Module math

Expand description

The math module.

Modules§

distributions: Statistical distributions.
fft: Fast fourier transform.
integration: Numerical integration routines. The primary (useful) integrator is the Tanh-Sinh (double exponential) implementation. This module contains functions for numerical integration.
interpolation: Interpolation routines.
optimization: Numerical optimization and root-finding routines.
risk_reward: Simple risk/reward measures.
rootfinding: Root-finding routines.
sequences: Sequences of numbers and associated functions. Sequences of numbers in the style of R’s seq and rep functions.
statistic: Statistic trait.

Bernoulli: Bernoulli distribution: X ~ Bern(p)
Binomial: Binomial distribution: X ~ Bin(n, p)
ChiSquared: Chi-Squared distribution: X ~ ChiSq(k)
Exponential: Exponential distribution: X ~ Exp(lambda)
ExponentialInterpolator: Exponential Interpolator.
Gamma: Gamma distribution
Gaussian: Gaussian (normal) distribution: X ~ N(mu, sigma^2) https://en.wikipedia.org/wiki/Normal_distribution
GradientDescent: Gradient descent optimizer. NOTE: Only for functions $f: \mathbb{R}^n \rightarrow \mathbb{R}$ for now. The gradient descent optimizer is an iterative algorithm that finds the local minimum of a function. The algorithm starts with an initial guess for the local minimum and moves iteratively in the direction of the negative gradient until the gradient is close to zero.
GradientDescentResult: Result of the gradient descent optimization.
LinearInterpolator: Linear Interpolator.
Poisson: Poisson distribution: X ~ Pois(lambda)
PortfolioMeasures: Portfolio struct for risk-reward measures.
Uniform: Uniform distribution: X ~ Uni(a, b)

Distribution: Base trait for all distributions. Provides common methods for all distributions. All distributions must implement this trait.
InterpolationIndex: Trait describing requirements to be an index of interpolation.
InterpolationValue: Trait describing requirements to be interpolated.
Interpolator: Interpolator trait. This trait is implemented by all interpolation models.
Sequence: Trait for generating sequences of numbers.
Statistic: Statistics trait for vectors of floating point numbers.

fft_complex: Complex FFT and returns a new vector, x length must be a power of 2
fft_complex_inplace: Complex FFT inplace, x length must be a power of 2
fft_real: Real FFT and returns a new vector, x length must be a power of 2
fft_real_inplace: Real FFT inplace, x length must be a power of 2
integrate: Integrates a function from a to b. Uses the Tanh-Sinh quadrature over [-1, +1] and then transforms to an integral over [a, b].
is_valid_length: Helper function to check if a vector length is a power of 2