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"""Tests for the brute force algorithm (aka 'grid-search').
Use example problem described in the SciPy documentation:
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.brute.html
"""
import pickle
import numpy as np
from numpy.testing import assert_allclose, assert_equal
import pytest
from scipy import optimize
import lmfit
def func_scipy(z, *params):
x, y = z
a, b, c, d, e, f, g, h, i, j, k, l, scale = params
f1 = a * x**2 + b*x*y + c * y**2 + d*x + e*y + f
f2 = -g*np.exp(-((x-h)**2 + (y-i)**2) / scale)
f3 = -j*np.exp(-((x-k)**2 + (y-l)**2) / scale)
return f1 + f2 + f3
params = (2, 3, 7, 8, 9, 10, 44, -1, 2, 26, 1, -2, 0.5)
def func_lmfit(p):
par = p.valuesdict()
f1 = (par['a'] * par['x']**2 + par['b']*par['x']*par['y'] +
par['c'] * par['y']**2 + par['d']*par['x'] + par['e']*par['y'] +
par['f'])
f2 = (-1.0*par['g']*np.exp(-((par['x']-par['h'])**2 +
(par['y']-par['i'])**2) / par['scale']))
f3 = (-1.0*par['j']*np.exp(-((par['x']-par['k'])**2 +
(par['y']-par['l'])**2) / par['scale']))
return f1 + f2 + f3
@pytest.fixture
def params_lmfit():
"""Return lmfit.Parameters class with initial values and bounds."""
params = lmfit.Parameters()
params.add_many(
('a', 2, False), ('b', 3, False), ('c', 7, False), ('d', 8, False),
('e', 9, False), ('f', 10, False), ('g', 44, False), ('h', -1, False),
('i', 2, False), ('j', 26, False), ('k', 1, False), ('l', -2, False),
('scale', 0.5, False), ('x', -4.0, True, -4.0, 4.0, None, None),
('y', -2.0, True, -2.0, 2.0, None, None))
return params
def test_brute_lmfit_vs_scipy_default(params_lmfit):
"""TEST 1: using finite bounds with Ns=20, keep=50 and brute_step=None."""
assert params_lmfit['x'].brute_step is None
assert params_lmfit['y'].brute_step is None
rranges = ((-4, 4), (-2, 2))
ret = optimize.brute(func_scipy, rranges, args=params, full_output=True,
Ns=20, finish=None)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=20)
assert out.method == 'brute'
assert_equal(out.nfev, 20**len(out.var_names)) # Ns * nmb varying params
assert_equal(len(out.candidates), 50) # top-50 candidates are stored
assert_equal(ret[2], out.brute_grid) # grid identical
assert_equal(ret[3], out.brute_Jout) # function values on grid identical
# best-fit values identical / stored correctly in MinimizerResult
assert_equal(ret[0][0], out.brute_x0[0])
assert_equal(ret[0][0], out.params['x'].value)
assert_equal(ret[0][1], out.brute_x0[1])
assert_equal(ret[0][1], out.params['y'].value)
assert_equal(ret[1], out.brute_fval)
assert_equal(ret[1], out.residual)
def test_brute_lmfit_vs_scipy_Ns(params_lmfit):
"""TEST 2: using finite bounds, with Ns=40 and brute_step=None."""
rranges = ((-4, 4), (-2, 2))
ret = optimize.brute(func_scipy, rranges, args=params, full_output=True,
Ns=40, finish=None)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=40)
assert_equal(ret[2], out.brute_grid) # grid identical
assert_equal(ret[3], out.brute_Jout) # function values on grid identical
assert_equal(out.nfev, 40**len(out.var_names)) # Ns * nmb varying params
# best-fit values and function value identical
assert_equal(ret[0][0], out.brute_x0[0])
assert_equal(ret[0][1], out.brute_x0[1])
assert_equal(ret[1], out.brute_fval)
def test_brute_lmfit_vs_scipy_stepsize(params_lmfit):
"""TEST 3: using finite bounds and brute_step for both parameters."""
# set brute_step for parameters and assert whether that worked correctly
params_lmfit['x'].set(brute_step=0.25)
params_lmfit['y'].set(brute_step=0.25)
assert_equal(params_lmfit['x'].brute_step, 0.25)
assert_equal(params_lmfit['y'].brute_step, 0.25)
rranges = (slice(-4, 4, 0.25), slice(-2, 2, 0.25))
ret = optimize.brute(func_scipy, rranges, args=params, full_output=True,
Ns=20, finish=None)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute')
assert_equal(ret[2], out.brute_grid) # grid identical
assert_equal(ret[3], out.brute_Jout) # function values on grid identical
# best-fit values and function value identical
assert_equal(ret[0][0], out.brute_x0[0])
assert_equal(ret[0][1], out.brute_x0[1])
assert_equal(ret[1], out.brute_fval)
points_x = np.arange(rranges[0].start, rranges[0].stop, rranges[0].step).size
points_y = np.arange(rranges[1].start, rranges[1].stop, rranges[1].step).size
nmb_evals = points_x * points_y
assert_equal(out.nfev, nmb_evals)
def test_brute_lmfit_vs_scipy_Ns_stepsize(params_lmfit):
"""TEST 4: using finite bounds, using Ns, brute_step for 'x'."""
