smile.math

package smile.math

Mathematical and statistical functions.

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Members list

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Distance functions.

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Type members

Classlikes

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Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

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class Any
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Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

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Supertypes: class Object

trait Matchable

class Any
Known subtypes: class AbsMatrix

class AcosMatrix

class AsinMatrix

class AtanMatrix

class CbrtMatrix

class CeilMatrix

class ExpMatrix

class Expm1Matrix

class FloorMatrix

class Log10Matrix

class Log1pMatrix

class Log2Matrix

class LogMatrix

class MatrixAddMatrix

class MatrixAddValue

class MatrixDivMatrix

class MatrixDivValue

class MatrixLift

class MatrixMulMatrix

class MatrixMulValue

class MatrixMultiplication

class MatrixMultiplicationChain

class MatrixSubMatrix

class MatrixSubValue

class MatrixTranspose

class RoundMatrix

class SinMatrix

class SqrtMatrix

class TanMatrix

class TanhMatrix

class ValueAddMatrix

class ValueDivMatrix

class ValueMulMatrix

class ValueSubMatrix
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Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

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

Value parameters

dims: Matrix A[i] has dimension dims[i-1] x dims[i] for i = 1..n

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Supertypes: trait LazyLogging

class Object

trait Matchable

class Any

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Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

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Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Python like slicing.

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait MatrixExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Vector Expression.

Attributes

Supertypes: class Object

trait Matchable

class Any
Known subtypes: class AbsVector

class AcosVector

class AsinVector

class AtanVector

class Ax

class CbrtVector

class CeilVector

class ExpVector

class Expm1Vector

class FloorVector

class Log10Vector

class Log1pVector

class Log2Vector

class LogVector

class RoundVector

class SinVector

class SqrtVector

class TanVector

class TanhVector

class ValueAddVector

class ValueDivVector

class ValueMulVector

class ValueSubVector

class VectorAddValue

class VectorAddVector

class VectorDivValue

class VectorDivVector

class VectorLift

class VectorMulValue

class VectorMulVector

class VectorSubValue

class VectorSubVector
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
Show all

Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Attributes

Supertypes: trait Serializable

trait Product

trait Equals

trait VectorExpression

class Object

trait Matchable

class Any
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Value members

Concrete methods

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).

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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.

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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.

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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.

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Cholesky decomposition.

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Cholesky decomposition.

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Cholesky decomposition.

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Returns the determinant of matrix.

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Returns the determinant of matrix.

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Returns the diagonal elements of matrix.

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

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Returns eigen values.

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Returns eigen values.

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Returns eigen values.

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Eigen decomposition.

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Eigen decomposition.

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Eigen decomposition.

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Returns k largest eigenvectors.

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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.

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The complementary error function.

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

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Returns an n-by-n identity matrix.

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Returns an m-by-n identity matrix.

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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.

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Gamma function. Lanczos approximation (6 terms).

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Returns the inverse of matrix.

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Returns the inverse of matrix.

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The inverse error function.

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The inverse complementary error function.

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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.

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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.

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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.

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

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LU decomposition.

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LU decomposition.

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LU decomposition.

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

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

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Pearson correlation coefficient test.

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QR decomposition.

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QR decomposition.

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QR decomposition.

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

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

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Returns the rank of matrix.

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Returns the rank of matrix.

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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.

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SVD decomposition.

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SVD decomposition.

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SVD decomposition.

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Returns k largest singular vectors.

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Returns the trace of matrix.

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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.

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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.

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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.

Value parameters

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.

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Returns an n-by-n zero matrix.

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Returns an m-by-n zero matrix.

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Implicits

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