Vector Operations

open FsAlg.Generic

let v1 = vector [1.; 2.; 3.]
let v2 = Vector.create 3 1.
let v3 = Vector.init 3 (fun i -> exp (float i))

let v4  = v1 + v2  // Vector addition
let v5  = v1 - v2  // Vector substraction
let v6  = v1 * v2  // Vector inner product (dot / scalar product)
let v7  = v1 %* v2 // Vector cross product
let v8  = v1 .* v2 // Vector element-wise (Hadamard) product
let v9  = v1 ./ v2 // Vector element-wise (Hadamard) division
let v10 = v1 + 2.  // Add scalar to vector
let v11 = v1 - 2.  // Subtract scalar from vector
let v12 = 2. - v1  // Subtract each element of vector from scalar
let v13 = v1 * 2.  // Vector-scalar multiplication
let v14 = v1 / 2.  // Vector-scalar division
let v15 = 2. / v1  // Divides each element of vector by scalar
let v16 = -v1      // Unary negation

let n1 = Vector.l1norm v1    // L1 norm
let n2 = Vector.l2norm v1    // L2 norm
let n3 = Vector.l2normSq v1  // Squared L2 norm
let n4 = Vector.lpnorm 3. v1 // Lp norm

let e1 = v1.[0]          // 1st element of v1
let e2 = Vector.get v1 1 // 2nd element of v1
let e3 = v1.[..1]        // Slice, until 2nd element
let e4 = v1.[1..2]       // Slice, between 2nd and 3rd elements
let v20 = Vector.ofSeq [1.; 2.; 3.] // Convert sequence to vector
let v21 = vector [1.; 2.; 3.]       // Same with above, supports lists,
let v22 = vector [|1.; 2.; 3.|]     // arrays,
let v23 = vector (seq {yield 1.})   // and sequences.
let aa1 = Vector.toArray v1 // Convert vector to array
let sq1 = Vector.toSeq v1   // Convert vector to sequence

v1.[0] <- 4. // Mutate an element
Vector.replace (fun x -> x + 2.) v1 // Replace by mapping a function, mutating in place
Vector.replacei (fun i x -> x + float i) v1 // Replace in place, with index
Vector.replace2 (fun x y -> x - y) v1 v2 // Replace v1 in place, using a function of v1 and v2
Vector.replacei2 (fun i x y -> x - y + float i) v1 v2 // Replace v1 in place, with index
Vector.replaceWith v1 v2 // Replace elements of v1 with v2, mutating in place

let ss1 = Vector.splitEqual 3 (vector [1.; 2.; 3.; 4.; 5.; 6.]) // Split into 3 vectors of equal length
let ss2 = Vector.split [2; 4] (vector [1.; 2.; 3.; 4.; 5.; 6.]) // Split into vectors of given lengths
let cc1 = Vector.concat ss1 // Concatenate vectors into one

let s1 = v1.ToMathematicaString()
let s2 = v1.ToMatlabString()

let len = Vector.length v1 // Length of vector
let min = Vector.min v1  // Minimum element of vector
let max = Vector.max v1  // Maximum element of vector
let sum = Vector.sum v1  // Sum elements of vector
let v17 = Vector.unitVector v1 // Get unit vector codirectional with v1
let v18 = Vector.map (fun x -> sin x) v1 // Map function to vector
let v19 = Vector.fold (fun s x -> s + sin x) 0. v1 // Fold a vector