def __init__(self, setup):
self.setup = setup
sigma2 = pow(setup.sigma, 2)
dx_opt = abs(setup.C_opt / (.5 * sigma2 - setup.r) * setup.l2_opt *
sigma2)
dt_opt = pow(dx_opt, 2) / sigma2 / setup.l2_opt
# adjusting dt so that nt is integer
self.dt = setup.T
self.nt = 0
while self.dt > dt_opt:
self.nt += 1
self.dt = setup.T / self.nt
# adjusting dx to match requested l^2
dx = np.sqrt(setup.l2_opt * self.dt) * setup.sigma
# calculating actual u number and lambda
self.C = -(.5 * sigma2 - setup.r) * (-self.dt) / dx
self.l2 = dx * dx / sigma2 / self.dt
# adjusting nx and setting S_beg, S_end
S_beg = setup.S_match
self.nx = 1
while S_beg > setup.S_min:
self.nx += 1
S_beg = np.exp(np.log(setup.S_match) - self.nx * dx)
self.ix_match = self.nx
S_end = setup.S_match
while S_end < setup.S_max:
self.nx += 1
S_end = np.exp(np.log(S_beg) + (self.nx - 1) * dx)
# asset price
self.S = np.exp(np.log(S_beg) + np.arange(self.nx) * dx)
self.mu_coeff = (0.5 / self.l2, )
self.solvers = {}
self.solvers[1] = Factories.advection_diffusion_1d(
advectee=setup.payoff(self.S),
advector=self.C,
options=Options(n_iters=1, non_zero_mu_coeff=True),
boundary_conditions=(ExtrapolatedBoundaryCondition(), ))
self.solvers[2] = Factories.advection_diffusion_1d(
advectee=setup.payoff(self.S),
advector=self.C,
options=Options(**OPTIONS),
boundary_conditions=(ExtrapolatedBoundaryCondition(), ))
def test_diffusion_only_2d(data0=np.array([[0, 0, 0], [0, 1., 0], [0, 0, 0]]),
mu_coeff=(.1, .1),
n_steps=1):
# Arrange
options = Options(non_zero_mu_coeff=True)
boundary_conditions = tuple([Periodic()] * 2)
advectee = ScalarField(data0, options.n_halo, boundary_conditions)
advector = VectorField(data=(np.zeros(
(data0.shape[0] + 1, data0.shape[1])),
np.zeros(
(data0.shape[0], data0.shape[1] + 1))),
halo=options.n_halo,
boundary_conditions=boundary_conditions)
solver = Solver(stepper=Stepper(options=options, grid=data0.shape),
advector=advector,
advectee=advectee)
# Act
solver.advance(n_steps=n_steps, mu_coeff=mu_coeff)
# Assert
data1 = solver.advectee.get()
np.testing.assert_almost_equal(actual=np.sum(data1), desired=np.sum(data0))
assert np.amax(data0) > np.amax(data1)
assert np.amin(data1) >= 0
assert np.count_nonzero(data1) == 5
def test_double_pass_donor_cell(n_iters):
courant = .5
options = Options(n_iters=n_iters, DPDC=True, nonoscillatory=True)
state = np.array([0, 1, 0], dtype=options.dtype)
boundary_conditions = (Periodic(),)
mpdata = Solver(
stepper=Stepper(options=options, n_dims=state.ndim, non_unit_g_factor=False),
advectee=ScalarField(
state,
halo=options.n_halo,
boundary_conditions=boundary_conditions
),
advector=VectorField(
(np.full(state.shape[0] + 1, courant, dtype=options.dtype),),
halo=options.n_halo,
boundary_conditions=boundary_conditions
)
)
steps = 1
conserved = np.sum(mpdata.advectee.get())
mpdata.advance(steps)
assert np.sum(mpdata.advectee.get()) == conserved
def __init__(self, nz, dt, advector_of_t, advectee_of_zZ_at_t0,
g_factor_of_zZ, mpdata_settings):
self.t = 0
self.dt = dt
self.advector_of_t = advector_of_t
grid = (nz, )
options = Options(n_iters=mpdata_settings['n_iters'],
infinite_gauge=mpdata_settings['iga'],
flux_corrected_transport=mpdata_settings['fct'],
third_order_terms=mpdata_settings['tot'])
stepper = Stepper(options=options, grid=grid, non_unit_g_factor=True)
bcs = (ExtrapolatedBoundaryCondition(), )
