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#include "computeJumps.h"
#include "talRandom.h"
#include "someUtil.h"
#include "matrixUtils.h"
#include <algorithm>
computeJumps::computeJumps(const MDOUBLE Lambda1, const MDOUBLE Lambda2 , const MDOUBLE r, const int maxNumOfChangesPerBranchSum)
: _Lambda1(Lambda1), _Lambda2(Lambda2),_maxNumOfChangesPerBranchSum(maxNumOfChangesPerBranchSum)
{
if(_Lambda1==_Lambda2)
_Lambda1+=EPSILON; // Patch: fix a BUG, if gain==loss the probability of transition from 0 to 1 given states start==End==1, is NA, thus add epsilon
_gFuncStart0 = gFunc(_Lambda1, _Lambda2, r);
_gFuncStart0MinusR = gFunc(_Lambda1, _Lambda2, -r);
_gFuncStart1 = gFunc(_Lambda2, _Lambda1, r);
_gFuncStart1MinusR = gFunc(_Lambda2, _Lambda1, -r);
}
computeJumps::~computeJumps()
{
}
/********************************************************************************************
getExpectation
*********************************************************************************************/
MDOUBLE computeJumps::getExpectation(const MDOUBLE BranchLength, int terminalStart, int terminalEnd, int fromId, int toId)
{
if(BranchLength>=0){
if(fromId==0 && toId==1){ // Gain
if(terminalStart==0 && terminalEnd==1)
return gainExpGiven01(BranchLength);
if(terminalStart==0 && terminalEnd==0)
return gainExpGiven00(BranchLength);
if(terminalStart==1 && terminalEnd==1)
return gainExpGiven11(BranchLength);
else //(terminalStart==1 && terminalEnd==0)
return gainExpGiven10(BranchLength);
}
if(fromId==1 && toId==0){ // Loss
if(terminalStart==0 && terminalEnd==1)
return lossExpGiven01(BranchLength);
if(terminalStart==0 && terminalEnd==0)
return lossExpGiven00(BranchLength);
if(terminalStart==1 && terminalEnd==1)
return lossExpGiven11(BranchLength);
else //(terminalStart==1 && terminalEnd==0)
return lossExpGiven10(BranchLength);
}
else
return 0;
}
else
return 0;
}
/********************************************************************************************
*********************************************************************************************/
MDOUBLE computeJumps::getTotalExpectation(const MDOUBLE BranchLength, int terminalStart, int terminalEnd)
{
if(BranchLength>=0){
if(terminalStart==0 && terminalEnd==1)
return m01(BranchLength);
if(terminalStart==0 && terminalEnd==0)
return m00(BranchLength);
if(terminalStart==1 && terminalEnd==1)
return m11(BranchLength);
else //(terminalStart==1 && terminalEnd==0)
return m10(BranchLength);
}
else
return 0;
}
/********************************************************************************************
gainExpGivenXY lossExpGivenXY
// Note: divide by Pij, since the computation is gainExp and End=0 given start=0
*********************************************************************************************/
MDOUBLE computeJumps::gainExpGiven01(MDOUBLE BranchLength){
return 0.5*(m01(BranchLength) +Pij_t(0,1,BranchLength))/Pij_t(0,1,BranchLength);
}
MDOUBLE computeJumps::gainExpGiven00(MDOUBLE BranchLength){
return 0.5*(m00(BranchLength)/Pij_t(0,0,BranchLength));
}
MDOUBLE computeJumps::gainExpGiven11(MDOUBLE BranchLength){
return 0.5*(m11(BranchLength)/Pij_t(1,1,BranchLength) ); //???
}
MDOUBLE computeJumps::gainExpGiven10(MDOUBLE BranchLength){
return m10(BranchLength)/Pij_t(1,0,BranchLength) - lossExpGiven10(BranchLength); //???
}
//////////////////////////////////////////////////////////////////////////
MDOUBLE computeJumps::lossExpGiven01(MDOUBLE BranchLength){
return m01(BranchLength)/Pij_t(0,1,BranchLength) - gainExpGiven01(BranchLength); //???
}
MDOUBLE computeJumps::lossExpGiven00(MDOUBLE BranchLength){
return m00(BranchLength)/Pij_t(0,0,BranchLength) - gainExpGiven00(BranchLength); //???
}
MDOUBLE computeJumps::lossExpGiven11(MDOUBLE BranchLength){
return m11(BranchLength)/Pij_t(1,1,BranchLength) - gainExpGiven11(BranchLength); //???
