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// $Id: chebyshevAccelerator.cpp 962 2006-11-07 15:13:34Z privmane $
#include "chebyshevAccelerator.h"
#include <cmath>
#include <cassert>
chebyshevAccelerator::chebyshevAccelerator(const chebyshevAccelerator& other):
_alphabetSize(other._alphabetSize),
_totalNumOfCoef(other._totalNumOfCoef),
_usingNumberOfCoef(other._usingNumberOfCoef),
_pb(NULL),
_rightRange(other._rightRange),
_leftRange(other._leftRange){
if (other._pb != NULL) _pb = other._pb->clone();
chebi_coff=other.chebi_coff;
chebi_dervation_coff=other.chebi_dervation_coff;
chebi_sec_dervation_coff=other.chebi_sec_dervation_coff;
}
chebyshevAccelerator::chebyshevAccelerator(
replacementModel* pb,
const int alphanetSize,
const int totalNumOfCoef,
const int usingNumberOfCoef,
const MDOUBLE rightRange,
const MDOUBLE leftRange
): _alphabetSize(alphanetSize),
_totalNumOfCoef(totalNumOfCoef), _usingNumberOfCoef(usingNumberOfCoef),_pb(pb->clone()), _rightRange(rightRange), _leftRange(leftRange)
//----------------------------------------------------------------------------------
//input: non
//output: non
//doing: filling the member chebi_coff[][][]; chebi_coff[1][2][4] is the forth
// chebichev coefficient in the chebichev polynom of the function
// slow_pij(1,2,t);
//----------------------------------------------------------------------------------
{
int tmp, tmp1;
for (tmp = 0; tmp < _alphabetSize ; tmp ++) {
chebi_coff.resize(_alphabetSize);
chebi_dervation_coff.resize(_alphabetSize);
chebi_sec_dervation_coff.resize(_alphabetSize);
for (tmp1 = 0; tmp1 < _alphabetSize ; tmp1 ++) {
chebi_coff[tmp].resize(_alphabetSize);
chebi_dervation_coff[tmp].resize(_alphabetSize);
chebi_sec_dervation_coff[tmp].resize(_alphabetSize);
for (tmp1 = 0; tmp1 < _alphabetSize ; tmp1 ++) {
chebi_coff[tmp][tmp1].resize(_totalNumOfCoef);
chebi_dervation_coff[tmp][tmp1].resize(_totalNumOfCoef);
chebi_sec_dervation_coff[tmp][tmp1].resize(_totalNumOfCoef);
}
}
}
Vdouble coffij(_totalNumOfCoef);
Vdouble coffij_of_derviation(_totalNumOfCoef);
Vdouble coffij_of_second_derivation(_totalNumOfCoef);
for (int from_aa =0; from_aa<_alphabetSize ; ++ from_aa)
{
for (int to_aa =0; to_aa<_alphabetSize ; ++ to_aa)
{
chebft(coffij,_totalNumOfCoef,from_aa,to_aa);
chder(coffij,coffij_of_derviation,_totalNumOfCoef);
chder(coffij_of_derviation,coffij_of_second_derivation,_totalNumOfCoef);
for (int tmp=0; tmp<_totalNumOfCoef;++tmp)
{
chebi_coff[from_aa][to_aa][tmp] = coffij[tmp];
chebi_dervation_coff[from_aa][to_aa][tmp] = coffij_of_derviation[tmp];
chebi_sec_dervation_coff[from_aa][to_aa][tmp] = coffij_of_second_derivation[tmp];
}
}
}
}
void chebyshevAccelerator::chebft(Vdouble& c, int n, int from_aa, int to_aa) {
//----------------------------------------------------------------------------------
//input: c[] is the vector where the cofficient will be
// from aa and to_aa are for chosing the right function to be developed
//output: non
//doing: calculating the chebichev coefficient in the chebichev polynom of the function
// slow_pij(from_aa,to_aa,t), and put them in the c[] vector
//----------------------------------------------------------------------------------
int k,j;
MDOUBLE fac,bpa,bma;
Vdouble f;
f.resize(n);
bma=0.5*(_rightRange-_leftRange);
bpa=0.5*(_rightRange+_leftRange);
for (k=0;k<n;k++) {
MDOUBLE y=cos(3.141592653589793*(k+0.5)/n);
