def residual_cubic(param):
'''Function which computes the residual (as sum of squares) comparing the
ratio of expt to theoretical intensity ratio to the sensitivity profile
modelled as a line, ( 1+ c1*x + c2*x**2 + c3*x**3 )
param : T, c1, c2, c3
'''
TK = 298
sosD2 = bp.sumofstate_D2(TK)
sosHD = bp.sumofstate_HD(TK)
computed_D2 = compute_series_para.spectra_D2(TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
computed_HD = compute_series_para.spectra_HD(TK, OJ_HD, QJ_HD,
SJ_HD, sosHD)
# ------ D2 ------
trueR_D2 = gen_intensity_mat(computed_D2, 2)
expt_D2 = gen_intensity_mat(dataD2, 0)
I_D2 = np.divide(expt_D2, trueR_D2)
#I_D2 = clean_mat(I_D2)
# ----------------
# ------ HD ------
trueR_HD = gen_intensity_mat(computed_HD, 2)
expt_HD = gen_intensity_mat(dataHD, 0)
I_HD = np.divide(expt_HD, trueR_HD)
#I_HD = clean_mat(I_HD)
# ----------------
# I_HD = clean_and_scale_elements(I_HD, index_HD, 2)
# I_D2 = clean_and_scale_elements(I_D2, index_D2, 2)
# generate the RHS : sensitivity factor
sD2 = gen_s_cubic(computed_D2, param)
sHD = gen_s_cubic(computed_HD, param)
# residual matrix
eD2 = I_D2 - sD2
eHD = I_HD - sHD
eD2 = np.multiply(wMat_D2, eD2)
eHD = np.multiply(wMat_HD, eHD)
eD2 = clean_mat(eD2)
eHD = clean_mat(eHD)
# E = np.sum(np.square(eD2)) + np.sum(np.square(eHD))
eD2[indexD2] = 0
eHD[indexHD] = 0
#E = np.sum(np.abs(eD2)) + np.sum(np.abs(eHD))
E = np.sum(np.square(eD2)) + np.sum(np.square(eHD))
return(E)
def T_independent_D2_set_nan(array):
'''
elements in 'array' which correspond to frequencies not
analyzed are set to nan, for D2
'''
TK = 298 # --------------------------------
sosD2 = bp.sumofstate_D2(TK)
computed_D2 = compute_series_para.spectra_D2( TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
calc_298_D2 = gen_intensity_mat(computed_D2, 2)
TK = 1000 # -------------------------------
sosD2 = bp.sumofstate_D2(TK)
computed_D2 = compute_series_para.spectra_D2( TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
calc_600_D2=gen_intensity_mat (computed_D2, 2)
diff_D2 = calc_298_D2 - calc_600_D2
cr_D2 = clean_mat(diff_D2)
return set_nan_if_foundzero(cr_D2, array)
def T_independent_index():
TK = 298 # --------------------------------
sosD2 = bp.sumofstate_D2(TK)
sosHD = bp.sumofstate_HD(TK)
computed_D2 = compute_series_para.spectra_D2( TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
computed_HD = compute_series_para.spectra_HD( TK, OJ_HD, QJ_HD,
SJ_HD, sosHD)
calc_298_D2 = gen_intensity_mat(computed_D2, 2)
calc_298_HD = gen_intensity_mat(computed_HD, 2)
TK = 1000 # -------------------------------
sosD2 = bp.sumofstate_D2(TK)
sosHD = bp.sumofstate_HD(TK)
computed_D2 = compute_series_para.spectra_D2( TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
computed_HD = compute_series_para.spectra_HD( TK, OJ_HD, QJ_HD,
SJ_HD, sosHD)
calc_600_D2=gen_intensity_mat (computed_D2, 2)
calc_600_HD=gen_intensity_mat (computed_HD, 2)
diff_D2 = calc_298_D2 - calc_600_D2
diff_HD = calc_298_HD - calc_600_HD
cr_D2 = clean_mat(diff_D2)
cr_HD = clean_mat(diff_HD)
index_D2 = np.nonzero(np.abs(cr_D2) >1e-10)
index_HD = np.nonzero(np.abs(cr_HD) >1e-10)
return index_D2, index_HD
def spectra_D2(T, Js, Jas):
"""Compute in intensities and position for rotational Raman bands of D2 """
#--- nuclear spin statistics ------------
g_even = 6 # deuterium
g_odd = 3
# ---------------------------------------
sos = bp.sumofstate_D2(T)
# define arrays for intensity, position and J_{i}
specD2 = np.zeros(shape=(Js + Jas, 4))
posnD2 = np.zeros(shape=(Js + Jas, 1))
spectraD2 = np.zeros(shape=(Js + Jas, 1))
# Stokes lines
for i in range(0, Js + 1):
E = eJD2v0[i]
energy = (-1 * E * H * C)
popn = (2 * i + 1) * math.exp(energy / (K * T))
