Change minimizer¶

This example shows how to change the minimization engine for refinement.

Import EasyDiffraction¶

In [2]:

import easydiffraction as ed

import easydiffraction as ed

Create a job¶

Create a job — the main object to store all the information

In [3]:

job = ed.Job()

job = ed.Job()

Define a model¶

Download the CIF file from the EasyDiffraction repository on GitHub

In [4]:

ed.download_from_repository('lbco_adp.cif', destination='data')

ed.download_from_repository('lbco_adp.cif', destination='data')

Load a phase from the downloaded CIF file

In [5]:

job.add_phase_from_file('data/lbco_adp.cif')
print(job.phases)

job.add_phase_from_file('data/lbco_adp.cif') print(job.phases)

Collection of 1 phases: ['lbco']

Show phase info in CIF format

In [6]:

phase = job.phases['lbco']
print(phase.cif)

phase = job.phases['lbco'] print(phase.cif)

data_lbco
_cell_length_a 3.89
_cell_length_b 3.89
_cell_length_c 3.89
_cell_angle_alpha 90.00000000
_cell_angle_beta 90.00000000
_cell_angle_gamma 90.00000000
_space_group_name_H-M_ref 'P m -3 m'

loop_
_atom_site_label
_atom_site_type_symbol
_atom_site_fract_x
_atom_site_fract_y
_atom_site_fract_z
_atom_site_occupancy
_atom_site_adp_type
_atom_site_B_iso_or_equiv
La La 0.00000000 0.00000000 0.00000000 0.5 Biso 0.4958
Ba Ba 0.00000000 0.00000000 0.00000000 0.5 Biso 0.4943
Co Co 0.5 0.5 0.5 1.00000000 Biso 0.2567
O O 0.00000000 0.5 0.5 1.00000000 Biso 1.4041

Display the crystal structure of a given model

In [7]:

job.show_crystal_structure(id='lbco')

job.show_crystal_structure(id='lbco')

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Define an experiment¶

Download the data file from the EasyDiffraction repository on GitHub

In [8]:

ed.download_from_repository('hrpt.xye', destination='data')

ed.download_from_repository('hrpt.xye', destination='data')

Show content of the downloaded file (first 6 lines)

In [9]:

with open('data/hrpt.xye') as f:
    print(''.join(f.readlines()[:6]))

with open('data/hrpt.xye') as f: print(''.join(f.readlines()[:6]))

#  2theta intensity   su
   10.00    167.00   12.60
   10.05    157.00   12.50
   10.10    187.00   13.30
   10.15    197.00   14.00
   10.20    164.00   12.50

Load experimentally measured data from a file in XYE format

In [10]:

job.add_experiment_from_file('data/hrpt.xye')

job.add_experiment_from_file('data/hrpt.xye')

Display the experimentally measured data

In [11]:

job.show_experiment_chart()

job.show_experiment_chart()

Define a point background

In [12]:

background_points = [(10.0, 170),
                    (165.0, 170)]

job.set_background(background_points)

background_points = [(10.0, 170), (165.0, 170)] job.set_background(background_points)

Display the experiment chart after setting the background

In [13]:

job.show_experiment_chart()

job.show_experiment_chart()

Perform an analysis¶

Display the analysis chart before setting initial parameter values

In [14]:

job.show_analysis_chart()

job.show_analysis_chart()

Create aliases for the two types of experimental parameters

In [15]:

pattern = job.pattern
instrument = job.instrument

pattern = job.pattern instrument = job.instrument

Change the default value of the wavelength used in the experiment and display the analysis chart again

In [16]:

instrument.wavelength = 1.494
job.show_analysis_chart()

instrument.wavelength = 1.494 job.show_analysis_chart()

Select parameters to be refined

In [17]:

phase.scale.free = True
phase.cell.length_a.free = True
pattern.zero_shift.free = True
instrument.resolution_u.free = True
instrument.resolution_v.free = True
instrument.resolution_w.free = True
instrument.resolution_y.free = True

phase.scale.free = True phase.cell.length_a.free = True pattern.zero_shift.free = True instrument.resolution_u.free = True instrument.resolution_v.free = True instrument.resolution_w.free = True instrument.resolution_y.free = True

Set the initial values of the parameters to be refined and display the analysis chart again

