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EukPhylo/PTL2/Scripts-DEV/guidance.v2.02/libs/phylogeny/numRec.h
Katzlab dd76ab1d12 Added PTL2 Scripts 
These are PTL2 files from Auden 2/9
2023-02-14 11:20:52 -05:00

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// $Id: numRec.h 9652 2011-07-12 13:59:26Z rubi $
// version 1.00
// last modified 2 Nov 2002
#ifndef ___NUM_REC
#define ___NUM_REC
#include <cmath>
#include <cassert>
#include <iostream>
using namespace std;
#include "definitions.h"
#include "errorMsg.h"
#include "uniformDistribution.h"
#include "logFile.h"
//#define VERBOS
#define SIGN(a,b) ((b) >= 0.0 ? fabs(a) : -fabs(a))
//========================== function brent =========================================
template <typename regF>
MDOUBLE brent(MDOUBLE ax, MDOUBLE bx, MDOUBLE cx, regF f, MDOUBLE tol,
MDOUBLE *xmin) {
const int ITMAX = 100;
const MDOUBLE CGOLD = 0.3819660f;
const MDOUBLE ZEPS = 1.0e-10f;
int iter;
MDOUBLE a,b,d=0.0,etemp,fu,fv,fw,fx,p,q,r,tol1,tol2,u,v,w,x,xm;
MDOUBLE e=0.0;
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
x=w=v=bx;
fw=fv=fx=f(x);
LOG(10,<<"brent, f("<<x<<")="<<fx<<endl);
for (iter=1;iter<=ITMAX;iter++) {
xm=0.5*(a+b);
tol2=2.0*(tol1=tol*fabs(x)+ZEPS);
if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
*xmin=x;
return fx;
}
if (fabs(e) > tol1) {
r=(x-w)*(fx-fv);
q=(x-v)*(fx-fw);
p=(x-v)*q-(x-w)*r;
q=2.0*(q-r);
if (q > 0.0) p = -p;
q=fabs(q);
etemp=e;
e=d;
if (fabs(p) >= fabs(0.5*q*etemp) || p <= q*(a-x) || p >= q*(b-x))
d=CGOLD*(e=(x >= xm ? a-x : b-x));
else {
d=p/q;
u=x+d;
if (u-a < tol2 || b-u < tol2)
d=SIGN(tol1,xm-x);
}
} else {
d=CGOLD*(e=(x >= xm ? a-x : b-x));
}
u=(fabs(d) >= tol1 ? x+d : x+SIGN(tol1,d));
fu=f(u);
LOG(10,<<"brent, f("<<u<<")="<<fu<<endl);
if (fu <= fx) {
if (u >= x) a=x; else b=x;
v=w;w=x;x=u;
fv=fw;fw=fx; fx=fu;
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else if (fu <= fv || v == x || v == w) {
v=u;
fv=fu;
}
}
}
errorMsg::reportError(" too many iterations in function, brent. "); // also quit the program
return -1;
}
/*
//A doubleRep implementation of brent cause return type function overloading is forbidden in c++
template <typename regF>
doubleRep brentDoubleRep(doubleRep ax, doubleRep bx, doubleRep cx, regF f, doubleRep tol,
MDOUBLE *xmin) {
const int ITMAX = 100;
const doubleRep CGOLD(0.3819660f);
const doubleRep ZEPS(1.0e-10f);
doubleRep minusOne(-1.0);
int iter;
doubleRep fu,fv,fw,fx,a,b,etemp,p,q,r,u,v,w,x;
doubleRep d(0.0);
doubleRep e(0.0);
doubleRep half(0.5);
doubleRep two(2.0);
doubleRep zero(0.0);
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
x=w=v=bx;
fw=fv=fx=f(convert(x));
LOG(10,<<"brent, f("<<x<<")="<<fx<<endl);
for (iter=1;iter<=ITMAX;iter++) {
doubleRep xm(0.5*convert(a+b));
doubleRep tol1(convert(tol)*fabs(convert(x)));
doubleRep tol2(2.0*convert((tol1+ZEPS)));
if (fabs(convert(x+minusOne*xm)) <= convert(tol2+minusOne*half*(b+minusOne*a))) {
*xmin=convert(x);
return fx;
}
if (fabs(convert(e)) > convert(tol1)) {
r=(x+minusOne*w)*(fx+minusOne*fv);
