VStats 0.0.1

A (very) basic Linear Algebra, Statistics, and Machine Learning library written from scratch and without dependencies

Modules implemented

The following is the list of functions implemented so far

Linear Algebra (linalg)

Vectors

• add(v []f64, w []f64) []f64: Adds two vectors a and b: (a + b)
• subtract(v []f64, w []f64) []f64: Subtracts two vectors a and b: (a - b)
• vector_sum(vector_list [][]f64) []f64: Sums a list of vectors, example: vector_sum([[f64(1),2],[3,4]]) => [4.0, 6.0]
• scalar_multiply(c f64, v []f64) []f64: Multiplies an scalar value c to each element of a vector v
• vector_mean(vector_list [][]f64) []f64: Calculates 1/n sum_j (v[j])
• dot(v []f64, w []f64) f64: Dot product of v and w
• sum_of_squares(v []f64) f64: Squares each term of a vector, example: [1,2,3]^2 = [1^2, 2^2, 3^2]
• magnitude(v []f64) f64: Module of a vector, example: || [3,4] || = 5
• squared_distance(v []f64, w []f64) f64: Calculates sqrt[(v1-w1)^2 + (v2-w2)^2...]
• distance(v []f64, w []f64) f64: Calculates the distance between v and w

Matrices

• shape(a [][]f64) (int, int): Returns the shape of a matrix (rows, columns)
• get_row(a [][]f64, i int) []f64: Gets the i-th row of a matrix as a vector
• get_column(a [][]f64, j int) []f64: Gets the j-th column of a matrix as a vector
• make_matrix(num_rows int, num_cols int, op fn (int, int) f64) [][]f64: Makes a matrix using a formula given by function op
• identity_matrix(n int) [][]f64: Returns a n-identity matrix
• matmul(a [][]f64, b [][]f64) [][]f64: Multuplies matrix a with b

Probabilites

Distributions (CDF and PDF)

• beta_function(x f64, y f64) f64
• normal_cdf(x f64, mu f64, sigma f64) f64
• inverse_normal_cdf(p f64, mu f64, sigma f64, dp DistribParams) f64
• bernoulli_pdf(x f64, p f64) f64
• bernoulli_cdf(x f64, p f64) f64
• binomial_pdf(k int, n int, p f64) f64
• poisson_pdf(k int, lambda f64) f64
• poisson_cdf(k int, lambda f64) f64
• exponential_pdf(x f64, lambda f64) f64
• exponential_cdf(x f64, lambda f64) f64
• gamma_pdf(x f64, k f64, theta f64) f64
• chi_squared_pdf(x f64, df int) f64
• students_t_pdf(x f64, df int) f64
• f_distribution_pdf(x f64, d1 int, d2 int) f64
• beta_pdf(x f64, alpha f64, beta f64) f64
• uniform_pdf(x f64, a f64, b f64) f64
• uniform_cdf(x f64, a f64, b f64) f64
• negative_binomial_pdf(k int, r int, p f64) f64
• negative_binomial_cdf(k int, r int, p f64) f64
• multinomial_pdf(x []int, p []f64) f64
• expectation(x []f64, p []f64) f64

Statistics

• sum(x []f64) f64
• mean(x []f64) f64
• median(x []f64) f64
• quantile(x []f64, p f64) f64
• mode(x []f64) []f64
• data_range(x []f64) f64
• dev_mean(x []f64) []f64
• variance(x []f64) f64
• standard_deviation(x []f64) f64
• interquartile_range(x []f64) f64
• covariance(x []f64, y []f64) f64
• correlation(x []f64, y []f64) f64

Optimization

• difference_quotient(f fn (f64) f64, x f64, h f64) f64
• partial_difference_quotient(f fn([]f64) f64, v []f64, i int, h f64) f64
• gradient(f fn([]f64) f64, v []f64, h f64) []f64
• gradient_step(v []f64, gradient_vector []f64, step_size f64) []f64
• sum_of_squares_gradient(v []f64) []f64

Disclaimer

• This was written as an exercise to get V closer to Data Analytics and Machine Learning tasks
• Heavily inspired by the book from Joel Grus "Data Science from Scratch: First principles with Python"
• It is not optimized in any way (at least for now)
• Documentation es an ongoing effort

Roadmap

• Add more optimization algorithms
• Complete Hypothesis testing module
• Complete Machine Learning module
• Complete Neural Network module
• Symbolic calculation

Pull requests are welcome!