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stringlengths 2
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⌀ | name
stringlengths 1
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| docstring
stringlengths 0
281k
⌀ | code
stringlengths 4
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| signature
stringlengths 2
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⌀ | embed_func_code
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43,019 | linearmodels.panel.model | _drop_singletons | null | def _drop_singletons(self) -> None:
if self._singletons or not self._has_effect:
return
effects = self._collect_effects()
retain = in_2core_graph(effects)
if np.all(retain):
return
import warnings as warn
nobs = retain.shape[0]
ndropped = nobs - retain.sum()
warn.warn(
f"{ndropped} singleton observations dropped",
SingletonWarning,
stacklevel=3,
)
drop = ~retain
self._singleton_index = cast(BoolArray, drop)
self.dependent.drop(drop)
self.exog.drop(drop)
self.weights.drop(drop)
if self.other_effects:
assert self._other_effect_cats is not None
self._other_effect_cats.drop(drop)
# Reverify exog matrix
self._check_exog_rank()
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|
43,022 | linearmodels.panel.model | _fast_path | Dummy-variable free estimation without weights | def _fast_path(
self, low_memory: bool
) -> tuple[Float64Array, Float64Array, Float64Array]:
"""Dummy-variable free estimation without weights"""
_y = self.dependent.values2d
_x = self.exog.values2d
ybar = np.asarray(_y.mean(0))
if not self._has_effect:
return _y, _x, ybar
y_gm = ybar
x_gm = _x.mean(0)
y = self.dependent
x = self.exog
if self.other_effects:
assert self._other_effect_cats is not None
groups = self._other_effect_cats
if self.entity_effects or self.time_effects:
groups = groups.copy()
if self.entity_effects:
effect = self.dependent.entity_ids
else:
effect = self.dependent.time_ids
col = ensure_unique_column("additional.effect", groups.dataframe)
groups.dataframe[col] = effect
y = cast(PanelData, y.general_demean(groups))
x = cast(PanelData, x.general_demean(groups))
elif self.entity_effects and self.time_effects:
y = cast(PanelData, y.demean("both", low_memory=low_memory))
x = cast(PanelData, x.demean("both", low_memory=low_memory))
elif self.entity_effects:
y = cast(PanelData, y.demean("entity"))
x = cast(PanelData, x.demean("entity"))
else: # self.time_effects
y = cast(PanelData, y.demean("time"))
x = cast(PanelData, x.demean("time"))
y_arr = y.values2d
x_arr = x.values2d
if self.has_constant:
y_arr = y_arr + y_gm
x_arr = x_arr + x_gm
else:
ybar = np.asarray(0.0)
return y_arr, x_arr, ybar
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|
43,023 | linearmodels.panel.model | _info | Information about model effects and panel structure | def _info(self) -> tuple[Series, Series, DataFrame | None]:
"""Information about model effects and panel structure"""
entity_info, time_info, other_info = super()._info()
if self.other_effects:
other_info_values: list[Series] = []
assert self._other_effect_cats is not None
oe = self._other_effect_cats.dataframe
for c in oe:
name = "Observations per group (" + str(c) + ")"
other_info_values.append(
panel_structure_stats(oe[c].values.astype(np.int32), name)
)
other_info = DataFrame(other_info_values)
return entity_info, time_info, other_info
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|
43,024 | linearmodels.panel.model | _is_effect_nested | Determine whether an effect is nested by the covariance clusters | @staticmethod
def _is_effect_nested(effects: NumericArray, clusters: NumericArray) -> bool:
"""Determine whether an effect is nested by the covariance clusters"""
is_nested = np.zeros(effects.shape[1], dtype=bool)
for i, e in enumerate(effects.T):
e = (e - e.min()).astype(np.int64)
e_count = len(np.unique(e))
for c in clusters.T:
c = (c - c.min()).astype(np.int64)
cmax = c.max()
ec = e * (cmax + 1) + c
is_nested[i] = len(np.unique(ec)) == e_count
return bool(np.all(is_nested))
| (effects: numpy.ndarray, clusters: numpy.ndarray) -> bool | [
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|
43,025 | linearmodels.panel.model | _lsmr_path | Sparse implementation, works for all scenarios | def _lsmr_path(
self,
) -> tuple[Float64Array, Float64Array, Float64Array, Float64Array, Float64Array]:
"""Sparse implementation, works for all scenarios"""
y = cast(Float64Array, self.dependent.values2d)
x = cast(Float64Array, self.exog.values2d)
w = cast(Float64Array, self.weights.values2d)
root_w = np.sqrt(w)
wybar = root_w * (w.T @ y / w.sum())
wy = root_w * y
wx = root_w * x
if not self._has_effect:
y_effect, x_effect = np.zeros_like(wy), np.zeros_like(wx)
return wy, wx, wybar, y_effect, x_effect
wy_gm = wybar
wx_gm = root_w * (w.T @ x / w.sum())
root_w_sparse = csc_matrix(root_w)
cats_l: list[IntArray | Float64Array] = []
if self.entity_effects:
cats_l.append(self.dependent.entity_ids)
if self.time_effects:
cats_l.append(self.dependent.time_ids)
if self.other_effects:
assert self._other_effect_cats is not None
cats_l.append(self._other_effect_cats.values2d)
cats = np.concatenate(cats_l, 1)
wd, cond = dummy_matrix(cats, precondition=True)
assert isinstance(wd, csc_matrix)
if self._is_weighted:
wd = wd.multiply(root_w_sparse)
wx_mean_l = []
for i in range(x.shape[1]):
cond_mean = lsmr(wd, wx[:, i], atol=1e-8, btol=1e-8)[0]
cond_mean /= cond
wx_mean_l.append(cond_mean)
wx_mean = np.column_stack(wx_mean_l)
wy_mean = lsmr(wd, wy, atol=1e-8, btol=1e-8)[0]
wy_mean /= cond
wy_mean = wy_mean[:, None]
wx_mean = csc_matrix(wx_mean)
wy_mean = csc_matrix(wy_mean)
# Purge fitted, weighted values
sp_cond = diags(cond, format="csc")
wx = wx - (wd @ sp_cond @ wx_mean).A
wy = wy - (wd @ sp_cond @ wy_mean).A
if self.has_constant:
wy += wy_gm
wx += wx_gm
else:
wybar = 0
y_effects = y - wy / root_w
x_effects = x - wx / root_w
return wy, wx, wybar, y_effects, x_effects
| (self) -> tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray] | [
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|
43,031 | linearmodels.panel.model | _slow_path | Frisch-Waugh-Lovell implementation, works for all scenarios | def _slow_path(
self,
) -> tuple[Float64Array, Float64Array, Float64Array, Float64Array, Float64Array]:
"""Frisch-Waugh-Lovell implementation, works for all scenarios"""
w = cast(Float64Array, self.weights.values2d)
root_w = np.sqrt(w)
y = root_w * cast(Float64Array, self.dependent.values2d)
x = root_w * cast(Float64Array, self.exog.values2d)
if not self._has_effect:
ybar = root_w @ _lstsq(root_w, y, rcond=None)[0]
y_effect, x_effect = np.zeros_like(y), np.zeros_like(x)
return y, x, ybar, y_effect, x_effect
drop_first = self._constant
d_l = []
if self.entity_effects:
d_l.append(self.dependent.dummies("entity", drop_first=drop_first).values)
drop_first = True
if self.time_effects:
d_l.append(self.dependent.dummies("time", drop_first=drop_first).values)
drop_first = True
if self.other_effects:
assert self._other_effect_cats is not None
oe = self._other_effect_cats.dataframe
for c in oe:
dummies = get_dummies(oe[c], drop_first=drop_first).astype(np.float64)
d_l.append(dummies.values)
drop_first = True
d = np.column_stack(d_l)
wd = root_w * d
if self.has_constant:
wd -= root_w * (w.T @ d / w.sum())
z = np.ones_like(root_w)
d -= z * (z.T @ d / z.sum())
x_mean = _lstsq(wd, x, rcond=None)[0]
y_mean = _lstsq(wd, y, rcond=None)[0]
# Save fitted unweighted effects to use in eps calculation
x_effects = d @ x_mean
y_effects = d @ y_mean
# Purge fitted, weighted values
x = x - wd @ x_mean
y = y - wd @ y_mean
ybar = root_w @ _lstsq(root_w, y, rcond=None)[0]
return y, x, ybar, y_effects, x_effects
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|
43,033 | linearmodels.panel.model | _validate_effects | Check model effects | def _validate_effects(self, effects: PanelDataLike | None) -> bool:
"""Check model effects"""
if effects is None:
return False
effects = PanelData(effects, var_name="OtherEffect", convert_dummies=False)
if effects.shape[1:] != self._original_shape[1:]:
raise ValueError(
"other_effects must have the same number of "
"entities and time periods as dependent."
