void GLaguer::GetPhylipLaguer(const int categs, MDOUBLE alpha, Vdouble & points, Vdouble & weights)
{
/* calculate rates and probabilities to approximate Gamma distribution
of rates with "categs" categories and shape parameter "alpha" using
rates and weights from Generalized Laguerre quadrature */
points.resize(categs, 0.0);
weights.resize(categs, 0.0);
long i;
raterootarray lgroot; /* roots of GLaguerre polynomials */
double f, x, xi, y;
alpha = alpha - 1.0;
lgroot[1][1] = 1.0+alpha;
for (i = 2; i <= categs; i++)
{
cerr<<lgroot[i][1]<<"\t";
lgr(i, alpha, lgroot); /* get roots for L^(a)_n */
cerr<<lgroot[i][1]<<endl;
}
/* here get weights */
/* Gamma weights are (1+a)(1+a/2) ... (1+a/n)*x_i/((n+1)^2 [L_{n+1}^a(x_i)]^2) */
f = 1;
for (i = 1; i <= categs; i++)
f *= (1.0+alpha/i);
for (i = 1; i <= categs; i++) {
xi = lgroot[categs][i];
y = glaguerre(categs+1, alpha, xi);
x = f*xi/((categs+1)*(categs+1)*y*y);
points[i-1] = xi/(1.0+alpha);
weights[i-1] = x;
}
}
MDOUBLE siteSpecificRateGL::computeML_siteSpecificRate(Vdouble & ratesV,
Vdouble & likelihoodsV,
const Vint& spAttributesVec,
const Vint& treeAttributesVec,
const vector<tree> & etVec,
const vector<const stochasticProcess *> & spVec,
const sequenceContainer& sc,
const MDOUBLE maxRate,
const MDOUBLE tol){
MDOUBLE Lsum = 0.0;
ratesV.resize(sc.seqLen()); // the rates themselves
likelihoodsV.resize(sc.seqLen()); // the log likelihood of each position
for (int pos=0; pos < sc.seqLen(); ++pos) {
LOG(5,<<".");
MDOUBLE bestR=-1.0; // tree1
// MDOUBLE LmaxR1=0;
// getting the right tree for the specific position:
const tree* treeForThisPosition=NULL;
if ((etVec.size() >0 ) && (treeAttributesVec[pos]>0)) {
treeForThisPosition = & etVec[ treeAttributesVec[pos] -1];
} else {
errorMsg::reportError("tree vector is empty, or treeAttribute is empty, or treeAttribute[pos] is zero (it should be one)");
}
// getting the right stochastic process for the specific position:
const stochasticProcess* spForThisPosition=NULL;
if ((spVec.size() >0 ) && (spAttributesVec[pos]>0)) {
spForThisPosition = spVec[ spAttributesVec[pos] -1];
} else {
errorMsg::reportError("stochastic process vector is empty, or spAttributesVec is empty, or spAttribute[pos] is zero (it should be one)");
}
siteSpecificRateGL::computeML_siteSpecificRate(pos,sc,*spForThisPosition,*treeForThisPosition,bestR,likelihoodsV[pos],maxRate,tol);
ratesV[pos] = bestR;
assert(likelihoodsV[pos]>0.0);
Lsum += log(likelihoodsV[pos]);
LOG(5,<<" rate of pos: "<<pos<<" = "<<ratesV[pos]<<endl);
}
LOG(5,<<" number of sites: "<<sc.seqLen()<<endl);
return Lsum;
}
//Input: alf = the alpha parameter of the Laguerre polynomials
// pointsNum = the polynom order
//Output: the abscissas and weights are stored in the vecotrs x and w, respectively.
//Discreption: given alf, the alpha parameter of the Laguerre polynomials, the function returns the abscissas and weights
// of the n-point Guass-Laguerre quadrature formula.
// The smallest abscissa is stored in x[0], the largest in x[pointsNum - 1].
void GLaguer::gaulag(Vdouble &x, Vdouble &w, const MDOUBLE alf, const int pointsNum)
{
x.resize(pointsNum, 0.0);
w.resize(pointsNum, 0.0);
const int MAXIT=10000;
const MDOUBLE EPS=1.0e-6;
int i,its,j;
MDOUBLE ai,p1,p2,p3,pp,z=0.0,z1;
int n= x.size();
for (i=0;i<n;i++) {
//loops over the desired roots
if (i == 0) { //initial guess for the smallest root
z=(1.0+alf)*(3.0+0.92*alf)/(1.0+2.4*n+1.8*alf);
} else if (i == 1) {//initial guess for the second smallest root
z += (15.0+6.25*alf)/(1.0+0.9*alf+2.5*n);
} else { //initial guess for the other roots
ai=i-1;
z += ((1.0+2.55*ai)/(1.9*ai)+1.26*ai*alf/
(1.0+3.5*ai))*(z-x[i-2])/(1.0+0.3*alf);
}
for (its=0;its<MAXIT;its++) { //refinement by Newton's method
p1=1.0;
p2=0.0;
for (j=0;j<n;j++) { //Loop up the recurrence relation to get the Laguerre polynomial evaluated at z.
p3=p2;
p2=p1;
p1=((2*j+1+alf-z)*p2-(j+alf)*p3)/(j+1);
}
//p1 is now the desired Laguerre polynomial. We next compute pp, its derivative,
//by a standard relation involving also p2, the polynomial of one lower order.
pp=(n*p1-(n+alf)*p2)/z;
z1=z;
z=z1-p1/pp; //Newton's formula
if (fabs(z-z1) <= EPS)
break;
}
if (its >= MAXIT)
errorMsg::reportError("too many iterations in gaulag");
x[i]=z;
w[i] = -exp(gammln(alf+n)-gammln(MDOUBLE(n)))/(pp*n*p2);
}
}
MDOUBLE siteSpecificRateGL::computeML_siteSpecificRate(Vdouble & ratesV,
Vdouble & likelihoodsV,
const sequenceContainer& sc,
const stochasticProcess& sp,
const tree& et,
const MDOUBLE maxRate,//20.0f
const MDOUBLE tol){//=0.0001f;
ratesV.resize(sc.seqLen());
likelihoodsV.resize(sc.seqLen());
MDOUBLE Lsum = 0.0;
for (int pos=0; pos < sc.seqLen(); ++pos) {
siteSpecificRateGL::computeML_siteSpecificRate(pos,sc,sp,et,ratesV[pos],likelihoodsV[pos],maxRate,tol);
assert(likelihoodsV[pos]>0.0);
Lsum += log(likelihoodsV[pos]);
LOG(5,<<" rate of pos: "<<pos<<" = "<<ratesV[pos]<<endl);
}
LOG(5,<<" number of sites: "<<sc.seqLen()<<endl);
return Lsum;
}