q=(x+minusOne*v)*(fx+minusOne*fw);
p=(x+minusOne*v)*q+minusOne*(x+minusOne*w)*r;
q=two*(q+minusOne*r);
if (q > zero) p = minusOne*p;
doubleRep newQ(fabs(convert(q)));
q=newQ;
etemp=e;
e=d;
if (fabs(convert(p)) >= fabs(convert(half*q*etemp)) || p <= q*(a+minusOne*x) || p >= q*(b+minusOne*x))
d=CGOLD*(e=(x >= xm ? a+minusOne*x : b+minusOne*x));
else {
d=p/q;
u=x+d;
if (u+minusOne*a < tol2 || b+minusOne*u < tol2){
doubleRep newD(SIGN(convert(tol1),convert(xm+minusOne*x)));
d=newD;
}
}
} else {
d=CGOLD*(e=(x >= xm ? a+minusOne*x : b+minusOne*x));
}
u=(fabs(convert(d)) >= convert(tol1) ? x+d : x+SIGN(convert(tol1),convert(d)));
fu=f(convert(u));
LOG(10,<<"brent, f("<<u<<")="<<fu<<endl);
if (fu <= fx) {
if (u >= x) a=x; else b=x;
v=w;w=x;x=u;
fv=fw;fw=fx; fx=fu;
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
v=w;
w=u;
fv=fw;
fw=fu;
} else if (fu <= fv || v == x || v == w) {
v=u;
fv=fu;
}
}
}
errorMsg::reportError(" too many iterations in function, brentDoubleRep. "); // also quit the program
return minusOne;
}
*/
// ===================================== function dbrent ========================================
/* The efficiency of this function for likelihood computations can be improved by replacing
functors regF f and dF df with one objects that preforms the likelihood computation once
and produces both L(t) and dL(t)/dt. This object will provide methods:
MDOUBLE f(MDOUBLE x)
MDOUBLE df(MDOUBLE x)
*/
#define ITMAX 100
#define ZEPS 1.0e-10
#define MOV3(a,b,c, d,e,f) (a)=(d);(b)=(e);(c)=(f);
template <typename regF, typename dF>
MDOUBLE dbrent(MDOUBLE ax, MDOUBLE bx, MDOUBLE cx, regF f,
dF df, MDOUBLE tol, MDOUBLE *xmin) {
int iter,ok1,ok2;
MDOUBLE a,b,d=0.0,d1,d2,du,dv,dw,dx,e=0.0;
MDOUBLE fu,fv,fw,fx,olde,tol1,tol2,u,u1,u2,v,w,x,xm;
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
//ensuring x is between a and b
if (bx>b) { x=w=v=b;b=bx;}
else if (bx<a) {x=w=v=a; a=bx;}
else x=w=v=bx;
fw=fv=fx=f(x);
assert(fv==fv);// throw an exception if answer is nan = not a number.
dw=dv=dx=df(x);
for (iter=1;iter<=ITMAX;iter++) {
xm=0.5*(a+b);
#ifdef VERBOS
//if (iter>10) cout<<"iteration: "<<iter<<" xm = "<<xm<<" x= "<<x<<" a= "<<a<<" b= "<<b<<" fx= "<<fx<<endl;
#endif
tol1=tol*fabs(x)+ZEPS;
tol2=2.0*tol1;
if (fabs(x-xm) <= (tol2-0.5*(b-a))) {
*xmin=x;
return fx;
}
if (fabs(e) > tol1) {
d1=2.0*(b-a);
d2=d1;
if (dw != dx) d1=(w-x)*dx/(dx-dw);
if (dv != dx) d2=(v-x)*dx/(dx-dv);
u1=x+d1;
u2=x+d2;
ok1 = (a-u1)*(u1-b) > 0.0 && dx*d1 <= 0.0;
ok2 = (a-u2)*(u2-b) > 0.0 && dx*d2 <= 0.0;
olde=e;
e=d;
if (ok1 || ok2) {
if (ok1 && ok2)
d=(fabs(d1) < fabs(d2) ? d1 : d2);
else if (ok1)
d=d1;
else
d=d2;
if (fabs(d) <= fabs(0.5*olde)) {
u=x+d;
if (u-a < tol2 || b-u < tol2)
d=SIGN(tol1,xm-x);
} else {
d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
}
} else {
d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
}
} else {
d=0.5*(e=(dx >= 0.0 ? a-x : b-x));
}
if (fabs(d) >= tol1) {
u=x+d;
fu=f(u);
} else {
u=x+SIGN(tol1,d);
if (u<ax) u=x; // MY LATEST ADDITION!
