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/***************************************************************************
* Copyright (C) 2009-2015 by *
* BUI Quang Minh <minh.bui@univie.ac.at> *
* Lam-Tung Nguyen <nltung@gmail.com> *
* *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License for more details. *
* *
* You should have received a copy of the GNU General Public License *
* along with this program; if not, write to the *
* Free Software Foundation, Inc., *
* 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. *
***************************************************************************/
#include "tree/phylotree.h"
#include "rategamma.h"
#include <cmath>
RateGamma::RateGamma(int ncat, double shape, bool median, PhyloTree *tree) : RateHeterogeneity()
{
ncategory = ncat;
phylo_tree = tree;
cut_median = median;
//gamma_shape = MAX_GAMMA_SHAPE-1.0;
gamma_shape = max(tree->params->min_gamma_shape, fabs(shape));
fix_gamma_shape = false;
rates = NULL;
if (shape > 0.0) {
// true unless -optfromgiven cmd line option
fix_gamma_shape = !(Params::getInstance().optimize_from_given_params);
} else if (shape == 0.0) {
gamma_shape = max(tree->params->min_gamma_shape*5.0, random_double());
cout << "Randomize initial gamma shape (alpha): " << gamma_shape << endl;
}
setNCategory(ncat);
}
void RateGamma::startCheckpoint() {
checkpoint->startStruct("RateGamma");
}
void RateGamma::saveCheckpoint() {
startCheckpoint();
CKP_SAVE(gamma_shape);
// CKP_SAVE(fix_gamma_shape);
// CKP_SAVE(cut_median);
// CKP_SAVE(ncategory);
endCheckpoint();
RateHeterogeneity::saveCheckpoint();
}
void RateGamma::restoreCheckpoint() {
RateHeterogeneity::restoreCheckpoint();
startCheckpoint();
CKP_RESTORE(gamma_shape);
// CKP_RESTORE(fix_gamma_shape);
// CKP_RESTORE(cut_median);
// CKP_RESTORE(ncategory);
endCheckpoint();
// necessary compute rates after restoring gamma_shape
computeRates();
}
void RateGamma::setNCategory(int ncat) {
ncategory = ncat;
if (rates) delete [] rates;
rates = new double[ncategory];
for (int cat = 0; cat < ncategory; cat++)
rates[cat] = 1.0;
name = "+G" + convertIntToString(ncategory);
full_name = "Gamma with " + convertIntToString(ncategory) + " categories";
computeRates();
}
string RateGamma::getNameParams() {
ostringstream str;
str << "+G" << ncategory << '{' << gamma_shape << '}';
return str.str();
}
RateGamma::~RateGamma()
{
if (rates) delete [] rates;
rates = NULL;
}
void RateGamma::computeRates() {
int cat; /* category id */
double sum_rates = 0.0;
if (ncategory == 1) {
rates[0] = 1.0;
return;
}
double curScale = 0.0;
for (cat = 0; cat < ncategory; cat++)
curScale += rates[cat];
if (!cut_median) {
computeRatesMean();
} else {
for (cat = 0; cat < ncategory; cat ++) {
double prob = ( 2.0 * cat + 1 ) / (2.0 * ncategory);
double perPoint_ = cmpPointChi2 (prob, 2.0 * gamma_shape) / (2.0 * gamma_shape);
perPoint_ = perPoint_ < 0.0 ? -perPoint_ : perPoint_;
rates[ cat ] = perPoint_;
}
//rescale in order to make mean equal to 1.0
for (cat = 0; cat < ncategory; cat ++)
sum_rates += rates[ cat];
for (cat = 0; cat < ncategory; cat ++)
rates[ cat ] = rates[ cat ] * ncategory / sum_rates;
}
/* BQM 2015-02-25: Testing if RAxML forgot this rate rescaling step */
if (phylo_tree && phylo_tree->params && phylo_tree->params->no_rescale_gamma_invar)
return;
double newScale = 0.0;
for (cat = 0; cat < ncategory; cat++)
newScale += rates[cat];
if (newScale != curScale) {
for (cat = 0; cat < ncategory; cat++)
rates[cat] *= curScale/newScale;
}
/* if invariable sites are present */
// if (Params::getInstance().optimize_alg_gammai != "EM") {
// double p_inv = getPInvar();
// for (cat = 0; cat < ncategory; cat++)
// rates[cat] = rates[cat]/(1.0 - p_inv);
// }
