-- HNumeric-0.3.0.0 Documentation
let a = vector [1,2,3] -- Vector declaration
let b = Vector [4,5,6] -- small v and large V are same (for convenient)
-- Print Vector
print a
-- You can (+1) by fmap (Vector is functor)
(+1) <$> a
-- Or MATLAB-like operator (.+, .-, .*, ./, .^)
a .+ 1 -- do not 1 .+ a (. means position of vector)
-- You can make list from vector
toList a -- [1, 2, 3]
-- You can make vector from list
fromList [1,2,3] -- Vector [1,2,3]
-- You can add (subtract, multiply, divide) vectors
a + b -- Vector [5,7,9]
-- Also dot product is here.
a .*. b -- 1*4 + 2*5 + 3*6 = 32
-- Declare Matrix (Syntactic Sugar)
let c = matrix [[1,2],[3,4]]
-- or Declare using R Syntax
let d = Matrix {val = Vector [5,6,7,8], row = 2, col = 2, byRow = True}
-- Determinant
det c
-- Inverse
inv c
-- Transpose
transpose c
-- Matrix ops with Constant (+, -, *, /, ^)
c .+ 1 -- Matrix [[2,3],[4,5]]
-- Matrix ops with Matrix (+, -)
c + c -- Matrix [[2,4],[6,8]]
-- Matrix Multiplication
c %*% d
-- Matrix - Inverse Multiplication
c %/% d
-- Vector Concatenate
hcat a b -- Vector [1,2,3,4,5,6]
vcat a b -- Matrix [[1,2,3],[4,5,6]]
-- Matrix Concatenate
hcat c d -- Matrix [[1,2,5,6],[3,4,7,8]]
vcat c d -- Matrix [[1,2],[3,4],[5,6],[7,8]]
-- Insert Vector to Matrix
vector [1, 2] .: c -- Matrix [[1,2],[1,2],[3,4]]

-- Sample Vector (import Vector)
v = vector [1..10]
w = vector [10, 9 .. 1]
-- Mean
mean v
-- Var
var v
-- Std
std v
-- Cov Matrix
cov v w
-- Only Cov
cov' v w
-- Linear Fit
(intercept, slope) = lm v w -- (11.0, -1.0) -- (Intercept, Slope)
-- Linear Fit function
lineFit (intercept, slope) (Vector [1 .. 20])
-- RSS
rss v w
-- RSE
rse v w