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double_analysis.py
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'''
Author: Rajnandini Mukherjee
Double fitting analysis code which runs loops of fit ranges of both the C_Kpi
correlators - with point-like kaon sources and smeared kaon sources,in a
combined fit with pion and kaon two-point functions, and other correlation
functions with information on around-the-world (ATW) matrix elements, to single
out the value of Delta E_Kpi and hence the scattering length. The data for point
and smeared sources is also combined for one big global fit in each of the
isospin channels.'''
data_dir = 'correlators/'
import numpy as np
import matplotlib.pyplot as plt
from plot_settings import plotparams
plt.rcParams.update(plotparams)
T, K = 96, 500 # lattice time extent, number of bootstrap samples
from fit_routine import *
from scipy.linalg import block_diag
from numpy.linalg import svd, inv
def svd_model(cov, cuts=1, **kwargs):
''' models the covariance matrix by removing smallest
singular values of the inverse matrix'''
u, s, vt = svd(cov)
s_inv = 1/s
for i in range(cuts):
s_inv[np.argmax(s_inv)] = 0
L = vt.T@np.diag(s_inv**0.5)
return L
def cov_block_diag(obj):
'''gives block diagonal form to the covarianc matrix'''
N = len(obj.corrs)
covs = np.empty(N,dtype=object)
for n in range(N):
(s,e,t) = obj.corrs[n].interval
covs[n] = obj.corrs[n].COV[s:e+1:t, s:e+1:t]
return block_diag(*covs)
delta = 1
def KKpipi_ansatz(params, t, **kwargs):
c0, A, m_p = params
if 'm_pion' in kwargs.keys():
m_p = kwargs['m_pion']
return c0 + A*np.exp(2*m_p*t)
def piKpiK_ansatz(params, t, **kwargs):
c0, A, m_p = params
if 'm_pion' in kwargs.keys():
m_p = kwargs['m_pion']
return c0 + A*np.exp(-2*m_p*t)
def CKpi_ansatz(params, t, **kwargs):
A_CKpi, m_p, m_k, DE, c0_KKpipi, c0_piKpiK = params
EKpi = m_p + m_k + DE
denom = cosh([1,m_p],t,T=T)*cosh([1,m_k],t,T=T)
interesting = A_CKpi*cosh([1,EKpi],t,T=T)/denom
c0_KKpipi = c0_KKpipi*np.exp(m_k*delta)
c0_piKpiK = c0_piKpiK*np.exp(-m_k*delta)
RTW_KKpipi = c0_KKpipi*np.exp(-m_p*t -m_k*(T-t))/denom
RTW_piKpiK = c0_piKpiK*np.exp(-m_k*t -m_p*(T-t))/denom
return interesting + RTW_KKpipi + RTW_piKpiK
L = 48
c1 = -2.837297
c2 = 6.375183
def scat_length(params, **kwargs):
A_p, m_p = params[:2]
A_k, A_k_sm, m_k = params[2:5]
A_KKpipi, A_KKpipi_sm, c0_KKpipi, c0_KKpipi_sm = params[5:9]
A_piKpiK, A_piKpiK_sm, c0_piKpiK, c0_piKpiK_sm = params[9:13]
A_CKpi, A_CKpi_sm, DE = params[13:16]
k0 = DE
k1 = 2*np.pi*(m_p+m_k)/(m_p*m_k*(L**3))
k2 = k1*c1/L
k3 = k1*c2/(L**2)
roots = np.roots([k3,k2,k1,k0])
a = np.real(roots[np.isreal(roots)][0])
return a*m_p
def alt_scat_length(params, **kwargs):
A_p, m_p = params[:2]
A_k, A_k_sm, m_k = params[2:5]
A_KKpipi, A_KKpipi_sm, c0_KKpipi, c0_KKpipi_sm = params[5:9]
A_piKpiK, A_piKpiK_sm, c0_piKpiK, c0_piKpiK_sm = params[9:13]
A_CKpi, A_CKpi_sm, DE = params[13:16]
mu = m_p*m_k/(m_p+m_k)
k0 = DE
k1 = 2*np.pi/(mu*(L**3))
k2 = k1*c1/L
k3 = k1*c2/(L**2)
roots = np.roots([k3,k2,k1,k0])
a = np.real(roots[np.isreal(roots)][0])
return a*mu
def combined_ansatz(params, t, **kwargs):
A_p, m_p, A_k, m_k = params[:4]
A_KKpipi, c0_KKpipi = params[4:6]
A_piKpiK, c0_piKpiK = params[6:8]
A_CKpi, DE = params[8:]
pion_part = cosh([A_p,m_p],pion.x,T=T)
kaon_part = cosh([A_k,m_k],kaon.x,T=T)
I_idx = int(kwargs['I']-0.5)
KKpipi_part = KKpipi_ansatz([c0_KKpipi,A_KKpipi,m_p],ratios[0+I_idx,2].x)
piKpiK_part = piKpiK_ansatz([c0_piKpiK,A_piKpiK,m_p],ratios[2+I_idx,2].x)
CKpi_part = CKpi_ansatz([A_CKpi, m_p, m_k, DE, c0_KKpipi, c0_piKpiK],
KpiI12_ratio.x if I_idx==0 else KpiI32_ratio.x)
return np.concatenate((pion_part, kaon_part, KKpipi_part, piKpiK_part,
