#include "models.h"

#include "data_loader.h"

#include "parameters.h"

#include "alpha_s.h"

#include <math.h>

#include <string.h>

#include <latan/latan_nunits.h>

#include <latan/latan_mass.h>

#include <latan/latan_math.h>

#include <latan/latan_tabfunc.h>

#define QED_FVOL_KAPPA 2.83729747947876

static void polynom(double *res, const mat *par, const size_t i0,\

const double x, const int deg)

{

int d;

size_t i;

if ((deg) > 0)

{

*res += mat_get(par,i0,0)*(x);

for (d=2;d<=(deg);d++)

{

i = (size_t)(d) - 1;

*res += mat_get(par,(i0)+i,0)*pow(x,(double)(d));

}

}

}

#define I_ud(i) (i+(size_t)((param)->with_const ? 1 : 0))

#define I_s(i) (I_ud(i)+(size_t)((param)->M_ud_deg))

#define I_a2(i) (I_s(i)+(size_t)((param)->M_s_deg))

#define I_alpha_sa(i) (I_a2(i)+(size_t)((param)->with_a2 ? 1 : 0))

#define I_a2ud(i) (I_alpha_sa(i)+(size_t)((param)->with_alpha_sa ? 1 : 0))

#define I_a2s(i) (I_a2ud(i)+(size_t)((param)->with_a2ud ? 1 : 0))

#define I_umd(i) (I_a2s(i)+(size_t)((param)->with_a2s ? 1 : 0))

#define I_udumd(i) (I_umd(i)+(size_t)((param)->umd_deg))

#define I_sumd(i) (I_udumd(i)+(size_t)((param)->with_udumd))

#define I_a2umd(i) (I_sumd(i)+(size_t)((param)->with_sumd))

#define I_alpha_saumd(i) (I_a2umd(i)+(size_t)((param)->with_a2umd ? 1 : 0))

#define I_alpha(i) (I_alpha_saumd(i)+(size_t)((param)->with_alpha_saumd ? 1 : 0))

#define I_udalpha(i) (I_alpha(i)+(size_t)((param)->alpha_deg))

#define I_salpha(i) (I_udalpha(i)+(size_t)((param)->with_udalpha))

#define I_aalpha(i) (I_salpha(i)+(size_t)((param)->with_salpha))

#define I_qedfv(i) (I_aalpha(i)+(size_t)((param)->with_aalpha ? 1 : 0))

#define LAST_IND (I_qedfv(0)+(size_t)(param->with_qed_fvol-1-param->with_qed_fvol_monopmod))

#define I_a_val(i) (LAST_IND+1+i)

double a_error_chi2_ext(const mat *p, void *vd)

{

size_t i,s;

double a,a_err,res;

fit_param *param;

fit_data *d;

res = 0.0;

d = (fit_data *)(vd);

param = (fit_param *)(d->model_param);

s = fit_data_get_sample_counter(d);

for (i=0;i<param->nbeta;i++)

{

if (s == 0)

{

a = mat_get(rs_sample_pt_cent_val(param->s_a),i,0);

}

else

{

a = mat_get(rs_sample_pt_sample(param->s_a,s-1),i,0);

}

a_err = mat_get(param->a_err,i,0);

res += SQ(mat_get(p,I_a_val(i),0) - a)/SQ(a_err);

d->matperf += 5.0;

}

return res;

}

double fm_phypt_taylor_func(const mat *X, const mat *p, void *vparam)

{

double res,lo,ex,buf,M_ud,M_s,M_fvol,a,dimfac,umd,Linv,ToL,a2mud,a2ms,\

alpha,alpha_sa,d,Lambda;

size_t s,bind;

fit_param *param;

param = (fit_param *)vparam;

bind = (size_t)(mat_get(X,i_bind,0));

/* what is the lattice spacing ? */

if (IS_AN(param,AN_PHYPT))

{

if (IS_AN(param,AN_SCALE))

{

/** a fit parameter from the scale setting model **/

a = (!param->scale_model) ? mat_get(p,bind,0) : mat_get(X,i_a,0);

s = fm_scaleset_taylor_npar(param);

}

else

{

/** a global parameter with error (with external scale samples) **/

if (strbufcmp(param->with_ext_a,"") != 0)

