All Implemented Interfaces:


public class Maths

Mathematical functions and utilities.

Nested Class Summary

Nested Classes
Modifier and Type	Class	Description
`public class`	`Maths.laplaceApproxComplexReturn`
`public class`	`Maths.laplaceApproxReturn`
`public class`	`Maths.simplexQuadResult`

Field Summary

Fields
Modifier and Type	Field	Description

Constructor Summary

Constructors
Constructor	Description
`Maths()`

Enum Constant Summary

Enum Constants
Enum Constant	Description

Method Summary

Modifier and Type	Method	Description
`static double`	`binomialCoeff(int n, int k)`	Computes the binomial coefficient "n choose k" by doing the work in log-space then exponentiating with FastMath.exp().
`static Matrix`	`circul(int c)`	Returns a circulant matrix of order c.
`static Matrix`	`circul(Matrix c)`	Returns a circulant matrix from the given first column.
`static Array<int>`	`cumSum(Array<int> ar)`	Cumulative sum of an array, where the value at each index of the result is the sum of all the previous values of the input.
`static Array<double>`	`cumSum(Array<double> ar)`	Cumulative sum of an array, where the value at each index of the result is the sum of all the previous values of the input.
`static void`	`elementAdd(Array<int> ar, int i)`	Helper method that adds an integer to every element of an integer array.
`static double`	`normalErf(double x)`	Computes the error function (erf) of a value.
`static Matrix`	`matrixExp(Matrix matrix)`	Adapted from jblas and IHMC Original documentation: Calculate matrix exponential of a square matrix.
`static int`	`fact(int n)`	Computes the factorial of an integer.
`static double`	`fact(double n)`	Computes the factorial of a double value using the gamma function.
`static double`	`factln(int n)`	Computes the natural logarithm of the factorial.
`static double`	`factln(double n)`	Computes the natural logarithm of the factorial for a double value.
`static double`	`gammaFunction(double x)`	Computes the gamma function via Lanczos approximation formula.
`static Maths.simplexQuadResult`	`grnmol(Function<Array<double>, Double> f, Array<Array<double>> V, int s, double tol)`	Grundmann-Moeller simplex integration
`static Matrix`	`binHist(Matrix v, int minVal, int maxVal)`	Implementation of MATLAB "hist": puts elements of v into k bins
`static Maths.laplaceApproxReturn`	`laplaceapprox_h(Matrix x0, SerializableFunction<Matrix, Matrix> h)`
`static Maths.laplaceApproxComplexReturn`	`laplaceapprox_h_complex(Matrix x0, SerializableFunction<Matrix, ComplexMatrix> h)`
`static Array<double>`	`linSpace(double start, double end, int num)`
`static double`	`logBinomial(int n, int k)`	Computes log(n choose k) = log Γ(n+1) − log Γ(k+1) − log Γ(n−k+1).
`static double`	`logmeanexp(Matrix x)`
`static Array<double>`	`logSpace(double min, double max, int n)`
`static Array<int>`	`logSpacei(int start, int stop, int n)`	Generates an integer list of n logarithmically spaced values.
`static double`	`max(double x, double y)`	Returns the max of two numbers.
`static double`	`min(double x, double y)`	Returns the min of two numbers.
`static List<Matrix>`	`multiChooseCombinations(int k, int n)`	Generate all combinations of distributing n items into k bins
`static Matrix`	`multiChooseCon(Matrix n, double S)`
`static Matrix`	`multichoose(double n, double k)`
`static double`	`multinomialln(Matrix n)`
`static double`	`nCk(double n, double k)`
`static Matrix`	`nCk(Matrix v, int k)`	Computes the combinations of the elements in v taken k at a time
`static int`	`nextPowerOfTwo(int x)`	Given an integer x input, find the next integer y greater than x such that y is a power of 2.
`static Matrix`	`num_grad_h(Matrix x0, double h, SerializableFunction<Matrix, Matrix> hfun)`