/* check for very small rates */
// for (cat = 0; cat < ncategory; cat ++)
// if (rates[cat] < MIN_GAMMA_RATE)
// rates[cat] = MIN_GAMMA_RATE;
}
/*double RateGamma::cmpPerPointGamma (const double prob, const double shape) {
}*/
void RateGamma::computeRatesMean () {
int i;
double lnga1=cmpLnGamma(gamma_shape+1);
double *freqK = new double[ncategory];
for (i=0; i<ncategory-1; i++) /* cutting points, Eq. 9 */
freqK[i]=cmpPointChi2((i+1.0)/ncategory, 2.0 * gamma_shape) / (2.0 * gamma_shape);
for (i=0; i<ncategory-1; i++) /* Eq. 10 */
freqK[i]=cmpIncompleteGamma(freqK[i]*gamma_shape, gamma_shape+1, lnga1);
rates[0] = freqK[0]*ncategory;
rates[ncategory-1] = (1-freqK[ncategory-2])*ncategory;
for (i=1; i<ncategory-1; i++) rates[i] = (freqK[i]-freqK[i-1])*ncategory;
delete [] freqK;
}
void RateGamma::setGammaShape(double gs) {
gamma_shape = gs;
computeRates();
}
double RateGamma::computeFunction(double shape) {
if (gamma_shape != shape) {
gamma_shape = shape;
computeRates();
phylo_tree->clearAllPartialLH();
}
return -phylo_tree->computeLikelihood();
}
double RateGamma::targetFunk(double x[]) {
getVariables(x);
phylo_tree->clearAllPartialLH();
return -phylo_tree->computeLikelihood();
}
void RateGamma::setBounds(double *lower_bound, double *upper_bound, bool *bound_check) {
if (getNDim() == 0) return;
lower_bound[1] = phylo_tree->params->min_gamma_shape;
upper_bound[1] = MAX_GAMMA_SHAPE;
bound_check[1] = false;
}
void RateGamma::setVariables(double *variables) {
if (getNDim() == 0) return;
variables[1] = gamma_shape;
}
bool RateGamma::getVariables(double *variables) {
if (getNDim() == 0) return false;
bool changed = (gamma_shape != variables[1]);
gamma_shape = variables[1];
if (changed)
computeRates();
return changed;
}
double RateGamma::optimizeParameters(double gradient_epsilon, double min_gamma, double max_gamma) {
if (fix_gamma_shape)
return phylo_tree->computeLikelihood();
if (verbose_mode >= VB_MAX)
cout << "Optimizing gamma shape..." << endl;
double negative_lh;
double current_shape = gamma_shape;
double ferror, optx;
optx = minimizeOneDimen(min_gamma, current_shape, max_gamma, max(gradient_epsilon, TOL_GAMMA_SHAPE), &negative_lh, &ferror);
// if (gamma_shape != optx) {
// gamma_shape = optx;
// computeRates();
// phylo_tree->clearAllPartialLH();
// }
// return phylo_tree->computeLikelihood();
return -computeFunction(optx);
}
double RateGamma::optimizeParameters(double gradient_epsilon) {
if (fix_gamma_shape)
return phylo_tree->computeLikelihood();
if (verbose_mode >= VB_MAX)
cout << "Optimizing gamma shape..." << endl;
double negative_lh;
double current_shape = gamma_shape;
double ferror, optx;
optx = minimizeOneDimen(phylo_tree->params->min_gamma_shape, current_shape, MAX_GAMMA_SHAPE, max(gradient_epsilon, TOL_GAMMA_SHAPE), &negative_lh, &ferror);
// gamma_shape = optx;
// computeRates();
// phylo_tree->clearAllPartialLH();
// return -negative_lh;
return -computeFunction(optx);
}
void RateGamma::writeInfo(ostream &out) {
out << "Gamma shape alpha: " << gamma_shape << endl;
//out << " (" << (cut_median ? "median" : "mean") << " rate per category)" << endl;
//out << "Number of categories: " << ncategory << endl;
}
void RateGamma::writeParameters(ostream &out) {
out << "\t" << gamma_shape;
}
int RateGamma::computePatternRates(DoubleVector &pattern_rates, IntVector &pattern_cat) {
//cout << "Computing Gamma site rates by empirical Bayes..." << endl;
phylo_tree->computePatternLhCat(WSL_RATECAT);
int npattern = phylo_tree->aln->getNPattern();
pattern_rates.resize(npattern);
pattern_cat.resize(npattern);
double *lh_cat = phylo_tree->_pattern_lh_cat;
for (int i = 0; i < npattern; i++) {
double sum_rate = 0.0, sum_lh = 0.0;
int best = 0;
for (int c = 0; c < ncategory; c++) {