fu=f(u);
if (fu > fx) {
*xmin=x;
return fx;
}
}
du=df(u);
if (fu <= fx) {
if (u >= x) a=x; else b=x;
MOV3(v,fv,dv, w,fw,dw)
MOV3(w,fw,dw, x,fx,dx)
MOV3(x,fx,dx, u,fu,du)
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
MOV3(v,fv,dv, w,fw,dw)
MOV3(w,fw,dw, u,fu,du)
} else if (fu < fv || v == x || v == w) {
MOV3(v,fv,dv, u,fu,du)
}
}
}
errorMsg::reportError("Too many iterations in routine dbrent"); // also quit the program
return -1;
}
/*
//A doubleRep implementation of dbrent cause return type function overloading is forbidden in c++
template <typename regF, typename dF>
doubleRep dbrentDoubleRep(doubleRep ax, doubleRep bx, doubleRep cx, regF f,
dF df, doubleRep tol, MDOUBLE *xmin) {
int iter,ok1,ok2;
doubleRep a,b,d1,d2;
doubleRep d(0.0);
doubleRep e(0.0);
doubleRep olde,u,u1,u2,v,w,x,xm;
doubleRep fu,fv,fw,fx,du,dv,dw,dx;
doubleRep minusOne(-1.0);
doubleRep half(0.5);
doubleRep two(2.0);
doubleRep zero(0.0);
a=(ax < cx ? ax : cx);
b=(ax > cx ? ax : cx);
//ensuring x is between a and b
if (bx>b) { x=w=v=b;b=bx;}
else if (bx<a) {x=w=v=a; a=bx;}
else x=w=v=bx;
fw=fv=fx=f(convert(x));
assert(fv==fv);// throw an exception if answer is nan = not a number.
dw=dv=dx=df(convert(x));
for (iter=1;iter<=ITMAX;iter++) {
xm=half*(a+b);
#ifdef VERBOS
//if (iter>10) cout<<"iteration: "<<iter<<" xm = "<<xm<<" x= "<<x<<" a= "<<a<<" b= "<<b<<" fx= "<<fx<<endl;
#endif
doubleRep tol1(convert(tol)*fabs(convert(x)));
doubleRep tol2(2.0*(convert(tol1)+ZEPS));
if (fabs(convert(x+minusOne*xm)) <= convert((tol2+minusOne*half*(b+minusOne*a)))) {
*xmin=convert(x);
return fx;
}
if (fabs(convert(e)) > convert(tol1)) {
d1=two*(b+minusOne*a);
d2=d1;
if (dw != dx) d1=(w+minusOne*x)*dx/(dx+minusOne*dw);
if (dv != dx) d2=(v+minusOne*x)*dx/(dx+minusOne*dv);
u1=x+d1;
u2=x+d2;
ok1 = (a+minusOne*u1)*(u1+minusOne*b) > zero && dx*d1 <= zero;
ok2 = (a+minusOne*u2)*(u2+minusOne*b) > zero && dx*d2 <= zero;
olde=e;
e=d;
if (ok1 || ok2) {
if (ok1 && ok2)
d=(fabs(convert(d1)) < fabs(convert(d2)) ? d1 : d2);
else if (ok1)
d=d1;
else
d=d2;
if (fabs(convert(d)) <= fabs(convert(half*olde))) {
u=x+d;
if (u+minusOne*a < tol2 || b+minusOne*u < tol2){
doubleRep sign(SIGN(convert(tol1),convert(xm+minusOne*x)));
d=sign;
}
} else {
d=half*(e=(dx >= zero ? a+minusOne*x : b+minusOne*x));
}
} else {
d=half*(e=(dx >= zero ? a+minusOne*x : b+minusOne*x));
}
} else {
d=half*(e=(dx >= zero ? a+minusOne*x : b+minusOne*x));
}
if (fabs(convert(d)) >= convert(tol1)) {
u=x+d;
fu=f(convert(u));
} else {
doubleRep sign(SIGN(convert(tol1),convert(d)));
u=x+sign;
if (u<ax) u=x; // MY LATEST ADDITION!
