[doc] adding inter and union for IntervalVector and IntervalMatrix, lessonB and C in Matlab

.gitignore

@@ -69,4 +69,7 @@ wheelhouse/
 
 # Graphics files
 examples/**/*.xml
-*.ipe
+*.ipe
+
+# Matlab files
+*.asv

doc/manual/tuto/cp_robotics/lesson_a_static_range_and_bearing.rst

@@ -128,6 +128,31 @@ where :math:`a,b,\dots,e` are intermediate variables used for the decomposition.
     Interval d(4.5,5); // interval for y
     ctc_g.contract(a,d,b);
 
+  .. code-tab:: matlab
+
+    import py.codac4matlab.*
+
+    % Symbolic variables:
+    y = ScalarVar();
+    [x,m] = deal(VectorVar(2),VectorVar(2));
+
+    % Analytic scalar function g(x,m,y) involved in the constraint:
+    g = AnalyticFunction({x,y,m}, sqrt(((x(1)-m(1))^2)+((x(2)-m(2))^2))-y);
+
+    % Contractor associated with the constraint g(x,m,y)\in[u], with [u]=[0,0]
+    ctc_g = CtcInverse(g, 0);
+
+    // Now ctc_g can be called with the .contract(..) method to contract all domains:
+    // Example:
+    a = IntervalVector(2); // box for x
+    b = IntervalVector({{2,3},{5,6.2}}); // box for m
+    d = Interval(4.5,5); // interval for y
+
+    res = ctc_g.contract(cart_prod(a,d,b));
+    a = res.subvector(1,2);
+    b = res.subvector(3,4);
+    c = res(5);
+
 
 Optimality of contractors
 -------------------------
@@ -176,6 +201,17 @@ could be implemented by
     // Contractor associated with the constraint g(x,m,y)\in[u] with [u]=[[0,0],[0,0]]
     CtcInverse ctc_g(g, {0,0}) // {0,0} is equivalent to Vector::zero(2)
 
+  .. code-tab:: matlab
+
+    % Symbolic variables:
+    [x,m,y] = deal(VectorVar(3),VectorVar(2),VectorVar(2));
+
+    % Analytic vectorial function g(x,y,m) involved in the constraint:
+    g = AnalyticFunction({x,y,m}, vec(x(1)+y(1)*cos(x(3)+y(2))-m(1), x(2)+y(1)*sin(x(3)+y(2))-m(2)));
+
+    % Contractor associated with the constraint g(x,m,y)\in[u] with [u]=[[0,0],[0,0]]
+    ctc_g = CtcInverse(g, Vector([0,0])); % [0,0] is equivalent to Vector.zero(2)
+
 However, this involves a multi-occurrence of variables which leads to pessimism. For instance, the sum :math:`(x_3+y_2)` appears twice in functions :math:`\cos` and :math:`\sin`, which is hardly handled by a classical decomposition.
 
 
@@ -266,6 +302,13 @@ A robot depicted by the state :math:`\mathbf{x}=\left(2,1,\pi/6\right)^\intercal
 
       Vector x_truth = {2,1,PI/6}; // actual state vector (pose = position + bearing)
 
+    .. code-tab:: matlab
+
+      % We recall that you can use the Vector class for
+      % representing mathematical vectors. For instance:
+
+      x_truth = Vector([2,1,PI/6]); % actual state vector (pose = position + bearing)
+
   .. container:: toggle, toggle-hidden
 
     .. tabs::
@@ -309,6 +352,10 @@ A robot depicted by the state :math:`\mathbf{x}=\left(2,1,\pi/6\right)^\intercal
 
       x[2] &= x_truth[2]; // the heading is assumed to be known
 
+    .. code-tab:: matlab
+
+      x(3).self_inter(x_truth(3)); % the heading is assumed to be known
+
   .. container:: toggle, toggle-hidden
 
