[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

2.3 Data handling

Class mglData contains all functions for the data handling in MathGL (see section Data processing). There are several matters why I use class mglData but not a single array: it does not depend on type of data (mreal or double), sizes of data arrays are kept with data, memory working is simpler and safer.


[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

2.3.1 Array creation

There are many ways in MathGL how data arrays can be created and filled.

One can put the data in mglData instance by several ways. Let us do it for sinus function:

Creation of 2d- and 3d-arrays is mostly the same. But one should keep in mind that class mglData uses flat data representation. For example, matrix 30*40 is presented as flat (1d-) array with length 30*40=1200 (nx=30, ny=40). The element with indexes {i,j} is a[i+nx*j]. So for 2d array we have:

  mglData z(30,40);
  for(int i=0;i<30;i++)   for(int j=0;j<40;j++)
    z.a[i+30*j] = sin(M_PI*i/29.)*sin(M_PI*j/39.);

or by using Modify() function

  mglData z(30,40);
  z.Modify("sin(pi*x)*cos(pi*y)");

The only non-obvious thing here is using multidimensional arrays in C/C++, i.e. arrays defined like mreal dat[40][30];. Since, formally these elements dat[i] can address the memory in arbitrary place you should use the proper function to convert such arrays to mglData object. For C++ this is functions like mglData::Set(mreal **dat, int N1, int N2);. For C this is functions like mgl_data_set_mreal2(HMDT d, const mreal **dat, int N1, int N2);. At this, you should keep in mind that nx=N2 and ny=N1 after conversion.


[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

2.3.2 Linking array

Sometimes the data arrays are so large, that one couldn’t’ copy its values to another array (i.e. into mglData). In this case, he can define its own class derived from mglDataA (see User defined types (mglDataA class)) or can use Link function.

In last case, MathGL just save the link to an external data array, but not copy it. You should provide the existence of this data array for whole time during which MathGL can use it. Another point is that MathGL will automatically create new array if you’ll try to modify data values by any of mglData functions. So, you should use only function with const modifier if you want still using link to the original data array.

Creating the link is rather simple – just the same as using Set function

  double *a = new double[50];
  for(int i=0;i<50;i++)   a[i] = sin(M_PI*i/49.);

  mglData y;
  y.Link(a,50);

[ < ] [ > ]   [ << ] [ Up ] [ >> ]         [Top] [Contents] [Index] [ ? ]

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;
}
Example of data differentiation and integration

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;
}
Example of data manipulation

Also 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.

Another interesting feature of MathGL is interpolation and root-finding. There are several functions for linear and cubic spline interpolation (see Interpolation). Also there is a function evaluate which do interpolation of data array for values of each data element of index data. It look as indirect access to the data elements.

This function have inverse function solve which find array of indexes at which data array is equal to given value (i.e. work as root finding). But solve function have the issue – usually multidimensional data (2d and 3d ones) have an infinite number of indexes which give some value. This is contour lines for 2d data, or isosurface(s) for 3d data. So, solve function will return index only in given direction, assuming that other index(es) are the same as equidistant index(es) of original data. If data have multiple roots then second (and later) branches can be found by consecutive call(s) of solve function. Let me demonstrate this on the following sample.

int sample(mglGraph *gr)
{
  gr->SetRange('z',0,1);
  mglData x(20,30), y(20,30), z(20,30), xx,yy,zz;
  gr->Fill(x,"(x+2)/3*cos(pi*y)");
  gr->Fill(y,"(x+2)/3*sin(pi*y)");
  gr->Fill(z,"exp(-6*x^2-2*sin(pi*y)^2)");

  gr->SubPlot(2,1,0); gr->Title("Cartesian space");   gr->Rotate(30,-40);
  gr->Axis("xyzU");   gr->Box();  gr->Label('x',"x"); gr->Label('y',"y");
  gr->SetOrigin(1,1); gr->Grid("xy");
  gr->Mesh(x,y,z);

  // section along 'x' direction
  mglData u = x.Solve(0.5,'x');
  mglData v(u.nx);  v.Fill(0,1);
  xx = x.Evaluate(u,v);   yy = y.Evaluate(u,v);   zz = z.Evaluate(u,v);
  gr->Plot(xx,yy,zz,"k2o");

  // 1st section along 'y' direction
  mglData u1 = x.Solve(-0.5,'y');
  mglData v1(u1.nx);  v1.Fill(0,1);
  xx = x.Evaluate(v1,u1); yy = y.Evaluate(v1,u1); zz = z.Evaluate(v1,u1);
  gr->Plot(xx,yy,zz,"b2^");

  // 2nd section along 'y' direction
  mglData u2 = x.Solve(-0.5,'y',u1);
  xx = x.Evaluate(v1,u2); yy = y.Evaluate(v1,u2); zz = z.Evaluate(v1,u2);
  gr->Plot(xx,yy,zz,"r2v");

  gr->SubPlot(2,1,1); gr->Title("Accompanied space");
  gr->SetRanges(0,1,0,1); gr->SetOrigin(0,0);
  gr->Axis(); gr->Box();  gr->Label('x',"i"); gr->Label('y',"j");
  gr->Grid(z,"h");

  gr->Plot(u,v,"k2o");    gr->Line(mglPoint(0.4,0.5),mglPoint(0.8,0.5),"kA");
  gr->Plot(v1,u1,"b2^");  gr->Line(mglPoint(0.5,0.15),mglPoint(0.5,0.3),"bA");
  gr->Plot(v1,u2,"r2v");  gr->Line(mglPoint(0.5,0.7),mglPoint(0.5,0.85),"rA");
}
Example of data interpolation and root finding
[ < ] [ > ]   [ << ] [ Up ] [ >> ]

This document was generated on August 12, 2013 using texi2html 1.82.