def setUp(self):
self.md = (gr.Model() >> gr.cp_function(
fun=lambda x: x, var=1, out=1, runtime=1) >>
gr.cp_marginals(x0={
"dist": "uniform",
"loc": 0,
"scale": 1
}) >> gr.cp_copula_independence())
self.md_2d = (gr.Model() >> gr.cp_function(
fun=lambda x: x[0], var=2, out=1) >> gr.cp_marginals(
x0={
"dist": "uniform",
"loc": 0,
"scale": 1
},
x1={
"dist": "uniform",
"loc": 0,
"scale": 1
},
) >> gr.cp_copula_independence())
self.md_mixed = (gr.Model() >> gr.cp_function(
fun=lambda x: x[0] + x[1], var=2,
out=1) >> gr.cp_bounds(x0=(-1, +1)) >> gr.cp_marginals(x1={
"dist": "uniform",
"loc": 0,
"scale": 1
}, ) >> gr.cp_copula_independence())
def setUp(self):
## Smooth model
self.md_smooth = (gr.Model() >> gr.cp_function(
fun=lambda x: [x, x + 1], var=["x"], out=["y", "z"]) >>
gr.cp_marginals(x={
"dist": "uniform",
"loc": 0,
"scale": 2
}) >> gr.cp_copula_independence())
self.df_smooth = self.md_smooth >> gr.ev_df(
df=pd.DataFrame(dict(x=[0, 1, 2])))
## Tree model
self.md_tree = (gr.Model() >> gr.cp_function(
fun=lambda x: [0, x < 5], var=["x"], out=["y", "z"]) >>
gr.cp_marginals(x={
"dist": "uniform",
"loc": 0,
"scale": 2
}) >> gr.cp_copula_independence())
self.df_tree = self.md_tree >> gr.ev_df(
df=pd.DataFrame(dict(x=np.linspace(0, 10, num=8))))
## Cluster model
self.df_cluster = pd.DataFrame(
dict(
x=[0.1, 0.2, 0.3, 0.4, 1.1, 1.2, 1.3, 1.4],
y=[0.3, 0.2, 0.1, 0.0, 1.3, 1.2, 1.1, 1.0],
c=[0, 0, 0, 0, 1, 1, 1, 1],
))
def test_opt(self):
# invariant checks
self.inv_test.md_arg(gr.eval_min, df_arg="df_start")
self.inv_test.df_arg(gr.eval_min, df_arg="df_start", acc_none="always")
md_bowl = (gr.Model("Constrained bowl") >> gr.cp_function(
fun=lambda x: x[0]**2 + x[1]**2,
var=["x", "y"],
out=["f"],
) >> gr.cp_function(
fun=lambda x: (x[0] + x[1] + 1),
var=["x", "y"],
out=["g1"],
) >> gr.cp_function(
fun=lambda x: -(-x[0] + x[1] - np.sqrt(2 / 10)),
var=["x", "y"],
out=["g2"],
) >> gr.cp_bounds(
x=(-1, +1),
y=(-1, +1),
))
df_res = md_bowl >> gr.ev_min(
out_min="f",
out_geq=["g1"],
out_leq=["g2"],
)
# Check result
self.assertTrue(abs(df_res.x[0] + np.sqrt(1 / 20)) < 1e-6)
self.assertTrue(abs(df_res.y[0] - np.sqrt(1 / 20)) < 1e-6)
# Check errors for violated invariants
with self.assertRaises(ValueError):
gr.eval_min(md_bowl, out_min="FALSE")
with self.assertRaises(ValueError):
gr.eval_min(md_bowl, out_min="f", out_geq=["FALSE"])
with self.assertRaises(ValueError):
gr.eval_min(md_bowl, out_min="f", out_eq=["FALSE"])
# Test multiple restarts
df_multi = gr.eval_min(
md_bowl,
out_min="f",
out_geq=["g1"],
out_leq=["g2"],
n_restart=2,
)
self.assertTrue(df_multi.shape[0] == 2)
def test_grad_fd(self):
"""Checks the FD code
"""
## Accuracy
df_grad = gr.eval_grad_fd(
self.model_2d, df_base=self.df_2d_nominal, append=False
)
self.assertTrue(np.allclose(df_grad[self.df_2d_grad.columns], self.df_2d_grad))
## Subset
df_grad_sub = gr.eval_grad_fd(
self.model_2d, df_base=self.df_2d_nominal, var=["x"], append=False
)
self.assertTrue(set(df_grad_sub.columns) == set(["Df_Dx", "Dg_Dx"]))
## Flags
md_test = (
gr.Model()
