bernoulli
The nth Bernoulli number
Parameters
Name Type Description n number | BigNumber | bigint | Fraction
Returns
number | BigNumber | Fraction —
Examples
bernoulli(4)
combinations
Compute the number of combinations of n items taken k at a time
Syntax
combinations(n | k)
Type Signatures
BigNumber, BigNumber
Parameters
Name Type Description n number | BigNumber Total number of objects in the set k number | BigNumber Number of objects in the subset
Returns
number | BigNumber — Number of possible combinations.
Examples
combinations(7
combinationsWithRep
Compute the number of combinations of n items taken k at a time with replacements.
Syntax
combinationsWithRep(n | k)
Type Signatures
number, number, BigNumber, BigNumber
Parameters
Name Type Description n number | BigNumber Total number of objects in the set k number | BigNumber Number of objects in the subset
Returns
number | BigNumber — Number of possible combinations with replacement.
Examples
combinationsWithRep(7
factorial
Compute the factorial of a value
Parameters
Name Type Description n number | BigNumber | Array | Matrix An integer number
Returns
number | BigNumber | Array | Matrix — The factorial of `n`
Examples
5!
gamma
Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.
Parameters
Name Type Description n number | BigNumber | Complex A real or complex number
Returns
number | BigNumber | Complex — The gamma of `n`
Examples
gamma(4)
kldivergence
Calculate the Kullback-Leibler (KL) divergence between two distributions.
Syntax
kldivergence(x | y)
Type Signatures
Array, Array, Matrix, Array, Array, Matrix, Matrix, Matrix
Parameters
Name Type Description q Array | Matrix First vector p Array | Matrix Second vector
Returns
number — Returns distance between q and p
Examples
kldivergence([0.7
lgamma
Logarithm of the gamma function for real, positive numbers and complex numbers,
Examples
lgamma(4)
multinomial
Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.
Type Signatures
Array | Matrix
Parameters
Name Type Description a number[] | BigNumber[] Integer numbers of objects in the subset
Returns
Number | BigNumber — Multinomial coefficient.
Examples
multinomial([1
permutations
Compute the number of permutations of n items taken k at a time
Syntax
permutations(n) | permutations(n | k)
Type Signatures
number, number, BigNumber, BigNumber
Parameters
Name Type Description n number | BigNumber The number of objects in total k number | BigNumber The number of objects in the subset
Returns
number | BigNumber — The number of permutations
Examples
permutations(5)
pickRandom
Pick a random entry from a given array.
Syntax
pickRandom(array) | pickRandom(array | number)
Type Signatures
Array | Matrix, Array | Matrix, Object, Array | Matrix, number, Array | Matrix, Array | Matrix, Array | Matrix, Array | Matrix, number, Array | Matrix, number, Array | Matrix
Parameters
Name Type Description array Array | Matrix A one dimensional array number Int An int or float weights Array | Matrix An array of ints or floats
Returns
number | Array — Returns a single random value from array when number is undefined.
Examples
pickRandom(0:10)
random
Return a random number.
Syntax
random() | random(max) | random(min
Parameters
Name Type Description size Array | Matrix If provided, an array or matrix with given min number Minimum boundary for the random value, included max number Maximum boundary for the random value, excluded
Returns
number | Array | Matrix — A random number
Examples
random()
randomInt
Return a random integer number
Syntax
randomInt(max) | randomInt(min | max)
Parameters
Name Type Description size Array | Matrix If provided, an array or matrix with given min number Minimum boundary for the random value, included max number Maximum boundary for the random value, excluded
Returns
number | Array | Matrix — A random integer value
Examples
randomInt(10