Fit - inequality constraint

import nexus as nx
#import numpy as np

# load example spectrum
detuning, intensity = nx.data.Load("spectrum_equality.txt",
                                    x_index = 0,
                                    intensity_index = 1)

#setup fit parameters
isomer = nx.Var(0.8, min = 0, max = 2, fit = True, id="isomer")

# assign to sites
site1 = nx.Hyperfine(
    id = "site 1",
    weight = 0.5,
    isomer = isomer,
    magnetic_field = nx.Var(value = 32, min = 0, max = 35, fit = True, id = "mag field 1"),
    isotropic = False)

site2 = nx.Hyperfine(
    id = "site 2",
    weight = 0.5,
    isomer = isomer,
    magnetic_field = nx.Var(value = 14, min = 0, max = 35, fit = True, id = "mag field 2"),
    isotropic = False)

mat_Fe = nx.Material.Template(nx.lib.material.Fe_enriched)

mat_Fe.hyperfine_sites = [site1, site2]

#create sample
lay_Fe = nx.Layer(id = "Fe",
                  material = mat_Fe,
                  thickness = 2800)

sample = nx.Sample(id = "sample",
                   layers = [lay_Fe],
                   geometry = "f")

beam  = nx.Beam()
beam.LinearSigma()

exp = nx.Experiment(beam = beam,
                    objects = [sample],
                    isotope = nx.moessbauer.Fe57,
                    id = "my exp")

energy_spec = nx.EnergySpectrum(exp,
                                detuning,
                                intensity_data = intensity,
                                id = "energy spec")

fit = nx.Fit([energy_spec],
             inequalities = [lambda: site1.magnetic_field.value < site2.magnetic_field.value])

fit.options.method = "PagmoDiffEvol"

fit()

Run Fit instance with id:

Starting fit with 1 measurement data set(s) and 5 fit parameter(s):

  no. |                           id |       initial value |              min |              max
    0 |                   ES scaling |             88182.9 |                0 |      8.81829e+06
    1 |                    ES backgr |             7777.25 |                0 |           777725
    2 |                       isomer |                 0.8 |                0 |                2
    3 |                  mag field 1 |                  32 |                0 |               35
    4 |                  mag field 2 |                  14 |                0 |               35

Using 0 equality constraint(s) on parameter(s):

Using 1 inequality constraint(s).


Calling Pagmo solver with fit method PagmoDiffEvol

  population: 60
  iterations: 100

  cost = 5.335555e+02

Calling ceres solver with fit method LevMar

Ceres Solver Report: Iterations: 4, Initial cost: 5.335555e+02, Final cost: 3.432344e+02, Termination: CONVERGENCE

Gradient error analysis.


Fit performed with algorithm:
PagmoDiffEvol
Local algorithm:
LevMar
Error analysis:
Gradient

Using 5 fit parameter(s):

  no. |                           id |          fit value |   +/- std dev | initial value |          min |          max
    0 |                   ES scaling |             100154 |       223.664 |       88182.9 |            0 |  8.81829e+06
    1 |                    ES backgr |                  0 |         170.2 |       7777.25 |            0 |       777725
    2 |                       isomer |            1.00011 |   0.000490228 |           0.8 |            0 |            2
    3 |                  mag field 1 |            9.99901 |    0.00644206 |            32 |            0 |           35
    4 |                  mag field 2 |            33.0033 |    0.00650444 |            14 |            0 |           35

Correlation matrix:

  no. |        0        1        2        3        4
 -----|---------------------------------------------
    0 |    1.000   -0.978    0.001    0.055   -0.002
    1 |   -0.978    1.000   -0.001   -0.056    0.002
    2 |    0.001   -0.001    1.000    0.002    0.001
    3 |    0.055   -0.056    0.002    1.000    0.010
    4 |   -0.002    0.002    0.001    0.010    1.000

Using 0 equality constraint(s) on parameter(s):

and 1 inequality constraint(s).

Total cost = 3.432e+02

cost for each FitMeasurement is:

  no. |                           id |                cost |                   %
    0 |                  energy spec |           3.432e+02 |             100.000

Fit instance with id "" finished.

energy_spec.Plot()