A new language is best learned through examples. In this section, we collected a number of examples of math scenarios using S2, so you have a better idea of what S2 is capable of. In the other sections of the course, you will learn S2 APIs and math concepts in depth. The S2 platform also allows us to develop data-driven solutions for scientific and business issues.
Using S2 on S2 IDE
If you are using S2 on S2 IDE, please make sure to write the magical keyword %use s2 on a cell and execute the cell before running any line of code. When you have this magic keyword, the S2 IDE will recognize that you are using the S2.
// ALWAYS START THIS MAGICAL KEYWORD USING S2 or nothing will work
%use s2
Using S2 for Linear Algebra
// define a vector
var v = DenseVector(arrayOf(1.1, -2.2, 3.3))
println(v)
// define a matrix
var A = DenseMatrix(arrayOf(
doubleArrayOf(1.0, 2.0, 3.0),
doubleArrayOf(4.0, 5.0, 6.0)))
println(A)
// B = Av
val B = A.multiply(v)
println(B)
OUTPUT: [1.100000, -2.200000, 3.300000] 2x3 [,1] [,2] [,3] [1,] 1.000000, 2.000000, 3.000000, [2,] 4.000000, 5.000000, 6.000000, [6.600000, 13.200000]
Using S2 for Calculus
// define a function f(x)
val f: UnivariateRealFunction = object : AbstractUnivariateRealFunction() {
override fun evaluate(x: Double): Double {
return x.pow(2) + 2*x + 1 // x^2 + 2x + 1
}
}
// find root for a function
val solver = NewtonRoot(1e-9, 10)
val root: Double = solver.solve(f, 0.5)
println(String.format("f(%f) = %f", root, f.evaluate(root)))
OUTPUT: f(-0.998535) = 0.000002
// plot a function
val p = JGnuplot(false)
p.addPlot("x*x + 2*x + 1")
p.plot()
OUTPUT:
// optimization
val solver = BrentMinimizer(1e-15, 20)
val soln = solver.solve(f)
val xmin: Double = soln.minimizer()
val fmin: Double = f.evaluate(xmin)
println(String.format("f(%f) = %f", xmin, fmin))
OUTPUT: f(0.000000) = 1.000000
// differentiate f w.r.t. x once
val df1: UnivariateRealFunction = FiniteDifference(f, 1, FiniteDifference.Type.CENTRAL) // 2x + 2
df1.evaluate(1.0)
// integration
val integrator: Integrator = Riemann()
val I: Double = integrator.integrate(df1, 0.0, 1.0) // ∫_[0,1] (2x + 2) dx = x^2 + 2x
I
OUTPUT: 3.000000000218579
Using S2 for Statistics
// statistics
val gaussian = NormalRNG(0.0, 1.0) // a standard Gaussian random number generator
val numbers: MutableList = mutableListOf()
for (i in 1..10000) { // generate random numbers
val x: Double = gaussian.nextDouble()
numbers.add(x)
}
val arr = numbers.toDoubleArray()
println(Mean(arr).value())
println(Variance(arr).standardDeviation())
println(Skewness(arr).value())
println(Kurtosis(arr).value())
OUTPUT: 0.007440710227587757 0.9934094869218749 -3.733142452297809E-4 -0.003197798050856182
Using S2 to Process Large-scale Data
// Download stock data for "AAPL" between two dates.
val aapl = s2.dataFrame("stock", "AAPL", "2020-01-01", "2020-11-01")
aapl
OUTPUT: A DataFrame: 211 x 10
ticker date open high low close volume dividends closeunadj
1 AAPL 2020-01-02 74.06 75.15 73.797 75.088 135647456 0 300.35
2 AAPL 2020-01-03 74.287 75.145 74.125 74.358 146535512 0 297.43
3 AAPL 2020-01-06 73.448 74.99 73.188 74.95 117288824 0 299.8
4 AAPL 2020-01-07 74.96 75.225 74.37 74.597 111510620 0 298.39
5 AAPL 2020-01-08 74.29 76.11 74.289 75.797 132363784 0 303.19
6 AAPL 2020-01-09 76.809 77.608 76.55 77.407 167082252 0 309.63
7 AAPL 2020-01-10 77.65 78.168 77.062 77.582 140869088 0 310.33
8 AAPL 2020-01-13 77.91 79.267 77.787 79.24 120114968 0 316.96
9 AAPL 2020-01-14 79.175 79.392 78.043 78.17 162613828 0 312.68
10 AAPL 2020-01-15 77.963 78.875 77.388 77.835 121923528 0 311.34
and 201 more rows, and and 1 more variables: 