)
num_effects = effects.nvar
if num_effects + self.entity_effects + self.time_effects > 2:
raise ValueError("At most two effects supported.")
cats = {}
effects_frame = effects.dataframe
for col in effects_frame:
cat = Categorical(effects_frame[col])
# TODO: Bug in pandas-stube
# https://github.com/pandas-dev/pandas-stubs/issues/111
cats[col] = cat.codes.astype(np.int64) # type: ignore
cats_df = DataFrame(cats, index=effects_frame.index)
cats_df = cats_df[effects_frame.columns]
other_effects = PanelData(cats_df)
other_effects.drop(~self.not_null)
self._other_effect_cats = other_effects
cats_array = other_effects.values2d
nested = False
nesting_effect = ""
if cats_array.shape[1] == 2:
nested = self._is_effect_nested(cats_array[:, [0]], cats_array[:, [1]])
nested |= self._is_effect_nested(cats_array[:, [1]], cats_array[:, [0]])
nesting_effect = "other effects"
elif self.entity_effects:
nested = self._is_effect_nested(
cats_array[:, [0]], self.dependent.entity_ids
)
nested |= self._is_effect_nested(
self.dependent.entity_ids, cats_array[:, [0]]
)
nesting_effect = "entity effects"
elif self.time_effects:
nested = self._is_effect_nested(cats_array[:, [0]], self.dependent.time_ids)
nested |= self._is_effect_nested(
self.dependent.time_ids, cats_array[:, [0]]
)
nesting_effect = "time effects"
if nested:
raise ValueError(
"Included other effects nest or are nested "
"by {effect}".format(effect=nesting_effect)
)
return True
| (self, effects: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType]) -> bool | [
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|
43,034 | linearmodels.panel.model | _weighted_fast_path | Dummy-variable free estimation with weights | def _weighted_fast_path(
self, low_memory: bool
) -> tuple[Float64Array, Float64Array, Float64Array, Float64Array, Float64Array]:
"""Dummy-variable free estimation with weights"""
y_arr = self.dependent.values2d
x_arr = self.exog.values2d
w = self.weights.values2d
root_w = cast(Float64Array, np.sqrt(w))
wybar = root_w * (w.T @ y_arr / w.sum())
if not self._has_effect:
wy_arr = root_w * self.dependent.values2d
wx_arr = root_w * self.exog.values2d
y_effect, x_effect = np.zeros_like(wy_arr), np.zeros_like(wx_arr)
return wy_arr, wx_arr, wybar, y_effect, x_effect
wy_gm = wybar
wx_gm = root_w * (w.T @ x_arr / w.sum())
y = self.dependent
x = self.exog
if self.other_effects:
assert self._other_effect_cats is not None
groups = self._other_effect_cats
if self.entity_effects or self.time_effects:
groups = groups.copy()
if self.entity_effects:
effect = self.dependent.entity_ids
else:
effect = self.dependent.time_ids
col = ensure_unique_column("additional.effect", groups.dataframe)
groups.dataframe[col] = effect
wy = y.general_demean(groups, weights=self.weights)
wx = x.general_demean(groups, weights=self.weights)
elif self.entity_effects and self.time_effects:
wy = cast(
PanelData, y.demean("both", weights=self.weights, low_memory=low_memory)
)
wx = cast(
PanelData, x.demean("both", weights=self.weights, low_memory=low_memory)
)
elif self.entity_effects:
wy = cast(PanelData, y.demean("entity", weights=self.weights))
wx = cast(PanelData, x.demean("entity", weights=self.weights))
else: # self.time_effects
wy = cast(PanelData, y.demean("time", weights=self.weights))
wx = cast(PanelData, x.demean("time", weights=self.weights))
wy_arr = wy.values2d
wx_arr = wx.values2d
if self.has_constant:
wy_arr += wy_gm
wx_arr += wx_gm
else:
wybar = 0
wy_effects = y.values2d - wy_arr / root_w
wx_effects = x.values2d - wx_arr / root_w
return wy_arr, wx_arr, wybar, wy_effects, wx_effects
| (self, low_memory: bool) -> tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray] | [
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|
43,035 | linearmodels.panel.model | fit |
Estimate model parameters
Parameters
----------
use_lsdv : bool
Flag indicating to use the Least Squares Dummy Variable estimator
to eliminate effects. The default value uses only means and does
note require constructing dummy variables for each effect.
use_lsmr : bool
Flag indicating to use LSDV with the Sparse Equations and Least
Squares estimator to eliminate the fixed effects.
low_memory : {bool, None}
Flag indicating whether to use a low-memory algorithm when a model
contains two-way fixed effects. If `None`, the choice is taken
automatically, and the low memory algorithm is used if the
required dummy variable array is both larger than then array of
regressors in the model and requires more than 1 GiB .
cov_type : str
Name of covariance estimator. See Notes.
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
auto_df : bool
Flag indicating that the treatment of estimated effects in degree
of freedom adjustment is automatically handled. This is useful
since clustered standard errors that are clustered using the same
variable as an effect do not require degree of freedom correction
while other estimators such as the unadjusted covariance do.
count_effects : bool
Flag indicating that the covariance estimator should be adjusted
to account for the estimation of effects in the model. Only used
if ``auto_df=False``.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
PanelEffectsResults
Estimation results
Examples
--------
>>> from linearmodels import PanelOLS
>>> mod = PanelOLS(y, x, entity_effects=True)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Three covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer valued, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
| def fit(
self,
*,
use_lsdv: bool = False,
use_lsmr: bool = False,
low_memory: bool | None = None,
cov_type: str = "unadjusted",
debiased: bool = True,
auto_df: bool = True,
count_effects: bool = True,
**cov_config: bool | float | str | IntArray | DataFrame | PanelData,
) -> PanelEffectsResults:
"""
Estimate model parameters
Parameters
----------
use_lsdv : bool
Flag indicating to use the Least Squares Dummy Variable estimator
to eliminate effects. The default value uses only means and does
note require constructing dummy variables for each effect.
use_lsmr : bool
Flag indicating to use LSDV with the Sparse Equations and Least
Squares estimator to eliminate the fixed effects.
low_memory : {bool, None}
Flag indicating whether to use a low-memory algorithm when a model
contains two-way fixed effects. If `None`, the choice is taken
automatically, and the low memory algorithm is used if the
required dummy variable array is both larger than then array of
regressors in the model and requires more than 1 GiB .
cov_type : str
Name of covariance estimator. See Notes.
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
auto_df : bool
Flag indicating that the treatment of estimated effects in degree
of freedom adjustment is automatically handled. This is useful
since clustered standard errors that are clustered using the same
variable as an effect do not require degree of freedom correction
while other estimators such as the unadjusted covariance do.
count_effects : bool
Flag indicating that the covariance estimator should be adjusted
to account for the estimation of effects in the model. Only used
if ``auto_df=False``.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
PanelEffectsResults
Estimation results
Examples
--------
>>> from linearmodels import PanelOLS
>>> mod = PanelOLS(y, x, entity_effects=True)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Three covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer valued, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
"""
weighted = np.any(self.weights.values2d != 1.0)
if use_lsmr:
y, x, ybar, y_effects, x_effects = self._lsmr_path()
elif use_lsdv:
y, x, ybar, y_effects, x_effects = self._slow_path()
else:
low_memory = (
self._choose_twoway_algo() if low_memory is None else low_memory
)
if not weighted:
y, x, ybar = self._fast_path(low_memory=low_memory)
y_effects = np.array([0.0])
x_effects = np.zeros(x.shape)
else:
y, x, ybar, y_effects, x_effects = self._weighted_fast_path(
low_memory=low_memory
)
neffects = 0
drop_first = self.has_constant
if self.entity_effects:
neffects += self.dependent.nentity - drop_first
drop_first = True
if self.time_effects:
neffects += self.dependent.nobs - drop_first
drop_first = True
if self.other_effects:
assert self._other_effect_cats is not None
oe = self._other_effect_cats.dataframe
for c in oe:
neffects += oe[c].nunique() - drop_first
drop_first = True
if self.entity_effects or self.time_effects or self.other_effects:
if not self._drop_absorbed:
check_absorbed(x, [str(var) for var in self.exog.vars])
else:
# TODO: Need to special case the constant here when determining which
# to retain since we always want to retain the constant if present
retain = not_absorbed(x, self._constant, self._constant_index)
if not retain:
raise ValueError(
"All columns in exog have been fully absorbed by the included"
" effects. This model cannot be estimated."
)
if len(retain) != x.shape[1]:
drop = set(range(x.shape[1])).difference(retain)
dropped = ", ".join([str(self.exog.vars[i]) for i in drop])
import warnings
warnings.warn(
absorbing_warn_msg.format(absorbed_variables=dropped),
AbsorbingEffectWarning,
stacklevel=2,
)
x = x[:, retain]
# Update constant index loc
if self._constant:
assert isinstance(self._constant_index, int)
self._constant_index = int(
np.squeeze(
np.argwhere(np.array(retain) == self._constant_index)
)
)
# Adjust exog
self.exog = PanelData(self.exog.dataframe.iloc[:, retain])
x_effects = x_effects[:, retain]
params = _lstsq(x, y, rcond=None)[0]
nobs = self.dependent.dataframe.shape[0]
df_model = x.shape[1] + neffects
df_resid = nobs - df_model
# Check clusters if singletons were removed
cov_config = self._setup_clusters(cov_config)
if auto_df:
count_effects = self._determine_df_adjustment(cov_type, **cov_config)
extra_df = neffects if count_effects else 0
cov = setup_covariance_estimator(
self._cov_estimators,
cov_type,
y,
x,
params,
self.dependent.entity_ids,
self.dependent.time_ids,
debiased=debiased,
extra_df=extra_df,
**cov_config,
)
weps = y - x @ params
eps = weps
_y = self.dependent.values2d
_x = self.exog.values2d
if weighted:
eps = (_y - y_effects) - (_x - x_effects) @ params
if self.has_constant:
# Correction since y_effects and x_effects @ params add mean
w = self.weights.values2d
eps -= (w * eps).sum() / w.sum()
index = self.dependent.index
fitted = DataFrame(_x @ params, index, ["fitted_values"])
idiosyncratic = DataFrame(eps, index, ["idiosyncratic"])
eps_effects = _y - fitted.values
sigma2_tot = float(np.squeeze(eps_effects.T @ eps_effects) / nobs)
sigma2_eps = float(np.squeeze(eps.T @ eps) / nobs)
sigma2_effects = sigma2_tot - sigma2_eps
rho = sigma2_effects / sigma2_tot if sigma2_tot > 0.0 else 0.0
resid_ss = float(np.squeeze(weps.T @ weps))
if self.has_constant:
mu = ybar
else:
mu = np.array([0.0])
total_ss = float(np.squeeze((y - mu).T @ (y - mu)))
r2 = 1 - resid_ss / total_ss if total_ss > 0.0 else 0.0
root_w = cast(Float64Array, np.sqrt(self.weights.values2d))
y_ex = root_w * self.dependent.values2d
mu_ex = 0
if (
self.has_constant
or self.entity_effects
or self.time_effects
or self.other_effects
):
mu_ex = root_w * ((root_w.T @ y_ex) / (root_w.T @ root_w))
total_ss_ex_effect = float(np.squeeze((y_ex - | (self, *, use_lsdv: bool = False, use_lsmr: bool = False, low_memory: Optional[bool] = None, cov_type: str = 'unadjusted', debiased: bool = True, auto_df: bool = True, count_effects: bool = True, **cov_config: bool | float | str | numpy.ndarray | pandas.core.frame.DataFrame | linearmodels.panel.data.PanelData) -> linearmodels.panel.results.PanelEffectsResults | [
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|
43,038 | linearmodels.panel.model | PooledOLS |
Pooled coefficient estimator for panel data
Parameters
----------
dependent : array_like
Dependent (left-hand-side) variable (time by entity)
exog : array_like
Exogenous or right-hand-side variables (variable by time by entity).
weights : array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual time
the weight should be homoskedastic.
check_rank : bool
Flag indicating whether to perform a rank check on the exogenous
variables to ensure that the model is identified. Skipping this
check can reduce the time required to validate a model specification.
