testing?

  //var e2_scale = e2_abc.join(",");

  //x3dom_draw_ellipsoid("e2","green",e2_c.toString(),"",e2_scale);

  /*

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e2","green",{

    O:  e2_c,

    Ox: new x3dom.fields.SFVec3f(e2_abc[0],         0,         0),

    Oy: new x3dom.fields.SFVec3f(        0, e2_abc[1],         0),

    Oz: new x3dom.fields.SFVec3f(        0,         0, e2_abc[2])

  },transparency=0.5);

  */

  var RE2 = x3dom.fields.SFMatrix4f.identity();

  //RE2.setValue(xa,ya,za);

  $("#helper_line0").remove();

  $("#helper_line1").remove();

  $("#helper_line3").remove();

  // e1 direction

  x3dom_draw_line("helper_line0","white", e1_c, new x3dom.fields.SFVec3f(0,0,0));

  //x3dom_draw_line("helper_line0","white", e1_c, new x3dom.fields.SFVec3f(0,0,0));

  // e1 direction from e2_c

  x3dom_draw_line("helper_line1","white", e2_c.add(e1_c), e2_c.subtract(e1_c));

  //x3dom_draw_line("helper_line1","white", e2_c.add(e1_c), e2_c.subtract(e1_c));

  x3dom_draw_line("helper_line3","white", e1_c, e2_c);

  // E1: draw tilted ellipsoid

  console.log(RE1.toString());

  /*

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e1b","green",{

    O:  e2_c,

    Ox: xa.multiply(e1_abc[0]),

    Oy: ya.multiply(e1_abc[1]),

    Oz: za.multiply(e1_abc[2])

  },transparency=0.0);

  },transparency=0.5);

  */

  // now let's get to covariance matrix

  var JE1 = x3dom_ellipsoid_inertia_tensor_v2(1,e1_abc[0],e1_abc[1],e1_abc[2]);

  var C2 = RE2xJE2.mult(RE2xJE2.transpose());

  var C = C1.add(C2);

  // testing

  //var C = C1.add(C1);

  Cn = matrix_x3dom_to_numeric(C);

  Bn = numeric.eig(Cn);

  console.log(Bn);

  //console.log(Bn);

  var ee_a = Math.sqrt(Bn.lambda.x[0]);

  var ee_b = Math.sqrt(Bn.lambda.x[1]);

  var ee_c = Math.sqrt(Bn.lambda.x[2]);

  var es_a = Math.sqrt(Bn.lambda.x[0]);

  var es_b = Math.sqrt(Bn.lambda.x[1]);

  var es_c = Math.sqrt(Bn.lambda.x[2]);

  console.log("e1 restored abc: "+[ee_a,ee_b,ee_c].join(" "));

  console.log("e1 restored abc: "+[es_a,es_b,es_c].join(" "));

  var RE1n = new x3dom.fields.SFMatrix4f(

  var RES = new x3dom.fields.SFMatrix4f(

               Bn.E.x[0][0], Bn.E.x[0][1], Bn.E.x[0][2], 0,

               Bn.E.x[1][0], Bn.E.x[1][1], Bn.E.x[1][2], 0,

               Bn.E.x[2][0], Bn.E.x[2][1], Bn.E.x[2][2], 0,

                          0,            0,            0, 1

             );

  console.log(RE1n.toString());

  console.log(RES.toString());

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e1c","red",{

    O:  e2_c,

    Ox: RE1n.e0().multiply(ee_a),

    Oy: RE1n.e1().multiply(ee_b),

    Oz: RE1n.e2().multiply(ee_c)

  },transparency=0.5);

    Ox: RES.e0().multiply(es_a),

    Oy: RES.e1().multiply(es_b),

    Oz: RES.e2().multiply(es_c)

  },transparency=0.7);

  // now get error:

  // we have:

  // 1. e1_c

  // 2. RES and es_a, es_b, es_c

  // RES x e1_c

  var RESi = RES.inverse();

  var E = RESi.multMatrixVec(e1_c.subtract(e2_c));

  console.log("delta vector in ellipsoid:");

  console.log(E.toString());

  E = E.multComponents(new x3dom.fields.SFVec3f(1/es_a, 1/es_b, 1/es_c));

  console.log(E.toString());

  console.log(E.length()*E.length());

  // scale the result ellipsoid so it with touch another marker

  // and it did - it only tests that the scale is correct

  x3dom_draw_ellipsoid_by_semiaxes_and_center("e1d","gold",{

    O:  e2_c,

    Ox: RES.e0().multiply(E.length()*es_a),

    Oy: RES.e1().multiply(E.length()*es_b),

    Oz: RES.e2().multiply(E.length()*es_c)

  },transparency=0.7);

  return 0;