Proportional Constaints - Molass Technical Report

from molass import get_version
assert get_version() >= '0.7.4', "This tutorial requires molass version 0.7.4 or higher."
from molass_data import get_version
assert get_version() >= '0.3.0', "This tutorial requires molass_data version 0.3.0 or higher."
from molass_data import SAMPLE4
from molass.DataObjects import SecSaxsData as SSD
ssd = SSD(SAMPLE4)
trimmed_ssd = ssd.trimmed_copy()
corrected_ssd = trimmed_ssd.corrected_copy()

import numpy as np
import matplotlib.pyplot as plt
from molass.Decompose.Proportional import decompose_proportionally
icurve  = corrected_ssd.xr.get_icurve()
result = decompose_proportionally(icurve, [3,2,1], debug=True)

[0.47908885 0.28660209 0.23430906]

[0.50000694 0.33332614 0.16666691]

result

       message: Maximum number of function evaluations has been exceeded.
       success: False
        status: 1
           fun: -4.226653800002927
             x: [ 5.477e-02  8.259e+01  7.101e+00 -1.572e-05  2.702e-02
                  9.666e+01  9.439e+00  3.990e+00  1.152e-02  1.111e+02
                  1.095e+01  5.995e+00]
           nit: 1658
          nfev: 2400
 final_simplex: (array([[ 5.477e-02,  8.259e+01, ...,  1.095e+01,
                         5.995e+00],
                       [ 5.477e-02,  8.259e+01, ...,  1.095e+01,
                         5.995e+00],
                       ...,
                       [ 5.477e-02,  8.259e+01, ...,  1.095e+01,
                         5.995e+00],
                       [ 5.477e-02,  8.259e+01, ...,  1.095e+01,
                         5.995e+00]], shape=(13, 12)), array([-4.227e+00, -4.227e+00, ..., -4.227e+00, -4.227e+00],
                      shape=(13,)))

rgcurve = corrected_ssd.xr.compute_rgcurve()

num_trails = 8
species1_proportions = np.ones(num_trails) * 3
species2_proportions = np.linspace(1, 3, num_trails)
proportions = np.array([species1_proportions, species2_proportions]).T
proportions

array([[3.        , 1.        ],
       [3.        , 1.28571429],
       [3.        , 1.57142857],
       [3.        , 1.85714286],
       [3.        , 2.14285714],
       [3.        , 2.42857143],
       [3.        , 2.71428571],
       [3.        , 3.        ]])

from importlib import reload
import molass.Decompose.VaryUtils
reload(molass.Decompose.VaryUtils)
from molass.Decompose.VaryUtils import _plot_varied_decompositions_impl
_plot_varied_decompositions_impl(icurve, proportions, rgcurve=rgcurve, best=3)

species3_proportions = np.ones(num_trails) * 1
proportions = np.array([species1_proportions, species2_proportions, species3_proportions]).T
proportions

array([[3.        , 1.        , 1.        ],
       [3.        , 1.28571429, 1.        ],
       [3.        , 1.57142857, 1.        ],
       [3.        , 1.85714286, 1.        ],
       [3.        , 2.14285714, 1.        ],
       [3.        , 2.42857143, 1.        ],
       [3.        , 2.71428571, 1.        ],
       [3.        , 3.        , 1.        ]])

_plot_varied_decompositions_impl(icurve, proportions, rgcurve=rgcurve, best=3)

from molass_data import SAMPLE1
ssd = SSD(SAMPLE1)
trimmed_ssd = ssd.trimmed_copy()
corrected_ssd = trimmed_ssd.corrected_copy()

zeros at the angular ends of error data have been replaced with the adjacent values.

modified_decomposition = corrected_ssd.quick_decomposition(num_components=3, proportions=[0.32, 0.20, 0.48])
plot2 = modified_decomposition.plot_components(title="Modified Decomposition of Sample1 (num_components=3, proportions=[0.32, 0.20, 0.48])")