bj = (3 * (i + 1) * (i + 2)) / (2 * (2 * i + 1) * (2 * i + 3))
position = (eJD2v0[i + 2] - eJD2v0[i])
gamma = ME_D2_532[i + 1][2]
if i % 2 == 0:
factor = popn * g_even * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
else:
factor = popn * g_odd * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
specD2[(Jas - 1) + i][0] = i
specD2[(Jas - 1) + i][1] = position
specD2[(Jas - 1) +
i][2] = factor # unnormalized intensity, arbitrary unit
specD2[(Jas - 1) + i][3] = omega - position
posnD2[(Jas - 1) + i] = position
spectraD2[(Jas - 1) + i] = factor
# Anti-Stokes lines
i = Jas
for i in range(Jas, 1, -1):
E = eJD2v0[i]
energy = (-1 * E * H * C)
popn = (2 * i + 1) * math.exp(energy / (K * T))
bj = (3 * (i) * (i - 1)) / (2 * (2 * i - 1) * (2 * i + 1))
position = -1 * (eJD2v0[i] - eJD2v0[i - 2])
gamma = ME_D2_532[i - 1][2]
if i % 2 == 0:
factor = popn * g_even * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
else:
factor = popn * g_odd * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
specD2[Jas - i][0] = i
specD2[Jas - i][1] = position
specD2[Jas - i][2] = factor # unnormalized intensity, arbitrary unit
specD2[Jas - i][3] = omega - position
posnD2[Jas - i] = position
spectraD2[Jas - i] = factor
# return the output
normalize1d(spectraD2)
specD2[:, 2] = spectraD2[:, 0] # assign normalized intensity
return specD2
def residual_linear(param):
'''Function which computes the residual (as sum of squares) comparing the
ratio of expt to theoretical intensity ratio to the sensitivity profile
modelled as a line, ( 1+ c1*x )
param : T, c1
'''
TK = 298
sosD2 = bp.sumofstate_D2(TK)
sosHD = bp.sumofstate_HD(TK)
computed_D2 = compute_series_para.spectra_D2(TK, OJ_D2, QJ_D2,
SJ_D2, sosD2)
computed_HD = compute_series_para.spectra_HD(TK, OJ_HD, QJ_HD,
SJ_HD, sosHD)
# ------ D2 ------
trueR_D2 = gen_intensity_mat(computed_D2, 2)
expt_D2 = gen_intensity_mat(dataD2, 0)
I_D2 = np.divide(expt_D2, trueR_D2)
#I_D2 = clean_mat(I_D2)
# ----------------
# ------ HD ------
trueR_HD = gen_intensity_mat(computed_HD, 2)
expt_HD = gen_intensity_mat(dataHD, 0)
I_HD = np.divide(expt_HD, trueR_HD)
#I_HD = clean_mat(I_HD)
# ----------------
#I_D2[indexD2] = 0
#I_HD[indexHD] = 0
# generate the RHS : sensitivity factor
sD2 = gen_s_linear(computed_D2, param)
sHD = gen_s_linear(computed_HD, param)
# weight
#errD2 = gen_weight(expt_D2)
#errHD = gen_weight(expt_HD)
#errD2 = clean_mat(errD2)
#errD2[indexD2] = 0
#np.savetxt("error_test", errD2, fmt='%3.3f')
# residual matrix
eD2 = I_D2 - sD2
eHD = I_HD - sHD
eD2 = np.multiply(wMat_D2, eD2)
eHD = np.multiply(wMat_HD, eHD)
eD2 = clean_mat(eD2)
eHD = clean_mat(eHD)
# E = np.sum(np.square(eD2)) + np.sum(np.square(eHD))
eD2[indexD2] = 0
eHD[indexHD] = 0
np.savetxt("errD2_test", eD2, fmt='%3.3f')
np.savetxt("errHD_test", eHD, fmt='%3.3f')
#E = np.sum(np.abs(eD2)) + np.sum(np.abs(eHD))
E = np.sum(np.square(eD2)) + np.sum(np.square(eHD))
return(E)
# ******************** CHECKS FOR INPUTS ************************
# ***************************************************************
# ------------------------------------------------
wMat_D2 = 1
wMat_HD = 1.2
wMat_H2 = 1
# checks for input done here
# generate calculated data for the entered J values
TK=299
sosD2 = bp.sumofstate_D2(TK)
sosHD = bp.sumofstate_HD(TK)
sosH2 = bp.sumofstate_H2(TK)
computed_D2 = compute_series_para.spectra_D2(TK, OJ_D2, QJ_D2, SJ_D2, sosD2)
computed_HD = compute_series_para.spectra_HD(TK, OJ_HD, QJ_HD, SJ_HD, sosHD)
computed_H2 = compute_series_para.spectra_H2_c(TK, OJ_H2, QJ_H2, sosH2)
# checks for dimension match done here
if (computed_D2.shape[0] != dataD2.shape[0]):
print('D2 : Dimension of input data does not match with the calculated\
spectra. Check input expt data or the J-indices entered.')