sum_rate += rates[c] * lh_cat[c];
sum_lh += lh_cat[c];
if (lh_cat[c] > lh_cat[best] || (lh_cat[c] == lh_cat[best] && random_double()<0.5)) // break tie at random
best = c;
}
pattern_rates[i] = sum_rate / sum_lh;
pattern_cat[i] = best;
lh_cat += ncategory;
}
return ncategory;
// pattern_rates.clear();
// pattern_rates.insert(pattern_rates.begin(), ptn_rates, ptn_rates + npattern);
// pattern_cat.resize(npattern, 0);
// for (int i = 0; i < npattern; i++)
// for (int j = 1; j < ncategory; j++)
// if (fabs(rates[j] - ptn_rates[i]) < fabs(rates[pattern_cat[i]] - ptn_rates[i]))
// pattern_cat[i] = j;
// delete [] ptn_rates;
}
/*NUMERICAL SUBROUTINES
**************************************************************************************
**************************************************************************************
**************************************************************************************
**************************************************************************************
**************************************************************************************/
/* THE FOLLOWING CODE COMES FROM tools.c in Yang's PAML package */
//----------------------------------------------------------------------------------------
double RateGamma::cmpLnGamma (double alpha) {
/* returns ln(gamma(alpha)) for alpha>0, accurate to 10 decimal places.
Stirling's formula is used for the central polynomial part of the procedure.
Pike MC & Hill ID (1966) Algorithm 291: Logarithm of the gamma function.
Communications of the Association for Computing Machinery, 9:684
*/
double x=alpha, f=0, z;
if (x<7) {
f=1; z=x-1;
while (++z<7) f*=z;
x=z; f=-log(f);
}
z = 1/(x*x);
return f + (x-0.5)*log(x) - x + .918938533204673
+ (((-.000595238095238*z+.000793650793651)*z-.002777777777778)*z
+.083333333333333)/x;
} //end of function cmpLnGamma
//----------------------------------------------------------------------------------------
double RateGamma::cmpIncompleteGamma (double x, double alpha, double ln_gamma_alpha) {
/* returns the incomplete gamma ratio I(x,alpha) where x is the upper
limit of the integration and alpha is the shape parameter.
returns (-1) if in error
(1) series expansion if (alpha>x || x<=1)
(2) continued fraction otherwise
RATNEST FORTRAN by
Bhattacharjee GP (1970) The incomplete gamma integral. Applied Statistics,
19: 285-287 (AS32)
*/
int i;
double p=alpha, g=ln_gamma_alpha;
double accurate=1e-8, overflow=1e30;
double factor, gin=0, rn=0, a=0,b=0,an=0,dif=0, term=0, pn[6];
if (x==0) return (0);
if (x<0 || p<=0) return (-1);
factor=exp(p*log(x)-x-g);
if (x>1 && x>=p) goto l30;
/* (1) series expansion */
gin=1; term=1; rn=p;
l20:
rn++;
term*=x/rn; gin+=term;
if (term > accurate) goto l20;
gin*=factor/p;
goto l50;
l30:
/* (2) continued fraction */
a=1-p; b=a+x+1; term=0;
pn[0]=1; pn[1]=x; pn[2]=x+1; pn[3]=x*b;
gin=pn[2]/pn[3];
l32:
a++; b+=2; term++; an=a*term;
for (i=0; i<2; i++) pn[i+4]=b*pn[i+2]-an*pn[i];
if (pn[5] == 0) goto l35;
rn=pn[4]/pn[5]; dif=fabs(gin-rn);
if (dif>accurate) goto l34;
if (dif<=accurate*rn) goto l42;
l34:
gin=rn;
l35:
for (i=0; i<4; i++) pn[i]=pn[i+2];
if (fabs(pn[4]) < overflow) goto l32;
for (i=0; i<4; i++) pn[i]/=overflow;
goto l32;
l42:
gin=1-factor*gin;
l50:
return (gin);
} //end of function cmpIncompleteGamma
//----------------------------------------------------------------------------------------
/* functions concerning the CDF and percentage points of the gamma and
Chi2 distribution
*/
double RateGamma::cmpPointNormal (double prob) {
/* returns z so that Prob{x<z}=prob where x ~ N(0,1) and (1e-12)<prob<1-(1e-12)
returns (-9999) if in error
Odeh RE & Evans JO (1974) The percentage points of the normal distribution.