Results may be numerically unstable if this check is skipped and
the matrix is not full rank.
Notes
-----
The model is given by
.. math::
y_{it}=\beta^{\prime}x_{it}+\epsilon_{it}
| class PooledOLS(_PanelModelBase):
r"""
Pooled coefficient estimator for panel data
Parameters
----------
dependent : array_like
Dependent (left-hand-side) variable (time by entity)
exog : array_like
Exogenous or right-hand-side variables (variable by time by entity).
weights : array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual time
the weight should be homoskedastic.
check_rank : bool
Flag indicating whether to perform a rank check on the exogenous
variables to ensure that the model is identified. Skipping this
check can reduce the time required to validate a model specification.
Results may be numerically unstable if this check is skipped and
the matrix is not full rank.
Notes
-----
The model is given by
.. math::
y_{it}=\beta^{\prime}x_{it}+\epsilon_{it}
"""
def __init__(
self,
dependent: PanelDataLike,
exog: PanelDataLike,
*,
weights: PanelDataLike | None = None,
check_rank: bool = True,
) -> None:
super().__init__(dependent, exog, weights=weights, check_rank=check_rank)
@classmethod
def from_formula(
cls,
formula: str,
data: PanelDataLike,
*,
weights: PanelDataLike | None = None,
check_rank: bool = True,
) -> PooledOLS:
"""
Create a model from a formula
Parameters
----------
formula : str
Formula to transform into model. Conforms to formulaic formula
rules.
data : array_like
Data structure that can be coerced into a PanelData. In most
cases, this should be a multi-index DataFrame where the level 0
index contains the entities and the level 1 contains the time.
weights: array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual times
the weight should be homoskedastic.
check_rank : bool
Flag indicating whether to perform a rank check on the exogenous
variables to ensure that the model is identified. Skipping this
check can reduce the time required to validate a model
specification. Results may be numerically unstable if this check
is skipped and the matrix is not full rank.
Returns
-------
PooledOLS
Model specified using the formula
Notes
-----
Unlike standard formula syntax, it is necessary to explicitly include
a constant using the constant indicator (1)
Examples
--------
>>> from linearmodels import PooledOLS
>>> from linearmodels.panel import generate_panel_data
>>> panel_data = generate_panel_data()
>>> mod = PooledOLS.from_formula("y ~ 1 + x1", panel_data.data)
>>> res = mod.fit()
"""
parser = PanelFormulaParser(formula, data, context=capture_context(1))
dependent, exog = parser.data
mod = cls(dependent, exog, weights=weights, check_rank=check_rank)
mod.formula = formula
return mod
def fit(
self,
*,
cov_type: str = "unadjusted",
debiased: bool = True,
**cov_config: bool | float | str | IntArray | DataFrame | PanelData,
) -> PanelResults:
"""
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator. See Notes.
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
PanelResults
Estimation results
Examples
--------
>>> from linearmodels import PooledOLS
>>> mod = PooledOLS(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
"""
y = self.dependent.values2d
x = self.exog.values2d
w = self.weights.values2d
root_w = cast(Float64Array, np.sqrt(w))
wx = root_w * x
wy = root_w * y
params = _lstsq(wx, wy, rcond=None)[0]
nobs = y.shape[0]
df_model = x.shape[1]
df_resid = nobs - df_model
cov_config = self._setup_clusters(cov_config)
extra_df = 0
if "extra_df" in cov_config:
cov_config = cov_config.copy()
_extra_df = cov_config.pop("extra_df")
assert isinstance(_extra_df, (str, int))
extra_df = int(_extra_df)
cov = setup_covariance_estimator(
self._cov_estimators,
cov_type,
wy,
wx,
params,
self.dependent.entity_ids,
self.dependent.time_ids,
debiased=debiased,
extra_df=extra_df,
**cov_config,
)
weps = wy - wx @ params
index = self.dependent.index
fitted = DataFrame(x @ params, index, ["fitted_values"])
effects = DataFrame(
np.full_like(np.asarray(fitted), np.nan), index, ["estimated_effects"]
)
eps = y - fitted.values
idiosyncratic = DataFrame(eps, index, ["idiosyncratic"])
residual_ss = float(np.squeeze(weps.T @ weps))
e = y
if self._constant:
e = e - (w * y).sum() / w.sum()
total_ss = float(np.squeeze(w.T @ (e**2)))
r2 = 1 - residual_ss / total_ss
res = self._postestimation(
params, cov, debiased, df_resid, weps, wy, wx, root_w
)
res.update(
dict(
df_resid=df_resid,
df_model=df_model,
nobs=y.shape[0],
residual_ss=residual_ss,
total_ss=total_ss,
r2=r2,
wresids=weps,
resids=eps,
index=self.dependent.index,
fitted=fitted,
effects=effects,
idiosyncratic=idiosyncratic,
)
)
return PanelResults(res)
def predict(
self,
params: ArrayLike,
*,
exog: PanelDataLike | None = None,
data: PanelDataLike | None = None,
eval_env: int = 1,
context: Mapping[str, Any] | None = None,
) -> DataFrame:
"""
Predict values for additional data
Parameters
----------
params : array_like
Model parameters (nvar by 1)
exog : array_like
Exogenous regressors (nobs by nvar)
data : DataFrame
Values to use when making predictions from a model constructed
from a formula
context : int
D | (dependent: 'PanelDataLike', exog: 'PanelDataLike', *, weights: 'PanelDataLike | None' = None, check_rank: 'bool' = True) -> 'None' | [
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|
43,039 | linearmodels.panel.model | __init__ | null | def __init__(
self,
dependent: PanelDataLike,
exog: PanelDataLike,
*,
weights: PanelDataLike | None = None,
check_rank: bool = True,
) -> None:
super().__init__(dependent, exog, weights=weights, check_rank=check_rank)
| (self, dependent: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series], exog: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series], *, weights: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType] = None, check_rank: bool = True) -> NoneType | [
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|
43,053 | linearmodels.panel.model | fit |
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator. See Notes.
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
PanelResults
Estimation results
Examples
--------
>>> from linearmodels import PooledOLS
>>> mod = PooledOLS(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
| def fit(
self,
*,
cov_type: str = "unadjusted",
debiased: bool = True,
**cov_config: bool | float | str | IntArray | DataFrame | PanelData,
) -> PanelResults:
"""
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator. See Notes.
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
PanelResults
Estimation results
Examples
--------
>>> from linearmodels import PooledOLS
>>> mod = PooledOLS(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
"""
y = self.dependent.values2d
x = self.exog.values2d
w = self.weights.values2d
root_w = cast(Float64Array, np.sqrt(w))
wx = root_w * x
wy = root_w * y
params = _lstsq(wx, wy, rcond=None)[0]
nobs = y.shape[0]
df_model = x.shape[1]
df_resid = nobs - df_model
cov_config = self._setup_clusters(cov_config)
extra_df = 0
if "extra_df" in cov_config:
cov_config = cov_config.copy()
_extra_df = cov_config.pop("extra_df")
assert isinstance(_extra_df, (str, int))
extra_df = int(_extra_df)
cov = setup_covariance_estimator(
self._cov_estimators,
cov_type,
wy,
wx,
params,
self.dependent.entity_ids,
self.dependent.time_ids,
debiased=debiased,
extra_df=extra_df,
**cov_config,
)
weps = wy - wx @ params
index = self.dependent.index
fitted = DataFrame(x @ params, index, ["fitted_values"])
effects = DataFrame(
np.full_like(np.asarray(fitted), np.nan), index, ["estimated_effects"]
)
eps = y - fitted.values
idiosyncratic = DataFrame(eps, index, ["idiosyncratic"])
residual_ss = float(np.squeeze(weps.T @ weps))
e = y
if self._constant:
e = e - (w * y).sum() / w.sum()
total_ss = float(np.squeeze(w.T @ (e**2)))
r2 = 1 - residual_ss / total_ss
res = self._postestimation(
params, cov, debiased, df_resid, weps, wy, wx, root_w
)
res.update(
dict(
df_resid=df_resid,
df_model=df_model,
nobs=y.shape[0],
residual_ss=residual_ss,
total_ss=total_ss,
r2=r2,
wresids=weps,
resids=eps,
index=self.dependent.index,
fitted=fitted,
effects=effects,
idiosyncratic=idiosyncratic,
)
)
return PanelResults(res)
| (self, *, cov_type: str = 'unadjusted', debiased: bool = True, **cov_config: bool | float | str | numpy.ndarray | pandas.core.frame.DataFrame | linearmodels.panel.data.PanelData) -> linearmodels.panel.results.PanelResults | [
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|
43,054 | linearmodels.panel.model | predict |
Predict values for additional data
Parameters
----------
params : array_like
Model parameters (nvar by 1)
exog : array_like
Exogenous regressors (nobs by nvar)
data : DataFrame
Values to use when making predictions from a model constructed
from a formula
context : int
Depth to use when evaluating formulas.
Returns
-------
DataFrame
Fitted values from supplied data and parameters
Notes
-----
If `data` is not None, then `exog` must be None.