g_factor = ScalarField(data=g_factor_of_zZ(
arakawa_c.z_scalar_coord(grid)),
halo=options.n_halo,
boundary_conditions=bcs)
advector = VectorField(data=(np.full(nz + 1, advector_of_t(0)), ),
halo=options.n_halo,
boundary_conditions=bcs)
self.advectee = ScalarField(data=advectee_of_zZ_at_t0(
arakawa_c.z_scalar_coord(grid)),
halo=options.n_halo,
boundary_conditions=bcs)
self.solver = Solver(stepper=stepper,
advectee=self.advectee,
advector=advector,
g_factor=g_factor)
def __init__(self, *, fields,
n_iters=2, infinite_gauge=True,
flux_corrected_transport=True, third_order_terms=False):
self.grid = fields.g_factor.shape
self.asynchronous = False
self.thread: (Thread, None) = None
options = Options(
n_iters=n_iters,
infinite_gauge=infinite_gauge,
flux_corrected_transport=flux_corrected_transport,
third_order_terms=third_order_terms
)
disable_threads_if_needed = {}
if not conf.JIT_FLAGS['parallel']:
disable_threads_if_needed['n_threads'] = 1
stepper = Stepper(options=options, grid=self.grid, non_unit_g_factor=True, **disable_threads_if_needed)
# CFL condition
for d in range(len(fields.advector)):
np.testing.assert_array_less(np.abs(fields.advector[d]), 1)
self.advector = fields.advector
advector_impl = VectorField(fields.advector, halo=options.n_halo,
boundary_conditions=(PeriodicBoundaryCondition(), PeriodicBoundaryCondition()))
self.g_factor = fields.g_factor
g_factor_impl = ScalarField(fields.g_factor.astype(dtype=options.dtype), halo=options.n_halo,
boundary_conditions=(PeriodicBoundaryCondition(), PeriodicBoundaryCondition()))
self.mpdatas = {}
for k, v in fields.advectees.items():
advectee = ScalarField(np.full(self.grid, v, dtype=options.dtype), halo=options.n_halo,
boundary_conditions=(PeriodicBoundaryCondition(), PeriodicBoundaryCondition()))
self.mpdatas[k] = Solver(stepper=stepper, advectee=advectee, advector=advector_impl, g_factor=g_factor_impl)
def test_make_upwind(self):
# Arrange
psi_data = np.array((0, 1, 0))
flux_data = np.array((0, 0, 1, 0))
options = Options()
halo = options.n_halo
traversals = Traversals(grid=psi_data.shape,
halo=halo,
jit_flags={},
n_threads=1)
upwind = make_upwind(options=options,
non_unit_g_factor=False,
traversals=traversals)
bc = [PeriodicBoundaryCondition()]
psi = ScalarField(psi_data, halo, bc)
psi_impl = psi.impl
flux_impl = VectorField((flux_data, ), halo, bc).impl
null_impl = ScalarField.make_null(len(psi_data.shape)).impl
# Act
upwind(psi_impl[0], *flux_impl, *null_impl)
# Assert
np.testing.assert_array_equal(psi.get(), np.roll(psi_data, 1))
def analysis(setup, grid_layout, psi_coord, options_dict, GC_max):
options_str = str(options_dict)
options = Options(**options_dict)
simulation = Simulation(setup, grid_layout, psi_coord, options, GC_max)
result = {
"n": [],
"n_analytical": [],
"error_norm_L2": [],
"wall_time": []
}
last_step = 0
for n_steps in simulation.out_steps:
steps = n_steps - last_step
wall_time = simulation.step(steps) if steps > 0 else 0
last_step += steps
result['n'].append(simulation.n_of_r.copy())
result['wall_time'].append(wall_time)
result['r'] = simulation.r.copy()
result['rh'] = simulation.rh.copy()
result['dx'] = simulation.dx
return Result(grid_layout_str=grid_layout.__class__.__name__,
option_str=options_str,
result=result,
out_steps=simulation.out_steps,
dt=simulation.dt)
def test_upwind(shape, ij0, out, courant_number):
value = 44
scalar_field_init = np.zeros(shape)
