def test_301(): d = example(300, 'd') m = Model(dataservice=d) v = [ "timeperiod==2", "timeperiod==3", "timeperiod==4", "timeperiod==5", "timeperiod==6", "timeperiod==7", "timeperiod==8", "timeperiod==9", "carrier==2", "carrier==3", "carrier==4", "carrier==5", "equipment==2", "fare_hy", "fare_ly", "elapsed_time", "nb_cnxs", ] m.utility_ca = sum(PX(i) for i in v) m.choice_ca_var = 'choice' m.load_data() result = m.maximize_loglike() assert result.loglike == approx(-777770.0688722526) assert result.x['carrier==2'] == approx(0.11720047917232307) assert result.logloss == approx(3.306873650593341)
def test_utility_function_output():
k = Model()
k.utility_ca = P.Aaa * X.Aaa + P.Bbb * X.Bbb + P.Ccc
k.utility_co[1] = P.Dx1 + P.Dy1 * X.Yyy
k.utility_co[2] = P.Dx2 + P.Dy2 * X.Yyy
k.quantity_ca = P.Qaa * X.Aaa + P.Qbb * X.Bbb + P.Qcc
k.set_values(Aaa=12, Bbb=20, Ccc=2, Dx1=0, Dy1=0.001, Dx2=0.33, Dy2=-0.002)
u1 = k.utility_functions(resolve_parameters=False)
assert u1.tostring() == '<div><table class="floatinghead" style="margin-top:1px;"><thead>' \
'<tr><th>alt</th><th style="text-align:left;">formula</th></tr></thead>' \
'<tbody><tr><td>1</td><td style="text-align:left;"><div></div> + ' \
'<div class="tooltipped">P.Aaa<span class="tooltiptext">12</span></div> * ' \
'<div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span>' \
'</div><br> + <div class="tooltipped">P.Bbb<span class="tooltiptext">20</span>' \
'</div> * <div class="tooltipped">X.Bbb<span class="tooltiptext">This is Data' \
'</span></div><br> + <div class="tooltipped">P.Ccc<span class="tooltiptext">2' \
'</span></div><br> + <div class="tooltipped">P.Dx1<span class="tooltiptext">0' \
'</span></div><br> + <div class="tooltipped">P.Dy1<span class="tooltiptext">0.001' \
'</span></div> * <div class="tooltipped">X.Yyy<span class="tooltiptext">' \
'This is Data</span></div><br> + log(<br>\xa0\xa0 + <span></span>exp(' \
'<div class="tooltipped">P.Qaa<span class="tooltiptext">exp(0) = 0</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">P.Qbb<span class="tooltiptext">' \
'exp(0) = 0</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'P.Qcc<span class="tooltiptext">exp(0) = 0</span></div>)<br>)</td></tr><tr><td>2</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">P.Aaa' \
'<span class="tooltiptext">12</span></div> * <div class="tooltipped">X.Aaa' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'P.Bbb<span class="tooltiptext">20</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'P.Ccc<span class="tooltiptext">2</span></div><br> + <div class="tooltipped">P.Dx2' \
'<span class="tooltiptext">0.33</span></div><br> + <div class="tooltipped">P.Dy2' \
'<span class="tooltiptext">-0.002</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + ' \
'<span></span>exp(<div class="tooltipped">P.Qaa<span class="tooltiptext">exp(0) = 0' \
'</span></div>) * <div class="tooltipped">X.Aaa<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'P.Qbb<span class="tooltiptext">exp(0) = 0</span></div>) * <div class="tooltipped">' \
'X.Bbb<span class="tooltiptext">This is Data</span></div><br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">P.Qcc<span class="tooltiptext">exp(0) = 0</span>' \
'</div>)<br>)</td></tr></tbody></table></div>'
u2 = k.utility_functions(resolve_parameters=True)
assert u2.tostring() == '<div><table class="floatinghead" style="margin-top:1px;"><thead><tr><th>alt</th>' \
'<th style="text-align:left;">formula</th></tr></thead><tbody><tr><td>1</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">12' \
