#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Feb 23 09:17:34 2022
@author: haascp
"""
[docs]def get_non_comp_sum(parafac_factors, start_slice, end_slice):
"""
Get summed integrals from all components except the highest inegral component
in one slice of the PARAFAC factors.
"""
n_comps = parafac_factors[0].shape[1]
non_comp_sum_list = []
for i in range(n_comps):
sorted_integrals = sorted(parafac_factors[2][:, i][start_slice:end_slice])
non_comp_sum_i = sum(sorted_integrals)
non_comp_sum_list.append(non_comp_sum_i)
sorted_sums_ex_max = sorted(non_comp_sum_list)[:-1]
return sum(sorted_sums_ex_max)
[docs]def get_all_non_comp_sum(parafac_factors, comp_tensor_shape,
show_parafac_analytics):
"""
Iterative PARAFAC approach is a minimization problem. Based on the component
tensor data shape, the maximal sum of integrals is found for every component
part in the data tensor. The integrals of all other components in this
component part are summed up and should be ideally zero (only component
spectrum contributes to component part of tensor). This final sum
is the minimization objective for the iterative PARAFAC approach.
"""
start_slice = 0
end_slice = 0
non_comp_sum_list = []
for i in range(len(comp_tensor_shape)):
end_slice += comp_tensor_shape[i]
non_comp_sum = get_non_comp_sum(parafac_factors, start_slice, end_slice)
non_comp_sum_list.append(non_comp_sum)
start_slice += comp_tensor_shape[i]
if show_parafac_analytics:
print(f"objective_val_non_comp = {sum(non_comp_sum_list)}")
return sum(non_comp_sum_list)
[docs]def get_comp_sum(parafac_factors, start_slice, end_slice):
"""
Get summed integrals from the highest inegral component in one slice of
PARAFAC factors.
"""
n_comps = parafac_factors[0].shape[1]
non_comp_sum_list = []
for i in range(n_comps):
sorted_integrals = sorted(parafac_factors[2][:, i][start_slice:end_slice])
non_comp_sum_i = sum(sorted_integrals)
non_comp_sum_list.append(non_comp_sum_i)
max_sum = sorted(non_comp_sum_list)[-1]
return max_sum
[docs]def get_all_comp_sum(parafac_factors, comp_tensor_shape, show_parafac_analytics):
"""
Iterative PARAFAC approach is a maximization problem. Based on the component
tensor data shape, the maximal sum of integrals is found for every component
part in the data tensor. The integrals of these component integrals are
summed up. This sum is the maximization objective for the iterative PARAFAC
approach.
"""
start_slice = 0
end_slice = 0
comp_sum_list = []
for i in range(len(comp_tensor_shape)):
end_slice += comp_tensor_shape[i]
comp_sum = get_comp_sum(parafac_factors, start_slice, end_slice)
comp_sum_list.append(comp_sum)
start_slice += comp_tensor_shape[i]
if show_parafac_analytics:
print(f"objective_val_comp = {sum(comp_sum_list)}")
return sum(comp_sum_list)
[docs]def get_total_integral_sum(parafac_factors, show_parafac_analytics):
"""
Iterative PARAFAC approach is a maximization problem. This objective function
assumes that the PARAFAC model is best, when the overall integral over all
slices is maximized.
"""
n_comps = parafac_factors[0].shape[1]
sum_list = []
for i in range(n_comps):
integrals = parafac_factors[2][:, i]
sum_i = sum(integrals)
sum_list.append(sum_i)
total_sum = sum(sum_list)
if show_parafac_analytics:
print(f"objective_total_sum = {total_sum}")
return total_sum
[docs]def get_impure_integral_sum(parafac_factors, show_parafac_analytics):
"""
This objective function assumes that the PARAFAC model is best, when the
summed integral of all components in the impure peak slice is maximized.
"""
integrals = parafac_factors[2][-1, :]
sum_i = sum(integrals)
if show_parafac_analytics:
print(f"impure_peak_sum = {sum_i}")
return sum_i