scalar_field_init[ij0] = value
vector_field_init = (
np.full((shape[0] + 1, shape[1]), courant_number[0]),
np.full((shape[0], shape[1] + 1), courant_number[1])
)
options = Options(n_iters=1)
bcs = (Periodic(), Periodic())
advectee = ScalarField(scalar_field_init, halo=options.n_halo, boundary_conditions=bcs)
advector = VectorField(vector_field_init, halo=options.n_halo, boundary_conditions=bcs)
mpdata = Solver(
stepper=Stepper(options=options, grid=shape, n_threads=1),
advector=advector,
advectee=advectee
)
mpdata.advance(n_steps=1)
np.testing.assert_array_equal(
mpdata.advectee.get(),
out
)
def test_mu_arg_handling(case):
opt = Options(non_zero_mu_coeff=case['non_zero_mu_coeff'])
advector = VectorField((np.asarray([1., 2, 3]),), opt.n_halo, BCS)
advectee = ScalarField(np.asarray([4., 5]), opt.n_halo, BCS)
stepper = Stepper(options=opt, n_dims=1)
sut = Solver(stepper, advectee, advector, case['g_factor'])
sut.advance(1, mu_coeff=case['mu'])
def test_timing_3d(benchmark, options, dtype, static, num_threads):
numba.set_num_threads(num_threads)
settings = Settings(n=20, dt=1)
simulation = Simulation(settings, Options(**options, dtype=dtype), static=static)
def reset():
simulation.solver.advectee.get()[:] = settings.advectee
n_steps = 10
benchmark.pedantic(simulation.run, (n_steps,), setup=reset, warmup_rounds=1, rounds=1)
def test_shared_advector():
n_x = 100
arr = np.zeros(n_x)
opt1 = Options(n_iters=2, DPDC=True)
opt2 = Options(n_iters=2)
b_c = (Periodic(),)
halo = opt1.n_halo
assert opt2.n_halo == halo
advector = VectorField(data=(np.zeros(n_x + 1),), halo=halo, boundary_conditions=b_c)
_ = Solver(
stepper=Stepper(options=opt1, grid=(n_x,)),
advectee=ScalarField(data=arr, halo=halo, boundary_conditions=b_c),
advector=advector
)
solver = Solver(
stepper=Stepper(options=opt2, grid=(n_x,)),
advectee=ScalarField(data=arr, halo=halo, boundary_conditions=b_c),
advector=advector
)
solver.advance(1)
def make_data(setup, grid, opts):
options = Options(**opts)
simulation = Simulation(setup=setup,
grid_layout=grid,
psi_coord=x_id(),
opts=options,
GC_max=default_GC_max)
result = {"wall_time": []}
last_step = 0
for n_steps in simulation.out_steps:
steps = n_steps - last_step
wall_time_per_timestep = simulation.step(steps)
last_step += steps
result['wall_time'].append(wall_time_per_timestep)
return result
def __init__(
self,
nz,
dt,
advector_of_t,
advectee_of_zZ_at_t0,
g_factor_of_zZ,
mpdata_settings,
):
self.__t = 0
self.dt = dt
self.advector_of_t = advector_of_t
grid = (nz, )
options = Options(
n_iters=mpdata_settings["n_iters"],
infinite_gauge=mpdata_settings["iga"],
nonoscillatory=mpdata_settings["fct"],
third_order_terms=mpdata_settings["tot"],
)
stepper = Stepper(options=options, grid=grid, non_unit_g_factor=True)
bcs = (Extrapolated(), )
zZ_scalar = arakawa_c.z_scalar_coord(grid) / nz
g_factor = ScalarField(
data=g_factor_of_zZ(zZ_scalar),
halo=options.n_halo,
boundary_conditions=bcs,
)
advector = VectorField(
data=(np.full(nz + 1, advector_of_t(0)), ),
halo=options.n_halo,
boundary_conditions=bcs,
)
self.advectee = ScalarField(
data=advectee_of_zZ_at_t0(zZ_scalar),
halo=options.n_halo,
boundary_conditions=bcs,
)
self.solver = Solver(
stepper=stepper,
advectee=self.advectee,
advector=advector,
g_factor=g_factor,
)
def test_formulae_upwind():
# Arrange
psi_data = np.array((0, 1, 0))