>> gr.cp_function(fun=lambda x: x[0] + x[1] ** 2, var=2, out=1)
>> gr.cp_marginals(x0={"dist": "norm", "loc": 0, "scale": 1})
)
df_base = pd.DataFrame(dict(x0=[0, 1], x1=[0, 1]))
## Multiple base points
df_true = pd.DataFrame(dict(Dy0_Dx0=[1, 1], Dy0_Dx1=[0, 2]))
df_rand = gr.eval_grad_fd(md_test, df_base=df_base, var="rand", append=False)
self.assertTrue(gr.df_equal(df_true[["Dy0_Dx0"]], df_rand, close=True))
df_det = gr.eval_grad_fd(md_test, df_base=df_base, var="det", append=False)
self.assertTrue(gr.df_equal(df_true[["Dy0_Dx1"]], df_det, close=True))
def setUp(self):
self.md = (gr.Model() >> gr.cp_function(
fun=lambda x: x,
var=["x"],
out=["y"],
) >> gr.cp_marginals(x=dict(dist="norm", loc=0, scale=1)) >>
gr.cp_copula_independence())
def __init__(self):
"""Setup necessary values"""
self.md = (gr.Model() >> gr.cp_function(
fun=lambda x: x, var=1, out=1, runtime=1))
self.md_var_det = self.md >> gr.cp_bounds(x1=(0, 1))
self.df = pd.DataFrame(data={"x": [0.0], "y": [0.5]})
# declare tests
self.type_tests = [(1, 2), 2, [1, 8]]
def test_nls(self):
## Setup
md_feat = (
gr.Model()
>> gr.cp_function(fun=lambda x: x[0] * x[1] + x[2], var=3, out=1,)
>> gr.cp_bounds(x0=[-1, +1], x2=[0, 0])
>> gr.cp_marginals(x1=dict(dist="norm", loc=0, scale=1))
)
md_const = (
gr.Model()
>> gr.cp_function(fun=lambda x: x[0], var=1, out=1)
>> gr.cp_bounds(x0=(-1, +1))
)
df_response = md_feat >> gr.ev_df(
df=gr.df_make(x0=0.1, x1=[-1, -0.5, +0, +0.5, +1], x2=0)
)
df_data = df_response[["x1", "y0"]]
## Model with features
df_true = gr.df_make(x0=0.1)
df_fit = md_feat >> gr.ev_nls(df_data=df_data, append=False)
pd.testing.assert_frame_equal(
df_fit,
df_true,
check_exact=False,
check_dtype=False,
check_column_type=False,
)
## Fitting synonym
md_feat_fit = df_data >> gr.ft_nls(md=md_feat, verbose=False)
self.assertTrue(set(md_feat_fit.var) == set(["x1", "x2"]))
## Constant model
df_const = gr.df_make(x0=0)
df_fit = md_const >> gr.ev_nls(df_data=gr.df_make(y0=[-1, 0, +1]))
pd.testing.assert_frame_equal(
df_fit,
df_const,
check_exact=False,
check_dtype=False,
check_column_type=False,
)
def test_drop_out(self):
"""Checks that output column names are properly dropped"""
md = gr.Model() >> gr.cp_function(lambda x: x[0] + 1, var=1, out=1)
df_in = gr.df_make(x0=[0, 1, 2], y0=[0, 1, 2])
df_true = gr.df_make(x0=[0, 1, 2], y0=[1, 2, 3])
df_res = md >> gr.ev_df(df=df_in)
self.assertTrue(gr.df_equal(df_res, df_true, close=True))
def test_dag(self):
md = (gr.Model("model") >> gr.cp_function(lambda x: x, var=1, out=1) >>
gr.cp_function(lambda x: x[0] + x[1], var=["x0", "y0"], out=1))
G_true = nx.DiGraph()
G_true.add_edge("(var)", "f0", label="{}".format({"x0"}))
G_true.add_edge("f0", "(out)", label="{}".format({"y0"}))
G_true.add_edge("(var)", "f1", label="{}".format({"x0"}))
G_true.add_edge("f0", "f1", label="{}".format({"y0"}))
G_true.add_edge("f1", "(out)", label="{}".format({"y1"}))
nx.set_node_attributes(G_true, "model", "parent")
self.assertTrue(
nx.is_isomorphic(
md.make_dag(),
G_true,
node_match=lambda u, v: u == v,
edge_match=lambda u, v: u == v,
))
def setUp(self):