Predictions from models constructed using formulas can
be computed using either `exog`, which will treat these are
arrays of values corresponding to the formula-processed data, or using
`data` which will be processed using the formula used to construct the
values corresponding to the original model specification.
| def predict(
self,
params: ArrayLike,
*,
exog: PanelDataLike | None = None,
data: PanelDataLike | None = None,
eval_env: int = 1,
context: Mapping[str, Any] | None = None,
) -> DataFrame:
"""
Predict values for additional data
Parameters
----------
params : array_like
Model parameters (nvar by 1)
exog : array_like
Exogenous regressors (nobs by nvar)
data : DataFrame
Values to use when making predictions from a model constructed
from a formula
context : int
Depth to use when evaluating formulas.
Returns
-------
DataFrame
Fitted values from supplied data and parameters
Notes
-----
If `data` is not None, then `exog` must be None.
Predictions from models constructed using formulas can
be computed using either `exog`, which will treat these are
arrays of values corresponding to the formula-processed data, or using
`data` which will be processed using the formula used to construct the
values corresponding to the original model specification.
"""
if data is not None and self.formula is None:
raise ValueError(
"Unable to use data when the model was not " "created using a formula."
)
if data is not None and exog is not None:
raise ValueError(
"Predictions can only be constructed using one "
"of exog or data, but not both."
)
if exog is not None:
exog = PanelData(exog).dataframe
else:
assert self._formula is not None
assert data is not None
if context is None:
context = capture_context(eval_env)
parser = PanelFormulaParser(self._formula, data, context=context)
exog = parser.exog
x = exog.values
params = np.atleast_2d(np.asarray(params))
if params.shape[0] == 1:
params = params.T
if x.shape[1] != params.shape[0]:
raise ValueError(
EXOG_PREDICT_MSG.format(
x_shape=x.shape[1], params_shape=params.shape[0]
)
)
pred = DataFrame(x @ params, index=exog.index, columns=["predictions"])
return pred
| (self, params: Union[numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series], *, exog: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType] = None, data: Union[linearmodels.panel.data.PanelData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType] = None, eval_env: int = 1, context: Optional[collections.abc.Mapping[str, Any]] = None) -> pandas.core.frame.DataFrame | [
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|
43,056 | linearmodels.panel.model | RandomEffects |
One-way Random Effects model for panel data
Parameters
----------
dependent : array_like
Dependent (left-hand-side) variable (time by entity)
exog : array_like
Exogenous or right-hand-side variables (variable by time by entity).
weights : array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual time
the weight should be homoskedastic.
Notes
-----
The model is given by
.. math::
y_{it} = \beta^{\prime}x_{it} + u_i + \epsilon_{it}
where :math:`u_i` is a shock that is independent of :math:`x_{it}` but
common to all entities i.
| class RandomEffects(_PanelModelBase):
r"""
One-way Random Effects model for panel data
Parameters
----------
dependent : array_like
Dependent (left-hand-side) variable (time by entity)
exog : array_like
Exogenous or right-hand-side variables (variable by time by entity).
weights : array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual time
the weight should be homoskedastic.
Notes
-----
The model is given by
.. math::
y_{it} = \beta^{\prime}x_{it} + u_i + \epsilon_{it}
where :math:`u_i` is a shock that is independent of :math:`x_{it}` but
common to all entities i.
"""
def __init__(
self,
dependent: PanelDataLike,
exog: PanelDataLike,
*,
weights: PanelDataLike | None = None,
check_rank: bool = True,
) -> None:
super().__init__(dependent, exog, weights=weights, check_rank=check_rank)
@classmethod
def from_formula(
cls,
formula: str,
data: PanelDataLike,
*,
weights: PanelDataLike | None = None,
check_rank: bool = True,
) -> RandomEffects:
"""
Create a model from a formula
Parameters
----------
formula : str
Formula to transform into model. Conforms to formulaic formula
rules.
data : array_like
Data structure that can be coerced into a PanelData. In most
cases, this should be a multi-index DataFrame where the level 0
index contains the entities and the level 1 contains the time.
weights: array_like
Weights to use in estimation. Assumes residual variance is
proportional to inverse of weight to that the residual times
the weight should be homoskedastic.
check_rank : bool
Flag indicating whether to perform a rank check on the exogenous
variables to ensure that the model is identified. Skipping this
check can reduce the time required to validate a model
specification. Results may be numerically unstable if this check
is skipped and the matrix is not full rank.
Returns
-------
RandomEffects
Model specified using the formula
Notes
-----
Unlike standard formula syntax, it is necessary to explicitly include
a constant using the constant indicator (1)
Examples
--------
>>> from linearmodels import RandomEffects
>>> from linearmodels.panel import generate_panel_data
>>> panel_data = generate_panel_data()
>>> mod = RandomEffects.from_formula("y ~ 1 + x1", panel_data.data)
>>> res = mod.fit()
"""
parser = PanelFormulaParser(formula, data, context=capture_context(1))
dependent, exog = parser.data
mod = cls(dependent, exog, weights=weights, check_rank=check_rank)
mod.formula = formula
return mod
def fit(
self,
*,
small_sample: bool = False,
cov_type: str = "unadjusted",
debiased: bool = True,
**cov_config: bool | float | str | IntArray | DataFrame | PanelData,
) -> RandomEffectsResults:
"""
Estimate model parameters
Parameters
----------
small_sample : bool
Apply a small-sample correction to the estimate of the variance of
the random effect.
cov_type : str
Name of covariance estimator (see notes). Default is "unadjusted".
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
RandomEffectsResults
Estimation results
Examples
--------
>>> from linearmodels import RandomEffects
>>> mod = RandomEffects(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
"""
w = self.weights.values2d
root_w = cast(Float64Array, np.sqrt(w))
demeaned_dep = self.dependent.demean("entity", weights=self.weights)
demeaned_exog = self.exog.demean("entity", weights=self.weights)
assert isinstance(demeaned_dep, PanelData)
assert isinstance(demeaned_exog, PanelData)
y = demeaned_dep.values2d
x = demeaned_exog.values2d
if self.has_constant:
w_sum = w.sum()
y_gm = (w * self.dependent.values2d).sum(0) / w_sum
x_gm = (w * self.exog.values2d).sum(0) / w_sum
y += root_w * y_gm
x += root_w * x_gm
params = _lstsq(x, y, rcond=None)[0]
weps = y - x @ params
wybar = self.dependent.mean("entity", weights=self.weights)
wxbar = self.exog.mean("entity", weights=self.weights)
params = _lstsq(np.asarray(wxbar), np.asarray(wybar), rcond=None)[0]
wu = np.asarray(wybar) - np.asarray(wxbar) @ params
nobs = weps.shape[0]
neffects = wu.shape[0]
nvar = x.shape[1]
sigma2_e = float(np.squeeze(weps.T @ weps)) / (nobs - nvar - neffects + 1)
ssr = float(np.squeeze(wu.T @ wu))
t = np.asarray(self.dependent.count("entity"))
unbalanced = np.ptp(t) != 0
if small_sample and unbalanced:
ssr = float(np.squeeze((t * wu).T @ wu))
wx_df = cast(DataFrame, root_w * self.exog.dataframe)
means = wx_df.groupby(level=0).transform("mean").values
denom = means.T @ means
sums = wx_df.groupby(level=0).sum().values
num = sums.T @ sums
tr = np.trace(np.linalg.inv(denom) @ num)
sigma2_u = max(0, (ssr - (neffects - nvar) * sigma2_e) / (nobs - tr))
else:
t_bar = neffects / ((1.0 / t).sum())
sigma2_u = max(0, ssr / (neffects - nvar) - sigma2_e / t_bar)
rho = sigma2_u / (sigma2_u + sigma2_e)
theta = 1.0 - np.sqrt(sigma2_e / (t * sigma2_u + sigma2_e))
theta_out = DataFrame(theta, columns=["theta"], index=wybar.index)
wy: Float64Array = np.asarray(root_w * self.dependent.values2d, dtype=float)
wx: Float64Array = np.asarray(root_w * self.exog.values2d, dtype=float)
index = self.dependent.index
reindex = index.levels[0][index.codes[0]]
wybar = (theta * wybar).loc[reindex]
wxbar = (theta * wxbar).loc[reindex]
wy -= wybar.values
wx -= wxbar.values
params = _lstsq(wx, wy, rcond=None)[0]
df_resid = wy.shape[0] - wx.shape[1]
cov_config = self._setup_clusters(cov_config)
extra_df = 0
if "extra_df" in cov_config:
cov_config = cov_config.copy()
_extra_df = cov_config.pop("extra_df")
| (dependent: 'PanelDataLike', exog: 'PanelDataLike', *, weights: 'PanelDataLike | None' = None, check_rank: 'bool' = True) -> 'None' | [
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|
43,071 | linearmodels.panel.model | fit |
Estimate model parameters
Parameters
----------
small_sample : bool
Apply a small-sample correction to the estimate of the variance of
the random effect.
cov_type : str
Name of covariance estimator (see notes). Default is "unadjusted".
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
RandomEffectsResults
Estimation results
Examples
--------
>>> from linearmodels import RandomEffects
>>> mod = RandomEffects(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
| def fit(
self,
*,
small_sample: bool = False,
cov_type: str = "unadjusted",
debiased: bool = True,
**cov_config: bool | float | str | IntArray | DataFrame | PanelData,
) -> RandomEffectsResults:
"""
Estimate model parameters
Parameters
----------
small_sample : bool
Apply a small-sample correction to the estimate of the variance of
the random effect.
cov_type : str
Name of covariance estimator (see notes). Default is "unadjusted".
debiased : bool
Flag indicating whether to debiased the covariance estimator using
a degree of freedom adjustment.
**cov_config
Additional covariance-specific options. See Notes.
Returns
-------
RandomEffectsResults
Estimation results
Examples
--------
>>> from linearmodels import RandomEffects
>>> mod = RandomEffects(y, x)
>>> res = mod.fit(cov_type="clustered", cluster_entity=True)
Notes
-----
Four covariance estimators are supported:
* "unadjusted", "homoskedastic" - Assume residual are homoskedastic
* "robust", "heteroskedastic" - Control for heteroskedasticity using
White's estimator
* "clustered` - One- or two-way clustering. Configuration options are:
* ``clusters`` - Input containing 1 or 2 variables.