`static ComplexMatrix`	`num_grad_h_complex(Matrix x0, double h, SerializableFunction<Matrix, ComplexMatrix> hfun)`
`static Matrix`	`num_hess_h(Matrix x0, double h, SerializableFunction<Matrix, Matrix> hfun)`
`static ComplexMatrix`	`num_hess_h_complex(Matrix x0, double h, SerializableFunction<Matrix, ComplexMatrix> hfun)`
`static Matrix`	`permutations(Matrix vec)`
`static double`	`rand()`
`static double`	`randn()`
`static int`	`probchoose(List<Double> p)`	Choose an element index according to probability vector.
`static int`	`probchoose(Matrix p)`	Choose an element index according to probability vector.
`static List<Integer>`	`primes(int N)`
`static int`	`maxpos(Matrix v)`	Returns the position of the maximum value in a vector.
`static Array<int>`	`maxpos(Matrix v, int n)`	Returns the positions of the n largest values in a vector.
`static int`	`minpos(Matrix v)`	Returns the position of the minimum value in a vector.
`static Array<int>`	`minpos(Matrix v, int n)`	Returns the positions of the n smallest values in a vector.
`static boolean`	`randomMatlabStyle()`
`static Array<Complex>`	`roots(Matrix coefficients)`
`static Array<Complex>`	`roots(Array<double> coefficients)`
`static void`	`setMatlabRandomSeed(long seed)`
`static void`	`setRandomNumbersMatlab(boolean matlab_style)`
`static double`	`simplex_fun(Array<double> x, Matrix L, Matrix N)`	Computes a specialized function used in simplex-based optimization algorithms.
`static Maths.simplexQuadResult`	`simplexquad(Function<Array<double>, Double> f, int n, int order, double tol)`
`static double`	`softmin(double x, double y, double alpha)`	Softmin function.
`static List<Integer>`	`sub2ind(Matrix dims, Matrix row, Matrix col)`
`static Array<Array<double>>`	`transpose(Array<Array<double>> data)`	Transposes a 2D array of values.
`static Matrix`	`uniqueAndSort(Matrix space)`
`static Matrix`	`uniquePerms(Matrix vec)`
`static Matrix`	`setdiff(Matrix A, Matrix B)`	Set difference operation for Matrix objects that are vectors.
`static Matrix`	`multichoose(int n, int k)`	Generates all combinations of n objects taken k at a time with repetition (multichoose).
`static List<Array<int>>`	`multichooseList(int n, int k)`	Generates all combinations of n objects taken k at a time with repetition (multichoose).
`static List<Array<int>>`	`sortByNnzPos(List<Array<int>> combinations)`	Sorts combinations by number of non-zeros and their positions.
`static int`	`nnzcmp(Array<int> i1, Array<int> i2)`	Compares two arrays by number of zeros and their positions.
`static int`	`matchRow(List<Array<int>> rows, Array<int> target)`	Finds the index of a matching row in a list.
`static int`	`nchoosek(int n, int k)`	Computes binomial coefficient "n choose k".
`static Array<double>`	`goldenSectionSearch(Function<Double, Double> function, double a, double b, double tol)`	Golden section search for finding the minimum of a unimodal function.
`static Array<double>`	`goldenSectionSearch(Function<Double, Double> function, double a, double b)`	Golden section search with default tolerance.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - Maths
```
Maths()
```
- Method Detail
  - binomialCoeff
```
 static double binomialCoeff(int n, int k)
```
    Computes the binomial coefficient "n choose k" by doing the work in log-space then exponentiating with FastMath.exp().
    
    Parameters:
    
    n - total items
    
    k - items chosen
    
    Returns:
    
    the binomial coefficient, or 0.0 if k<0 or k>n
  - circul
```
 static Matrix circul(int c)
```
    Returns a circulant matrix of order c. Creates a circulant matrix where each row is a cyclic shift of the previous row.
    