self.md = models.make_test()
self.md_mixed = (
gr.Model()
>> gr.cp_function(fun=lambda x: x[0], var=3, out=1)
>> gr.cp_bounds(x2=(0, 1))
>> gr.cp_marginals(
x0={"dist": "uniform", "loc": 0, "scale": 1},
x1={"dist": "uniform", "loc": 0, "scale": 1},
)
>> gr.cp_copula_independence()
)
def setUp(self):
## Linear limit state w/ MPP off initial guess
self.beta_true = 3
self.md = (
gr.Model()
>> gr.cp_function(
fun=lambda x: self.beta_true * 2 - x[0] - np.sqrt(3) * x[1],
var=2,
out=["g"],
)
>> gr.cp_marginals(
x0=dict(dist="norm", loc=0, scale=1, sign=1),
x1=dict(dist="norm", loc=0, scale=1, sign=1),
)
>> gr.cp_copula_independence()
)
def test_var_outer(self):
## Test pass-throughs
df_test = pd.DataFrame(dict(x0=[0]))
md_no_rand = gr.Model() >> gr.cp_function(
fun=lambda x: x, var=1, out=1)
md_no_rand.var_outer(pd.DataFrame(), df_det="nom")
md_no_det = md_no_rand >> gr.cp_marginals(x0={
"dist": "uniform",
"loc": 0,
"scale": 1
})
md_no_det.var_outer(df_test, df_det="nom")
## Test assertions
with self.assertRaises(ValueError):
self.model_3d.var_outer(self.df_2d, df_det=self.df_2d)
def test_function_model(self):
md_base = gr.Model() >> gr.cp_function(
fun=lambda x: x, var=1, out=1, name="name", runtime=1)
## Base constructor
func = gr.FunctionModel(md_base)
self.assertTrue(md_base.var == func.var)
self.assertTrue(md_base.out == func.out)
self.assertTrue(md_base.name == func.name)
self.assertTrue(md_base.runtime(1) == func.runtime)
## Test copy
func_copy = func.copy()
self.assertTrue(func_copy.var == func.var)
self.assertTrue(func_copy.out == func.out)
self.assertTrue(func_copy.name == func.name)
self.assertTrue(func_copy.runtime == func.runtime)
def setUp(self):
## Linear limit state w/ MPP off initial guess
self.beta_true = 3
self.md = (
gr.Model()
>> gr.cp_function(
fun=lambda x: self.beta_true * 2 - x[0] - np.sqrt(3) * x[1],
var=2,
out=["g"],
)
>> gr.cp_marginals(
x0=dict(dist="norm", loc=0, scale=1, sign=1),
x1=dict(dist="norm", loc=0, scale=1, sign=1),
)
>> gr.cp_copula_independence()
)
## Linear limit state w/ lognormal marginals
self.md_log = (
gr.Model()
>> gr.cp_vec_function(
fun=lambda df: gr.df_make(
g=gr.exp(gr.sqrt(2) * 1) - df.x * df.y
),
var=["x", "y"],
out=["g"]
)
>> gr.cp_marginals(
x=dict(dist="lognorm", loc=0, scale=1, s=1),
y=dict(dist="lognorm", loc=0, scale=1, s=1),
)
>> gr.cp_copula_independence()
)
self.df_mpp = gr.df_make(
x=gr.exp(gr.sqrt(2)/2),
y=gr.exp(gr.sqrt(2)/2),
beta_g=1.0,
g=0.0,
)
## Cantilever beam for flatten test
self.md_beam = models.make_cantilever_beam()
def test_comp_model(self):
"""Test model composition"""
md_inner = (
gr.Model("inner")
>> gr.cp_function(fun=lambda x: x[0] + x[1], var=2, out=1)
>> gr.cp_marginals(x0=dict(dist="norm", loc=0, scale=1))
>> gr.cp_copula_independence()
)
## Deterministic composition
md_det = gr.Model("outer_det") >> gr.cp_md_det(md=md_inner)
self.assertTrue(set(md_det.var) == {"x0", "x1"})
self.assertTrue(md_det.out == ["y0"])
gr.eval_df(md_det, df=gr.df_make(x0=0, x1=0))
## Deterministic composition
md_sample = gr.Model("outer_det") >> gr.cp_md_sample(