Clusters should be integer values, although other types will
be coerced to integer values by treating as categorical variables
* ``cluster_entity`` - Boolean flag indicating to use entity
clusters
* ``cluster_time`` - Boolean indicating to use time clusters
* "kernel" - Driscoll-Kraay HAC estimator. Configurations options are:
* ``kernel`` - One of the supported kernels (bartlett, parzen, qs).
Default is Bartlett's kernel, which is produces a covariance
estimator similar to the Newey-West covariance estimator.
* ``bandwidth`` - Bandwidth to use when computing the kernel. If
not provided, a naive default is used.
"""
w = self.weights.values2d
root_w = cast(Float64Array, np.sqrt(w))
demeaned_dep = self.dependent.demean("entity", weights=self.weights)
demeaned_exog = self.exog.demean("entity", weights=self.weights)
assert isinstance(demeaned_dep, PanelData)
assert isinstance(demeaned_exog, PanelData)
y = demeaned_dep.values2d
x = demeaned_exog.values2d
if self.has_constant:
w_sum = w.sum()
y_gm = (w * self.dependent.values2d).sum(0) / w_sum
x_gm = (w * self.exog.values2d).sum(0) / w_sum
y += root_w * y_gm
x += root_w * x_gm
params = _lstsq(x, y, rcond=None)[0]
weps = y - x @ params
wybar = self.dependent.mean("entity", weights=self.weights)
wxbar = self.exog.mean("entity", weights=self.weights)
params = _lstsq(np.asarray(wxbar), np.asarray(wybar), rcond=None)[0]
wu = np.asarray(wybar) - np.asarray(wxbar) @ params
nobs = weps.shape[0]
neffects = wu.shape[0]
nvar = x.shape[1]
sigma2_e = float(np.squeeze(weps.T @ weps)) / (nobs - nvar - neffects + 1)
ssr = float(np.squeeze(wu.T @ wu))
t = np.asarray(self.dependent.count("entity"))
unbalanced = np.ptp(t) != 0
if small_sample and unbalanced:
ssr = float(np.squeeze((t * wu).T @ wu))
wx_df = cast(DataFrame, root_w * self.exog.dataframe)
means = wx_df.groupby(level=0).transform("mean").values
denom = means.T @ means
sums = wx_df.groupby(level=0).sum().values
num = sums.T @ sums
tr = np.trace(np.linalg.inv(denom) @ num)
sigma2_u = max(0, (ssr - (neffects - nvar) * sigma2_e) / (nobs - tr))
else:
t_bar = neffects / ((1.0 / t).sum())
sigma2_u = max(0, ssr / (neffects - nvar) - sigma2_e / t_bar)
rho = sigma2_u / (sigma2_u + sigma2_e)
theta = 1.0 - np.sqrt(sigma2_e / (t * sigma2_u + sigma2_e))
theta_out = DataFrame(theta, columns=["theta"], index=wybar.index)
wy: Float64Array = np.asarray(root_w * self.dependent.values2d, dtype=float)
wx: Float64Array = np.asarray(root_w * self.exog.values2d, dtype=float)
index = self.dependent.index
reindex = index.levels[0][index.codes[0]]
wybar = (theta * wybar).loc[reindex]
wxbar = (theta * wxbar).loc[reindex]
wy -= wybar.values
wx -= wxbar.values
params = _lstsq(wx, wy, rcond=None)[0]
df_resid = wy.shape[0] - wx.shape[1]
cov_config = self._setup_clusters(cov_config)
extra_df = 0
if "extra_df" in cov_config:
cov_config = cov_config.copy()
_extra_df = cov_config.pop("extra_df")
assert isinstance(_extra_df, (str, int))
extra_df = int(_extra_df)
cov = setup_covariance_estimator(
self._cov_estimators,
cov_type,
wy,
np.asarray(wx),
params,
self.dependent.entity_ids,
self.dependent.time_ids,
debiased=debiased,
extra_df=extra_df,
**cov_config,
)
weps = wy - wx @ params
eps = weps / root_w
index = self.dependent.index
fitted = DataFrame(self.exog.values2d @ params, index, ["fitted_values"])
effects = DataFrame(
self.dependent.values2d - np.asarray(fitted) - eps,
index,
["estimated_effects"],
)
idiosyncratic = DataFrame(eps, index, ["idiosyncratic"])
residual_ss = float(np.squeeze(weps.T @ weps))
wmu: float | Float64Array = 0.0
if self.has_constant:
wmu = root_w * _lstsq(root_w, wy, rcond=None)[0]
wy_demeaned = wy - wmu
total_ss = float(np.squeeze(wy_demeaned.T @ wy_demeaned))
r2 = 1 - residual_ss / total_ss
res = self._postestimation(
params, cov, debiased, df_resid, weps, wy, wx, root_w
)
res.update(
dict(
df_resid=df_resid,
df_model=x.shape[1],
nobs=y.shape[0],
residual_ss=residual_ss,
total_ss=total_ss,
r2=r2,
resids=eps,
wresids=weps,
index=index,
sigma2_eps=sigma2_e,
sigma2_effects=sigma2_u,
rho=rho,
theta=theta_out,
fitted=fitted,
effects=effects,
idiosyncratic=idiosyncratic,
)
)
return RandomEffectsResults(res)
| (self, *, small_sample: bool = False, cov_type: str = 'unadjusted', debiased: bool = True, **cov_config: bool | float | str | numpy.ndarray | pandas.core.frame.DataFrame | linearmodels.panel.data.PanelData) -> linearmodels.panel.results.RandomEffectsResults | [
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|
43,074 | linearmodels.system.model | SUR |
Seemingly unrelated regression estimation (SUR/SURE)
Parameters
----------
equations : dict
Dictionary-like structure containing dependent and exogenous variable
values. Each key is an equations label and must be a string. Each
value must be either a tuple of the form (dependent,
exog, [weights]) or a dictionary with keys "dependent" and "exog" and
the optional key "weights".
sigma : array_like
Prespecified residual covariance to use in GLS estimation. If not
provided, FGLS is implemented based on an estimate of sigma.
Notes
-----
Estimates a set of regressions which are seemingly unrelated in the sense
that separate estimation would lead to consistent parameter estimates.
Each equation is of the form
.. math::
y_{i,k} = x_{i,k}\beta_i + \epsilon_{i,k}
where k denotes the equation and i denoted the observation index. By
stacking vertically arrays of dependent and placing the exogenous
variables into a block diagonal array, the entire system can be compactly
expressed as
.. math::
Y = X\beta + \epsilon
where
.. math::
Y = \left[\begin{array}{x}Y_1 \\ Y_2 \\ \vdots \\ Y_K\end{array}\right]
and
.. math::
X = \left[\begin{array}{cccc}
X_1 & 0 & \ldots & 0 \\
0 & X_2 & \dots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \dots & X_K
\end{array}\right]
The system OLS estimator is
.. math::
\hat{\beta}_{OLS} = (X'X)^{-1}X'Y
When certain conditions are satisfied, a GLS estimator of the form
.. math::
\hat{\beta}_{GLS} = (X'\Omega^{-1}X)^{-1}X'\Omega^{-1}Y
can improve accuracy of coefficient estimates where
.. math::
\Omega = \Sigma \otimes I_N
where :math:`\Sigma` is the covariance matrix of the residuals.
SUR is a special case of 3SLS where there are no endogenous regressors and
no instruments.
| class SUR(_LSSystemModelBase):
r"""
Seemingly unrelated regression estimation (SUR/SURE)
Parameters
----------
equations : dict
Dictionary-like structure containing dependent and exogenous variable
values. Each key is an equations label and must be a string. Each
value must be either a tuple of the form (dependent,
exog, [weights]) or a dictionary with keys "dependent" and "exog" and
the optional key "weights".
sigma : array_like
Prespecified residual covariance to use in GLS estimation. If not
provided, FGLS is implemented based on an estimate of sigma.
Notes
-----
Estimates a set of regressions which are seemingly unrelated in the sense
that separate estimation would lead to consistent parameter estimates.
Each equation is of the form
.. math::
y_{i,k} = x_{i,k}\beta_i + \epsilon_{i,k}
where k denotes the equation and i denoted the observation index. By
stacking vertically arrays of dependent and placing the exogenous
variables into a block diagonal array, the entire system can be compactly
expressed as
.. math::
Y = X\beta + \epsilon
where
.. math::
Y = \left[\begin{array}{x}Y_1 \\ Y_2 \\ \vdots \\ Y_K\end{array}\right]
and
.. math::
X = \left[\begin{array}{cccc}
X_1 & 0 & \ldots & 0 \\
0 & X_2 & \dots & 0 \\
\vdots & \vdots & \ddots & \vdots \\
0 & 0 & \dots & X_K
\end{array}\right]
The system OLS estimator is
.. math::
\hat{\beta}_{OLS} = (X'X)^{-1}X'Y
When certain conditions are satisfied, a GLS estimator of the form
.. math::
\hat{\beta}_{GLS} = (X'\Omega^{-1}X)^{-1}X'\Omega^{-1}Y
can improve accuracy of coefficient estimates where
.. math::
\Omega = \Sigma \otimes I_N
where :math:`\Sigma` is the covariance matrix of the residuals.
SUR is a special case of 3SLS where there are no endogenous regressors and
no instruments.
"""
def __init__(
self,
equations: Mapping[
str, Mapping[str, ArrayLike | None] | Sequence[ArrayLike | None]
],
*,
sigma: ArrayLike | None = None,
) -> None:
if not isinstance(equations, Mapping):
raise TypeError("equations must be a dictionary-like")
for key in equations:
if not isinstance(key, str):
raise ValueError("Equation labels (keys) must be strings")
reformatted = {}
for key in equations:
eqn = equations[key]
if isinstance(eqn, tuple):
if len(eqn) == 3:
w = eqn[-1]
eqn = eqn[:2]
eqn = eqn + (None, None) + (w,)
else:
eqn = eqn + (None, None)
reformatted[key] = eqn
super().__init__(reformatted, sigma=sigma)
self._model_name = "Seemingly Unrelated Regression (SUR)"
@classmethod
def multivariate_ls(cls, dependent: ArrayLike, exog: ArrayLike) -> SUR:
"""
Interface for specification of multivariate regression models
Parameters
----------
dependent : array_like
nobs by ndep array of dependent variables
exog : array_like
nobs by nvar array of exogenous regressors common to all models
Returns
-------
model : SUR
Model instance
Notes
-----
Utility function to simplify the construction of multivariate
regression models which all use the same regressors. Constructs
the dictionary of equations from the variables using the common
exogenous variable.