    Parameters:
    
    c - the order of the circulant matrix
    
    Returns:
    
    a c×c circulant matrix
  - circul
```
 static Matrix circul(Matrix c)
```
    Returns a circulant matrix from the given first column. Creates a circulant matrix where the first column is given by the input matrix, and each subsequent column is a cyclic shift of the previous one.
    
    Parameters:
    
    c - the first column of the circulant matrix
    
    Returns:
    
    a square circulant matrix
  - cumSum
```
 static Array<int> cumSum(Array<int> ar)
```
    Cumulative sum of an array, where the value at each index of the result is the sum of all the previous values of the input.
    
    Parameters:
    
    ar - Array we want the cumulative sum of.
    
    Returns:
    
    New array that is the cumulative sum of the input.
  - cumSum
```
 static Array<double> cumSum(Array<double> ar)
```
    Cumulative sum of an array, where the value at each index of the result is the sum of all the previous values of the input.
    
    Parameters:
    
    ar - Array we want the cumulative sum of.
    
    Returns:
    
    New array that is the cumulative sum of the input.
  - elementAdd
```
 static void elementAdd(Array<int> ar, int i)
```
    Helper method that adds an integer to every element of an integer array.
    
    Parameters:
    
    ar - Array to be added to.
    
    i - Integer to add.
  - normalErf
```
 static double normalErf(double x)
```
    Computes the error function (erf) of a value. The error function is the integral of the Gaussian distribution.
    
    Parameters:
    
    x - the input value
    
    Returns:
    
    the error function value erf(x)
  - matrixExp
```
 static Matrix matrixExp(Matrix matrix)
```
    Adapted from jblas and IHMC Original documentation:
    Calculate matrix exponential of a square matrix.
    A scaled Pade approximation algorithm from Golub and Van Loan "Matrix Computations", algorithm 11.3.1 and 11.2.
    
    Returns:
    
    matrix exponential of the matrix
  - fact
```
 static int fact(int n)
```
    Computes the factorial of an integer.
    
    Parameters:
    
    n - the input value
    
    Returns:
    
    n! (n factorial)
  - fact
```
 static double fact(double n)
```
    Computes the factorial of a double value using the gamma function.
    
    Parameters:
    
    n - the input value
    
    Returns:
    
    n! = Γ(n+1)
  - factln
```
 static double factln(int n)
```
    Computes the natural logarithm of the factorial.
    
    Parameters:
    
    n - the input value
    
    Returns:
    
    ln(n!)
  - factln
```
 static double factln(double n)
```
    Computes the natural logarithm of the factorial for a double value.
    
    Parameters:
    
    n - the input value
    
    Returns:
    
    ln(n!) = ln(Γ(n+1))
  - gammaFunction
```
 static double gammaFunction(double x)
```
    Computes the gamma function via Lanczos approximation formula. The gamma function is an extension of the factorial function to real and complex numbers.
    
    Parameters:
    
    x - the input value
    
    Returns:
    
    Γ(x)
  - grnmol
```
 static Maths.simplexQuadResult grnmol(Function<Array<double>, Double> f, Array<Array<double>> V, int s, double tol)
```
    Grundmann-Moeller simplex integration
  - binHist
```
 static Matrix binHist(Matrix v, int minVal, int maxVal)
```
    Implementation of MATLAB "hist": puts elements of v into k bins
    
    Parameters:
    
    v - - vector of elements
    
    minVal - - lowest number in v
    
    maxVal - - highest number in v
    
    Returns:
    
    - vector containing number of elements in each bin
  - laplaceapprox_h
```
 static Maths.laplaceApproxReturn laplaceapprox_h(Matrix x0, SerializableFunction<Matrix, Matrix> h)
```
  - laplaceapprox_h_complex
```
 static Maths.laplaceApproxComplexReturn laplaceapprox_h_complex(Matrix x0, SerializableFunction<Matrix, ComplexMatrix> h)
```
  - linSpace
```
 static Array<double> linSpace(double start, double end, int num)
```
  - logBinomial
```
 static double logBinomial(int n, int k)
```
    Computes log(n choose k) = log Γ(n+1) − log Γ(k+1) − log Γ(n−k+1). Uses Commons-Math Gamma but FastMath for everything else.
    