md=md_inner, param=dict(x0=("loc", "scale"))
)
self.assertTrue(set(md_sample.var) == {"x0_loc", "x0_scale", "x1"})
self.assertTrue(set(md_sample.out) == {"y0"})
gr.eval_df(md_sample, df=gr.df_make(x0_loc=0, x0_scale=1, x1=0))
def test_nls(self):
## Ground-truth model
c_true = 2
a_true = 1
md_true = (gr.Model() >> gr.cp_function(
fun=lambda x: a_true * np.exp(x[0] * c_true) + x[1],
var=["x", "epsilon"],
out=["y"],
) >> gr.cp_marginals(epsilon={
"dist": "norm",
"loc": 0,
"scale": 0.5
}) >> gr.cp_copula_independence())
df_data = md_true >> gr.ev_monte_carlo(
n=5, seed=101, df_det=gr.df_make(x=[0, 1, 2, 3, 4]))
## Model to fit
md_param = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] * np.exp(x[0] * x[1]),
var=["x", "c", "a"],
out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0]))
## Fit the model
md_fit = df_data >> gr.ft_nls(
md=md_param,
verbose=False,
uq_method="linpool",
)
## Unidentifiable model throws warning
# -------------------------
md_unidet = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] / x[3] * np.exp(x[0] * x[1]),
var=["x", "c", "a", "z"],
out=["y"],
) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0], z=[0, 1]))
with self.assertWarns(RuntimeWarning):
gr.fit_nls(
df_data,
md=md_unidet,
uq_method="linpool",
)
## True parameters in wide confidence region
# -------------------------
alpha = 1e-3
self.assertTrue(
(md_fit.density.marginals["c"].q(alpha / 2) <= c_true)
and (c_true <= md_fit.density.marginals["c"].q(1 - alpha / 2)))
self.assertTrue(
(md_fit.density.marginals["a"].q(alpha / 2) <= a_true)
and (a_true <= md_fit.density.marginals["a"].q(1 - alpha / 2)))
## Model with fixed parameter
# -------------------------
md_fixed = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] * np.exp(x[0] * x[1]),
var=["x", "c", "a"],
out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[1, 1]))
md_fit_fixed = df_data >> gr.ft_nls(
md=md_fixed, verbose=False, uq_method="linpool")
# Test that fixed model can evaluate successfully
gr.eval_monte_carlo(md_fit_fixed, n=1, df_det="nom")
## Trajectory model
# -------------------------
md_base = models.make_trajectory_linear()
md_fit = data.df_trajectory_windowed >> gr.ft_nls(
md=md_base, method="SLSQP", tol=1e-3)
df_tmp = md_fit >> gr.ev_nominal(df_det="nom")
def test_comp_function(self):
"""Test comp_function()"""
md_new0 = gr.comp_function(self.md, fun=lambda x: x, var=1, out=1)
md_new1 = gr.comp_function(md_new0, fun=lambda x: x, var=1, out=1)
## Operations above should not affect self.md
md_named = gr.comp_function(
self.md,
fun=lambda x: [x, 2 * x],
var=["foo"],
out=["bar1", "bar2"],
name="test",
)
## Default var and out names
self.assertEqual(md_new0.var, ["x0"])
self.assertEqual(md_new0.out, ["y0"])
## New default names iterate counter
self.assertEqual(set(md_new1.var), set(["x0", "x1"]))
self.assertEqual(set(md_new1.out), set(["y0", "y1"]))
## Output names assigned correctly
# Also tests for copy issues
self.assertEqual(set(md_named.out), set(["bar1", "bar2"]))
## Function name assigned correctly
self.assertEqual(md_named.functions[0].name, "test")
