issue #56:

fix names of variables

products/+elltool/+doc/+snip/s_chapter06_section06_snippet01.m

@@ -1,53 +1,53 @@
 % initialize all variables for this model
-m = [1; 2];
-J = [0; 0];
-phi_0 = [0; 0];
-L = [5; 5];
-s = [3; 3];
-alpha = [3; 10];
-k = [0; 0];
+mVec = [1; 2];
+jVec = [0; 0];
+phi0Vec = [0; 0];
+LVec = [5; 5];
+sVec = [3; 3];
+alphaVec = [3; 10];
+kVec = [0; 0];
 g = 9.8;
 
-a_1 = m(1) * s(1)^2 + J(1) + m(2) * L(1)^2;
-a_2 = L(1) * s(2) * cos(phi_0(1) - phi_0(2));
-b_1 = L(1) * s(2) * cos(phi_0(1) - phi_0(2));
-b_2 = m(2) * s(2)^2 + J(2);
+a1 = mVec(1) * sVec(1)^2 + jVec(1) + mVec(2) * LVec(1)^2;
+a2 = LVec(1) * sVec(2) * cos(phi0Vec(1) - phi0Vec(2));
+b1 = LVec(1) * sVec(2) * cos(phi0Vec(1) - phi0Vec(2));
+b2 = mVec(2) * sVec(2)^2 + jVec(2);
 
-d_1 = (m(1) * a_1 + m(2) * L(2)) * g;
-d_2 = m(2) * a_2 * g;
+d1 = (mVec(1) * a1 + mVec(2) * LVec(2)) * g;
+d2 = mVec(2) * a2 * g;
 
-X_1 = -k(1) * a_2 / (a_2 * b_1 - a_1 * b_2);
-X_2 = k(2) * a_1 / (a_2 * b_1 - a_1 * b_2);
-X_3 = a_2 / (a_2 * b_1 - a_1 * b_2);
-X_4 = -a_1 / (a_2 * b_1 - a_1 * b_2);
-X_5 = -(d_1 * a_2 + d_2 * a_1) / (a_2 * b_1 - a_1 * b_2);
+X1 = -kVec(1) * a2 / (a2 * b1 - a1 * b2);
+X2 = kVec(2) * a1 / (a2 * b1 - a1 * b2);
+X3 = a2 / (a2 * b1 - a1 * b2);
+X4 = -a1 / (a2 * b1 - a1 * b2);
+X5 = -(d1 * a2 + d2 * a1) / (a2 * b1 - a1 * b2);
 
-Y_1 = -k(1) * b_2 / (a_2 * b_1 - a_1 * b_2);
-Y_2 = k(2) * b_1 / (a_2 * b_1 - a_1 * b_2);
-Y_3 = b_2 / (a_2 * b_1 - a_1 * b_2);
-Y_4 = -b_1 / (a_2 * b_1 - a_1 * b_2);
-Y_5 = (d_2 * b_1 - d_1 * b_2) / (a_2 * b_1 - a_1 * b_2);
+Y1 = -kVec(1) * b2 / (a2 * b1 - a1 * b2);
+Y2 = kVec(2) * b1 / (a2 * b1 - a1 * b2);
+Y3 = b2 / (a2 * b1 - a1 * b2);
+Y4 = -b1 / (a2 * b1 - a1 * b2);
+Y5 = (d2 * b1 - d1 * b2) / (a2 * b1 - a1 * b2);
 
-X_11 = d_1 * a_2 * sin(phi_0(1)) / (a_2 * b_1 - a_1 * b_2);
-X_12 = d_2 * a_1 * sin(phi_0(2)) / (a_2 * b_1 - a_1 * b_2);
-X_13 = (-d_1 * a_2 * cos(phi_0(1)) - d_1 * a_2 * sin(phi_0(1)) * phi_0(1)) / ...
-    (a_2 * b_1 - a_1 * b_2) + (-d_2 * a_1 * cos(phi_0(2)) - ...
-    d_2 * a_1 * sin(phi_0(2)) * phi_0(2)) / (a_2 * b_1 - a_1 * b_2);
+X11 = d1 * a2 * sin(phi0Vec(1)) / (a2 * b1 - a1 * b2);
+X12 = d2 * a1 * sin(phi0Vec(2)) / (a2 * b1 - a1 * b2);
+X13 = (-d1 * a2 * cos(phi0Vec(1)) - d1 * a2 * sin(phi0Vec(1)) * phi0Vec(1)) / ...
+    (a2 * b1 - a1 * b2) + (-d2 * a1 * cos(phi0Vec(2)) - ...
+    d2 * a1 * sin(phi0Vec(2)) * phi0Vec(2)) / (a2 * b1 - a1 * b2);
 
-Y_11 = d_1 * b_2 * sin(phi_0(1)) / (a_2 * b_1 - a_1 * b_2);
-Y_12 = -d_2 * b_1 * sin(phi_0(2)) / (a_2 * b_1 - a_1 * b_2);
-Y_13 = (d_2 * b_1 * cos(phi_0(2)) + d_2 * b_1 * sin(phi_0(2)) * phi_0(2)) / ...
-    (a_2 * b_1 - a_1 * b_2) + (-d_1 * b_2 * cos(phi_0(1)) - ...
-    d_1 * b_2 * sin(phi_0(1)) * phi_0(1)) / (a_2 * b_1 - a_1 * b_2);
+Y11 = d1 * b2 * sin(phi0Vec(1)) / (a2 * b1 - a1 * b2);
+Y12 = -d2 * b1 * sin(phi0Vec(2)) / (a2 * b1 - a1 * b2);
+Y13 = (d2 * b1 * cos(phi0Vec(2)) + d2 * b1 * sin(phi0Vec(2)) * phi0Vec(2)) / ...
+    (a2 * b1 - a1 * b2) + (-d1 * b2 * cos(phi0Vec(1)) - ...
+    d1 * b2 * sin(phi0Vec(1)) * phi0Vec(1)) / (a2 * b1 - a1 * b2);
 
 %initialize A and B relying on theoretical materials
-aMat = [0 0 1 0; 0 0 0 1; Y_11 Y_12 Y_1 Y_2; X_11 X_12 X_1 X_2];
-bMat = [0 0; 0 0; Y_3 Y_4; X_3 X_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];
 
-x_0 = [0; 0; 0; 0];
+x0Vec = [0; 0; 0; 0];
 endTime=5;
 % after initializing we create ellipsoid for control function
-diagMat = diag([alpha(1), alpha(2)]);
+diagMat = diag(alphaVec);
 uEllObj = ellipsoid(diagMat);
 % define linear systems
 linSys=elltool.linsys.LinSysContinuous(aMat, bMat, uEllObj);
@@ -58,10 +58,8 @@
 for iElem = 1 : mSize
     dirMat(:, iElem) = dirMat(:, iElem) ./ norm(dirMat(:, iElem));
 end;
-% end position
-
 % set of start coordinates
-x0EllObj = 1E-2 * ell_unitball(4) + x_0;
+x0EllObj = 1E-2 * ell_unitball(4) + x0Vec;
 % calculate solvability set
 timeVec = [endTime, 0];
 rsTube = elltool.reach.ReachContinuous(linSys, x0EllObj, dirMat, ...
@@ -72,4 +70,11 @@
 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;