Examples
--------
A simple CAP-M can be estimated as a multivariate regression
>>> from linearmodels.datasets import french
>>> from linearmodels.system import SUR
>>> data = french.load()
>>> portfolios = data[["S1V1","S1V5","S5V1","S5V5"]]
>>> factors = data[["MktRF"]].copy()
>>> factors["alpha"] = 1
>>> mod = SUR.multivariate_ls(portfolios, factors)
"""
equations = {}
dependent_ivd = IVData(dependent, var_name="dependent")
exog_ivd = IVData(exog, var_name="exog")
for col in dependent_ivd.pandas:
# TODO: Bug in pandas-stubs
# https://github.com/pandas-dev/pandas-stubs/issues/97
equations[str(col)] = (dependent_ivd.pandas[[col]], exog_ivd.pandas)
return cls(equations)
@classmethod
def from_formula(
cls,
formula: str | dict[str, str],
data: DataFrame,
*,
sigma: ArrayLike | None = None,
weights: Mapping[str, ArrayLike] | None = None,
) -> SUR:
"""
Specify a SUR using the formula interface
Parameters
----------
formula : {str, dict[str, str]}
Either a string or a dictionary of strings where each value in
the dictionary represents a single equation. See Notes for a
description of the accepted syntax
data : DataFrame
Frame containing named variables
sigma : array_like
Prespecified residual covariance to use in GLS estimation. If
not provided, FGLS is implemented based on an estimate of sigma.
weights : dict[str, array_like]
Dictionary like object (e.g. a DataFrame) containing variable
weights. Each entry must have the same number of observations as
data. If an equation label is not a key weights, the weights will
be set to unity
Returns
-------
model : SUR
Model instance
Notes
-----
Models can be specified in one of two ways. The first uses curly
braces to encapsulate equations. The second uses a dictionary
where each key is an equation name.
Examples
--------
The simplest format uses standard formulas for each equation
in a dictionary. Best practice is to use an Ordered Dictionary
>>> import pandas as pd
>>> import numpy as np
>>> data = pd.DataFrame(np.random.randn(500, 4),
... columns=["y1", "x1_1", "y2", "x2_1"])
>>> from linearmodels.system import SUR
>>> formula = {"eq1": "y1 ~ 1 + x1_1", "eq2": "y2 ~ 1 + x2_1"}
>>> mod = SUR.from_formula(formula, data)
The second format uses curly braces {} to surround distinct equations
>>> formula = "{y1 ~ 1 + x1_1} {y2 ~ 1 + x2_1}"
>>> mod = SUR.from_formula(formula, data)
It is also possible to include equation labels when using curly braces
>>> formula = "{eq1: y1 ~ 1 + x1_1} {eq2: y2 ~ 1 + x2_1}"
>>> mod = SUR.from_formula(formula, data)
"""
context = capture_context(1)
parser = SystemFormulaParser(formula, data, weights, context=context)
eqns = parser.data
mod = cls(eqns, sigma=sigma)
mod.formula = formula
return mod
| (equations: 'Mapping[str, Mapping[str, ArrayLike | None] | Sequence[ArrayLike | None]]', *, sigma: 'ArrayLike | None' = None) -> 'None' | [
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|
43,075 | linearmodels.system.model | __init__ | null | def __init__(
self,
equations: Mapping[
str, Mapping[str, ArrayLike | None] | Sequence[ArrayLike | None]
],
*,
sigma: ArrayLike | None = None,
) -> None:
if not isinstance(equations, Mapping):
raise TypeError("equations must be a dictionary-like")
for key in equations:
if not isinstance(key, str):
raise ValueError("Equation labels (keys) must be strings")
reformatted = {}
for key in equations:
eqn = equations[key]
if isinstance(eqn, tuple):
if len(eqn) == 3:
w = eqn[-1]
eqn = eqn[:2]
eqn = eqn + (None, None) + (w,)
else:
eqn = eqn + (None, None)
reformatted[key] = eqn
super().__init__(reformatted, sigma=sigma)
self._model_name = "Seemingly Unrelated Regression (SUR)"
| (self, equations: collections.abc.Mapping[str, collections.abc.Mapping[str, typing.Union[numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType]] | collections.abc.Sequence[typing.Union[numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType]]], *, sigma: Union[numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series, NoneType] = None) -> NoneType | [
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|
43,094 | linearmodels.asset_pricing.model | TradedFactorModel |
Linear factor models estimator applicable to traded factors
Parameters
----------
portfolios : array_like
Test portfolio returns (nobs by nportfolio)
factors : array_like
Priced factor returns (nobs by nfactor)
Notes
-----
Implements both time-series estimators of risk premia, factor loadings
and zero-alpha tests.
The model estimated is
.. math::
r_{it}^e = \alpha_i + f_t \beta_i + \epsilon_{it}
where :math:`r_{it}^e` is the excess return on test portfolio i and
:math:`f_t` are the traded factor returns. The model is directly
tested using the estimated values :math:`\hat{\alpha}_i`. Risk premia,
:math:`\lambda_i` are estimated using the sample averages of the factors,
which must be excess returns on traded portfolios.
| class TradedFactorModel(_FactorModelBase):
r"""
Linear factor models estimator applicable to traded factors
Parameters
----------
portfolios : array_like
Test portfolio returns (nobs by nportfolio)
factors : array_like
Priced factor returns (nobs by nfactor)
Notes
-----
Implements both time-series estimators of risk premia, factor loadings
and zero-alpha tests.
The model estimated is
.. math::
r_{it}^e = \alpha_i + f_t \beta_i + \epsilon_{it}
where :math:`r_{it}^e` is the excess return on test portfolio i and
:math:`f_t` are the traded factor returns. The model is directly
tested using the estimated values :math:`\hat{\alpha}_i`. Risk premia,
:math:`\lambda_i` are estimated using the sample averages of the factors,
which must be excess returns on traded portfolios.
"""
def __init__(self, portfolios: IVDataLike, factors: IVDataLike):
super().__init__(portfolios, factors)
@classmethod
def from_formula(
cls, formula: str, data: DataFrame, *, portfolios: DataFrame | None = None
) -> TradedFactorModel:
"""
Parameters
----------
formula : str
Formula modified for the syntax described in the notes
data : DataFrame
DataFrame containing the variables used in the formula
portfolios : array_like
Portfolios to be used in the model
Returns
-------
TradedFactorModel
Model instance
Notes
-----
The formula can be used in one of two ways. The first specified only the
factors and uses the data provided in ``portfolios`` as the test portfolios.
The second specified the portfolio using ``+`` to separate the test portfolios
and ``~`` to separate the test portfolios from the factors.
Examples
--------
>>> from linearmodels.datasets import french
>>> from linearmodels.asset_pricing import TradedFactorModel
>>> data = french.load()
>>> formula = "S1M1 + S1M5 + S3M3 + S5M1 + S5M5 ~ MktRF + SMB + HML"
>>> mod = TradedFactorModel.from_formula(formula, data)
Using only factors
>>> portfolios = data[["S1M1", "S1M5", "S3M1", "S3M5", "S5M1", "S5M5"]]
>>> formula = "MktRF + SMB + HML"
>>> mod = TradedFactorModel.from_formula(formula, data, portfolios=portfolios)
"""
factors, portfolios, formula = cls._prepare_data_from_formula(
formula, data, portfolios
)
mod = cls(portfolios, factors)
mod.formula = formula
return mod
def fit(
self,
cov_type: str = "robust",
debiased: bool = True,
**cov_config: str | float,
) -> LinearFactorModelResults:
"""
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator
debiased : bool
Flag indicating whether to debias the covariance estimator using
a degree of freedom adjustment
**cov_config : dict
Additional covariance-specific options. See Notes.
Returns
-------
LinearFactorModelResults
Results class with parameter estimates, covariance and test statistics
Notes
-----
Supported covariance estimators are:
* "robust" - Heteroskedasticity-robust covariance estimator
* "kernel" - Heteroskedasticity and Autocorrelation consistent (HAC)
covariance estimator
The kernel covariance estimator takes the optional arguments
``kernel``, one of "bartlett", "parzen" or "qs" (quadratic spectral)
and ``bandwidth`` (a positive integer).