# set brute_step for x to 0.15 and reset to None for y and assert result
params_lmfit['x'].set(brute_step=0.15)
assert_equal(params_lmfit['x'].brute_step, 0.15)
rranges = (slice(-4, 4, 0.15), (-2, 2))
ret = optimize.brute(func_scipy, rranges, args=params, full_output=True,
Ns=10, finish=None)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=10)
assert_equal(ret[2], out.brute_grid) # grid identical
assert_equal(ret[3], out.brute_Jout) # function values on grid identical
points_x = np.arange(rranges[0].start, rranges[0].stop, rranges[0].step).size
points_y = 10
nmb_evals = points_x * points_y
assert_equal(out.nfev, nmb_evals)
# best-fit values and function value identical
assert_equal(ret[0][0], out.brute_x0[0])
assert_equal(ret[0][1], out.brute_x0[1])
assert_equal(ret[1], out.brute_fval)
def test_brute_upper_bounds_and_brute_step(params_lmfit):
"""TEST 5: using finite upper bounds, Ns=20, and brute_step specified."""
Ns = 20
params_lmfit['x'].set(min=-np.inf)
params_lmfit['x'].set(brute_step=0.25)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=Ns)
assert_equal(out.params['x'].min, -np.inf)
assert_equal(out.params['x'].brute_step, 0.25)
grid_x_expected = np.linspace(params_lmfit['x'].max -
Ns*params_lmfit['x'].brute_step,
params_lmfit['x'].max, Ns, False)
grid_x = np.unique([par.ravel() for par in out.brute_grid][0])
assert_allclose(grid_x, grid_x_expected)
grid_y_expected = np.linspace(params_lmfit['y'].min,
params_lmfit['y'].max, Ns)
grid_y = np.unique([par.ravel() for par in out.brute_grid][1])
assert_allclose(grid_y, grid_y_expected)
def test_brute_lower_bounds_and_brute_step(params_lmfit):
"""TEST 6: using finite lower bounds, Ns=15, and brute_step specified."""
Ns = 15
params_lmfit['y'].set(max=np.inf)
params_lmfit['y'].set(brute_step=0.1)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=Ns)
grid_x_expected = np.linspace(params_lmfit['x'].min,
params_lmfit['x'].max, Ns)
grid_x = np.unique([par.ravel() for par in out.brute_grid][0])
assert_allclose(grid_x, grid_x_expected)
grid_y_expected = np.linspace(params_lmfit['y'].min,
params_lmfit['y'].min +
Ns*params_lmfit['y'].brute_step, Ns, False)
grid_y = np.unique([par.ravel() for par in out.brute_grid][1])
assert_allclose(grid_y, grid_y_expected)
def test_brute_no_bounds_with_brute_step(params_lmfit):
"""TEST 7: using no bounds, but brute_step specified (Ns=15)."""
Ns = 15
params_lmfit['x'].set(min=-np.inf, max=np.inf, brute_step=0.1)
params_lmfit['y'].set(min=-np.inf, max=np.inf, brute_step=0.2)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute', Ns=15)
grid_x_expected = np.linspace(params_lmfit['x'].value -
(Ns//2)*params_lmfit['x'].brute_step,
params_lmfit['x'].value +
(Ns//2)*params_lmfit['x'].brute_step, Ns)
grid_x = np.unique([par.ravel() for par in out.brute_grid][0])
assert_allclose(grid_x, grid_x_expected)
grid_y_expected = np.linspace(params_lmfit['y'].value -
(Ns//2)*params_lmfit['y'].brute_step,
params_lmfit['y'].value +
(Ns//2)*params_lmfit['y'].brute_step, Ns)
grid_y = np.unique([par.ravel() for par in out.brute_grid][1])
assert_allclose(grid_y, grid_y_expected)
def test_brute_no_bounds_no_brute_step(params_lmfit):
"""TEST 8: insufficient information provided."""
params_lmfit['x'].set(min=-np.inf, max=np.inf)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
msg = r'Not enough information provided for the brute force method.'
with pytest.raises(ValueError, match=msg):
mini.minimize(method='brute')
def test_brute_one_parameter(params_lmfit):
"""TEST 9: only one varying parameter."""
params_lmfit['x'].set(vary=False)
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute')
assert out.candidates[0].score <= out.candidates[1].score
assert isinstance(out.candidates[0], lmfit.minimizer.Candidate)
assert isinstance(out.candidates[0].params, lmfit.Parameters)
assert isinstance(out.candidates[0].score, float)
def test_brute_keep(params_lmfit, capsys):
"""TEST 10: using 'keep' argument and check candidates attribute."""
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute')
assert_equal(len(out.candidates), 50) # default
out_keep_all = mini.minimize(method='brute', keep='all')
assert_equal(len(out_keep_all.candidates),
len(out_keep_all.brute_Jout.ravel()))
out_keep10 = mini.minimize(method='brute', keep=10)
assert_equal(len(out_keep10.candidates), 10)
assert isinstance(out.candidates[0], lmfit.minimizer.Candidate)
assert isinstance(out.candidates[0].params, lmfit.Parameters)
assert isinstance(out.candidates[0].score, float)
with pytest.raises(ValueError, match=r"'candidate_nmb' should be between"):
out_keep10.show_candidates(25)
with pytest.raises(ValueError, match=r"'candidate_nmb' should be between"):
out_keep10.show_candidates(0)
out_keep10.show_candidates(5)
captured = capsys.readouterr()
assert 'Candidate #5' in captured.out
# for coverage and to make sure the 'all' argument works; no assert...
out_keep10.show_candidates('all')
def test_brute_pickle(params_lmfit):
"""TEST 11: make sure the MinimizerResult can be pickle'd."""
mini = lmfit.Minimizer(func_lmfit, params_lmfit)
out = mini.minimize(method='brute')
pickle.dumps(out)
def test_nfev_workers(params_lmfit):
"""TEST 12: make sure the nfev is correct for workers != 1."""
mini = lmfit.Minimizer(func_lmfit, params_lmfit, workers=-1)
out = mini.minimize(method='brute')
assert_equal(out.nfev, 20**len(out.var_names))
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