2.3.3 Change data

MathGL has functions for data processing: differentiating, integrating, smoothing and so on (for more detail, see Data processing). Let us consider some examples. The simplest ones are integration and differentiation. The direction in which operation will be performed is specified by textual string, which may contain symbols ‘x’, ‘y’ or ‘z’. For example, the call of Diff("x") will differentiate data along ‘x’ direction; the call of Integral("xy") perform the double integration of data along ‘x’ and ‘y’ directions; the call of Diff2("xyz") will apply 3d Laplace operator to data and so on. Example of this operations on 2d array a=x*y is presented in code:

int sample(mglGraph *gr)
{
  gr->SetRanges(0,1,0,1,0,1);
  mglData a(30,40); a.Modify("x*y");
  gr->SubPlot(2,2,0); gr->Rotate(60,40);
  gr->Surf(a);    gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"a(x,y)");
  gr->SubPlot(2,2,1); gr->Rotate(60,40);
  a.Diff("x");    gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"da/dx");
  gr->SubPlot(2,2,2); gr->Rotate(60,40);
  a.Integral("xy"); gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"\\int da/dx dxdy");
  gr->SubPlot(2,2,3); gr->Rotate(60,40);
  a.Diff2("y"); gr->Surf(a);  gr->Box();
  gr->Puts(mglPoint(0.7,1,1.2),"\\int {d^2}a/dxdy dx");
  return 0;
}

Data smoothing (function Smooth()) is more interesting and important. This function has single argument which define type of smoothing and its direction. Now 3 methods are supported: ‘3’ – linear averaging by 3 points, ‘5’ – linear averaging by 5 points, and default one – quadratic averaging by 5 points.

MathGL also have some amazing functions which is not so important for data processing as useful for data plotting. There are functions for finding envelope (useful for plotting rapidly oscillating data), for data sewing (useful to removing jumps on the phase), for data resizing (interpolation). Let me demonstrate it:

int sample(mglGraph *gr)
{
  gr->SubPlot(2,2,0,"");  gr->Title("Envelop sample");
  mglData d1(1000); gr->Fill(d1,"exp(-8*x^2)*sin(10*pi*x)");
  gr->Axis();     gr->Plot(d1, "b");
  d1.Envelop('x');  gr->Plot(d1, "r");

  gr->SubPlot(2,2,1,"");  gr->Title("Smooth sample");
  mglData y0(30),y1,y2,y3;
  gr->SetRanges(0,1,0,1);
  gr->Fill(y0, "0.4*sin(pi*x) + 0.3*cos(1.5*pi*x) - 0.4*sin(2*pi*x)+0.5*rnd");

  y1=y0;  y1.Smooth("x3");
  y2=y0;  y2.Smooth("x5");
  y3=y0;  y3.Smooth("x");

  gr->Plot(y0,"{m7}:s", "legend 'none'"); //gr->AddLegend("none","k");
  gr->Plot(y1,"r", "legend ''3' style'");
  gr->Plot(y2,"g", "legend ''5' style'");
  gr->Plot(y3,"b", "legend 'default'");
  gr->Legend();   gr->Box();

  gr->SubPlot(2,2,2);   gr->Title("Sew sample");
  mglData d2(100, 100); gr->Fill(d2, "mod((y^2-(1-x)^2)/2,0.1)");
  gr->Rotate(50, 60);   gr->Light(true);  gr->Alpha(true);
  gr->Box();            gr->Surf(d2, "b");
  d2.Sew("xy", 0.1);  gr->Surf(d2, "r");

  gr->SubPlot(2,2,3);   gr->Title("Resize sample (interpolation)");
  mglData x0(10), v0(10), x1, v1;
  gr->Fill(x0,"rnd");     gr->Fill(v0,"rnd");
  x1 = x0.Resize(100);    v1 = v0.Resize(100);
  gr->Plot(x0,v0,"b+ ");  gr->Plot(x1,v1,"r-");
  gr->Label(x0,v0,"%n");
  return 0;
}

Finally one can create new data arrays on base of the existing one: extract slice, row or column of data (SubData()), summarize along a direction(s) (Sum()), find distribution of data elements (Hist()) and so on.

This document was generated on April 13, 2012 using texi2html 5.0.