    Parameters:
    
    n - total items
    
    k - items chosen
    
    Returns:
    
    log of the binomial coefficient, or NegInf if k<0 or k>n
  - logmeanexp
```
 static double logmeanexp(Matrix x)
```
  - logSpace
```
 static Array<double> logSpace(double min, double max, int n)
```
  - logSpacei
```
 static Array<int> logSpacei(int start, int stop, int n)
```
    Generates an integer list of n logarithmically spaced values.
    
    Parameters:
    
    start - First element of array.
    
    stop - Last element of array.
    
    n - Number of values.
    
    Returns:
    
    Array of logarithmically spaced values.
  - max
```
 static double max(double x, double y)
```
    Returns the max of two numbers. If one of the two is NaN, it returns the other.
    
    Parameters:
    
    x - - the first number to be compared
    
    y - - the second number to be compared
    
    Returns:
    
    - the max between the two
  - min
```
 static double min(double x, double y)
```
    Returns the min of two numbers. If one of the two is NaN, it returns the other.
    
    Parameters:
    
    x - - the first number to be compared
    
    y - - the second number to be compared
    
    Returns:
    
    - the min between the two
  - multiChooseCombinations
```
 static List<Matrix> multiChooseCombinations(int k, int n)
```
    Generate all combinations of distributing n items into k bins
  - multiChooseCon
```
 static Matrix multiChooseCon(Matrix n, double S)
```
  - multichoose
```
 static Matrix multichoose(double n, double k)
```
  - multinomialln
```
 static double multinomialln(Matrix n)
```
  - nCk
```
 static double nCk(double n, double k)
```
  - nCk
```
 static Matrix nCk(Matrix v, int k)
```
    Computes the combinations of the elements in v taken k at a time
    
    Parameters:
    
    v - - vector of elements
    
    k - - how many elements to pick at a time
    
    Returns:
    
    - the combinations of the elements in v taken k at a time
  - nextPowerOfTwo
```
 static int nextPowerOfTwo(int x)
```
    Given an integer x input, find the next integer y greater than x such that y is a power of 2.
    
    Parameters:
    
    x - Input to find next power
    
    Returns:
    
    Closest integer greater than input that is a power of two.
  - num_grad_h
```
 static Matrix num_grad_h(Matrix x0, double h, SerializableFunction<Matrix, Matrix> hfun)
```
  - num_grad_h_complex
```
 static ComplexMatrix num_grad_h_complex(Matrix x0, double h, SerializableFunction<Matrix, ComplexMatrix> hfun)
```
  - num_hess_h
```
 static Matrix num_hess_h(Matrix x0, double h, SerializableFunction<Matrix, Matrix> hfun)
```
  - num_hess_h_complex
```
 static ComplexMatrix num_hess_h_complex(Matrix x0, double h, SerializableFunction<Matrix, ComplexMatrix> hfun)
```
  - permutations
```
 static Matrix permutations(Matrix vec)
```
  - rand
```
 static double rand()
```
  - randn
```
 static double randn()
```
  - probchoose
```
 static int probchoose(List<Double> p)
```
    Choose an element index according to probability vector. Equivalent to MATLAB's probchoose function.
    
    Parameters:
    
    p - Probability vector (must sum to 1.
    
    Returns:
    
    Index of chosen element (0-based)
  - probchoose
```
 static int probchoose(Matrix p)
```
    Choose an element index according to probability vector. Overloaded version for Matrix input.
    