flux_data = np.array((0, 0, 1, 0))
options = Options()
halo = options.n_halo
traversals = Traversals(grid=psi_data.shape,
halo=halo,
jit_flags=options.jit_flags,
n_threads=1)
upwind = make_upwind(options=options,
non_unit_g_factor=False,
traversals=traversals)
boundary_conditions = (Periodic(), )
psi = ScalarField(psi_data, halo, boundary_conditions)
psi.assemble(traversals)
psi_impl = psi.impl
flux = VectorField((flux_data, ), halo, boundary_conditions)
flux.assemble(traversals)
flux_impl = flux.impl
# Act
with warnings.catch_warnings():
warnings.simplefilter('ignore',
category=NumbaExperimentalFeatureWarning)
upwind(
traversals.null_impl,
_Impl(field=psi_impl[IMPL_META_AND_DATA], bc=psi_impl[IMPL_BC]),
_Impl(field=flux_impl[IMPL_META_AND_DATA], bc=flux_impl[IMPL_BC]),
_Impl(field=traversals.null_impl.scalar[IMPL_META_AND_DATA],
bc=traversals.null_impl.scalar[IMPL_BC]))
# Assert
np.testing.assert_array_equal(psi.get(), np.roll(psi_data, 1))
def test_upwind_1d():
state = np.array([0, 1, 0])
courant = 1
options = Options(n_iters=1)
mpdata = Solver(
stepper=Stepper(options=options, n_dims=len(state.shape), non_unit_g_factor=False),
advectee=ScalarField(
state.astype(options.dtype),
halo=options.n_halo,
boundary_conditions=(Periodic(),)
),
advector=VectorField(
(np.full(state.shape[0] + 1, courant, dtype=options.dtype),),
halo=options.n_halo,
boundary_conditions=(Periodic(),)
)
)
n_steps = 5
conserved = np.sum(mpdata.advectee.get())
mpdata.advance(n_steps)
assert np.sum(mpdata.advectee.get()) == conserved
from PyMPDATA.arakawa_c.traversals import Traversals
from PyMPDATA.arakawa_c.meta import META_HALO_VALID
from PyMPDATA import Options, ScalarField, VectorField, ConstantBoundaryCondition
from PyMPDATA.arakawa_c.indexers import indexers
from PyMPDATA.arakawa_c.enumerations import MAX_DIM_NUM, INNER, MID3D, OUTER, IMPL_META_AND_DATA, IMPL_BC, \
META_AND_DATA_META, ARG_FOCUS, INVALID_INDEX
import pytest
import numba
import numpy as np
jit_flags = Options().jit_flags
@numba.njit(**jit_flags)
def cell_id(i, j, k):
if i == INVALID_INDEX:
i = 0
if j == INVALID_INDEX:
j = 0
return 100 * i + 10 * j + k
@numba.njit(**jit_flags)
def _cell_id_scalar(value, arg_1_vec, arg_2_scl, arg_3_scl, arg_4_scl):
focus = arg_1_vec[ARG_FOCUS]
if focus != arg_2_scl[ARG_FOCUS]:
raise Exception()
if focus != arg_3_scl[ARG_FOCUS]:
raise Exception()
if focus != arg_4_scl[ARG_FOCUS]:
raise Exception()
def rhod_of_z(arg):
return 1 - arg * 1e-4
RHOD = np.repeat(rhod_of_z((np.arange(GRID[1]) + 1 / 2) / GRID[1]).reshape(
(1, GRID[1])),
GRID[0],
axis=0)
VALUES = {'th': np.full(GRID, 300), 'qv': np.full(GRID, .001)}
@pytest.mark.parametrize(
"options",
(Options(n_iters=1), Options(n_iters=2),
Options(n_iters=2,
nonoscillatory=True), Options(n_iters=3, nonoscillatory=True),
Options(n_iters=2, nonoscillatory=True, infinite_gauge=True),
Options(nonoscillatory=True, infinite_gauge=True, third_order_terms=True),
Options(nonoscillatory=False, infinite_gauge=True),
Options(nonoscillatory=False, third_order_terms=True),
Options(nonoscillatory=False, infinite_gauge=True,
third_order_terms=True)))
def test_single_timestep(options):
# Arrange
stepper = Stepper(options=options, grid=GRID, non_unit_g_factor=True)
advector = nondivergent_vector_field_2d(GRID, SIZE, TIMESTEP,
stream_function, options.n_halo)
g_factor = ScalarField(RHOD.astype(dtype=options.dtype),
