): FTest

    Test if the arrays x and y have significantly different variances.

    Test if the arrays x and y have significantly different variances. Small values of p-value indicate that the two arrays have significantly different variances.

44.  def gamma(x: Double): Double

    Gamma function.

    Gamma function. Lanczos approximation (6 terms).

45.  def inv(A: MatrixExpression): DenseMatrix

    Returns the inverse of matrix.

46.  def inv(A: DenseMatrix): DenseMatrix

    Returns the inverse of matrix.

47.  def inverf(p: Double): Double

    The inverse error function.

48.  def inverfc(p: Double): Double

    The inverse complementary error function.

49.  def kendalltest(x: Array[Double], y: Array[Double]): CorTest

    Kendall rank correlation test.

    Kendall rank correlation test. The Kendall Tau Rank Correlation Coefficient is used to measure the degree of correspondence between sets of rankings where the measures are not equidistant. It is used with non-parametric data. The p-value is calculated by approximation, which is good for n > 10.

50.  def kstest(x: Array[Double], y: Array[Double]): KSTest

    The two-sample KS test for the null hypothesis that the data sets are drawn from the same distribution.

    The two-sample KS test for the null hypothesis that the data sets are drawn from the same distribution. Small values of p-value show that the cumulative distribution function of x is significantly different from that of y. The arrays x and y are modified by being sorted into ascending order.

51.  def kstest(x: Array[Double], y: Distribution): KSTest

    The one-sample KS test for the null hypothesis that the data set x is drawn from the given distribution.

    The one-sample KS test for the null hypothesis that the data set x is drawn from the given distribution. Small values of p-value show that the cumulative distribution function of x is significantly different from the given distribution. The array x is modified by being sorted into ascending order.

52.  def lgamma(x: Double): Double

    log of the Gamma function.

    log of the Gamma function. Lanczos approximation (6 terms)

53.  def log(x: MatrixExpression): LogMatrix
54.  def log(x: VectorExpression): LogVector
55.  def log10(x: MatrixExpression): Log10Matrix
56.  def log10(x: VectorExpression): Log10Vector
57.  def log1p(x: MatrixExpression): Log1pMatrix
58.  def log1p(x: VectorExpression): Log1pVector
59.  def log2(x: MatrixExpression): Log2Matrix
60.  def log2(x: VectorExpression): Log2Vector
61.  def lu(A: MatrixExpression): LU

    LU decomposition.

62.  def lu(A: DenseMatrix): LU

    LU decomposition.

63.  def lu(A: Array[Array[Double]]): LU

    LU decomposition.

64.  implicit def matrix2MatrixExpression(x: DenseMatrix): MatrixLift
65.  implicit def matrixExpression2Array(exp: MatrixExpression): DenseMatrix
66.  def ones(m: Int, n: Int): DenseMatrix

    Returns an m-by-n matrix of all ones.

67.  def ones(n: Int): DenseMatrix

    Returns an n-by-n matrix of all ones.

68.  def pearsontest(x: Array[Double], y: Array[Double]): CorTest

    Pearson correlation coefficient test.

69.  implicit def pimpArray2D(data: Array[Array[Double]]): PimpedArray2D
70.  implicit def pimpDouble(x: Double): PimpedDouble
71.  implicit def pimpDoubleArray(data: Array[Double]): PimpedDoubleArray
72.  implicit def pimpIntArray(data: Array[Int]): PimpedArray[Int]
73.  implicit def pimpMatrix(matrix: DenseMatrix): PimpedMatrix
74.  def qr(A: MatrixExpression): QR

    QR decomposition.

75.  def qr(A: DenseMatrix): QR

    QR decomposition.

76.  def qr(A: Array[Array[Double]]): QR

    QR decomposition.

77.  def randn(m: Int, n: Int, mu: Double = 0.0, sigma: Double = 1.0): DenseMatrix

    Returns an m-by-n matrix of normally distributed random numbers.

78.  def rank(A: MatrixExpression): Int

    Returns the rank of matrix.

79.  def rank(A: DenseMatrix): Int

    Returns the rank of matrix.

80.  def round(x: MatrixExpression): RoundMatrix
81.  def round(x: VectorExpression): RoundVector
82.  def sin(x: MatrixExpression): SinMatrix
83.  def sin(x: VectorExpression): SinVector
84.  def spearmantest(x: Array[Double], y: Array[Double]): CorTest

    Spearman rank correlation coefficient test.

    Spearman rank correlation coefficient test. The Spearman Rank Correlation Coefficient is a form of the Pearson coefficient with the data converted to rankings (ie. when variables are ordinal). It can be used when there is non-parametric data and hence Pearson cannot be used.

    The raw scores are converted to ranks and the differences between the ranks of each observation on the two variables are calculated.

    The p-value is calculated by approximation, which is good for n > 10.

85.  def sqrt(x: MatrixExpression): SqrtMatrix
86.  def sqrt(x: VectorExpression): SqrtVector
87.  def svd(A: DenseMatrix, k: Int, kappa: Double = 1E-8, maxIter: Int = -1): SVD

    SVD decomposition.

88.  def svd(A: MatrixExpression): SVD

    SVD decomposition.

89.  def svd(A: DenseMatrix): SVD

    SVD decomposition.

90.  def svd(A: Array[Array[Double]]): SVD

    SVD decomposition.

91.  def tan(x: MatrixExpression): TanMatrix
92.  def tan(x: VectorExpression): TanVector
93.  def tanh(x: MatrixExpression): TanhMatrix
94.  def tanh(x: VectorExpression): TanhVector
95.  def trace(A: Matrix): Double

    Returns the trace of matrix.

96.  def ttest(x: Array[Double], y: Array[Double]): TTest

    Given the paired arrays x and y, test if they have significantly different means.

    Given the paired arrays x and y, test if they have significantly different means. Small values of p-value indicate that the two arrays have significantly different means.

97.  def ttest(x: Array[Double], mean: Double): TTest

    Independent one-sample t-test whether the mean of a normally distributed population has a value specified in a null hypothesis.

    Independent one-sample t-test whether the mean of a normally distributed population has a value specified in a null hypothesis. Small values of p-value indicate that the array has significantly different mean.

98.  def ttest2(x: Array[Double], y: Array[Double], equalVariance: Boolean = false): TTest

    Test if the arrays x and y have significantly different means.

    Test if the arrays x and y have significantly different means. Small values of p-value indicate that the two arrays have significantly different means.

    equalVariance

    true if the data arrays are assumed to be drawn from populations with the same true variance. Otherwise, The data arrays are allowed to be drawn from populations with unequal variances.

99.  implicit def vectorExpression2Array(exp: VectorExpression): Array[Double]
100.  def zeros(m: Int, n: Int): DenseMatrix

     Returns an m-by-n zero matrix.

101.  def zeros(n: Int): DenseMatrix

     Returns an n-by-n zero matrix.