}
MDOUBLE computeJumps::lossExpGiven10(MDOUBLE BranchLength){
return 0.5*(m10(BranchLength) + Pij_t(1,0,BranchLength) )/Pij_t(1,0,BranchLength); //???
//return m10(BranchLength)/Pij_t(1,0,BranchLength) - gainExpGiven10(BranchLength); //???
}
/********************************************************************************************
getProbability
*********************************************************************************************/
MDOUBLE computeJumps::getProb(const MDOUBLE BranchLength, int terminalStart, int terminalEnd, int fromId, int toId)
{
if(BranchLength>=0){
if(fromId==0 && toId==1){ // Gain
if(terminalStart==0 && terminalEnd==1)
return gainProbGiven01(BranchLength);
if(terminalStart==0 && terminalEnd==0)
return gainProbGiven00(BranchLength);
if(terminalStart==1 && terminalEnd==1)
return gainProbGiven11(BranchLength);
else //(terminalStart==1 && terminalEnd==0)
return gainProbGiven10(BranchLength); // if g=l, return -NaN
}
if(fromId==1 && toId==0){ // Loss
if(terminalStart==0 && terminalEnd==1)
return lossProbGiven01(BranchLength); // if g=l, return -NaN
if(terminalStart==0 && terminalEnd==0)
return lossProbGiven00(BranchLength);
if(terminalStart==1 && terminalEnd==1)
return lossProbGiven11(BranchLength);
else //(terminalStart==1 && terminalEnd==0)
return lossProbGiven10(BranchLength);
}
else
return 0;
}
else
return 0;
}
//////////////////////////////////////////////////////////////////////////
MDOUBLE computeJumps::gainProbGiven01(MDOUBLE BranchLength){
MDOUBLE probSum = 1.0;
return probSum;
}
MDOUBLE computeJumps::gainProbGiven00(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(2,4,6,...) changes
//for(int k = 1; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart0.qFunc_2k(BranchLength,k);
//}
//B 1 - Sum(uneven changes) - zeroEvenChanges
probSum = 1 - 0.5*(_gFuncStart0.gFunc_(BranchLength) - _gFuncStart0MinusR.gFunc_(BranchLength)) - _gFuncStart0.qFunc_2k(BranchLength,0);
return probSum/Pij_t(0,0,BranchLength);
}
MDOUBLE computeJumps::gainProbGiven11(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(2,4,6,...) changes
//for(int k = 1; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart1.qFunc_2k(BranchLength,k); //? _gFuncStart1 or _gFuncStart0
//}
//B 1 - Sum(uneven changes) - zeroEvenChanges
probSum = 1 - 0.5*(_gFuncStart1.gFunc_(BranchLength) - _gFuncStart1MinusR.gFunc_(BranchLength)) - _gFuncStart1.qFunc_2k(BranchLength,0);
return probSum/Pij_t(1,1,BranchLength);
}
MDOUBLE computeJumps::gainProbGiven10(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(3,5,7,...) changes
//for(int k = 2; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart1.qFunc_2k_1(BranchLength,k);
//}
//B 1 - Sum(even changes) - oneUnEvenChanges
probSum = 1 - 0.5*(_gFuncStart1.gFunc_(BranchLength) + _gFuncStart1MinusR.gFunc_(BranchLength)) - _gFuncStart1.qFunc_2k_1(BranchLength,1);
return probSum/Pij_t(1,0,BranchLength);
}
//////////////////////////////////////////////////////////////////////////
MDOUBLE computeJumps::lossProbGiven01(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(3,5,7,...) changes
//for(int k = 2; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart0.qFunc_2k_1(BranchLength,k);
//}
//B 1 - Sum(even changes) - oneUnEvenChanges
probSum = 1 - 0.5*(_gFuncStart0.gFunc_(BranchLength) + _gFuncStart0MinusR.gFunc_(BranchLength)) - _gFuncStart0.qFunc_2k_1(BranchLength,1);