fu=f(convert(u));
if (fu > fx) {
*xmin=convert(x);
return fx;
}
}
du=df(convert(u));
if (fu <= fx) {
if (u >= x) a=x; else b=x;
MOV3(v,fv,dv, w,fw,dw)
MOV3(w,fw,dw, x,fx,dx)
MOV3(x,fx,dx, u,fu,du)
} else {
if (u < x) a=u; else b=u;
if (fu <= fw || w == x) {
MOV3(v,fv,dv, w,fw,dw)
MOV3(w,fw,dw, u,fu,du)
} else if (fu < fv || v == x || v == w) {
MOV3(v,fv,dv, u,fu,du)
}
}
}
errorMsg::reportError("Too many iterations in routine dbrentDoubleRep"); // also quit the program
return minusOne;
}
*/
/*================================== function rtbis =========================================
//Using bisection, find the root of the function func known to lie between
x1 and x2. The return value is the root will be refined until its accuracy is +- xacc
*/
template <typename regF>
MDOUBLE rtbis(regF func,MDOUBLE x1, MDOUBLE x2, MDOUBLE xacc) {
const int max_number_of_iter = 100;
MDOUBLE f = func(x1);
MDOUBLE fmid = func(x2);
if (f*fmid >=0.0) {
errorMsg::reportError(" error in function rtbis, root must be bracketed for bisection in rtbis ");
// also quit the program
}
MDOUBLE dx, rtb;
if (f<0.0) {
dx = x2-x1;
rtb = x1;
}
else {
dx = x1-x2;
rtb = x2;
}
for (int j=1; j <= max_number_of_iter; ++j) {
dx *= 0.5;
MDOUBLE xmid = rtb+dx;
MDOUBLE fmid = func(xmid);
if (fmid <= 0.0) rtb = xmid;
if ((fabs(dx) < xacc) || (fmid == 0.0)) return rtb;
}
errorMsg::reportError("Error in function rtbis..."); // also quit the program...
return -1.0;
}
//Given a function func and an initial guessed range (x1,x2), the routine expands the range
//geometrically until a root is bracketed by the returned values x1 and x2 (in which case zbrac retruns true)
//or until the range becomes large unacceptably large (in which case zbrac return false).
template <typename regF>
bool zbrac(regF func, MDOUBLE &x1, MDOUBLE &x2) {
const int NTRY=50;
const MDOUBLE FACTOR= 1.6;
int j;
MDOUBLE f1,f2;
if (x1 == x2)
errorMsg::reportError("Bad initial range in zbrac");
f1 = func(x1);
f2 = func(x2);
for (j = 0; j < NTRY; j++)
{
if (f1 * f2 < 0.0)
return true;
if (fabs(f1) < fabs(f2))
f1=func(x1 += FACTOR*(x1-x2));
else
f2=func(x2 += FACTOR*(x2-x1));
}
return false;
}
// ================================ function brent new ======================================
int MyJacobi(VVdouble &Insym, VVdouble &RightEigenV, Vdouble &EigenValues);
MDOUBLE sign(MDOUBLE a,MDOUBLE b);
MDOUBLE pythag(const MDOUBLE a, const MDOUBLE b);
void houseHolder(VVdouble &mat,VVdouble &Q);
void tred2(VVdouble &a, Vdouble &d, Vdouble &e);
void QL(Vdouble &d, Vdouble &e, VVdouble &z);
void computeEigenSystem(VVdouble &symmetricMatrix,VVdouble &eigenVectros,Vdouble &diagonal);
MDOUBLE performKSTest(const uniformDistribution& empiricalDist, Vdouble& observedDist); // perform Kolomogorov-Smirnoff test
MDOUBLE computeProbForKS (const MDOUBLE QsParam); // function called only by performKSTest
#endif
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