'<span class="tooltiptext">P.Aaa</span></div> * <div class="tooltipped">' \
'X.Aaa<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'20<span class="tooltiptext">P.Bbb</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'2<span class="tooltiptext">P.Ccc</span></div><br> + <div class="tooltipped">0' \
'<span class="tooltiptext">P.Dx1</span></div><br> + <div class="tooltipped">0.001' \
'<span class="tooltiptext">P.Dy1</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">0<span class="tooltiptext">exp(P.Qaa)</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0<span class="tooltiptext">' \
'exp(P.Qbb)</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0' \
'<span class="tooltiptext">exp(P.Qcc)</span></div>)<br>)</td></tr><tr><td>2</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">12' \
'<span class="tooltiptext">P.Aaa</span></div> * <div class="tooltipped">X.Aaa' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'20<span class="tooltiptext">P.Bbb</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">2' \
'<span class="tooltiptext">P.Ccc</span></div><br> + <div class="tooltipped">0.33' \
'<span class="tooltiptext">P.Dx2</span></div><br> + <div class="tooltipped">-0.002' \
'<span class="tooltiptext">P.Dy2</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">0<span class="tooltiptext">exp(P.Qaa)</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0<span class="tooltiptext">' \
'exp(P.Qbb)</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'0<span class="tooltiptext">exp(P.Qcc)</span></div>)<br>)</td></tr></tbody></table></div>'
def location_choice_model(
name="workplace_location",
edb_directory="output/estimation_data_bundle/{name}/",
coefficients_file="{name}_coefficients.csv",
spec_file="{name}_SPEC.csv",
size_spec_file="{name}_size_terms.csv",
alt_values_file="{name}_alternatives_combined.csv",
chooser_file="{name}_choosers_combined.csv",
settings_file="{name}_model_settings.yaml",
landuse_file="{name}_landuse.csv",
return_data=False,
):
model_selector = name.replace("_location", "")
model_selector = model_selector.replace("_destination", "")
model_selector = model_selector.replace("_subtour", "")
model_selector = model_selector.replace("_tour", "")
if model_selector == 'joint':
model_selector = 'non_mandatory'
edb_directory = edb_directory.format(name=name)
def _read_csv(filename, **kwargs):
filename = filename.format(name=name)
return pd.read_csv(os.path.join(edb_directory, filename), **kwargs)
coefficients = _read_csv(
coefficients_file,
index_col="coefficient_name",
)
spec = _read_csv(spec_file, comment="#")
alt_values = _read_csv(alt_values_file)
chooser_data = _read_csv(chooser_file)
landuse = _read_csv(landuse_file, index_col="zone_id")
master_size_spec = _read_csv(size_spec_file)
# remove temp rows from spec, ASim uses them to calculate the other values written
# to the EDB, but they are not actually part of the utility function themselves.
spec = spec.loc[~spec.Expression.isna()]
spec = spec.loc[~spec.Expression.str.startswith("_")].copy()
settings_file = settings_file.format(name=name)
with open(os.path.join(edb_directory, settings_file), "r") as yf:
settings = yaml.load(
yf,
Loader=yaml.SafeLoader,
)
include_settings = settings.get("include_settings")
if include_settings:
include_settings = os.path.join(edb_directory, include_settings)
if include_settings and os.path.exists(include_settings):
with open(include_settings, "r") as yf:
more_settings = yaml.load(
yf,