Applied Statistics 22: 96-97 (AS70)
Newer methods:
Wichura MJ (1988) Algorithm AS 241: the percentage points of the
normal distribution. 37: 477-484.
Beasley JD & Springer SG (1977). Algorithm AS 111: the percentage
points of the normal distribution. 26: 118-121.
*/
double a0=-.322232431088, a1=-1, a2=-.342242088547, a3=-.0204231210245;
double a4=-.453642210148e-4, b0=.0993484626060, b1=.588581570495;
double b2=.531103462366, b3=.103537752850, b4=.0038560700634;
double y, z=0, p=prob, p1;
p1 = (p<0.5 ? p : 1-p);
if (p1<1e-20) return (-9999);
y = sqrt (log(1/(p1*p1)));
z = y + ((((y*a4+a3)*y+a2)*y+a1)*y+a0) / ((((y*b4+b3)*y+b2)*y+b1)*y+b0);
return (p<0.5 ? -z : z);
} //end of function cmpPointNormal
//----------------------------------------------------------------------------------------
double RateGamma::cmpPointChi2 (double prob, double v) {
/* returns z so that Prob{x<z}=prob where x is Chi2 distributed with df=v
returns -1 if in error. 0.000002<prob<0.999998
RATNEST FORTRAN by
Best DJ & Roberts DE (1975) The percentage points of the
Chi2 distribution. Applied Statistics 24: 385-388. (AS91)
Converted into C by Ziheng Yang, Oct. 1993.
*/
double e=.5e-6, aa=.6931471805, p=prob, g;
double xx, c, ch, a=0,q=0,p1=0,p2=0,t=0,x=0,b=0,s1,s2,s3,s4,s5,s6;
if (p<.000002 || p>.999998 || v<=0) return (-1);
g = cmpLnGamma (v/2);
xx=v/2; c=xx-1;
if (v >= -1.24*log(p)) goto l1;
ch=pow((p*xx*exp(g+xx*aa)), 1/xx);
if (ch-e<0) return (ch);
goto l4;
l1:
if (v>.32) goto l3;
ch=0.4; a=log(1-p);
l2:
q=ch; p1=1+ch*(4.67+ch); p2=ch*(6.73+ch*(6.66+ch));
t=-0.5+(4.67+2*ch)/p1 - (6.73+ch*(13.32+3*ch))/p2;
ch-=(1-exp(a+g+.5*ch+c*aa)*p2/p1)/t;
if (fabs(q/ch-1)-.01 <= 0) goto l4;
else goto l2;
l3:
x=cmpPointNormal (p);
p1=0.222222/v; ch=v*pow((x*sqrt(p1)+1-p1), 3.0);
if (ch>2.2*v+6) ch=-2*(log(1-p)-c*log(.5*ch)+g);
l4:
do {
q=ch; p1=.5*ch;
if ((t=cmpIncompleteGamma (p1, xx, g))<0) {
return (-1);
}
p2=p-t;
t=p2*exp(xx*aa+g+p1-c*log(ch));
b=t/ch; a=0.5*t-b*c;
s1=(210+a*(140+a*(105+a*(84+a*(70+60*a))))) / 420;
s2=(420+a*(735+a*(966+a*(1141+1278*a))))/2520;
s3=(210+a*(462+a*(707+932*a)))/2520;
s4=(252+a*(672+1182*a)+c*(294+a*(889+1740*a)))/5040;
s5=(84+264*a+c*(175+606*a))/2520;
s6=(120+c*(346+127*c))/5040;
ch+=t*(1+0.5*t*s1-b*c*(s1-b*(s2-b*(s3-b*(s4-b*(s5-b*s6))))));
} while (fabs(q/ch-1) > e);
return (ch);
} //end of function cmpPointChi2
/* THE END OF THE CODES COMMING FROM tools.c in Yang's PAML package */
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