math

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. package distance

    

    Distance functions.

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

    

    Returns eigen values.

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

    

    Returns eigen values.

28. def eig(A: Array[Array[Double]]): Array[Double]

    

    Returns eigen values.

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

    

    Eigen decomposition.

30. def eigen(A: MatrixExpression): EVD

    

    Eigen decomposition.

31. def eigen(A: DenseMatrix): EVD

    

    Eigen decomposition.

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

    

    Eigen decomposition.

33. 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.

34. def erfc(x: Double): Double

    

    The complementary error function.

35. 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.

36. def exp(x: MatrixExpression): ExpMatrix

    

37. def exp(x: VectorExpression): ExpVector

    

38. def expm1(x: MatrixExpression): Expm1Matrix

    

39. def expm1(x: VectorExpression): Expm1Vector

    

40. def eye(m: Int, n: Int): DenseMatrix

    

    Returns an m-by-n identity matrix.

41. def eye(n: Int): DenseMatrix

    

    Returns an n-by-n identity matrix.

42. def floor(x: MatrixExpression): FloorMatrix

    

43. def floor(x: VectorExpression): FloorVector

    

44. 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.

45. def gamma(x: Double): Double

    

    Gamma function.

    Gamma function. Lanczos approximation (6 terms).

46. def inv(A: MatrixExpression): DenseMatrix

    

    Returns the inverse of matrix.

47. def inv(A: DenseMatrix): DenseMatrix

    

    Returns the inverse of matrix.

48. def inverf(p: Double): Double

    

    The inverse error function.

49. def inverfc(p: Double): Double

    

    The inverse complementary error function.

50. 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.

51. 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.

52. 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.

53. def lgamma(x: Double): Double

    

    log of the Gamma function.

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

54. def log(x: MatrixExpression): LogMatrix

    

55. def log(x: VectorExpression): LogVector

    

56. def log10(x: MatrixExpression): Log10Matrix

    

57. def log10(x: VectorExpression): Log10Vector

    

58. def log1p(x: MatrixExpression): Log1pMatrix

    

59. def log1p(x: VectorExpression): Log1pVector

    

60. def log2(x: MatrixExpression): Log2Matrix

    

61. def log2(x: VectorExpression): Log2Vector

    

62. def lu(A: MatrixExpression): LU

    

    LU decomposition.

63. def lu(A: DenseMatrix): LU

    

    LU decomposition.

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

    

    LU decomposition.

65. package matrix

    

66. implicit def matrix2MatrixExpression(x: DenseMatrix): MatrixLift

    

67. implicit def matrixExpression2Array(exp: MatrixExpression): DenseMatrix

    

68. def ones(m: Int, n: Int): DenseMatrix

    

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

69. def ones(n: Int): DenseMatrix

    

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

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

    

    Pearson correlation coefficient test.

71. implicit def pimpArray2D(data: Array[Array[Double]]): PimpedArray2D

    

72. implicit def pimpDouble(x: Double): PimpedDouble

    

73. implicit def pimpDoubleArray(data: Array[Double]): PimpedDoubleArray

    

74. implicit def pimpIntArray(data: Array[Int]): PimpedArray[Int]

    

75. implicit def pimpMatrix(matrix: DenseMatrix): PimpedMatrix

    

76. def qr(A: MatrixExpression): QR

    

    QR decomposition.

77. def qr(A: DenseMatrix): QR

    

    QR decomposition.

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

    

    QR decomposition.

79. 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.

80. def rank(A: MatrixExpression): Int

    

    Returns the rank of matrix.

81. def rank(A: DenseMatrix): Int

    

    Returns the rank of matrix.

82. def round(x: MatrixExpression): RoundMatrix

    

83. def round(x: VectorExpression): RoundVector

    

84. def sin(x: MatrixExpression): SinMatrix

    

85. def sin(x: VectorExpression): SinVector

    

86. 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.

87. def sqrt(x: MatrixExpression): SqrtMatrix

    

88. def sqrt(x: VectorExpression): SqrtVector

    

89. def svd(A: DenseMatrix, k: Int, kappa: Double = 1E-8, maxIter: Int = 1): SVD

    

    SVD decomposition.

90. def svd(A: MatrixExpression): SVD

    

    SVD decomposition.

91. def svd(A: DenseMatrix): SVD

    

    SVD decomposition.

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

    

    SVD decomposition.

93. def tan(x: MatrixExpression): TanMatrix

    

94. def tan(x: VectorExpression): TanVector

    

95. def tanh(x: MatrixExpression): TanhMatrix

    

96. def tanh(x: VectorExpression): TanhVector

    

97. def trace(A: Matrix): Double

    

    Returns the trace of matrix.

98. 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.

99. 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.

100. 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.

101. implicit def vectorExpression2Array(exp: VectorExpression): Array[Double]

     

102. def zeros(m: Int, n: Int): DenseMatrix

     

     Returns an m-by-n zero matrix.

103. def zeros(n: Int): DenseMatrix

     

     Returns an n-by-n zero matrix.