Loader=yaml.SafeLoader,
)
settings.update(more_settings)
CHOOSER_SEGMENT_COLUMN_NAME = settings.get("CHOOSER_SEGMENT_COLUMN_NAME")
SEGMENT_IDS = settings.get("SEGMENT_IDS")
if SEGMENT_IDS is None:
SEGMENTS = settings.get("SEGMENTS")
if SEGMENTS is not None:
SEGMENT_IDS = {i: i for i in SEGMENTS}
SIZE_TERM_SELECTOR = settings.get('SIZE_TERM_SELECTOR', model_selector)
# filter size spec for this location choice only
size_spec = (master_size_spec.query(
f"model_selector == '{SIZE_TERM_SELECTOR}'").drop(
columns="model_selector").set_index("segment"))
size_spec = size_spec.loc[:, size_spec.max() > 0]
size_coef = size_coefficients_from_spec(size_spec)
indexes_to_drop = [
"util_size_variable", # pre-computed size (will be re-estimated)
"util_size_variable_atwork", # pre-computed size (will be re-estimated)
"util_utility_adjustment", # shadow pricing (ignored in estimation)
"@df['size_term'].apply(np.log1p)", # pre-computed size (will be re-estimated)
]
if 'Label' in spec.columns:
indexes_to_drop = [
i for i in indexes_to_drop if i in spec.Label.to_numpy()
]
label_column_name = 'Label'
elif 'Expression' in spec.columns:
indexes_to_drop = [
i for i in indexes_to_drop if i in spec.Expression.to_numpy()
]
label_column_name = 'Expression'
else:
raise ValueError("cannot find Label or Expression in spec file")
expression_labels = None
if label_column_name == 'Expression':
expression_labels = {
expr: f"variable_label{n:04d}"
for n, expr in enumerate(spec.Expression.to_numpy())
}
# Remove shadow pricing and pre-existing size expression for re-estimation
spec = (spec.set_index(label_column_name).drop(
index=indexes_to_drop).reset_index())
if label_column_name == 'Expression':
spec.insert(0, "Label", spec['Expression'].map(expression_labels))
alt_values['variable'] = alt_values['variable'].map(expression_labels)
label_column_name = "Label"
if name == 'trip_destination':
CHOOSER_SEGMENT_COLUMN_NAME = 'primary_purpose'
primary_purposes = spec.columns[3:]
SEGMENT_IDS = {pp: pp for pp in primary_purposes}
chooser_index_name = chooser_data.columns[0]
x_co = chooser_data.set_index(chooser_index_name)
x_ca = cv_to_ca(
alt_values.set_index([chooser_index_name, alt_values.columns[1]]))
if CHOOSER_SEGMENT_COLUMN_NAME is not None:
# label segments with names
SEGMENT_IDS_REVERSE = {v: k for k, v in SEGMENT_IDS.items()}
x_co["_segment_label"] = x_co[CHOOSER_SEGMENT_COLUMN_NAME].apply(
lambda x: SEGMENT_IDS_REVERSE[x])
else:
x_co["_segment_label"] = size_spec.index[0]
# compute total size values by segment
for segment in size_spec.index:
total_size_segment = pd.Series(0, index=landuse.index)
x_co["total_size_" + segment] = 0
for land_use_field in size_spec.loc[segment].index:
total_size_segment += (landuse[land_use_field] *
size_spec.loc[segment, land_use_field])
x_co["total_size_" + segment] = total_size_segment.loc[
x_co["override_choice"]].to_numpy()
# for each chooser, collate the appropriate total size value
x_co["total_size_segment"] = 0
for segment in size_spec.index:
labels = "total_size_" + segment
rows = x_co["_segment_label"] == segment
x_co.loc[rows, "total_size_segment"] = x_co[labels][rows]
# Remove choosers with invalid observed choice (appropriate total size value = 0)
valid_observed_zone = x_co["total_size_segment"] > 0
x_co = x_co[valid_observed_zone]
x_ca = x_ca[x_ca.index.get_level_values(chooser_index_name).isin(
x_co.index)]
# Merge land use characteristics into CA data
try:
x_ca_1 = pd.merge(x_ca, landuse, on="zone_id", how="left")
except KeyError:
# Missing the zone_id variable?
# Use the alternative id's instead, which assumes no sampling of alternatives
x_ca_1 = pd.merge(x_ca,
landuse,
left_on=x_ca.index.get_level_values(1),
right_index=True,
how="left")
x_ca_1.index = x_ca.index
# Availability of choice zones
if "util_no_attractions" in x_ca_1:
av = x_ca_1["util_no_attractions"].apply(
lambda x: False if x == 1 else True).astype(np.int8)
elif "@df['size_term']==0" in x_ca_1:
av = x_ca_1["@df['size_term']==0"].apply(
lambda x: False if x == 1 else True).astype(np.int8)
else:
av = 1
d = DataFrames(co=x_co, ca=x_ca_1, av=av)
m = Model(dataservice=d)
if len(spec.columns) == 4 and all(
spec.columns ==
['Label', 'Description', 'Expression', 'coefficient']):
m.utility_ca = linear_utility_from_spec(
spec,
x_col="Label",
p_col=spec.columns[-1],
ignore_x=("local_dist", ),
)
elif len(spec.columns) == 4 \
and all(spec.columns[:3] == ['Label', 'Description', 'Expression']) \
and len(SEGMENT_IDS) == 1 \
and spec.columns[3] == list(SEGMENT_IDS.values())[0]:
m.utility_ca = linear_utility_from_spec(
spec,
x_col="Label",
p_col=spec.columns[-1],
ignore_x=("local_dist", ),
)
else:
m.utility_ca = linear_utility_from_spec(
spec,
x_col=label_column_name,
p_col=SEGMENT_IDS,
ignore_x=("local_dist", ),
segment_id=CHOOSER_SEGMENT_COLUMN_NAME,
)
if CHOOSER_SEGMENT_COLUMN_NAME is None:
assert len(size_spec) == 1
m.quantity_ca = sum(
P(f"{i}_{q}") * X(q) for i in size_spec.index
for q in size_spec.columns if size_spec.loc[i, q] != 0)
else:
m.quantity_ca = sum(
P(f"{i}_{q}") * X(q) *
X(f"{CHOOSER_SEGMENT_COLUMN_NAME}=={str_repr(SEGMENT_IDS[i])}")
for i in size_spec.index for q in size_spec.columns
if size_spec.loc[i, q] != 0)
apply_coefficients(coefficients, m)
apply_coefficients(size_coef, m, minimum=-6, maximum=6)
m.choice_co_code = "override_choice"
if return_data:
return (
m,
Dict(
edb_directory=Path(edb_directory),
alt_values=alt_values,
chooser_data=chooser_data,
coefficients=coefficients,
landuse=landuse,
spec=spec,
size_spec=size_spec,
master_size_spec=master_size_spec,
model_selector=model_selector,
settings=settings,
),
)
return m
def schedule_choice_model(
name,
edb_directory="output/estimation_data_bundle/{name}/",
coefficients_file="{name}_coefficients.csv",
spec_file="{name}_SPEC.csv",
alt_values_file="{name}_alternatives_combined.csv",
chooser_file="{name}_choosers_combined.csv",
settings_file="{name}_model_settings.yaml",
return_data=False,
):
model_selector = name.replace("_location", "")
model_selector = model_selector.replace("_destination", "")
model_selector = model_selector.replace("_subtour", "")
model_selector = model_selector.replace("_tour", "")
edb_directory = edb_directory.format(name=name)
def _read_csv(filename, optional=False, **kwargs):
filename = filename.format(name=name)
try:
return pd.read_csv(os.path.join(edb_directory, filename), **kwargs)
except FileNotFoundError:
if optional:
return None
else:
raise
settings_file = settings_file.format(name=name)
with open(os.path.join(edb_directory, settings_file), "r") as yf:
settings = yaml.load(
yf,
Loader=yaml.SafeLoader,
)
try:
coefficients = _read_csv(
coefficients_file,
index_col="coefficient_name",
)
except FileNotFoundError:
# possibly mis-named file is shown in settings
coefficients_file = settings.get('COEFFICIENTS', coefficients_file)
coefficients = _read_csv(
coefficients_file,
index_col="coefficient_name",
)
spec = _read_csv(spec_file, comment='#')
alt_values = _read_csv(alt_values_file)
chooser_data = _read_csv(chooser_file)