{

a = (!param->scale_model) ? mat_get(p,I_a_val(bind),0) :\

mat_get(X,i_a,0);

}

/** a x coordinate (with the ratio method) **/

else

{

a = mat_get(X,i_a,0);

}

s = 0;

}

}

else

{

fprintf(stderr,"error: this model should not ne used in program %s\n",\

param->analyze);

exit(EXIT_FAILURE);

}

/* x values */

dimfac = (!param->scale_model) ? a : 1.0;

Lambda = LAMBDA_MSBAR_2500MEV;

M_ud = mat_get(X,i_ud,0)/SQ(dimfac);

M_s = mat_get(X,i_s,0)/SQ(dimfac);

umd = mat_get(X,i_umd,0)/SQ(dimfac);

Linv = mat_get(X,i_Linv,0)/dimfac;

ToL = mat_get(X,i_ToL,0);

a2mud = SQ(a)*mat_get(X,i_ud,0)/SQ(dimfac);

a2ms = SQ(a)*mat_get(X,i_s,0)/SQ(dimfac);

alpha = mat_get(X,i_alpha,0);

alpha_sa = alpha_s_msbar(1.0/a,Lambda,3,4)*a;

M_fvol = mat_get(X,i_fvM,0)/dimfac;

d = (double)param->q_dim;

res = 0.0;

/* Taylor/Pade isospin symmetric expansion */

lo = (param->with_const) ? mat_get(p,s,0) : 0.0;

ex = 0.0;

polynom(&ex,p,I_ud(0)+s,M_ud-SQ(param->M_ud),param->M_ud_deg);

polynom(&ex,p,I_s(0)+s,M_s-SQ(param->M_s),param->M_s_deg);

ex += (param->with_a2) ? mat_get(p,I_a2(0)+s,0)*SQ(a) : 0.0;

ex += (param->with_alpha_sa) ? mat_get(p,I_alpha_sa(0)+s,0)*alpha_sa : 0.0;

ex += (param->with_a2ud) ? mat_get(p,I_a2ud(0)+s,0)*a2mud : 0.0;

ex += (param->with_a2s) ? mat_get(p,I_a2s(0)+s,0)*a2ms : 0.0;

res += (param->with_pade) ? lo/(1.0-ex/lo) : lo+ex;

/* Taylor/Pade m_u-m_d expansion */

lo = (param->umd_deg) ? mat_get(p,I_umd(0)+s,0) : 0.0;

ex = 0.0;

polynom(&ex,p,I_udumd(0)+s,M_ud-SQ(param->M_ud),param->with_udumd);

polynom(&ex,p,I_sumd(0)+s,M_s-SQ(param->M_s),param->with_sumd);

ex += (param->with_a2umd) ? mat_get(p,I_a2umd(0)+s,0)*SQ(a) : 0.0;

ex += (param->with_alpha_saumd) ? \

mat_get(p,I_alpha_saumd(0)+s,0)*alpha_sa : 0.0;

res += (param->with_umd_pade) ? umd*lo/(1.0-ex/lo) : umd*lo+umd*ex;

/* Taylor/Pade alpha expansion */

lo = (param->alpha_deg) ? mat_get(p,I_alpha(0)+s,0) : 0.0;

ex = 0.0;

polynom(&ex,p,I_udalpha(0)+s,M_ud-SQ(param->M_ud),param->with_udalpha);

polynom(&ex,p,I_salpha(0)+s,M_s-SQ(param->M_s),param->with_salpha);

ex += (param->with_aalpha) ? mat_get(p,I_aalpha(0)+s,0)*a : 0.0;

res += (param->with_alpha_pade) ? alpha*lo/(1.0-ex/lo) : alpha*lo+alpha*ex;

/** QED finite volume effects **/

if (param->have_alpha)

{

buf = 0.0;

if (param->with_qed_fvol_monopmod)

{

if (param->with_qed_fvol >= 1)

{

buf += -0.5*QED_FVOL_KAPPA*Linv*d*pow(M_fvol,d-1.0);

}

if (param->with_qed_fvol >= 2)