f[k]= _pb->Pij_t(from_aa,to_aa,y*bma+bpa); //(*func)(y*bma+bpa);
}
fac=2.0/n;
for (j=0;j<n;j++) {
MDOUBLE sum=0.0;
for (k=0;k<n;k++)
sum += f[k]*cos(3.141592653589793*j*(k+0.5)/n);
c[j]=fac*sum;
}
}
const MDOUBLE chebyshevAccelerator::Pij_t(const int from_aa, const int to_aa, const MDOUBLE x) const
//----------------------------------------------------------------------------------
//input: like pij_t
//output: the probabilty
//doing: calculating with the polinom of chebi and via eigenvalue decomposition
//----------------------------------------------------------------------------------
{
MDOUBLE d=0.0,dd=0.0,sv,y,y2,check;
int j;
if ((x-_leftRange)*(x-_rightRange) > 0.0) {
return _pb->Pij_t(from_aa,to_aa,x);
// errorMsg::reportError("x not in range in routine fast_Pij_t");// also quit the program
}
y2=2.0*(y=(2.0*x-_leftRange-_rightRange)/(_rightRange-_leftRange));
for (j=_usingNumberOfCoef;j>0;j--) {
sv=d;
d=y2*d-dd+chebi_coff[from_aa][to_aa][j];
dd=sv;
}
check = y*d-dd+0.5*chebi_coff[from_aa][to_aa][0];
if ((check>1) || (check<=0)) check = _pb->Pij_t(from_aa,to_aa,x);
assert(check<=1);
assert(check>=0);
return check;
}
const MDOUBLE chebyshevAccelerator::dPij_dt(const int from_aa, const int to_aa, const MDOUBLE x) const
//----------------------------------------------------------------------------------
//input: like pij_t
//output: the derivation of probabilty
//doing: calculating with the polinom of chebi and via eigenvalue decomposition
//----------------------------------------------------------------------------------
{
MDOUBLE d=0.0,dd=0.0,sv,y,y2;
int j;
if ((x-_leftRange)*(x-_rightRange) > 0.0) {
return _pb->dPij_dt(from_aa,to_aa,x);
}
y2=2.0*(y=(2.0*x-_leftRange-_rightRange)/(_rightRange-_leftRange));
for (j=_usingNumberOfCoef;j>0;j--) {
sv=d;
d=y2*d-dd+chebi_dervation_coff[from_aa][to_aa][j];
dd=sv;
}
return y*d-dd+0.5*chebi_dervation_coff[from_aa][to_aa][0];
}
const MDOUBLE chebyshevAccelerator::d2Pij_dt2(const int from_aa, const int to_aa, const MDOUBLE x) const {
//----------------------------------------------------------------------------------
//input: like pij_t
//output: the second derivation of the probabilty
//doing: calculating with the polynom of chebi and via eigenvalue decomposition
//----------------------------------------------------------------------------------
MDOUBLE d=0.0,dd=0.0,sv,y,y2;
int j;
if ((x-_leftRange)*(x-_rightRange) > 0.0) {
return _pb->d2Pij_dt2(from_aa,to_aa,x);
}
y2=2.0*(y=(2.0*x-_leftRange-_rightRange)/(_rightRange-_leftRange));
for (j=_usingNumberOfCoef;j>0;j--) {
sv=d;
d=y2*d-dd+chebi_sec_dervation_coff[from_aa][to_aa][j];
dd=sv;
}
return y*d-dd+0.5*chebi_sec_dervation_coff[from_aa][to_aa][0];
}
void chebyshevAccelerator::chder(Vdouble &c, Vdouble &cder, int n) {
//----------------------------------------------------------------------------------
//input: chebicev coff of f(x) i.e. in c[]. n is the vector size
//output: chebicev coff of df(x)/dx i.e. in cder[]
//doing: calculating the coff of the dervation from the coff of f.
//reference:numercal recepies in c, pg 195.
//----------------------------------------------------------------------------------
int j;
MDOUBLE con;
cder[n-1]=0.0;
cder[n-2]=2*(n-1)*c[n-1];
for (j=n-3;j>=0;j--)
cder[j]=cder[j+2]+2*(j+1)*c[j+1];
con=2.0f/(_rightRange-_leftRange);
for (j=0;j<n;j++)
cder[j] *= con;
}
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