# remove temp rows from spec, ASim uses them to calculate the other values written
# to the EDB, but they are not actually part of the utility function themselves.
spec = spec.loc[~spec.Expression.str.startswith("_")].copy()
include_settings = settings.get("include_settings")
if include_settings:
with open(os.path.join(edb_directory, include_settings), "r") as yf:
more_settings = yaml.load(
yf,
Loader=yaml.SafeLoader,
)
settings.update(more_settings)
CHOOSER_SEGMENT_COLUMN_NAME = settings.get("CHOOSER_SEGMENT_COLUMN_NAME")
SEGMENT_IDS = settings.get("SEGMENT_IDS")
if SEGMENT_IDS is None:
SEGMENTS = settings.get("SEGMENTS")
if SEGMENTS is not None:
SEGMENT_IDS = {i: i for i in SEGMENTS}
if 'Label' in spec.columns:
label_column_name = 'Label'
elif 'Expression' in spec.columns:
label_column_name = 'Expression'
else:
raise ValueError("cannot find Label or Expression in spec file")
m = Model()
if len(spec.columns) == 4 and ([c.lower() for c in spec.columns] == [
'label', 'description', 'expression', 'coefficient'
]):
m.utility_ca = linear_utility_from_spec(
spec,
x_col="Label",
p_col=spec.columns[-1],
ignore_x=("local_dist", ),
)
elif len(spec.columns) == 4 \
and all(spec.columns[:3] == ['Label', 'Description', 'Expression']) \
and len(SEGMENT_IDS) == 1 \
and spec.columns[3] == list(SEGMENT_IDS.values())[0]:
m.utility_ca = linear_utility_from_spec(
spec,
x_col="Label",
p_col=spec.columns[-1],
ignore_x=("local_dist", ),
)
else:
m.utility_ca = linear_utility_from_spec(
spec,
x_col=label_column_name,
p_col=SEGMENT_IDS,
ignore_x=("local_dist", ),
segment_id=CHOOSER_SEGMENT_COLUMN_NAME,
)
apply_coefficients(coefficients, m, minimum=-25, maximum=25)
chooser_index_name = chooser_data.columns[0]
x_co = chooser_data.set_index(chooser_index_name)
alt_values.fillna(0, inplace=True)
x_ca = cv_to_ca(
alt_values.set_index([chooser_index_name, alt_values.columns[1]]),
required_labels=spec[label_column_name],
)
# if CHOOSER_SEGMENT_COLUMN_NAME is not None:
# # label segments with names
# SEGMENT_IDS_REVERSE = {v: k for k, v in SEGMENT_IDS.items()}
# x_co["_segment_label"] = x_co[CHOOSER_SEGMENT_COLUMN_NAME].apply(
# lambda x: SEGMENT_IDS_REVERSE[x]
# )
# else:
# x_co["_segment_label"] = size_spec.index[0]
alt_codes = np.arange(len(x_ca.index.levels[1])) + 1
x_ca.index = x_ca.index.set_levels(alt_codes, 1)
x_co["override_choice_plus1"] = x_co["override_choice"] + 1
x_co["model_choice_plus1"] = x_co["model_choice"] + 1
unavail_coefs = coefficients.query(
"(constrain == 'T') & (value < -900)").index
unavail_data = [i.data for i in m.utility_ca if i.param in unavail_coefs]
if len(unavail_data):
joint_unavail = "|".join(f"({i}>0)" for i in unavail_data)
joint_avail = f"~({joint_unavail})"
else:
joint_avail = 1
d = DataFrames(co=x_co, ca=x_ca, av=joint_avail)
m.dataservice = d
m.choice_co_code = "override_choice_plus1"
# m.choice_co_code = "model_choice_plus1"
if return_data:
return (
m,
Dict(
edb_directory=Path(edb_directory),
alt_values=alt_values,
chooser_data=chooser_data,
coefficients=coefficients,
spec=spec,
model_selector=model_selector,
joint_avail=joint_avail,
),
)
return m
def test_utility_function_output():
k = Model()
k.utility_ca = P.Aaa * X.Aaa + P.Bbb * X.Bbb + P.Ccc
k.utility_co[1] = P.Dx1 + P.Dy1 * X.Yyy
k.utility_co[2] = P.Dx2 + P.Dy2 * X.Yyy
k.quantity_ca = P.Qaa * X.Aaa + P.Qbb * X.Bbb + P.Qcc
k.set_values(Aaa=12, Bbb=20, Ccc=2, Dx1=0, Dy1=0.001, Dx2=0.33, Dy2=-0.002)
u1 = k.utility_functions(resolve_parameters=False)
assert u1.tostring() == '<div><table class="floatinghead" style="margin-top:1px;"><thead>' \
'<tr><th>alt</th><th style="text-align:left;">formula</th></tr></thead>' \
'<tbody><tr><td>1</td><td style="text-align:left;"><div></div> + ' \
'<div class="tooltipped">P.Aaa<span class="tooltiptext">12</span></div> * ' \
'<div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span>' \
'</div><br> + <div class="tooltipped">P.Bbb<span class="tooltiptext">20</span>' \
'</div> * <div class="tooltipped">X.Bbb<span class="tooltiptext">This is Data' \