"""
p = self.portfolios.ndarray
f = self.factors.ndarray
nportfolio = p.shape[1]
nobs, nfactor = f.shape
fc = np.c_[np.ones((nobs, 1)), f]
rp = f.mean(0)[:, None]
fe = f - f.mean(0)
b = np.linalg.pinv(fc) @ p
eps = p - fc @ b
alphas = b[:1].T
nloading = (nfactor + 1) * nportfolio
xpxi = np.eye(nloading + nfactor)
xpxi[:nloading, :nloading] = np.kron(
np.eye(nportfolio), np.linalg.pinv(fc.T @ fc / nobs)
)
f_rep = np.tile(fc, (1, nportfolio))
eps_rep = np.tile(eps, (nfactor + 1, 1)) # 1 2 3 ... 25 1 2 3 ...
eps_rep = eps_rep.ravel(order="F")
eps_rep = np.reshape(eps_rep, (nobs, (nfactor + 1) * nportfolio), order="F")
xe = f_rep * eps_rep
xe = np.c_[xe, fe]
if cov_type in ("robust", "heteroskedastic"):
cov_est = HeteroskedasticCovariance(
xe, inv_jacobian=xpxi, center=False, debiased=debiased, df=fc.shape[1]
)
rp_cov_est = HeteroskedasticCovariance(
fe, jacobian=np.eye(f.shape[1]), center=False, debiased=debiased, df=1
)
elif cov_type == "kernel":
kernel = get_string(cov_config, "kernel")
bandwidth = get_float(cov_config, "bandwidth")
cov_est = KernelCovariance(
xe,
inv_jacobian=xpxi,
center=False,
debiased=debiased,
df=fc.shape[1],
bandwidth=bandwidth,
kernel=kernel,
)
bw = cov_est.bandwidth
_cov_config = {k: v for k, v in cov_config.items()}
_cov_config["bandwidth"] = bw
rp_cov_est = KernelCovariance(
fe,
jacobian=np.eye(f.shape[1]),
center=False,
debiased=debiased,
df=1,
bandwidth=bw,
kernel=kernel,
)
else:
raise ValueError(f"Unknown cov_type: {cov_type}")
full_vcv = cov_est.cov
rp_cov = rp_cov_est.cov
vcv = full_vcv[:nloading, :nloading]
# Rearrange VCV
order = np.reshape(
np.arange((nfactor + 1) * nportfolio), (nportfolio, nfactor + 1)
)
order = order.T.ravel()
vcv = vcv[order][:, order]
# Return values
alpha_vcv = vcv[:nportfolio, :nportfolio]
stat = float(np.squeeze(alphas.T @ np.linalg.pinv(alpha_vcv) @ alphas))
jstat = WaldTestStatistic(
stat, "All alphas are 0", nportfolio, name="J-statistic"
)
params = b.T
betas = b[1:].T
residual_ss = (eps**2).sum()
e = p - p.mean(0)[None, :]
total_ss = (e**2).sum()
r2 = 1 - residual_ss / total_ss
param_names = []
for portfolio in self.portfolios.cols:
param_names.append(f"alpha-{portfolio}")
for factor in self.factors.cols:
param_names.append(f"beta-{portfolio}-{factor}")
for factor in self.factors.cols:
param_names.append(f"lambda-{factor}")
res = AttrDict(
params=params,
cov=full_vcv,
betas=betas,
rp=rp,
rp_cov=rp_cov,
alphas=alphas,
alpha_vcv=alpha_vcv,
jstat=jstat,
rsquared=r2,
total_ss=total_ss,
residual_ss=residual_ss,
param_names=param_names,
portfolio_names=self.portfolios.cols,
factor_names=self.factors.cols,
name=self._name,
cov_type=cov_type,
model=self,
nobs=nobs,
rp_names=self.factors.cols,
cov_est=cov_est,
)
return LinearFactorModelResults(res)
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|
43,095 | linearmodels.asset_pricing.model | __init__ | null | def __init__(self, portfolios: IVDataLike, factors: IVDataLike):
super().__init__(portfolios, factors)
| (self, portfolios: Union[linearmodels.iv.data.IVData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series], factors: Union[linearmodels.iv.data.IVData, numpy.ndarray, pandas.core.frame.DataFrame, pandas.core.series.Series]) | [
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|
43,097 | linearmodels.asset_pricing.model | __str__ | null | def __str__(self) -> str:
out = self.__class__.__name__
f, p = self.factors.shape[1], self.portfolios.shape[1]
out += f" with {f} factors, {p} test portfolios"
return out
| (self) -> str | [
0.016933120787143707,
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|
43,101 | linearmodels.asset_pricing.model | fit |
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator
debiased : bool
Flag indicating whether to debias the covariance estimator using
a degree of freedom adjustment
**cov_config : dict
Additional covariance-specific options. See Notes.
Returns
-------
LinearFactorModelResults
Results class with parameter estimates, covariance and test statistics
Notes
-----
Supported covariance estimators are:
* "robust" - Heteroskedasticity-robust covariance estimator
* "kernel" - Heteroskedasticity and Autocorrelation consistent (HAC)
covariance estimator
The kernel covariance estimator takes the optional arguments
``kernel``, one of "bartlett", "parzen" or "qs" (quadratic spectral)
and ``bandwidth`` (a positive integer).
| def fit(
self,
cov_type: str = "robust",
debiased: bool = True,
**cov_config: str | float,
) -> LinearFactorModelResults:
"""
Estimate model parameters
Parameters
----------
cov_type : str
Name of covariance estimator
debiased : bool
Flag indicating whether to debias the covariance estimator using
a degree of freedom adjustment
**cov_config : dict
Additional covariance-specific options. See Notes.
Returns
-------
LinearFactorModelResults
Results class with parameter estimates, covariance and test statistics
Notes
-----
Supported covariance estimators are:
* "robust" - Heteroskedasticity-robust covariance estimator
* "kernel" - Heteroskedasticity and Autocorrelation consistent (HAC)
covariance estimator
The kernel covariance estimator takes the optional arguments
``kernel``, one of "bartlett", "parzen" or "qs" (quadratic spectral)
and ``bandwidth`` (a positive integer).
"""
p = self.portfolios.ndarray
f = self.factors.ndarray
nportfolio = p.shape[1]
nobs, nfactor = f.shape
fc = np.c_[np.ones((nobs, 1)), f]
rp = f.mean(0)[:, None]
fe = f - f.mean(0)
b = np.linalg.pinv(fc) @ p
eps = p - fc @ b
alphas = b[:1].T
nloading = (nfactor + 1) * nportfolio
xpxi = np.eye(nloading + nfactor)
xpxi[:nloading, :nloading] = np.kron(
np.eye(nportfolio), np.linalg.pinv(fc.T @ fc / nobs)
)
f_rep = np.tile(fc, (1, nportfolio))
eps_rep = np.tile(eps, (nfactor + 1, 1)) # 1 2 3 ... 25 1 2 3 ...
eps_rep = eps_rep.ravel(order="F")
eps_rep = np.reshape(eps_rep, (nobs, (nfactor + 1) * nportfolio), order="F")
xe = f_rep * eps_rep
xe = np.c_[xe, fe]
if cov_type in ("robust", "heteroskedastic"):
cov_est = HeteroskedasticCovariance(
xe, inv_jacobian=xpxi, center=False, debiased=debiased, df=fc.shape[1]
)
rp_cov_est = HeteroskedasticCovariance(
fe, jacobian=np.eye(f.shape[1]), center=False, debiased=debiased, df=1
)
elif cov_type == "kernel":
kernel = get_string(cov_config, "kernel")
bandwidth = get_float(cov_config, "bandwidth")
cov_est = KernelCovariance(
xe,
inv_jacobian=xpxi,
center=False,
debiased=debiased,
df=fc.shape[1],
bandwidth=bandwidth,
kernel=kernel,
)
bw = cov_est.bandwidth
_cov_config = {k: v for k, v in cov_config.items()}
_cov_config["bandwidth"] = bw
rp_cov_est = KernelCovariance(
fe,
jacobian=np.eye(f.shape[1]),
center=False,
debiased=debiased,
df=1,
bandwidth=bw,
kernel=kernel,
)
else:
raise ValueError(f"Unknown cov_type: {cov_type}")
full_vcv = cov_est.cov
rp_cov = rp_cov_est.cov
vcv = full_vcv[:nloading, :nloading]
# Rearrange VCV
order = np.reshape(
np.arange((nfactor + 1) * nportfolio), (nportfolio, nfactor + 1)
)
order = order.T.ravel()
vcv = vcv[order][:, order]
# Return values
alpha_vcv = vcv[:nportfolio, :nportfolio]
stat = float(np.squeeze(alphas.T @ np.linalg.pinv(alpha_vcv) @ alphas))
jstat = WaldTestStatistic(
stat, "All alphas are 0", nportfolio, name="J-statistic"
)
params = b.T
betas = b[1:].T
residual_ss = (eps**2).sum()
e = p - p.mean(0)[None, :]
total_ss = (e**2).sum()
r2 = 1 - residual_ss / total_ss
param_names = []
for portfolio in self.portfolios.cols:
param_names.append(f"alpha-{portfolio}")
for factor in self.factors.cols:
param_names.append(f"beta-{portfolio}-{factor}")
for factor in self.factors.cols:
param_names.append(f"lambda-{factor}")
res = AttrDict(
params=params,
cov=full_vcv,
betas=betas,
rp=rp,
rp_cov=rp_cov,
alphas=alphas,
alpha_vcv=alpha_vcv,
jstat=jstat,
rsquared=r2,
total_ss=total_ss,
residual_ss=residual_ss,
param_names=param_names,
portfolio_names=self.portfolios.cols,
factor_names=self.factors.cols,
name=self._name,
cov_type=cov_type,
model=self,
nobs=nobs,
rp_names=self.factors.cols,
cov_est=cov_est,
)
return LinearFactorModelResults(res)
| (self, cov_type: str = 'robust', debiased: bool = True, **cov_config: str | float) -> linearmodels.asset_pricing.results.LinearFactorModelResults | [
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|
43,123 | linearmodels | test | null | def test(
extra_args: str | list[str] | None = None,
exit: bool = True,
append: bool = True,
location: str = "",
) -> int:
import sys
try:
import pytest
except ImportError: # pragma: no cover
raise ImportError("Need pytest to run tests")
cmd = ["--tb=auto"]
if extra_args:
if not isinstance(extra_args, list):
pytest_args = [extra_args]
else:
pytest_args = extra_args
if append:
cmd += pytest_args[:]
else:
cmd = pytest_args
print(location)
pkg = os.path.dirname(__file__)
print(pkg)
if location:
pkg = os.path.abspath(os.path.join(pkg, location))
print(pkg)
if not os.path.exists(pkg):
raise RuntimeError(f"{pkg} was not found. Unable to run tests")
cmd = [pkg] + cmd
print("running: pytest {}".format(" ".join(cmd)))
status = pytest.main(cmd)
if exit: # pragma: no cover
sys.exit(status)
return status
| (extra_args: Union[str, list[str], NoneType] = None, exit: bool = True, append: bool = True, location: str = '') -> int | [
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|
43,125 | ltxpdflinks._extractor | ExtractedGraphicLinks | null | class ExtractedGraphicLinks:
def __init__(self, graphic_fname, size, links, *, unitlength='1bp', **kwargs):
self.graphic_fname = graphic_fname
self.unitlength = unitlength # LaTeX length
(w,h) = size
self.size = (float(w),float(h)) # (width, height)
self.links = links
self.dic = dict(kwargs)
def __repr__(self):
return self.__class__.__name__ + \
'({!r}, {!r}, {!r}, unitlength={!r}, **{!r})'.format(
self.graphic_fname,
self.size,
self.links,
self.unitlength,
self.dic
)
| (graphic_fname, size, links, *, unitlength='1bp', **kwargs) | [
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0.060809485614299774,
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|
43,126 | ltxpdflinks._extractor | __init__ | null | def __init__(self, graphic_fname, size, links, *, unitlength='1bp', **kwargs):
self.graphic_fname = graphic_fname
self.unitlength = unitlength # LaTeX length
(w,h) = size
self.size = (float(w),float(h)) # (width, height)
self.links = links
self.dic = dict(kwargs)
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|
43,127 | ltxpdflinks._extractor | __repr__ | null | def __repr__(self):
return self.__class__.__name__ + \
'({!r}, {!r}, {!r}, unitlength={!r}, **{!r})'.format(
self.graphic_fname,
self.size,
self.links,
self.unitlength,
self.dic
)
| (self) | [
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|
43,128 | ltxpdflinks._extractor | ExtractedLink |
..........