## Invariant checks
with self.assertRaises(ValueError):
# Missing function
gr.comp_function(self.md, fun=None, var=["foo"], out=["bar"])
with self.assertRaises(ValueError):
# Missing var
gr.comp_function(self.md, fun=lambda x: x, var=None, out=["bar"])
with self.assertRaises(ValueError):
# Missing out
gr.comp_function(self.md, fun=lambda x: x, var=["foo"], out=None)
with self.assertRaises(ValueError):
# Intersection var / out names
self.md >> gr.cp_function(lambda x: x, var=["x"], out=["x"], name="f0")
with self.assertRaises(ValueError):
# Non-unique function names
self.md >> gr.cp_function(
lambda x: x, var=1, out=1, name="f0"
) >> gr.cp_function(lambda x: x, var=1, out=1, name="f0")
## DAG invariant checks
with self.assertRaises(ValueError):
# Cycle by input
self.md >> gr.cp_function(
fun=lambda x: x[0], var=["y0"], out=1
) >> gr.cp_function(fun=lambda x: x[0], var=1, out=["y0"])
with self.assertRaises(ValueError):
# Non-unique output
self.md >> gr.cp_function(
fun=lambda x: x[0], var=1, out=["y0"]
) >> gr.cp_function(fun=lambda x: x[0], var=1, out=["y0"])
## Check vectorized builder
md_vec = gr.comp_vec_function(
self.md, fun=lambda df: df.assign(y0=df.x0), var=1, out=1,
)
self.assertTrue(
gr.df_equal(gr.df_make(x0=0, y0=0), md_vec >> gr.ev_df(df=gr.df_make(x0=0)))
)
def test_nls(self):
## Setup
md_feat = (gr.Model() >> gr.cp_function(
fun=lambda x: x[0] * x[1] + x[2],
var=3,
out=1,
) >> gr.cp_bounds(x0=[-1, +1], x2=[0, 0]) >>
gr.cp_marginals(x1=dict(dist="norm", loc=0, scale=1)))
md_const = (gr.Model() >> gr.cp_function(
fun=lambda x: x[0], var=1, out=1) >> gr.cp_bounds(x0=(-1, +1)))
df_response = md_feat >> gr.ev_df(
df=gr.df_make(x0=0.1, x1=[-1, -0.5, +0, +0.5, +1], x2=0))
df_data = df_response[["x1", "y0"]]
## Model with features
df_true = gr.df_make(x0=0.1)
df_fit = md_feat >> gr.ev_nls(df_data=df_data, append=False)
pd.testing.assert_frame_equal(
df_fit,
df_true,
check_exact=False,
check_dtype=False,
check_column_type=False,
)
## Fitting synonym
md_feat_fit = df_data >> gr.ft_nls(md=md_feat, verbose=False)
self.assertTrue(set(md_feat_fit.var) == set(["x1", "x2"]))
## Constant model
df_const = gr.df_make(x0=0)
df_fit = md_const >> gr.ev_nls(df_data=gr.df_make(y0=[-1, 0, +1]))
pd.testing.assert_frame_equal(
df_fit,
df_const,
check_exact=False,
check_dtype=False,
check_column_type=False,
)
## Multiple restarts works
df_multi = gr.eval_nls(md_feat, df_data=df_data, n_restart=2)
self.assertTrue(df_multi.shape[0] == 2)
## Specified initial guess
df_spec = gr.eval_nls(md_feat,
df_data=df_data,
df_init=gr.df_make(x0=0.5),
append=False)
pd.testing.assert_frame_equal(
df_spec,
df_true,
check_exact=False,
check_dtype=False,
check_column_type=False,
)
# Raises if incorrect guess data
with self.assertRaises(ValueError):
gr.eval_nls(md_feat, df_data=df_data, df_init=gr.df_make(foo=0.5))
def test_nls(self):
## Ground-truth model
c_true = 2
a_true = 1
md_true = (gr.Model() >> gr.cp_function(
fun=lambda x: a_true * np.exp(x[0] * c_true) + x[1],
var=["x", "epsilon"],
out=["y"],
