Issue #56:

Divided the initial snippet and added more snippets

products/+elltool/+doc/+snip/s_chapter06_section07_snippet01.m

@@ -4,7 +4,7 @@
 phi0Vec = [0; 0];
 lVec = [5; 5];
 sVec = [3; 3];
-alphaVec = [3; 10];
+
 kVec = [0; 0];
 g = 9.8;
 
@@ -44,37 +44,4 @@
 aMat = [0 0 1 0; 0 0 0 1; y11 y12 y1 y2; x11 x12 x1 x2];
 bMat = [0 0; 0 0; y3 y4; x3 x4];
 
-x0Vec = [0; 0; 0; 0];
-endTime=5;
-% after initializing we create ellipsoid for control function
-diagMat = diag(alphaVec);
-uEllObj = ellipsoid(diagMat);
-% define linear systems
-linSys=elltool.linsys.LinSysContinuous(aMat, bMat, uEllObj);
-% initialize direction matrix
-nShape = 4;
-mSize = 10;
-dirMat = 2*(rand(nShape, mSize) - 0.5);
-for iElem = 1 : mSize
-    dirMat(:, iElem) = dirMat(:, iElem) ./ norm(dirMat(:, iElem));
-end;
-% set of start coordinates
-x0EllObj = 1E-2 * ell_unitball(4) + x0Vec;
-% calculate solvability set
-timeVec = [endTime, 0];
-rsTube = elltool.reach.ReachContinuous(linSys, x0EllObj, dirMat, ...
-    timeVec, 'isRegEnabled', true, 'isJustCheck', false, 'regTol', 1e-3);
-% create projection matrix and draw projection on current axis (z_3, z_4)
-v1v2Mat = [0 0 1 0 ; 0 0 0 1]';
-prTube = rsTube.projection(v1v2Mat);
-prTube.plotByIa();
-hold on;
-ylabel('z_3'); zlabel('z_4');
-rotate3d on;
-% create projection matrix and draw projection on current axis (z_3, z_4)
-v1v2Mat = [1 0 0 0 ; 0 1 0 0]';
-prTube = rsTube.projection(v1v2Mat);
-prTube.plotByIa();
-hold on;
-ylabel('z_1'); zlabel('z_2');
-rotate3d on;
+endTime = 5;

products/+elltool/+doc/+snip/s_chapter06_section07_snippet02.m

@@ -0,0 +1 @@
+alphaVec = [3; 10];

products/+elltool/+doc/+snip/s_chapter06_section07_snippet03.m

@@ -0,0 +1 @@
+alphaVec = [10; 10];

products/+elltool/+doc/+snip/s_chapter06_section07_snippet04.m

@@ -0,0 +1 @@
+x0Vec = [0; 0; 0; 0];

products/+elltool/+doc/+snip/s_chapter06_section07_snippet05.m

@@ -0,0 +1 @@
+x0Vec = [pi / 8; pi / 8; 0; 0];

products/+elltool/+doc/+snip/s_chapter06_section07_snippet06.m

@@ -0,0 +1,24 @@
+% after initializing we create ellipsoid for control function
+diagMat = diag(alphaVec);
+uEllObj = ellipsoid(diagMat);
+% define linear systems
+linSysObj=elltool.linsys.LinSysContinuous(aMat, bMat, uEllObj);
+% initialize direction matrix
+nDims = 4;
+nDirs = 1;
+dirMeshVec = 0 : (2 * pi / nDirs) : 2 * pi;
+dirNum = length(dirMeshVec) ^ nDims;
+[a1, a2, a3, a4] = ndgrid(dirMeshVec, dirMeshVec, dirMeshVec, dirMeshVec);
+lineDir1Mat = reshape(a1, [1, dirNum]);
+lineDir2Mat = reshape(a2, [1, dirNum]);
+lineDir3Mat = reshape(a3, [1, dirNum]);
+lineDir4Mat = reshape(a4, [1, dirNum]);
+dirMat = [lineDir1Mat; lineDir2Mat; lineDir3Mat; lineDir4Mat];
+dirMat = dirMat(:, 2 : end);
+dirMat = dirMat ./ sqrt(repmat(sum(dirMat .^ 2, 1), nDims, 1));
+% set of start coordinates
+x0EllObj = 1E-2 * ell_unitball(4) + x0Vec;
+% calculate solvability set
+timeVec = [endTime, 0];
+rsTubeObj = elltool.reach.ReachContinuous(linSysObj, x0EllObj, dirMat, ...
+    timeVec, 'isRegEnabled', true, 'isJustCheck', false, 'regTol', 1e-3);

products/+elltool/+doc/+snip/s_chapter06_section07_snippet07.m

@@ -0,0 +1,8 @@
+% create projection matrix and draw projection on current axis (z_3, z_4)
+velBasisMat = [0 0 1 0 ; 0 0 0 1]';
+prTubeObj = rsTubeObj.projection(velBasisMat);
+prTubeObj.plotByIa();
+hold on;
+ylabel('z_3'); zlabel('z_4');
+title('Elipsoidal reach tube, proj. on subspace [0 0 1 0 ; 0 0 0 1]');
+rotate3d on; 

products/+elltool/+doc/+snip/s_chapter06_section07_snippet08.m

@@ -0,0 +1,8 @@
+% create projection matrix and draw projection on current axis (z_1, z_2)
+velBasisMat = [1 0 0 0 ; 0 1 0 0]';
+prTubeObj = rsTubeObj.projection(velBasisMat);
+prTubeObj.plotByIa();
+hold on;
+ylabel('z_1'); zlabel('z_2');
+title('Elipsoidal reach tube, proj. on subspace [1 0 0 0 ; 0 1 0 0]');
+rotate3d on;

products/+elltool/+doc/+snip/s_chapter06_section07_snippet09.m

@@ -0,0 +1,8 @@
+% create projection matrix and draw projection on current axis (z_1, z_3)
+velBasisMat = [1 0 0 0 ; 0 0 1 0]';
+prTubeObj = rsTubeObj.projection(velBasisMat);
+prTubeObj.plotByIa();
+hold on;
+ylabel('z_1'); zlabel('z_3');
+title('Elipsoidal reach tube, proj. on subspace [1 0 0 0 ; 0 0 1 0]');
+rotate3d on; 

products/+elltool/+doc/+snip/s_chapter06_section07_snippet10.m

@@ -0,0 +1,8 @@
+% create projection matrix and draw projection on current axis (z_2, z_4)
+velBasisMat = [0 1 0 0 ; 0 0 0 1]';
+prTubeObj = rsTubeObj.projection(velBasisMat);
+prTubeObj.plotByIa();
+hold on;
+ylabel('z_2'); zlabel('z_4');
+title('Elipsoidal reach tube, proj. on subspace [0 1 0 0 ; 0 0 0 1]');
+rotate3d on;