halo=options.n_halo,
from PyMPDATA_examples.Molenkamp_test_as_in_Jaruga_et_al_2015_Fig_12.simulation import Simulation
from PyMPDATA_examples.Molenkamp_test_as_in_Jaruga_et_al_2015_Fig_12.setup import Setup
from PyMPDATA import Options
from joblib import Parallel, delayed
options = {
'upwind':
Options(n_iters=1),
'2+fct':
Options(n_iters=2, flux_corrected_transport=True),
'3+fct+tot':
Options(n_iters=3, flux_corrected_transport=True, third_order_terms=True),
'2+fct+iga':
Options(n_iters=2, flux_corrected_transport=True, infinite_gauge=True)
}
def compute_panel(panel):
setup = Setup(n_rotations=6)
simulation = Simulation(setup, options[panel])
if panel == 'upwind':
return simulation.state
simulation.run()
return simulation.state
def fig_12_data():
data = Parallel(n_jobs=-2)(
delayed(compute_panel)(panel)
for panel in ['upwind', '2+fct', '3+fct+tot', '2+fct+iga'])
return data
# pylint: disable=missing-module-docstring,missing-class-docstring,missing-function-docstring
import pytest
from PyMPDATA import Options
from PyMPDATA.impl.domain_decomposition import make_subdomain
JIT_FLAGS = Options().jit_flags
@pytest.mark.parametrize(
"span, rank, size, result",
[(10, 0, 1, (0, 10)),
pytest.param(1, 1, 1, (0, 1), marks=pytest.mark.xfail(raises=ValueError)),
(10, 0, 3, (0, 4)), (10, 1, 3, (4, 8)), (10, 2, 3, (8, 10)),
(10, 0, 11, (0, 1)), (10, 9, 11, (9, 10))])
def test_subdomain(span, rank, size, result):
subdomain = make_subdomain(JIT_FLAGS)
assert subdomain(span, rank, size) == result
import numpy as np
import pytest
from PyMPDATA import Solver, Stepper, ScalarField, VectorField, Options
from PyMPDATA.boundary_conditions import Periodic
BCS = (Periodic(),)
@pytest.mark.parametrize("case", (
{'g_factor': None, 'non_zero_mu_coeff': True, 'mu': None},
{'g_factor': None, 'non_zero_mu_coeff': True, 'mu': (0,)},
pytest.param({
'g_factor': None,
'non_zero_mu_coeff': False,
'mu': (0,)
}, marks=pytest.mark.xfail(strict=True)),
pytest.param({
'g_factor': ScalarField(np.asarray([1., 1]), Options().n_halo, BCS),
'non_zero_mu_coeff': True,
'mu': None
}, marks=pytest.mark.xfail(strict=True))
))
def test_mu_arg_handling(case):
opt = Options(non_zero_mu_coeff=case['non_zero_mu_coeff'])
advector = VectorField((np.asarray([1., 2, 3]),), opt.n_halo, BCS)
advectee = ScalarField(np.asarray([4., 5]), opt.n_halo, BCS)
stepper = Stepper(options=opt, n_dims=1)
sut = Solver(stepper, advectee, advector, case['g_factor'])
sut.advance(1, mu_coeff=case['mu'])
def test_mpdata_2d(case_data):
case = {
"nx": case_data[0],
"ny": case_data[1],
"Cx": case_data[2],
"Cy": case_data[3],
"nt": case_data[4],
"ni": case_data[5],
"dimsplit": case_data[6],
"input": case_data[7],
"output": case_data[8]
}
# Arrange
data = case["input"].reshape((case["nx"], case["ny"]))
courant = [case["Cx"], case["Cy"]]
options = Options(n_iters=case["ni"], dimensionally_split=case["dimsplit"])
grid = data.shape
advector_data = [
np.full((grid[0] + 1, grid[1]), courant[0], dtype=options.dtype),
np.full((grid[0], grid[1] + 1), courant[1], dtype=options.dtype)
]
bcs = (Periodic(), Periodic())
advector = VectorField(advector_data,
halo=options.n_halo,
boundary_conditions=bcs)
advectee = ScalarField(data=data.astype(dtype=options.dtype),
halo=options.n_halo,
boundary_conditions=bcs)
stepper = Stepper(options=options, grid=grid, non_unit_g_factor=False)