In [18]:

phase.scale = 6
phase.cell.length_a = 3.88
pattern.zero_shift = 0.3
instrument.resolution_u = 0.1
instrument.resolution_v = -0.1
instrument.resolution_w = 0.1
instrument.resolution_y = 0
job.show_analysis_chart()

phase.scale = 6 phase.cell.length_a = 3.88 pattern.zero_shift = 0.3 instrument.resolution_u = 0.1 instrument.resolution_v = -0.1 instrument.resolution_w = 0.1 instrument.resolution_y = 0 job.show_analysis_chart()

Print parameters to be refined (free parameters) before fitting with Lmfit

In [19]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['lbco'].cell.length_a	3.88	Å	0.0
2	.phases['lbco'].scale	6.00		0.0
3	.instrument.resolution_u	0.10		0.0
4	.instrument.resolution_v	-0.10		0.0
5	.instrument.resolution_w	0.10		0.0
6	.instrument.resolution_y	0.00		0.0

Show the current minimization engine

In [20]:

print(job.analysis.current_minimizer)

print(job.analysis.current_minimizer)

LMFit_leastsq

Start minimization using the default minimizer (Least Squares method from the Lmfit library)

In [21]:

job.fit()

job.fit()

Fitting result
Status: 🥳 Success
Duration: ⌛ 2.10 s
Reduced χ²: 👍 1.31

Print the refined parameters after fitting with Lmfit

In [22]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['lbco'].cell.length_a	3.890880	Å	0.000040
2	.phases['lbco'].scale	9.202849		0.032388
3	.instrument.resolution_u	0.081730		0.003211
4	.instrument.resolution_v	-0.115064		0.006879
5	.instrument.resolution_w	0.118244		0.003306
6	.instrument.resolution_y	0.087071		0.001971
7	.pattern.zero_shift	0.622785	deg	0.001079

Display the analysis chart after the fitting with Lmfit

In [23]:

job.show_analysis_chart()

job.show_analysis_chart()

Show list of available minimisation engines

In [24]:

for mini in job.analysis.available_minimizers:
    print(mini)

for mini in job.analysis.available_minimizers: print(mini)

LMFit
LMFit_leastsq
LMFit_powell
LMFit_cobyla
LMFit_differential_evolution
LMFit_scipy_least_squares
Bumps
Bumps_simplex
Bumps_newton
Bumps_lm
DFO
DFO_leastsq

Change the minimization method to simplex from the Bumps library

In [25]:

job.analysis.current_minimizer = 'Bumps_lm'
print(job.analysis.current_minimizer)

job.analysis.current_minimizer = 'Bumps_lm' print(job.analysis.current_minimizer)

Bumps_lm

Reset the free parameters to their initial values (before fitting with Lmfit) and display the analysis chart

In [26]:

phase.scale = 6
phase.cell.length_a = 3.88
pattern.zero_shift = 0.3
instrument.resolution_u = 0.1
instrument.resolution_v = -0.1
instrument.resolution_w = 0.1
instrument.resolution_y = 0
job.show_analysis_chart()

phase.scale = 6 phase.cell.length_a = 3.88 pattern.zero_shift = 0.3 instrument.resolution_u = 0.1 instrument.resolution_v = -0.1 instrument.resolution_w = 0.1 instrument.resolution_y = 0 job.show_analysis_chart()

Print free parameters before the fitting with Bumps

In [27]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['lbco'].cell.length_a	3.88	Å	0.000040
2	.phases['lbco'].scale	6.00		0.032388
3	.instrument.resolution_u	0.10		0.003211
4	.instrument.resolution_v	-0.10		0.006879
5	.instrument.resolution_w	0.10		0.003306
6	.instrument.resolution_y	0.00		0.001971
7	.pattern.zero_shift	0.30	deg	0.001079

Start minimization with Bumps

In [28]:

job.fit()

job.fit()

Fitting result
Status: 🥳 Success
Duration: ⌛ 2.08 s
Reduced χ²: 👍 1.31

Print free parameters after the fitting with Bumps

In [29]:

job.show_free_parameters()

job.show_free_parameters()

	name	value		error
1	.phases['lbco'].cell.length_a	3.890896	Å	0.000035
2	.phases['lbco'].scale	9.202826		0.028286
3	.instrument.resolution_u	0.081818		0.002806
4	.instrument.resolution_v	-0.115158		0.006010
5	.instrument.resolution_w	0.118262		0.002888
6	.instrument.resolution_y	0.087064		0.001721
7	.pattern.zero_shift	0.623144	deg	0.000943

Display the analysis chart after the fitting with Bumps

In [30]:

job.show_analysis_chart()

job.show_analysis_chart()