    Parameters:
    
    p - Probability matrix (single row or column)
    
    Returns:
    
    Index of chosen element (0-based)
  - primes
```
 static List<Integer> primes(int N)
```
  - maxpos
```
 static int maxpos(Matrix v)
```
    Returns the position of the maximum value in a vector. Equivalent to MATLAB's maxpos function.
    
    Parameters:
    
    v - Input vector
    
    Returns:
    
    Index of maximum value (0-based)
  - maxpos
```
 static Array<int> maxpos(Matrix v, int n)
```
    Returns the positions of the n largest values in a vector. Equivalent to MATLAB's maxpos(v, n) function.
    
    Parameters:
    
    v - Input vector
    
    n - Number of positions to return
    
    Returns:
    
    Array of indices of n largest values (0-based), sorted by value (descending)
  - minpos
```
 static int minpos(Matrix v)
```
    Returns the position of the minimum value in a vector. Equivalent to MATLAB's minpos function.
    
    Parameters:
    
    v - Input vector
    
    Returns:
    
    Index of minimum value (0-based)
  - minpos
```
 static Array<int> minpos(Matrix v, int n)
```
    Returns the positions of the n smallest values in a vector. Equivalent to MATLAB's minpos(v, n) function.
    
    Parameters:
    
    v - Input vector
    
    n - Number of positions to return
    
    Returns:
    
    Array of indices of n smallest values (0-based), sorted by value (ascending)
  - randomMatlabStyle
```
 static boolean randomMatlabStyle()
```
  - roots
```
 static Array<Complex> roots(Matrix coefficients)
```
  - roots
```
 static Array<Complex> roots(Array<double> coefficients)
```
  - setMatlabRandomSeed
```
 static void setMatlabRandomSeed(long seed)
```
  - setRandomNumbersMatlab
```
 static void setRandomNumbersMatlab(boolean matlab_style)
```
  - simplex_fun
```
 static double simplex_fun(Array<double> x, Matrix L, Matrix N)
```
    Computes a specialized function used in simplex-based optimization algorithms. This function evaluates an exponential transformation of the input variables combined with matrix operations involving L and N matrices.
    The function performs the following computation:
    Creates a vector v where v[i] = exp(x[i]) for i = 0..M-2, and v[M-1] = 1
    Computes tmp = log(v * L)^T (element-wise logarithm of matrix product)
    Returns exp(N * tmp + sum(x) - (sum(N) + M) * log(sum(v)))
    This function is typically used in optimization contexts where the variables are constrained to a simplex and require exponential parameterization.
    Parameters:
    
    x - The input vector of optimization variables (length M-1)
    
    L - The transformation matrix for the exponential variables
    
    N - The weighting vector for the final computation
    
    Returns:
    
    The computed function value as a double
  - simplexquad
```
 static Maths.simplexQuadResult simplexquad(Function<Array<double>, Double> f, int n, int order, double tol)
```
  - softmin
```
 static double softmin(double x, double y, double alpha)
```
    Softmin function.
    
    Parameters:
    
    x - first term to compare
    
    y - second term to compare
    
    alpha - softmin smoothing parameter
    
    Returns:
    
    Softmin function value
  - sub2ind
```
 static List<Integer> sub2ind(Matrix dims, Matrix row, Matrix col)
```
  - transpose
```
 static Array<Array<double>> transpose(Array<Array<double>> data)
```
    Transposes a 2D array of values.
    
    Parameters:
    
    data - 2D array to be transposed.
    
    Returns:
    
    New 2D array of transposed data.
  - uniqueAndSort
```
 static Matrix uniqueAndSort(Matrix space)
```
  - uniquePerms
```
 static Matrix uniquePerms(Matrix vec)
```
  - setdiff
```
 static Matrix setdiff(Matrix A, Matrix B)
```
    Set difference operation for Matrix objects that are vectors. Returns elements in A that are not in B.
    