{

buf += mat_get(p,I_qedfv(0)+s,0)*SQ(Linv)*pow(M_fvol,d-2.0);

}

buf *= (double)param->qed_fvol_monopmod_sign;

}

else if (param->with_qed_fvol_qedtl)

{

buf += -QED_FVOL_KAPPA*Linv*M_fvol*\

(1.0 + 2.0*Linv/M_fvol*(1.0-0.5*C_PI*ToL/QED_FVOL_KAPPA));

buf += mat_get(p,I_qedfv(0)+s,0)*pow(Linv, 3.0);

}

else

{

if (param->with_qed_fvol)

{

buf += mat_get(p,I_qedfv(0)+s,0);

}

if (param->with_qed_fvol >= 2)

{

polynom(&buf,p,I_qedfv(1)+s,Linv/Lambda,param->with_qed_fvol-1);

}

buf *= Linv*pow(M_fvol,d-1.0);

}

res += alpha*buf;

}

/* dimensional factor */

res *= pow(dimfac,param->q_dim);

return res;

}

size_t fm_phypt_taylor_npar(void* vparam)

{

fit_param *param;

size_t npar;

param = (fit_param *)vparam;

npar = LAST_IND + 1;

if (IS_AN(param,AN_PHYPT)&&!IS_AN(param,AN_SCALE)&&\

(strbufcmp(param->with_ext_a,"") != 0))

{

npar += param->nbeta;

}

return npar;

}

#undef I_ud

#undef I_s

#undef I_a2

#undef I_aalpha

#undef I_a2ud

#undef I_a2s

#undef I_umd

#undef I_udumd

#undef I_sumd

#undef I_alpha

#undef I_udalpha

#undef I_salpha

#undef I_qedfv

#undef LAST_IND

#undef I_a

#define I_ud(i) (i+(param)->nbeta)

#define I_s(i) (I_ud(i)+(size_t)((param)->s_M_ud_deg))

#define I_a2ud(i) (I_s(i)+(size_t)((param)->s_M_s_deg))

#define I_a2s(i) (I_a2ud(i)+(size_t)(((param)->s_with_a2ud) ? 1 : 0))

#define I_umd(i) (I_a2s(i)+(size_t)(((param)->s_with_a2s) ? 1 : 0))

#define LAST_IND (I_umd(0)+(size_t)((param)->s_umd_deg-1))

double fm_scaleset_taylor_func(const mat *X, const mat *p, void *vparam)

{

double res,a,M_ud,M_s,umd,M_scale,a2mud,a2ms;

fit_param *param;

size_t bind;

param = (fit_param *)vparam;

res = 0.0;

bind = (size_t)(mat_get(X,i_bind,0));

M_scale = param->M_scale;

a = mat_get(p,bind,0);

a2ms = mat_get(X,i_s,0)/M_scale;

a2mud = mat_get(X,i_ud,0)/M_scale;

M_ud = mat_get(X,i_ud,0)/SQ(a*M_scale)-SQ(param->M_ud)/SQ(M_scale);

M_s = mat_get(X,i_s,0)/SQ(a*M_scale)-SQ(param->M_s)/SQ(M_scale);

umd = mat_get(X,i_umd,0)/SQ(a*M_scale)-param->M_umd_val/SQ(M_scale);

res += 1.0;

polynom(&res,p,I_ud(0),M_ud,param->s_M_ud_deg);

polynom(&res,p,I_s(0),M_s,param->s_M_s_deg);

polynom(&res,p,I_umd(0),umd,param->s_umd_deg);

if (param->s_with_a2ud)

{

res += mat_get(p,I_a2ud(0),0)*a2mud;

}

if (param->s_with_a2s)

{

res += mat_get(p,I_a2s(0),0)*a2ms;

}

res *= a*M_scale;

return res;

}

size_t fm_scaleset_taylor_npar(void* vparam)

{

fit_param *param;

param = (fit_param *)vparam;

return LAST_IND + 1;

}

#undef I_ud

#undef I_s

#undef I_umd

#undef LAST_IND

size_t fm_comb_phypt_taylor_scaleset_taylor_npar(void* vparam)

{

return fm_phypt_taylor_npar(vparam) + fm_scaleset_taylor_npar(vparam);

}