Package jline.util

Class Maths

java.lang.Object
jline.util.Maths
public class Maths extends Object
Mathematical functions and utilities.

  • Constructor Details

    • Maths

      public Maths()

  • Method Details

    • binomialCoeff

      public 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 kinvalid input: '<'0 or k>n

    • circul

      public 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

      public 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

      public static int[] cumSum(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

      public static double[] cumSum(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

      public static void elementAdd(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

      public 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

      public 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.

      Parameters:
      matrix -
      Returns:
      matrix exponential of the matrix

    • fact

      public static int fact(int n)
      Computes the factorial of an integer.
      Parameters:
      n - the input value
      Returns:
      n! (n factorial)

    • fact

      public 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

      public static double factln(int n)
      Computes the natural logarithm of the factorial.
      Parameters:
      n - the input value
      Returns:
      ln(n!)

    • factln

      public 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

      public 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

      public static Maths.simplexQuadResult grnmol(Function<double[],Double> f, double[][] V, int s, double tol)
      Grundmann-Moeller simplex integration

    • binHist

      public 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

      public static Maths.laplaceApproxReturn laplaceapprox_h(Matrix x0, SerializableFunction<Matrix,Matrix> h)

    • laplaceapprox_h_complex

      public static Maths.laplaceApproxComplexReturn laplaceapprox_h_complex(Matrix x0, SerializableFunction<Matrix,ComplexMatrix> h)

    • linSpace

      public static double[] linSpace(double start, double end, int num)

    • logBinomial

      public 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 kinvalid input: '<'0 or k>n

    • logmeanexp

      public static double logmeanexp(Matrix x)

    • logSpace

      public static double[] logSpace(double min, double max, int n)

    • logSpacei

      public static 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

      public 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

      public 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

      public static List<Matrix> multiChooseCombinations(int k, int n)
      Generate all combinations of distributing n items into k bins

    • multiChooseCon

      public static Matrix multiChooseCon(Matrix n, double S)

    • multichoose

      public static Matrix multichoose(double n, double k)

    • multinomialln

      public static double multinomialln(Matrix n)

    • nCk

      public static double nCk(double n, double k)

    • nCk

      public 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

      protected 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

      public static Matrix num_grad_h(Matrix x0, double h, SerializableFunction<Matrix,Matrix> hfun)

    • num_grad_h_complex

      public static ComplexMatrix num_grad_h_complex(Matrix x0, double h, SerializableFunction<Matrix,ComplexMatrix> hfun)

    • num_hess_h

      public static Matrix num_hess_h(Matrix x0, double h, SerializableFunction<Matrix,Matrix> hfun)

    • num_hess_h_complex

      public static ComplexMatrix num_hess_h_complex(Matrix x0, double h, SerializableFunction<Matrix,ComplexMatrix> hfun)

    • permutations

      public static Matrix permutations(Matrix vec)

    • rand

      public static double rand()

    • randn

      public static double randn()

    • probchoose

      public 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 1.0)
      Returns:
      Index of chosen element (0-based)

    • probchoose

      public 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

      public static List<Integer> primes(int N)

    • maxpos

      public 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

      public static 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

      public 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

      public static 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

      public static boolean randomMatlabStyle()

    • roots

      public static org.apache.commons.math3.complex.Complex[] roots(Matrix coefficients)

    • roots

      public static org.apache.commons.math3.complex.Complex[] roots(double[] coefficients)

    • setMatlabRandomSeed

      public static void setMatlabRandomSeed(long seed)

    • setRandomNumbersMatlab

      public static void setRandomNumbersMatlab(boolean matlab_style)

    • simplex_fun

      public static double simplex_fun(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:

      1. Creates a vector v where v[i] = exp(x[i]) for i = 0..M-2, and v[M-1] = 1
      2. Computes tmp = log(v * L)^T (element-wise logarithm of matrix product)
      3. 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
      Throws:
      IllegalArgumentException - if matrix dimensions are incompatible

    • simplexquad

      public static Maths.simplexQuadResult simplexquad(Function<double[],Double> f, int n, int order, double tol)

    • softmin

      public 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

      public static List<Integer> sub2ind(Matrix dims, Matrix row, Matrix col)

    • transpose

      public static double[][] transpose(double[][] data)
      Transposes a 2D array of values.
      Parameters:
      data - 2D array to be transposed.
      Returns:
      New 2D array of transposed data.

    • uniqueAndSort

      public static Matrix uniqueAndSort(Matrix space)

    • uniquePerms

      public static Matrix uniquePerms(Matrix vec)

    • setdiff

      public 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

      public 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

      public static List<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

      public static List<int[]> sortByNnzPos(List<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

      public static int nnzcmp(int[] i1, int[] i2)
      Compares two arrays by number of zeros and their positions. Returns 1 if a invalid input: '<' b, -1 if a > b, 0 if equal.
      Parameters:
      i1 - first array
      i2 - second array
      Returns:
      comparison result

    • matchRow

      public static int matchRow(List<int[]> rows, 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

      public static int nchoosek(int n, int k)
      Computes binomial coefficient "n choose k".
      Parameters:
      n - total items
      k - items chosen
      Returns:
      binomial coefficient

    • goldenSectionSearch

      public static 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

      public static 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]