tempest/resources/3rdparty/eigen/test/geo_homogeneous.cpp/tempest/examples/mdp/csma/csma2_4.nm

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Geometry>

template<typename Scalar,int Size> void homogeneous(void)
{
  /* this test covers the following files:
     Homogeneous.h
  */

  typedef Matrix<Scalar,Size,Size> MatrixType;
  typedef Matrix<Scalar,Size,1, ColMajor> VectorType;

  typedef Matrix<Scalar,Size+1,Size> HMatrixType;
  typedef Matrix<Scalar,Size+1,1> HVectorType;

  typedef Matrix<Scalar,Size,Size+1>   T1MatrixType;
  typedef Matrix<Scalar,Size+1,Size+1> T2MatrixType;
  typedef Matrix<Scalar,Size+1,Size> T3MatrixType;

  VectorType v0 = VectorType::Random(),
             ones = VectorType::Ones();

  HVectorType hv0 = HVectorType::Random();

  MatrixType m0 = MatrixType::Random();

  HMatrixType hm0 = HMatrixType::Random();

  hv0 << v0, 1;
  VERIFY_IS_APPROX(v0.homogeneous(), hv0);
  VERIFY_IS_APPROX(v0, hv0.hnormalized());

  hm0 << m0, ones.transpose();
  VERIFY_IS_APPROX(m0.colwise().homogeneous(), hm0);
  VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());
  hm0.row(Size-1).setRandom();
  for(int j=0; j<Size; ++j)
    m0.col(j) = hm0.col(j).head(Size) / hm0(Size,j);
  VERIFY_IS_APPROX(m0, hm0.colwise().hnormalized());

  T1MatrixType t1 = T1MatrixType::Random();
  VERIFY_IS_APPROX(t1 * (v0.homogeneous().eval()), t1 * v0.homogeneous());
  VERIFY_IS_APPROX(t1 * (m0.colwise().homogeneous().eval()), t1 * m0.colwise().homogeneous());

  T2MatrixType t2 = T2MatrixType::Random();
  VERIFY_IS_APPROX(t2 * (v0.homogeneous().eval()), t2 * v0.homogeneous());
  VERIFY_IS_APPROX(t2 * (m0.colwise().homogeneous().eval()), t2 * m0.colwise().homogeneous());

  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t2,
                    v0.transpose().rowwise().homogeneous() * t2);
                    m0.transpose().rowwise().homogeneous().eval();
  VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t2,
                    m0.transpose().rowwise().homogeneous() * t2);

  T3MatrixType t3 = T3MatrixType::Random();
  VERIFY_IS_APPROX((v0.transpose().rowwise().homogeneous().eval()) * t3,
                    v0.transpose().rowwise().homogeneous() * t3);
  VERIFY_IS_APPROX((m0.transpose().rowwise().homogeneous().eval()) * t3,
                    m0.transpose().rowwise().homogeneous() * t3);

  // test product with a Transform object
  Transform<Scalar, Size, Affine> aff;
  Transform<Scalar, Size, AffineCompact> caff;
  Transform<Scalar, Size, Projective> proj;
  Matrix<Scalar, Size, Dynamic>   pts;
  Matrix<Scalar, Size+1, Dynamic> pts1, pts2;

  aff.affine().setRandom();
  proj = caff = aff;
  pts.setRandom(Size,internal::random<int>(1,20));
  
  pts1 = pts.colwise().homogeneous();
  VERIFY_IS_APPROX(aff  * pts.colwise().homogeneous(), (aff  * pts1).colwise().hnormalized());
  VERIFY_IS_APPROX(caff * pts.colwise().homogeneous(), (caff * pts1).colwise().hnormalized());
  VERIFY_IS_APPROX(proj * pts.colwise().homogeneous(), (proj * pts1));
  
  VERIFY_IS_APPROX((aff  * pts1).colwise().hnormalized(),  aff  * pts);
  VERIFY_IS_APPROX((caff * pts1).colwise().hnormalized(), caff * pts);
  
  pts2 = pts1;
  pts2.row(Size).setRandom();
  VERIFY_IS_APPROX((aff  * pts2).colwise().hnormalized(), aff  * pts2.colwise().hnormalized());
  VERIFY_IS_APPROX((caff * pts2).colwise().hnormalized(), caff * pts2.colwise().hnormalized());
  VERIFY_IS_APPROX((proj * pts2).colwise().hnormalized(), (proj * pts2.colwise().hnormalized().colwise().homogeneous()).colwise().hnormalized());
}

void test_geo_homogeneous()
{
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1(( homogeneous<float,1>() ));
    CALL_SUBTEST_2(( homogeneous<double,3>() ));
    CALL_SUBTEST_3(( homogeneous<double,8>() ));
  }
}
// CSMA/CD protocol - probabilistic version of kronos model (3 stations)
// gxn/dxp 04/12/01

mdp

// note made changes since cannot have strict inequalities
// in digital clocks approach and suppose a station only sends one message

// simplified parameters scaled
const int sigma=1; // time for messages to propagate along the bus
const int lambda=30; // time to send a message

// actual parameters
const int N = 2; // number of processes
const int K = 4; // exponential backoff limit
const int slot = 2*sigma; // length of slot
const int M = 15 ; // max number of slots to wait
//const int lambda=782;
//const int sigma=26;


//----------------------------------------------------------------------------------------------------------------------------
// the bus
module bus
	
	b : [0..2];
	// b=0 - idle
	// b=1 - active
	// b=2 - collision
	
	// clocks of bus
	y1 : [0..sigma+1]; // time since first send (used find time until channel sensed busy)
	y2 : [0..sigma+1]; // time since second send (used to find time until collision detected)
	
