KotlinSci

Installation and Running

1. Download and unzip

2. Execute the KotlinSci.sh script

Then the Kotlin Interactive Shell is started, and it performs automatically some operations in order to initialize the KotlinSci environment. Also, the KotlinLab graphical environment is displayed, it is useful, but currently code can be executed only with the Kotlin Interactive Shell.

You type code in the embedded Kotlin Interactive Shell, since KotlinSci prepares it automatically by extending its classpath and performing the necessary import statements.

Some code examples follow.

Examples

Ikeda Chaotic map

import kotlin.math.sin as sin
import kotlin.math.cos as cos

// the Ikeda map
// avoids BigDecimal type by explicitly specifying double
var c1 = 0.4
var c2 = 0.9
var c3 = 9.0
var rho = 0.85

var x = 0.5; var y = 0.5
//niters = getInt("How many iterations of the Ikeda map");
var niters = 200000
var xall = DoubleArray(niters)
var yall = DoubleArray(niters)

tic()
for ( k in 0..niters-1 )  {
  var xp = x; var yp=y
  var taut = c1-c3/(1.0+xp*xp+yp*yp)
  x = rho + c2*xp*cos(taut)-yp*sin(taut)
  y = c2*(xp*sin(taut)+yp*cos(taut))
  xall[k] = x
  yall[k] = y
}

var tm = toc()
scatterPlotsOn()
figure(1)
plot(xall, yall, "time = "+tm)

Plotting

figure(1)

var t = inc(0.0, 0.01, 10.0)

var x = sin(t)

var lineSpecs="."
plot(t,x, lineSpecs)

println(t*8.8)
figure(2)
subplot(222)
var x11 = sin(t*4.56)
plot(t,x11)
hold(true)
lineSpecs = ":g"
plot(t,sin(x11*5.0), lineSpecs)
subplot(223)
lineSpecs = ":r"
plot(t,x11, lineSpecs)



// create a new figure and preform a plot at subplot 3,2,1
  figure(3)
 subplot(3,2,1)
 var t2 = inc(0.0, 0.01, 10.0);  var x2 = sin(t2*4.56)+cos(t2*8.7)
 plot(t2,x2, ".-")
 subplot(3,2,3)
var x3 = cos(t2*7.8)+sin(t2*8.9)*8.9
plot(t2, x3)
subplot(3,2,5)
var x4 = cos(t2*7.66)+sin(t2*3.23)*8.665
plot(t2, x4+x3)
subplot(3,2,6)
plot(t2, x4*8.77+x3)
title("x4*8.77+x3")

Plotting with JFreePlot

jfigure(1)

var t = inc(0.0, 0.01, 10.0)

var x = sin(t)

var lineSpecs="."
jplot(t,x, lineSpecs)

println(t*8.8)
jfigure(2)
jsubplot(222)
var x11 = sin(t*4.56)
jplot(t,x11)
jhold(true)
lineSpecs = ":g"
jplot(t,sin(x11*5.0), lineSpecs)
jsubplot(223)
lineSpecs = ":r"
jplot(t,x11, lineSpecs)



// create a new figure and preform a plot at subplot 3,2,1
  jfigure(3)
 jsubplot(3,2,1)
 var t2 = inc(0.0, 0.01, 10.0);  var x2 = sin(t2*4.56)+cos(t2*8.7)
 jplot(t2,x2, ".-")
jsubplot(3,2,3)
var x3 = cos(t2*7.8)+sin(t2*8.9)*8.9
jplot(t2, x3)
jlineColor(1, Color.RED)
jsubplot(3,2,5)
var x4 = cos(t2*7.66)+sin(t2*3.23)*8.665
jplot(t2, x4+x3)
jlineColor(1, Color.GREEN)
jsubplot(3,2,6)
jplot(t2, x4*8.77+x3)
jtitle("x4*8.77+x3")
jlineColor(1, Color.BLUE)

Interpolation using Apache Common Math

import org.apache.commons.math3.analysis.interpolation.*
var x = doubleArrayOf( 0.0, 0.5, 1.0, 1.6,  2.0)
var y = doubleArrayOf( 1.0, 0.7, -1.0, -1.6, 2.0)

var interpolator = SplineInterpolator()
var function  = interpolator.interpolate(x, y)
fun interpf (x: Double) = function.value(x)  // the constructed function from spline interpolation


var fig = figure(1)
var N = 1000
var taxis = linspace(0.0, 2.0, N)
var interpValues = taxis.map(::interpf)  // constructs a plot of the constructed function with spline interpolation
plot( taxis, interpValues, java.awt.Color.GREEN, "Interpolated Curve")
plotMarks(x!!,  y!!)
title( "Demonstration of the Apache Common Maths interpolation")

EigenDecomposition using Apache Common Maths

import org.apache.commons.math3.linear.Array2DRowRealMatrix


// make a Java 2D array
var a2d = arrayOf(
               doubleArrayOf(0.1, -0.3, 0.55, 1.3),
               doubleArrayOf(-0.7, -0.56, 1.23, 0.667),
               doubleArrayOf(-1.23, 0.9, -0.5, 1.8),
               doubleArrayOf(9.4, 0.44, -0.3, 9.2)
             )

// construct with it an Apache Common Maths Array2DRowRealMatrix
var rm = Array2DRowRealMatrix(a2d)

// construct an eigendecomposition object
var splitTolerance = 0.001
var ed =  EigenDecomposition(rm, splitTolerance)

var eigvecs  = ed.getV()