    Parameters:
    
    A - First vector (universe of values to check)
    
    B - Second vector (values to exclude from A)
    
    Returns:
    
    Matrix containing elements in A that are not in B, or empty matrix if inputs are invalid
  - multichoose
```
 static Matrix multichoose(int n, int k)
```
    Generates all combinations of n objects taken k at a time with repetition (multichoose). Returns a Matrix for compatibility with existing code.
    
    Parameters:
    
    n - number of distinct objects
    
    k - total number of selections
    
    Returns:
    
    Matrix where each row is a combination
  - multichooseList
```
 static List<Array<int>> multichooseList(int n, int k)
```
    Generates all combinations of n objects taken k at a time with repetition (multichoose). Each combination is an array where element i represents how many times object i is chosen.
    
    Parameters:
    
    n - number of distinct objects
    
    k - total number of selections
    
    Returns:
    
    list of combinations as int arrays
  - sortByNnzPos
```
 static List<Array<int>> sortByNnzPos(List<Array<int>> combinations)
```
    Sorts combinations by number of non-zeros and their positions.
    
    Parameters:
    
    combinations - list of combinations to sort
    
    Returns:
    
    sorted list of combinations
  - nnzcmp
```
 static int nnzcmp(Array<int> i1, Array<int> i2)
```
    Compares two arrays by number of zeros and their positions. Returns 1 if a <b, -1 if a >b, 0 if equal.
    
    Parameters:
    
    i1 - first array
    
    i2 - second array
    
    Returns:
    
    comparison result
  - matchRow
```
 static int matchRow(List<Array<int>> rows, Array<int> target)
```
    Finds the index of a matching row in a list.
    
    Parameters:
    
    rows - list of integer arrays
    
    target - array to find
    
    Returns:
    
    index of matching row, or -1 if not found
  - nchoosek
```
 static int nchoosek(int n, int k)
```
    Computes binomial coefficient "n choose k".
    
    Parameters:
    
    n - total items
    
    k - items chosen
    
    Returns:
    
    binomial coefficient
  - goldenSectionSearch
```
 static Array<double> goldenSectionSearch(Function<Double, Double> function, double a, double b, double tol)
```
    Golden section search for finding the minimum of a unimodal function. This is equivalent to Python's scipy.optimize.fminbound method.
    
    Parameters:
    
    function - The function to minimize
    
    a - Lower bound of search interval
    
    b - Upper bound of search interval
    
    tol - Tolerance for convergence (default: 1e-5)
    
    Returns:
    
    Array containing [optimal_x, optimal_value]
  - goldenSectionSearch
```
 static Array<double> goldenSectionSearch(Function<Double, Double> function, double a, double b)
```
    Golden section search with default tolerance.
    
    Parameters:
    
    function - The function to minimize
    
    a - Lower bound of search interval
    
    b - Upper bound of search interval
    
    Returns:
    
    Array containing [optimal_x, optimal_value]

Class Maths

Nested Class Summary

Field Summary

Constructor Summary

Enum Constant Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Maths

Method Detail

binomialCoeff

circul

circul

cumSum

cumSum

elementAdd

normalErf

matrixExp

fact

fact

factln

factln

gammaFunction

grnmol

binHist

laplaceapprox_h

laplaceapprox_h_complex

linSpace

logBinomial

logmeanexp

logSpace

logSpacei

max

min

multiChooseCombinations

multiChooseCon

multichoose

multinomialln

nCk

nCk

nextPowerOfTwo

num_grad_h

num_grad_h_complex

num_hess_h

num_hess_h_complex

permutations

rand

randn

probchoose

probchoose

primes

maxpos

maxpos

minpos

minpos

randomMatlabStyle

roots

roots

setMatlabRandomSeed

setRandomNumbersMatlab

simplex_fun

simplexquad

softmin

sub2ind

transpose

uniqueAndSort

uniquePerms

setdiff

multichoose

multichooseList

sortByNnzPos

nnzcmp

matchRow

nchoosek

goldenSectionSearch

goldenSectionSearch