mpdata = Solver(stepper=stepper, advectee=advectee, advector=advector)
sut = mpdata
def __init__(self,
*,
advectees,
stream_function,
rhod_of_zZ,
dt,
grid,
size,
displacement,
n_iters=2,
infinite_gauge=True,
nonoscillatory=True,
third_order_terms=False):
self.grid = grid
self.size = size
self.dt = dt
self.stream_function = stream_function
self.stream_function_time_dependent = (
"t" in inspect.signature(stream_function).parameters)
self.asynchronous = False
self.thread: (Thread, None) = None
self.displacement = displacement
self.t = 0
options = Options(
n_iters=n_iters,
infinite_gauge=infinite_gauge,
nonoscillatory=nonoscillatory,
third_order_terms=third_order_terms,
)
disable_threads_if_needed = {}
if not conf.JIT_FLAGS["parallel"]:
disable_threads_if_needed["n_threads"] = 1
stepper = Stepper(options=options,
grid=self.grid,
non_unit_g_factor=True,
**disable_threads_if_needed)
advector_impl = VectorField(
(
np.full((grid[0] + 1, grid[1]), np.nan),
np.full((grid[0], grid[1] + 1), np.nan),
),
halo=options.n_halo,
boundary_conditions=(Periodic(), Periodic()),
)
g_factor = make_rhod(self.grid, rhod_of_zZ)
g_factor_impl = ScalarField(
g_factor.astype(dtype=options.dtype),
halo=options.n_halo,
boundary_conditions=(Periodic(), Periodic()),
)
self.g_factor_vec = (
rhod_of_zZ(zZ=x_vec_coord(self.grid)[-1]),
rhod_of_zZ(zZ=z_vec_coord(self.grid)[-1]),
)
self.mpdatas = {}
for k, v in advectees.items():
advectee_impl = ScalarField(
np.asarray(v, dtype=options.dtype),
halo=options.n_halo,
boundary_conditions=(Periodic(), Periodic()),
)
self.mpdatas[k] = Solver(
stepper=stepper,
advectee=advectee_impl,
advector=advector_impl,
g_factor=g_factor_impl,
)
delta_y = (yrange[1] - yrange[0]) / gridsize[1]
for i in range(gridsize[0]):
for j in range(gridsize[1]):
psi[i, j] = pdf(xrange[0] + delta_x * (i + .5),
yrange[0] + delta_y * (j + .5))
coord_x = np.linspace(xrange[0] + delta_x / 2, xrange[1] - delta_x / 2,
gridsize[0])
coord_y = np.linspace(yrange[0] + delta_y / 2, yrange[1] - delta_y / 2,
gridsize[1])
return coord_x, coord_y, psi
@pytest.mark.parametrize(
"options",
[
Options(n_iters=1),
Options(n_iters=2),
Options(n_iters=3, infinite_gauge=True),
Options(n_iters=2, infinite_gauge=True, nonoscillatory=True),
# Options(n_iters=3, infinite_gauge=False, third_order_terms=True),
# Options(n_iters=3, infinite_gauge=True, third_order_terms=True, nonoscillatory=True),
])
@pytest.mark.parametrize("grid_static_str", ("static", "dynamic"))
# pylint: disable-next=redefined-outer-name
def test_timing_2d(benchmark,
options,
grid_static_str,
num_threads,
plot=False):
if grid_static_str == "static":
grid_static = True
# pylint: disable=missing-module-docstring,missing-class-docstring,missing-function-docstring
import pytest
import numpy as np
from PyMPDATA_examples.Smolarkiewicz_1984 import Settings, Simulation
from PyMPDATA import Options
# https://github.com/igfuw/libmpdataxx/blob/master/tests/paper_2015_GMD/4_revolving_sphere_3d/...
STATS = {
# ...refdata/stats_upwind.txt.gz
Options(n_iters=1): {
0: {
'min(solution)': 0.00000000,
'max(solution)': 4.00000000,
},
566: {
'max(solution)': 1.72131033,
'min(solution)': 0.00000000,
'Linf': 3.38441916,
'L2': 0.00567238,
'L1': 0.00128141,
}
},
# ...refdata/stats_basic.txt.gz
Options(n_iters=2): {
0: {
'min(solution)': 0.00000000,
'max(solution)': 4.00000000,
},
556: {
'max(solution)': 4.94170863,
'min(solution)': 0.00000000,