'</span></div><br> + <div class="tooltipped">P.Ccc<span class="tooltiptext">2' \
'</span></div><br> + <div class="tooltipped">P.Dx1<span class="tooltiptext">0' \
'</span></div><br> + <div class="tooltipped">P.Dy1<span class="tooltiptext">0.001' \
'</span></div> * <div class="tooltipped">X.Yyy<span class="tooltiptext">' \
'This is Data</span></div><br> + log(<br>\xa0\xa0 + <span></span>exp(' \
'<div class="tooltipped">P.Qaa<span class="tooltiptext">exp(0) = 0</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">P.Qbb<span class="tooltiptext">' \
'exp(0) = 0</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'P.Qcc<span class="tooltiptext">exp(0) = 0</span></div>)<br>)</td></tr><tr><td>2</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">P.Aaa' \
'<span class="tooltiptext">12</span></div> * <div class="tooltipped">X.Aaa' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'P.Bbb<span class="tooltiptext">20</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'P.Ccc<span class="tooltiptext">2</span></div><br> + <div class="tooltipped">P.Dx2' \
'<span class="tooltiptext">0.33</span></div><br> + <div class="tooltipped">P.Dy2' \
'<span class="tooltiptext">-0.002</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + ' \
'<span></span>exp(<div class="tooltipped">P.Qaa<span class="tooltiptext">exp(0) = 0' \
'</span></div>) * <div class="tooltipped">X.Aaa<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'P.Qbb<span class="tooltiptext">exp(0) = 0</span></div>) * <div class="tooltipped">' \
'X.Bbb<span class="tooltiptext">This is Data</span></div><br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">P.Qcc<span class="tooltiptext">exp(0) = 0</span>' \
'</div>)<br>)</td></tr></tbody></table></div>'
u2 = k.utility_functions(resolve_parameters=True)
assert u2.tostring() == '<div><table class="floatinghead" style="margin-top:1px;"><thead><tr><th>alt</th>' \
'<th style="text-align:left;">formula</th></tr></thead><tbody><tr><td>1</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">12' \
'<span class="tooltiptext">P.Aaa</span></div> * <div class="tooltipped">' \
'X.Aaa<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'20<span class="tooltiptext">P.Bbb</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'2<span class="tooltiptext">P.Ccc</span></div><br> + <div class="tooltipped">0' \
'<span class="tooltiptext">P.Dx1</span></div><br> + <div class="tooltipped">0.001' \
'<span class="tooltiptext">P.Dy1</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">0<span class="tooltiptext">exp(P.Qaa)</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0<span class="tooltiptext">' \
'exp(P.Qbb)</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0' \
'<span class="tooltiptext">exp(P.Qcc)</span></div>)<br>)</td></tr><tr><td>2</td>' \
'<td style="text-align:left;"><div></div> + <div class="tooltipped">12' \
'<span class="tooltiptext">P.Aaa</span></div> * <div class="tooltipped">X.Aaa' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">' \
'20<span class="tooltiptext">P.Bbb</span></div> * <div class="tooltipped">X.Bbb' \
'<span class="tooltiptext">This is Data</span></div><br> + <div class="tooltipped">2' \
'<span class="tooltiptext">P.Ccc</span></div><br> + <div class="tooltipped">0.33' \
'<span class="tooltiptext">P.Dx2</span></div><br> + <div class="tooltipped">-0.002' \
'<span class="tooltiptext">P.Dy2</span></div> * <div class="tooltipped">X.Yyy' \
'<span class="tooltiptext">This is Data</span></div><br> + log(<br>\xa0\xa0 + <span>' \
'</span>exp(<div class="tooltipped">0<span class="tooltiptext">exp(P.Qaa)</span></div>) ' \
'* <div class="tooltipped">X.Aaa<span class="tooltiptext">This is Data</span></div>' \
'<br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">0<span class="tooltiptext">' \
'exp(P.Qbb)</span></div>) * <div class="tooltipped">X.Bbb<span class="tooltiptext">' \
'This is Data</span></div><br>\xa0\xa0 + <span></span>exp(<div class="tooltipped">' \
'0<span class="tooltiptext">exp(P.Qcc)</span></div>)<br>)</td></tr></tbody></table></div>'