sys.exit("\tError: Quitting.")
if (computed_HD.shape[0] != dataHD.shape[0]):
print('H2 : Dimension of input data does not match with the calculated\
def spectra_D2(T, Js, Jas):
"""Compute in intensities and position for rotational Raman bands of D2 """
#--- nuclear spin statistics ------------
g_even = 6 # deuterium
g_odd = 3
# ---------------------------------------
sos = bp.sumofstate_D2(T)
# define arrays for intensity, position and J_{i}
specD2 = np.zeros(shape=(Js + Jas, 4))
posnD2 = np.zeros(shape=(Js + Jas, 1))
spectraD2 = np.zeros(shape=(Js + Jas, 1))
# Stokes lines
for i in range(0, Js + 1):
E = eJD2v0[i]
energy = (-1 * E * H * C)
popn = (2 * i + 1) * math.exp(energy / (K * T))
bj = (3 * (i + 1) * (i + 2)) / (2 * (2 * i + 1) * (2 * i + 3))
position = (eJD2v0[i + 2] - eJD2v0[i])
gamma = ME_D2_532[i + 1][2]
if i % 2 == 0:
factor = popn * g_even * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
else:
factor = popn * g_odd * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
specD2[(Jas - 1) + i][0] = i
specD2[(Jas - 1) + i][1] = position
specD2[(Jas - 1) +
i][2] = factor # unnormalized intensity, arbitrary unit
specD2[(Jas - 1) + i][3] = omega - position
posnD2[(Jas - 1) + i] = position
spectraD2[(Jas - 1) + i] = factor
# Anti-Stokes lines
i = Jas
for i in range(Jas, 1, -1):
E = eJD2v0[i]
energy = (-1 * E * H * C)
popn = (2 * i + 1) * math.exp(energy / (K * T))
bj = (3 * (i) * (i - 1)) / (2 * (2 * i - 1) * (2 * i + 1))
position = -1 * (eJD2v0[i] - eJD2v0[i - 2])
gamma = ME_D2_532[i - 1][2]
if i % 2 == 0:
factor = popn * g_even * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
else:
factor = popn * g_odd * bj * omega_sc * (
(omega_sc - position / 1e4)**3) * (gamma**2) / sos
specD2[Jas - i][0] = i
specD2[Jas - i][1] = position
specD2[Jas - i][2] = factor # unnormalized intensity, arbitrary unit
specD2[Jas - i][3] = omega - position
posnD2[Jas - i] = position
spectraD2[Jas - i] = factor
# return the output
normalize1d(spectraD2)
specD2[:, 2] = spectraD2[:, 0] # assign normalized intensity
return specD2
#print("Normalized spectra D2 :\n", spectraD2)
#np.savetxt('posnD2.txt', posnD2, fmt='%+6.6f') #save the band position.
#np.savetxt('spectraD2.txt', spectraD2, fmt='%+5.11f') #save the band intensity
#np.savetxt('specD2.txt', (specD2), fmt='%+5.12f') #save the 2D array which has data on
# initial J number, band position, band intensity and the position in abs. wavenumbers
#********************************************************************
#********************************************************************
#********************************************************************
#print(" Sum of state for H2 at 333 K : ", bp.sumofstate_H2(333))
#print(" Sum of state for HD at 375 K : ", bp.sumofstate_HD(375))
#print(" Sum of state for D2 at 298 K : ", bp.sumofstate_D2(298))
#********************************************************************
#print ("\n")
#spectra_H2(298, 6, 6)
#print ("\n")
#spectra_HD(298, 7, 7)
#print ("\n")
#spectra_D2(298, 6, 8)
# Spectra can be plotted using matplotlib simply using the band posn and the spectra
#********************************************************************