return probSum/Pij_t(0,1,BranchLength);
}
MDOUBLE computeJumps::lossProbGiven00(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(2,4,6,...) changes
//for(int k = 1; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart0.qFunc_2k(BranchLength,k);
//}
//B 1 - Sum(uneven changes) - zeroEvenChanges
probSum = 1 - 0.5*(_gFuncStart0.gFunc_(BranchLength) - _gFuncStart0MinusR.gFunc_(BranchLength)) - _gFuncStart0.qFunc_2k(BranchLength,0);
return probSum/Pij_t(0,0,BranchLength);
}
MDOUBLE computeJumps::lossProbGiven11(MDOUBLE BranchLength){
MDOUBLE probSum = 0.0;
//A Sum(2,4,6,...) changes
//for(int k = 1; k<=_maxNumOfChangesPerBranchSum; ++k){
// probSum += _gFuncStart1.qFunc_2k(BranchLength,k); //? _gFuncStart1 or _gFuncStart0
//}
//B 1 - Sum(uneven changes) - zeroEvenChanges
probSum = 1 - 0.5*(_gFuncStart1.gFunc_(BranchLength) - _gFuncStart1MinusR.gFunc_(BranchLength)) - _gFuncStart1.qFunc_2k(BranchLength,0);
return probSum/Pij_t(1,1,BranchLength);
}
MDOUBLE computeJumps::lossProbGiven10(MDOUBLE BranchLength){
MDOUBLE probSum = 1.0;
return probSum;
}
/********************************************************************************************
// mij(t) = E(N, end=j | start=i)
*********************************************************************************************/
MDOUBLE computeJumps::m01(MDOUBLE BranchLength){
return 0.5 *( _gFuncStart0.gFunc_dr(BranchLength) - _gFuncStart0MinusR.gFunc_dr(BranchLength));
}
MDOUBLE computeJumps::m00(MDOUBLE BranchLength){
return 0.5 *( _gFuncStart0.gFunc_dr(BranchLength) + _gFuncStart0MinusR.gFunc_dr(BranchLength));
}
MDOUBLE computeJumps::m11(MDOUBLE BranchLength){
return 0.5 *( _gFuncStart1.gFunc_dr(BranchLength) + _gFuncStart1MinusR.gFunc_dr(BranchLength));
}
MDOUBLE computeJumps::m10(MDOUBLE BranchLength){
return 0.5 *( _gFuncStart1.gFunc_dr(BranchLength) - _gFuncStart1MinusR.gFunc_dr(BranchLength));
}
/********************************************************************************************
gFunc_dr
*********************************************************************************************/
MDOUBLE computeJumps::gFunc_dr(MDOUBLE BranchLength, int startState){
// test:
if(startState == 0){
return _gFuncStart0.g1Func_dr(BranchLength) + _gFuncStart0.g2Func_dr(BranchLength);
}
if(startState == 1)
return _gFuncStart1.g1Func_dr(BranchLength) + _gFuncStart1.g2Func_dr(BranchLength);
else
return 0;
}
/********************************************************************************************
gFunc
*********************************************************************************************/
computeJumps::gFunc::gFunc(const MDOUBLE Lambda1, const MDOUBLE Lambda2 , const MDOUBLE r)
: _Lambda1(Lambda1), _Lambda2(Lambda2), _r(r)
{
_delta = sqrt((_Lambda1+_Lambda2)*(_Lambda1+_Lambda2) + 4*(_r*_r - 1)*_Lambda1*_Lambda2);
_delta_dr = (4*_r*_Lambda1*_Lambda2)/_delta;
_Alpha1 = 0.5*(-_Lambda1-_Lambda2 +_delta);
_Alpha2 = 0.5*(-_Lambda1-_Lambda2 -_delta);
_Alpha1_dr = 0.5*_delta_dr;
_Alpha2_dr = -0.5*_delta_dr;
_Alpha1_2 = _delta; //= _Alpha1 - _Alpha2;
_Alpha1_2_dr = _delta_dr; //= _Alpha1_dr - _Alpha2_dr;
_g1Part = ( (_r-1)*_Lambda1 - _Alpha2)/_Alpha1_2;
_g2Part = (-(_r-1)*_Lambda1 + _Alpha1)/_Alpha1_2;
_g1Part_dr = ( _Alpha1_2*( _Lambda1-_Alpha2_dr) - ( (_r-1)*_Lambda1 - _Alpha2)*_Alpha1_2_dr )/(_Alpha1_2*_Alpha1_2);
_g2Part_dr = ( _Alpha1_2*(-_Lambda1+_Alpha1_dr) - (-(_r-1)*_Lambda1 + _Alpha1)*_Alpha1_2_dr )/(_Alpha1_2*_Alpha1_2);
