FunctionalPlotsExample

Functional Style Plotting

Functional programming opens new opportunities for effective plotting. The following example demonstrates that fact.

Example

// Demonstrates functional style plotting in ScalaLab29

// define and plot the corresponding 1-D function
 val color = Color.BLUE
 val lineplotsFlag = true

  def  fx(x:Double) = { x -sin(x)*x }
  fplot(fx,  1, 10, color, lineplotsFlag)

 def fy(x: Double) = { x-2*cos(x)*x*x }
 fplot(fy, 1, 10, Color.GREEN, false, 1000)


// define as String and plot the corresponding 1-D function
splot("sin(x)", 1, 5, color, lineplotsFlag)

// plot with VISAD
 vsplot("sin(x)", 1, 5)

// plot with JFreeChart
 jsplot("sin(x)", 1, 5)

// define and plot the corresponding 2-D function
def  fxy(x:Double, y: Double) = { x*sin(x)+x*y*cos(y) }
  figure3d; fplot2d(fxy,  1, 10, 1,5)

// define directly as a String and plot the corresponding 1-D function
 figure3d; splot2d("x*y*cos(x*y)", -4, 4, -10, 10)

Adaptive Functional Plotting

Generally, we can improve the plot of a function significantly by adjusting the sampling density according to the rate of function change. The _faplot() method is a first attempt towards adaptive functional plotting. We illustrate it by means of an example: _

// Example: the function sin(x*x) changes generally more rapidly as x increases,
//  however, as can be seen from its derivative x*x*cos(x*x),
//  the rate of change oscilates also with increasing frequency as x increases 
 // Example: the function sin(x*x) changes generally more rapidly as x increases,
//  however, as can be seen from its derivative x*x*cos(x*x),
//  the rate of change oscilates also with increasing frequency as x increases

def f(x: Double) = sin(x*x)

closeAll
var Npoints = 200
figure(1)
subplot(2, 1, 1)
fplot(f, 0, 10, nP = Npoints )
xlabel("Fixed sampled x")
subplot(2, 1, 2)
var (ax, ay) = faplot(f, 0, 10, nP = Npoints)
xlabel("Adaptively sampled x")