) >> gr.cp_marginals(epsilon={
"dist": "norm",
"loc": 0,
"scale": 0.5
}) >> gr.cp_copula_independence())
df_data = md_true >> gr.ev_sample(
n=5, seed=101, df_det=gr.df_make(x=[0, 1, 2, 3, 4]))
## Model to fit
md_param = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] * np.exp(x[0] * x[1]),
var=["x", "c", "a"],
out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0]))
## Fit the model
md_fit = df_data >> gr.ft_nls(
md=md_param,
verbose=False,
uq_method="linpool",
)
## Unidentifiable model throws warning
# -------------------------
md_unidet = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] / x[3] * np.exp(x[0] * x[1]),
var=["x", "c", "a", "z"],
out=["y"],
) >> gr.cp_bounds(c=[0, 4], a=[0.1, 2.0], z=[0, 1]))
with self.assertWarns(RuntimeWarning):
gr.fit_nls(
df_data,
md=md_unidet,
uq_method="linpool",
)
## True parameters in wide confidence region
# -------------------------
alpha = 1e-3
self.assertTrue(
(md_fit.density.marginals["c"].q(alpha / 2) <= c_true)
and (c_true <= md_fit.density.marginals["c"].q(1 - alpha / 2)))
self.assertTrue(
(md_fit.density.marginals["a"].q(alpha / 2) <= a_true)
and (a_true <= md_fit.density.marginals["a"].q(1 - alpha / 2)))
## Model with fixed parameter
# -------------------------
md_fixed = (gr.Model() >> gr.cp_function(
fun=lambda x: x[2] * np.exp(x[0] * x[1]),
var=["x", "c", "a"],
out=["y"]) >> gr.cp_bounds(c=[0, 4], a=[1, 1]))
md_fit_fixed = df_data >> gr.ft_nls(
md=md_fixed, verbose=False, uq_method="linpool")
# Test that fixed model can evaluate successfully
gr.eval_sample(md_fit_fixed, n=1, df_det="nom")
## Trajectory model
# -------------------------
md_base = models.make_trajectory_linear()
md_fit = data.df_trajectory_windowed >> gr.ft_nls(
md=md_base, method="SLSQP", tol=1e-3)
df_tmp = md_fit >> gr.ev_nominal(df_det="nom")
## Select output for fitting
# -------------------------
# Split model has inconsistent "true" parameter value
md_split = (gr.Model("Split") >> gr.cp_vec_function(
fun=lambda df: gr.df_make(
f=1 * df.c * df.x,
g=2 * df.c * df.x,
),
var=["c", "x"],
out=["f", "g"],
) >> gr.cp_bounds(
x=(-1, +1),
c=(-1, +1),
))
df_split = (gr.df_make(x=gr.linspace(-1, +1, 100)) >> gr.tf_mutate(
f=X.x, g=X.x))
# Fitting both outputs: cannot achieve mse ~= 0
df_both = (df_split >> gr.ft_nls(md_split, out=["f", "g"]) >>
gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >>
gr.tf_summarize(
mse_f=gr.mse(X.f, X.f_t),
mse_g=gr.mse(X.g, X.g_t),
))
self.assertTrue(df_both.mse_f[0] > 0)
self.assertTrue(df_both.mse_g[0] > 0)
# Fitting "f" only
df_f = (df_split >> gr.ft_nls(md_split, out=["f"]) >>
gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >>
gr.tf_summarize(
mse_f=gr.mse(X.f, X.f_t),
mse_g=gr.mse(X.g, X.g_t),
))
self.assertTrue(df_f.mse_f[0] < 1e-16)
self.assertTrue(df_f.mse_g[0] > 0)
# Fitting "g" only
df_g = (df_split >> gr.ft_nls(md_split, out=["g"]) >>
gr.ev_df(df_split >> gr.tf_rename(f_t=X.f, g_t=X.g)) >>
gr.tf_summarize(
mse_f=gr.mse(X.f, X.f_t),
mse_g=gr.mse(X.g, X.g_t),
))
self.assertTrue(df_g.mse_f[0] > 0)
self.assertTrue(df_g.mse_g[0] < 1e-16)