     .. tabs::
@@ -351,6 +398,11 @@ A robot depicted by the state :math:`\mathbf{x}=\left(2,1,\pi/6\right)^\intercal
       DefaultFigure::draw_tank(x_truth, 1, {Color::black(),Color::yellow()}); // robot's size is 1
       DefaultFigure::draw_box(m, Color::red());
 
+    .. code-tab:: matlab
+
+      DefaultFigure().draw_tank(x_truth, 1, StyleProperties({Color().black(),Color().yellow()}));
+      DefaultFigure().draw_box(m,Color().red());
+
   **A.5.** Display the range-and-bearing measurement with its uncertainties. For this, we will use the function ``.draw_pie(<c>, <[rho]>, <[theta]>)`` to display a portion of a ring :math:`[\rho]\times[\theta]` centered on :math:`(x,y)^\intercal`. Here, we must add in :math:`[\theta]` the robot heading :math:`x_3` and the bounded bearing :math:`[y_2]`.
 
   You should obtain this figure:
@@ -370,6 +422,10 @@ A robot depicted by the state :math:`\mathbf{x}=\left(2,1,\pi/6\right)^\intercal
 
       DefaultFigure::draw_pie({<x>, <y>}, <[rho]> | 0, <[theta]>, Color::light_gray()); // with: <[rho]> | 0
 
+    .. code-tab:: matlab
+
+      DefaultFigure().draw_pie(Vector([<x>, <y>]), <[rho]>.union(0), <[theta]>, Color().light_gray()); % with: <[rho]> | 0
+
   .. container:: toggle, toggle-hidden
 
     .. tabs::
@@ -499,6 +555,10 @@ The following code illustrates how to implement such fixpoint:
       etc.
     }, <domains related to c1,c2,..>);
 
+  .. code-tab:: matlab
+
+    % Not supported yet
+
 The ``fixpoint`` function will execute the content of the function ``contractors_list`` until there are no more contractions on the sets listed in ``<domains related to c1,c2,..>``.
 
 .. admonition:: Exercise

doc/manual/tuto/cp_robotics/lesson_b_data_association.rst

@@ -136,6 +136,25 @@ where :math:`\bigsqcup`, called *squared union*, returns the smallest box enclos
           const std::vector<IntervalVector> _M;
       };
 
+    .. code-tab:: matlab
+
+      classdef MyCtc < handle
+
+          properties
+              M
+          end
+
+          methods
+              function obj = MyCtc(M_)
+                  obj.M = M_;
+              end
+
+              function a = contract(obj, a)
+                  % Insert contraction formula here                  
+              end
+          end
+      end
+
   | Note that:
 
   * ``M`` represents the set :math:`\mathbb{M}`, made of 2d ``IntervalVector`` objects;
@@ -169,6 +188,14 @@ where :math:`\bigsqcup`, called *squared union*, returns the smallest box enclos
           :end-before: [B-q2-end]
           :dedent: 2
 
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/MyCtc.m
+          :language: matlab
+          :start-after: [B-q2-beg]
+          :end-before: [B-q2-end]
+          :dedent: 0
+
   **B.3.** Test your contractor with:
 
   * a set :math:`\mathbb{M}=\big\{(1.5,2.5)^\intercal,(3,1)^\intercal,(2,2)^\intercal,(2.5,3)^\intercal,(3.5,2)^\intercal,(4,1)^\intercal,(1.5,0.5)^\intercal\big\}`, all boxes inflated by :math:`[-0.05,0.05]`;
@@ -214,6 +241,24 @@ where :math:`\bigsqcup`, called *squared union*, returns the smallest box enclos
       ctc_constell.contract(a2);
       ctc_constell.contract(a3);
 
+    .. code-tab:: matlab
+
+      M = {IntervalVector([...]),IntervalVector([...]),...
+
+      for i = 1:numel(M)
+          M{i}.inflate(0.05);
+      end
+
+      a1 = IntervalVector({...
+      a2 = IntervalVector({...
+      a3 = IntervalVector({...
+
+      ctc_constell = MyCtc(M);
+
+      a1 = ctc_constell.contract(a1)
+      a2 = ctc_constell.contract(a2)
+      a3 = ctc_constell.contract(a3)
+
   .. container:: toggle, toggle-hidden
 
