Added a bunch of functions including vector funcs

Sources/SwiftColabTools/SwiftColabTools.swift

@@ -1,9 +1,5 @@
 import Foundation
 
-struct SwiftColabTools {
-    var text = "Hello, World!"
-}
-
 public func normMarsaglia( ) -> Double {
   var S = 1.1
   var U = Double()
@@ -16,3 +12,92 @@ public func normMarsaglia( ) -> Double {
   }
   return U * sqrt((-2.0 * log(S))/S)
 }
+
+public func norm6Uniform() -> Double {
+  let numSamp = 6
+  var sum = 0.0
+  for k in 0..<numSamp {
+    sum += Double.random(in: 0..<1)
+  }
+  return (sum - Double(numSamp)/2)
+}
+
+public func fzero(fun: (Double)->Double, xzero: Double, xone: Double) -> Double {
+  let eps = 1e-6
+  var x0 = xzero
+  var x1 = xone
+  var y0 = fun(x0)
+  var y1 = fun(x1)
+  /*if y0 * y1 >= 0 {
+    print( "ERROR")
+    return x0
+  }*/
+  var m = (y1 - y0)/(x1 - x0)
+  var besty = min( abs(y0), abs(y1))
+  var bestx = x0
+  while besty > eps {
+    if abs(y1) > abs(y0) {
+      x1 = -y0 / m + x0
+      if x1 < -0.3 {x1 = -0.3}
+      y1 = fun(x1)
+      m = (y1 - y0)/(x1 - x0)
+      besty = min( abs(y0), abs(y1))
+      bestx = x1
+    } else {
+      x0 = -y1 / m + x1
+      if x0 < -0.3 {x0 = -0.3}
+      y0 = fun(x0)
+      m = (y1 - y0)/(x1 - x0)
+      besty = min( abs(y0), abs(y1))
+      bestx = x0
+    }
+    print( bestx)
+  }
+  return bestx
+}
+
+// A timing tool
+public func deltaT(begin: Date) -> Double {
+  let now = DateInterval(start: begin, end: Date())
+  return Double(now.duration)
+}
+
+// Vector tools
+public func vecDZeros(n: Int) -> [Double] {
+  return Array( repeating: 0.0, count: n)
+}
+
+public func vecIZeros(n: Int) -> [Int] {
+  return Array( repeating: 0, count: n)
+}
+
+public func vecsAdd(v1: [Double], v2: [Double]) -> [Double] {
+  return zip(v1, v2).map(+)
+}
+
+public func vecsSubtr(vp: [Double], vn: [Double]) -> [Double] {
+  return zip(vp, vn).map(-)
+}
+
+public func vecsProd(v1: [Double], v2: [Double]) -> [Double] {
+  return zip(v1, v2).map(*)
+}
+
+public func vecSqr(v: [Double]) -> [Double] {
+  return vecsProd(v1: v, v2: v)
+}
+
+public func vecSum(v: [Double]) -> Double {
+  return v.reduce(0.0, +)
+}
+
+public func vecMean(v: [Double]) -> Double {
+  return vecSum(v: v) / Double(v.count)
+}
+
+public func vecSDev(v: [Double]) -> Double {
+  let vbar = vecMean(v: v)
+  let v2bar = vecMean(v: vecSqr(v: v))
+  let n = v.count
+  return sqrt((v2bar - vbar * vbar) * Double(n) / Double((n-1)))
+}