}
//////////////////////////////////////////////////////////////////////////
MDOUBLE computeJumps::gFunc::gFunc_dr(MDOUBLE BranchLength){
return sign(_r)*(g1Func_dr(BranchLength) + g2Func_dr(BranchLength));
}
MDOUBLE computeJumps::gFunc::g1Func_dr(MDOUBLE BranchLength){
return _g1Part_dr*g1Exp(BranchLength) + _g1Part*g1Exp(BranchLength)*BranchLength*_Alpha1_dr;
}
MDOUBLE computeJumps::gFunc::g2Func_dr(MDOUBLE BranchLength){
return _g2Part_dr*g2Exp(BranchLength) + _g2Part*g2Exp(BranchLength)*BranchLength*_Alpha2_dr;
}
//////////////////////////////////////////////////////////////////////////
MDOUBLE computeJumps::gFunc::g1Exp(MDOUBLE BranchLength){
return exp(_Alpha1*BranchLength);
}
MDOUBLE computeJumps::gFunc::g2Exp(MDOUBLE BranchLength){
return exp(_Alpha2*BranchLength);
}
MDOUBLE computeJumps::gFunc::gFunc_(MDOUBLE BranchLength){
return _g1Part*g1Exp(BranchLength) + _g2Part*g2Exp(BranchLength);
};
MDOUBLE computeJumps::gFunc::_A_(int k, int i){return BinomialCoeff((k+i-1),i) * pow(-1.0,i)*pow(_Lambda1,k)*pow(_Lambda2,(k-1)) / pow((_Lambda2-_Lambda1),(k+i)) ; }
MDOUBLE computeJumps::gFunc::_B_(int k, int i){return BinomialCoeff((k+i-1),i) * pow(-1.0,i)*pow(_Lambda1,k)*pow(_Lambda2,(k-1)) / pow((_Lambda1-_Lambda2),(k+i)) ; }
MDOUBLE computeJumps::gFunc::_C_(int k, int i){return BinomialCoeff((k+i-1),i) * pow(-1.0,i)*pow(_Lambda1,k)*pow(_Lambda2,(k)) / pow((_Lambda2-_Lambda1),(k+i)) ; }
MDOUBLE computeJumps::gFunc::_D_(int k, int i){return BinomialCoeff((k+i),i) * pow(-1.0,i)*pow(_Lambda1,k)*pow(_Lambda2,(k)) / pow((_Lambda1-_Lambda2),(k+i+1)); }
// prob for (2k-1) transitions (gains and losses), given start=0
MDOUBLE computeJumps::gFunc::qFunc_2k_1 (MDOUBLE BranchLength, int k){
MDOUBLE qSUM = 0.0;
for(int i=1; i<=k; ++i){
qSUM += _A_(k,(k-i))* pow(BranchLength,(i-1))/factorial(i-1) * exp(-_Lambda1*BranchLength)
+ _B_(k,(k-i))* pow(BranchLength,(i-1))/factorial(i-1) * exp(-_Lambda2*BranchLength);
}
return qSUM;
}
// prob for (2k) transitions (gains and losses), given start=0
MDOUBLE computeJumps::gFunc::qFunc_2k (MDOUBLE BranchLength, int k){
MDOUBLE qSUM = 0.0;
for(int i=1; i<=(k+1); ++i){
qSUM += _C_(k,(k-i+1))* pow(BranchLength,(i-1))/factorial(i-1)*exp(-_Lambda1*BranchLength);
}
for(int i=1; i<=k; ++i){
qSUM += _D_(k,(k-i))* pow(BranchLength,(i-1))/factorial(i-1)*exp(-_Lambda2*BranchLength);
}
return qSUM;
}
/********************************************************************************************
Pij_t - Based on Analytic solution
*********************************************************************************************/
MDOUBLE computeJumps::Pij_t(const int i,const int j, const MDOUBLE d) {
MDOUBLE gain = _Lambda1;
MDOUBLE loss = _Lambda2;
MDOUBLE eigenvalue = -(gain + loss);
VVdouble Pt;
int AlphaSize = 2;
resizeMatrix(Pt,AlphaSize,AlphaSize);
int caseNum = i + j*2;
switch (caseNum) {
case 0 : Pt[0][0] = loss/(-eigenvalue) + exp(eigenvalue*d)*(1 - loss/(-eigenvalue)); break;
case 1 : Pt[1][0] = loss/(-eigenvalue) - exp(eigenvalue*d)*(1 - gain/(-eigenvalue)); break;
case 2 : Pt[0][1] = gain/(-eigenvalue) - exp(eigenvalue*d)*(1 - loss/(-eigenvalue)); break;
case 3 : Pt[1][1] = gain/(-eigenvalue) + exp(eigenvalue*d)*(1 - gain/(-eigenvalue)); break;
}
MDOUBLE val = (Pt[i][j]);
return val;
}
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