 smile

# math

#### package math

Mathematical and statistical functions.

Linear Supertypes
AnyRef, Any
Ordering
1. Alphabetic
2. By Inheritance
Inherited
1. math
2. AnyRef
3. Any
1. Hide All
2. Show All
Visibility
1. Public
2. All

### Type Members

38. #### class MatrixOrderOptimization extends LazyLogging

Optimizes the order of matrix multiplication chain.

Optimizes the order of matrix multiplication chain. Matrix multiplication is associative. However, the complexity of matrix multiplication chain is not associative.

64. #### sealed trait VectorExpression extends AnyRef

Vector Expression.

### Value Members

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 tx-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).

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: Matrix): 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: Matrix): 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): EVD

Returns eigen values.

27. #### def eig(A: Matrix): EVD

Returns eigen values.

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

Returns eigen values.

29. #### def eigen(A: SMatrix, k: Int): EVD

Returns k largest eigenvectors.

30. #### def eigen(A: DMatrix, k: Int): EVD

Returns k largest eigenvectors.

31. #### def eigen(A: MatrixExpression): EVD

Eigen decomposition.

32. #### def eigen(A: Matrix): EVD

Eigen decomposition.

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

Eigen decomposition.

34. #### 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) = 0x 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.

35. #### def erfc(x: Double): Double

The complementary error function.

36. #### 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.

41. #### def eye(m: Int, n: Int): Matrix

Returns an m-by-n identity matrix.

42. #### def eye(n: Int): Matrix

Returns an n-by-n identity matrix.

45. #### 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.

46. #### def gamma(x: Double): Double

Gamma function.

Gamma function. Lanczos approximation (6 terms).

47. #### def inv(A: MatrixExpression): Matrix

Returns the inverse of matrix.

48. #### def inv(A: Matrix): Matrix

Returns the inverse of matrix.

49. #### def inverf(p: Double): Double

The inverse error function.

50. #### def inverfc(p: Double): Double

The inverse complementary error function.

51. #### 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.

52. #### 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.

53. #### 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.

54. #### def lgamma(x: Double): Double

log of the Gamma function.

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

63. #### def lu(A: MatrixExpression): LU

LU decomposition.

64. #### def lu(A: Matrix): LU

LU decomposition.

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

LU decomposition.

69. #### def ones(m: Int, n: Int): Matrix

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

70. #### def ones(n: Int): Matrix

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

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

Pearson correlation coefficient test.

77. #### def qr(A: MatrixExpression): QR

QR decomposition.

78. #### def qr(A: Matrix): QR

QR decomposition.

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

QR decomposition.

80. #### def randn(m: Int, n: Int, mu: Double = 0.0, sigma: Double = 1.0): Matrix

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

81. #### def rank(A: MatrixExpression): Int

Returns the rank of matrix.

82. #### def rank(A: Matrix): Int

Returns the rank of matrix.

87. #### 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.

90. #### def svd(A: SMatrix, k: Int): SVD

Returns k largest singular vectors.

91. #### def svd(A: DMatrix, k: Int): SVD

Returns k largest singular vectors.

92. #### def svd(A: MatrixExpression): SVD

SVD decomposition.

93. #### def svd(A: Matrix): SVD

SVD decomposition.

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

SVD decomposition.

99. #### def trace(A: Matrix): Double

Returns the trace of matrix.

100. #### 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.

101. #### 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.

102. #### 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.

104. #### def zeros(m: Int, n: Int): Matrix

Returns an m-by-n zero matrix.

105. #### def zeros(n: Int): Matrix

Returns an n-by-n zero matrix.