CKpi_part), axis=0)
def pt_sm_combined(params, t, **kwargs):
A_p, m_p = params[:2]
A_k, A_k_sm, m_k = params[2:5]
A_KKpipi, A_KKpipi_sm, c0_KKpipi, c0_KKpipi_sm = params[5:9]
A_piKpiK, A_piKpiK_sm, c0_piKpiK, c0_piKpiK_sm = params[9:13]
A_CKpi, A_CKpi_sm, DE = params[13:16]
pion_part = cosh([A_p,m_p],pion.x,T=T)
kaon_part = cosh([A_k,m_k],kaon.x,T=T)
kaon_sm_part = cosh([A_k_sm, m_k], kaon_sm.x, T=T)
I_idx = int(kwargs['I']-0.5)
KKpipi_part = KKpipi_ansatz([c0_KKpipi,A_KKpipi,m_p],ratios[0+I_idx,2].x)
piKpiK_part = piKpiK_ansatz([c0_piKpiK,A_piKpiK,m_p],ratios[2+I_idx,2].x)
KKpipi_sm_part = KKpipi_ansatz([c0_KKpipi_sm,A_KKpipi_sm,m_p],ratios_sm[0+I_idx,2].x)
piKpiK_sm_part = piKpiK_ansatz([c0_piKpiK_sm,A_piKpiK_sm,m_p],ratios_sm[2+I_idx,2].x)
CKpi_part = CKpi_ansatz([A_CKpi, m_p, m_k, DE, c0_KKpipi, c0_piKpiK],
KpiI12_ratio.x if I_idx==0 else KpiI32_ratio.x)
CKpi_sm_part = CKpi_ansatz([A_CKpi_sm, m_p, m_k, DE, c0_KKpipi_sm, c0_piKpiK_sm], t)
return np.concatenate((pion_part, kaon_part, kaon_sm_part, KKpipi_part,
piKpiK_part, KKpipi_sm_part, piKpiK_sm_part,
CKpi_part, CKpi_sm_part))
from correlation_functions import *
pion, kaon, ratios, KpiI12_ratio, KpiI32_ratio = get_correlators(data_dir, False)
pion2, kaon_sm, ratios_sm, KpiI12_sm_ratio, KpiI32_sm_ratio = get_correlators(data_dir, True)
guess = [2e+4, 0.08, 1e+3, 1e+2, 0.28, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0.001]
# modified hyperweights for combined fits
hyperweights = {'pvalue_cost':1,
'fit_stbl_cost':1,
'err_cost':1,
'val_stbl_cost':1}
double_fit12_dict = {}
double_fit32_dict = {}
import warnings
warnings.filterwarnings('ignore')
from tqdm import tqdm
pbar = tqdm(total=5*6*5*6)
for pt_t_min in range(8,18,2):
for pt_delta_t in range(3,15,2):
KpiI12_ratio.interval = (pt_t_min, pt_t_min+pt_delta_t,1)
KpiI12_ratio.x = np.arange(pt_t_min, pt_t_min+pt_delta_t+1,1)
double_fit12_dict[str(KpiI12_ratio.interval)] = {}
KpiI32_ratio.interval = (pt_t_min, pt_t_min+pt_delta_t,1)
KpiI32_ratio.x = np.arange(pt_t_min, pt_t_min+pt_delta_t+1,1)
double_fit32_dict[str(KpiI32_ratio.interval)] = {}
for sm_t_min in range(8,18,2):
for sm_delta_t in range(3,15,2):
KpiI12_sm_ratio.interval = (sm_t_min, sm_t_min+sm_delta_t,1)
KpiI12_sm_ratio.x = np.arange(sm_t_min, sm_t_min+sm_delta_t+1,1)
double_fit12_dict[str(KpiI12_ratio.interval)][str(KpiI12_sm_ratio.interval)] = {}
KpiI32_sm_ratio.interval = (sm_t_min, sm_t_min+sm_delta_t,1)
KpiI32_sm_ratio.x = np.arange(sm_t_min, sm_t_min+sm_delta_t+1,1)
double_fit32_dict[str(KpiI32_ratio.interval)][str(KpiI32_sm_ratio.interval)] = {}
pt_sm_corrI12 = stat_object([pion, kaon, kaon_sm, ratios[0,2], ratios[2,2],
ratios_sm[0,2], ratios_sm[2,2], KpiI12_ratio,
KpiI12_sm_ratio], object_type='combined', K=K,
name='pt_sm_corrI12')
pt_sm_corrI12.fit((0,pt_sm_corrI12.T-1,1), pt_sm_combined, guess,
full_fit=False,
#correlated=False,
COV_model=cov_block_diag,
I=0.5, index=8,
calc_func=[scat_length, alt_scat_length])
double_fit12_dict[str(KpiI12_ratio.interval)][str(KpiI12_sm_ratio.interval)].update(pt_sm_corrI12.fit_dict)
pt_sm_corrI32 = stat_object([pion, kaon, kaon_sm, ratios[1,2], ratios[3,2],
ratios_sm[1,2], ratios_sm[3,2], KpiI32_ratio,
KpiI32_sm_ratio], object_type='combined', K=K,
name='pt_sm_corrI32')
pt_sm_corrI32.fit((0,pt_sm_corrI32.T-1,1), pt_sm_combined, guess,
full_fit=False,
#correlated=False,
COV_model=cov_block_diag,
I=1.5, index=8,
calc_func=[scat_length, alt_scat_length])
double_fit32_dict[str(KpiI32_ratio.interval)][str(KpiI32_sm_ratio.interval)].update(pt_sm_corrI32.fit_dict)
pbar.update()
import pickle
#df12, df32 = pickle.load(open('pickles/double_fit_dicts.p','rb'))
#df12.update(double_fit12_dict)
#df32.update(double_fit32_dict)