	// a sender sends (ok - no other message being sent)
	[send1] (b=0) -> (b'=1);
	[send2] (b=0) -> (b'=1);
	
	// a sender sends (bus busy - collision)
	[send1] (b=1|b=2) & (y1<sigma) -> (b'=2);
	[send2] (b=1|b=2) & (y1<sigma) -> (b'=2);
	
	// finish sending
	[end1] (b=1) -> (b'=0) & (y1'=0);
	[end2] (b=1) -> (b'=0) & (y1'=0);
	
	// bus busy
	[busy1] (b=1|b=2) & (y1>=sigma) -> (b'=b);  
	[busy2] (b=1|b=2) & (y1>=sigma) -> (b'=b);  
	
	// collision detected
	[cd] (b=2) & (y2<=sigma) -> (b'=0) & (y1'=0) & (y2'=0);
	
	// time passage
	[time] (b=0) -> (y1'=0); // value of y1/y2 does not matter in state 0
	[time] (b=1) -> (y1'=min(y1+1,sigma+1)); // no invariant in state 1
	[time] (b=2) & (y2<sigma) -> (y1'=min(y1+1,sigma+1)) & (y2'=min(y2+1,sigma+1)); // invariant in state 2 (time until collision detected)
	
endmodule

//----------------------------------------------------------------------------------------------------------------------------
// model of first sender
module station1
	
	// LOCAL STATE
	s1 : [0..5];
	// s1=0 - initial state
	// s1=1 - transmit
	// s1=2 - collision (set backoff)
	// s1=3 - wait (bus busy)
	// s1=4 - successfully sent
	
	// LOCAL CLOCK
	x1 : [0..max(lambda,slot)];
	
	// BACKOFF COUNTER (number of slots to wait)
	bc1 : [0..M];
	
	// COLLISION COUNTER
	cd1 : [0..K];
	
	// start sending
	[send1] (s1=0) -> (s1'=1) & (x1'=0); // start sending
	[busy1] (s1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // detects channel is busy so go into backoff
	
	// transmitting
	[time] (s1=1) & (x1<lambda) -> (x1'=min(x1+1,lambda)); // let time pass
	[end1]  (s1=1) & (x1=lambda) -> (s1'=4) & (x1'=0); // finished
	[cd]   (s1=1) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // collision detected (increment backoff counter)
	[cd] !(s1=1) -> (s1'=s1); // add loop for collision detection when not important
	
	// set backoff (no time can pass in this state)
	// probability depends on which transmission this is (cd1)
	[] s1=2 & cd1=1 ->  1/2 : (s1'=3) & (bc1'=0) + 1/2 : (s1'=3) & (bc1'=1) ;
	[] s1=2 & cd1=2 ->  1/4 : (s1'=3) & (bc1'=0) + 1/4 : (s1'=3) & (bc1'=1) + 1/4 : (s1'=3) & (bc1'=2) + 1/4 : (s1'=3) & (bc1'=3) ;
	[] s1=2 & cd1=3 ->  1/8 : (s1'=3) & (bc1'=0) + 1/8 : (s1'=3) & (bc1'=1) + 1/8 : (s1'=3) & (bc1'=2) + 1/8 : (s1'=3) & (bc1'=3) + 1/8 : (s1'=3) & (bc1'=4) + 1/8 : (s1'=3) & (bc1'=5) + 1/8 : (s1'=3) & (bc1'=6) + 1/8 : (s1'=3) & (bc1'=7) ;
	[] s1=2 & cd1=4 ->  1/16 : (s1'=3) & (bc1'=0) + 1/16 : (s1'=3) & (bc1'=1) + 1/16 : (s1'=3) & (bc1'=2) + 1/16 : (s1'=3) & (bc1'=3) + 1/16 : (s1'=3) & (bc1'=4) + 1/16 : (s1'=3) & (bc1'=5) + 1/16 : (s1'=3) & (bc1'=6) + 1/16 : (s1'=3) & (bc1'=7) + 1/16 : (s1'=3) & (bc1'=8) + 1/16 : (s1'=3) & (bc1'=9) + 1/16 : (s1'=3) & (bc1'=10) + 1/16 : (s1'=3) & (bc1'=11) + 1/16 : (s1'=3) & (bc1'=12) + 1/16 : (s1'=3) & (bc1'=13) + 1/16 : (s1'=3) & (bc1'=14) + 1/16 : (s1'=3) & (bc1'=15) ;
	
	// wait until backoff counter reaches 0 then send again
	[time] (s1=3) & (x1<slot) -> (x1'=x1+1); // let time pass (in slot)
	[time] (s1=3) & (x1=slot) & (bc1>0) -> (x1'=1) & (bc1'=bc1-1); // let time pass (move slots)
	[send1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=1) & (x1'=0); // finished backoff (bus appears free)
	[busy1] (s1=3) & (x1=slot) & (bc1=0) -> (s1'=2) & (x1'=0) & (cd1'=min(K,cd1+1)); // finished backoff (bus busy)
	
	// once finished nothing matters
	[time] (s1>=4) -> (x1'=0);

endmodule

//----------------------------------------------------------------------------------------------------------------------------

// construct further stations through renaming
module station2=station1[s1=s2,x1=x2,cd1=cd2,bc1=bc2,send1=send2,busy1=busy2,end1=end2] endmodule

//----------------------------------------------------------------------------------------------------------------------------

// reward structure for expected time
rewards "time"
	[time] true : 1;
endrewards

//----------------------------------------------------------------------------------------------------------------------------

// labels/formulae
label "all_delivered" = s1=4&s2=4;
label "one_delivered" = s1=4|s2=4;
label "collision_max_backoff" = (cd1=K & s1=1 & b=2)|(cd2=K & s2=1 & b=2);