     .. tabs::
@@ -234,6 +279,14 @@ where :math:`\bigsqcup`, called *squared union*, returns the smallest box enclos
           :end-before: [B-q3-end]
           :dedent: 2
 
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q3-beg]
+          :end-before: [B-q3-end]
+          :dedent: 0
+
 .. figure:: img/CtcConstell_constell.png
   :width: 600px
 
@@ -280,6 +333,14 @@ We will localize the robot in the map :math:`\mathbb{M}` created in Question **B
           :end-before: [B-q4-end]
           :dedent: 2
 
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q4-beg]
+          :end-before: [B-q4-end]
+          :dedent: 0
+
   **B.5.** Display the robot and the landmarks in a graphical view with:
 
   .. tabs::
@@ -300,6 +361,14 @@ We will localize the robot in the map :math:`\mathbb{M}` created in Question **B
         :end-before: [B-q5-end]
         :dedent: 2
 
+    .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q5-beg]
+          :end-before: [B-q5-end]
+          :dedent: 0
+
   You should obtain this result.
 
   .. figure:: img/loc_robot_landmarks.png
@@ -325,6 +394,14 @@ We will localize the robot in the map :math:`\mathbb{M}` created in Question **B
         :end-before: [B-q6-end]
         :dedent: 0
 
+    .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q6-beg]
+          :end-before: [B-q6-end]
+          :dedent: 0
+
   The returned value is a vector of [range]×[bearing] interval values.
 
   Compute and display the measurements in the view with ``.draw_pie()``, as we did in the previous lesson.
@@ -348,6 +425,14 @@ We will localize the robot in the map :math:`\mathbb{M}` created in Question **B
         :end-before: [B-q7-end]
         :dedent: 2
 
+    .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q7-beg]
+          :end-before: [B-q7-end]
+          :dedent: 0
+
   You should obtain a figure similar to this one:
 
   .. figure:: img/loc_robot_landmarks_obs.png
@@ -391,6 +476,14 @@ We will first reuse the fixpoint method of the previous Lesson, and apply it on
           :start-after: [B-q7b-beg]
           :end-before: [B-q7b-end]
           :dedent: 2
+
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q7b-beg]
+          :end-before: [B-q7b-end]
+          :dedent: 0
 
   **B.8.** Display the resulted contracted box :math:`[\mathbf{x}]` with:
 
@@ -414,6 +507,14 @@ We will first reuse the fixpoint method of the previous Lesson, and apply it on
           :end-before: [B-q8-end]
           :dedent: 2
 
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q8-beg]
+          :end-before: [B-q8-end]
+          :dedent: 0
+
   You should obtain this result in black (considering uncertainties proposed in Question **B.6**):
 
   .. figure:: img/loc_robot_landmarks_obs_box.png
@@ -453,6 +554,14 @@ We now assume that the identities of the landmarks are not known. This means tha
           :end-before: [B-q9-end]
           :dedent: 2
 
+      .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q9-beg]
+          :end-before: [B-q9-end]
+          :dedent: 0
+
 
   **B.11.** *Same result* means that the data association worked: each measurement has been automatically associated to the correct landmark without ambiguity.
 
@@ -480,6 +589,14 @@ We now assume that the identities of the landmarks are not known. This means tha
         :end-before: [B-q10-end]
         :dedent: 2
 
+    .. group-tab:: Matlab
+
+        .. literalinclude:: src/lesson_B.m
+          :language: matlab
+          :start-after: [B-q10-beg]
+          :end-before: [B-q10-end]
+          :dedent: 4
+
   Expected result:
 
   .. figure:: img/loc_robot_landmarks_obs_box_id.png