- `link_bbox` is relative to the page bottom left corner in user space
units, given as `(x, y, w, h)`
- `link_type` is one of 'URI', 'latex-ref', 'latex-cite'. When extracting
special types of URLs (e.g. 'latexpdf://xxx/xxx') then the extracted type
is 'URI' with the special URI, then use a relevant SpecialLinkConverter to
convert the special URI's to specialized types.
| class ExtractedLink:
"""
..........
- `link_bbox` is relative to the page bottom left corner in user space
units, given as `(x, y, w, h)`
- `link_type` is one of 'URI', 'latex-ref', 'latex-cite'. When extracting
special types of URLs (e.g. 'latexpdf://xxx/xxx') then the extracted type
is 'URI' with the special URI, then use a relevant SpecialLinkConverter to
convert the special URI's to specialized types.
"""
def __init__(self, link_bbox, link_type, link_target, **kwargs):
super().__init__()
x, y, w, h = link_bbox
self.link_bbox = (float(x), float(y), float(w), float(h))
self.link_type = link_type
self.link_target = link_target
self.dic = dict(kwargs)
def __repr__(self):
return self.__class__.__name__ + '({!r}, {!r}, {!r}, **{!r})'.format(
self.link_bbox,
self.link_type,
self.link_target,
self.dic
)
| (link_bbox, link_type, link_target, **kwargs) | [
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|
43,129 | ltxpdflinks._extractor | __init__ | null | def __init__(self, link_bbox, link_type, link_target, **kwargs):
super().__init__()
x, y, w, h = link_bbox
self.link_bbox = (float(x), float(y), float(w), float(h))
self.link_type = link_type
self.link_target = link_target
self.dic = dict(kwargs)
| (self, link_bbox, link_type, link_target, **kwargs) | [
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|
43,130 | ltxpdflinks._extractor | __repr__ | null | def __repr__(self):
return self.__class__.__name__ + '({!r}, {!r}, {!r}, **{!r})'.format(
self.link_bbox,
self.link_type,
self.link_target,
self.dic
)
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|
43,131 | ltxpdflinks._linkconverter | LatexRefsLinkConverter | null | class LatexRefsLinkConverter:
def __init__(self):
super().__init__()
def convertLinks(self, extracted_links):
"""
Go over URI hyperlinks, and convert those whose "protocol" in the URL is
"latexref".
Conversion is performed in-place, directly modifying the input object
hierarchy. This function doesn't return anything.
Argument `extracted_links` is a :py:class:`ExtractedGraphicLinks` instance.
"""
for lnk in extracted_links.links:
if lnk.link_type == 'URI':
uri = lnk.link_target
m = _rx_latexrefurl.match(uri)
if m is None:
continue
# found match! change link type.
ref_type, ref_target = m.group('ref_type'), m.group('ref_target')
ref_target = urllib.parse.unquote(ref_target)
if ref_type == 'ref':
lnk.link_type = 'latex-ref'
lnk.link_target = ref_target
continue
if ref_type == 'cite':
lnk.link_type = 'latex-cite'
lnk.link_target = ref_target
continue
logger.warning("Unsupported ref_type in special URL %r", uri)
# done! everything was modified in-place, so we don't return anything
return
| () | [
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|
43,132 | ltxpdflinks._linkconverter | __init__ | null | def __init__(self):
super().__init__()
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|
43,133 | ltxpdflinks._linkconverter | convertLinks |
Go over URI hyperlinks, and convert those whose "protocol" in the URL is
"latexref".
Conversion is performed in-place, directly modifying the input object
hierarchy. This function doesn't return anything.
Argument `extracted_links` is a :py:class:`ExtractedGraphicLinks` instance.
| def convertLinks(self, extracted_links):
"""
Go over URI hyperlinks, and convert those whose "protocol" in the URL is
"latexref".
Conversion is performed in-place, directly modifying the input object
hierarchy. This function doesn't return anything.
Argument `extracted_links` is a :py:class:`ExtractedGraphicLinks` instance.
"""
for lnk in extracted_links.links:
if lnk.link_type == 'URI':
uri = lnk.link_target
m = _rx_latexrefurl.match(uri)
if m is None:
continue
# found match! change link type.
ref_type, ref_target = m.group('ref_type'), m.group('ref_target')
ref_target = urllib.parse.unquote(ref_target)
if ref_type == 'ref':
lnk.link_type = 'latex-ref'
lnk.link_target = ref_target
continue
if ref_type == 'cite':
lnk.link_type = 'latex-cite'
lnk.link_target = ref_target
continue
logger.warning("Unsupported ref_type in special URL %r", uri)
# done! everything was modified in-place, so we don't return anything
return
| (self, extracted_links) | [
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|
43,134 | ltxpdflinks._lplxexporter | LplxPictureEnvExporter | null | class LplxPictureEnvExporter:
def __init__(self, *, include_comments_catcode=False):
super().__init__()
self.include_comments_catcode = include_comments_catcode
def export(self, extractedgraphiclinks):
e = extractedgraphiclinks # shorthand
graphic_basefname, graphic_ext = os.path.splitext(e.graphic_fname)
s = ""
if self.include_comments_catcode:
s += r"""\catcode`\%=14\relax""" + "\n"
s += (
r"""% Automatically generated by ltxpdflinks """ + version_str + r""" on """ +
datetime.datetime.now().isoformat() + r"""
%
% LPLX - """ + _makeltxsafe(e.graphic_fname) + r"""
%
\LPLX{version=0,ltxpdflinksversion={""" + version_str +
r"""},features={bbox}}{%
\lplxGraphic{""" + _makeltxsafe(graphic_basefname) + r"""}{"""
+ _makeltxsafe(graphic_ext) + r"""}%
\lplxUserSpaceUnitLength{""" + e.unitlength + r"""}%
\lplxSetBbox{0}{0}""" + "{{{:.6g}}}{{{:.6g}}}".format(e.size[0], e.size[1]) + r"""%
%%BoundingBox: 0 0 """ + "{:d} {:d}".format(int(e.size[0]+0.5), int(e.size[1]+0.5)) + r"""
%%HiResBoundingBox: 0 0 """ + "{:.6g} {:.6g}".format(e.size[0], e.size[1]) + r"""
\lplxPicture{%
"""
)
for el in e.links:
x, y, w, h = el.link_bbox
lplxcmd = r'\lplxPutLink'
lplxtailargs = ''
if el.link_type == 'URI':
hrstart = r"""\href{{{tgt}}}""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-ref':
hrstart = r"""\hyperref[{{{tgt}}}]""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-cite':
hrstart = r"""\hyperlink{{cite.{tgt}}}""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-box':
lplxcmd, lplxtailargs = _make_latexbox_from_url(el.link_target, el)
else:
logger.warning("Ignoring link with unsupported link_type: %r", el)
continue
# s += (
# r"\put({x},{y})".format(x=el.link_bbox[0], y=el.link_bbox[1]) +
# "{" + s2 + "}\n"
# )
s += (
r"{lplxcmd}{{{x:.8g}}}{{{y:.8g}}}{{{w:.8g}}}{{{h:.8g}}}{lplxtailargs}"
.format(lplxcmd=lplxcmd, x=x, y=y, w=w, h=h, lplxtailargs=lplxtailargs)
+ r"%" + "\n"
)
s += r"""}}%""" + "\n"
return s
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|
43,135 | ltxpdflinks._lplxexporter | __init__ | null | def __init__(self, *, include_comments_catcode=False):
super().__init__()
self.include_comments_catcode = include_comments_catcode
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|
43,136 | ltxpdflinks._lplxexporter | export | null | def export(self, extractedgraphiclinks):
e = extractedgraphiclinks # shorthand
graphic_basefname, graphic_ext = os.path.splitext(e.graphic_fname)
s = ""
if self.include_comments_catcode:
s += r"""\catcode`\%=14\relax""" + "\n"
s += (
r"""% Automatically generated by ltxpdflinks """ + version_str + r""" on """ +
datetime.datetime.now().isoformat() + r"""
%
% LPLX - """ + _makeltxsafe(e.graphic_fname) + r"""
%
\LPLX{version=0,ltxpdflinksversion={""" + version_str +
r"""},features={bbox}}{%
\lplxGraphic{""" + _makeltxsafe(graphic_basefname) + r"""}{"""
+ _makeltxsafe(graphic_ext) + r"""}%
\lplxUserSpaceUnitLength{""" + e.unitlength + r"""}%
\lplxSetBbox{0}{0}""" + "{{{:.6g}}}{{{:.6g}}}".format(e.size[0], e.size[1]) + r"""%
%%BoundingBox: 0 0 """ + "{:d} {:d}".format(int(e.size[0]+0.5), int(e.size[1]+0.5)) + r"""
%%HiResBoundingBox: 0 0 """ + "{:.6g} {:.6g}".format(e.size[0], e.size[1]) + r"""
\lplxPicture{%
"""
)
for el in e.links:
x, y, w, h = el.link_bbox
lplxcmd = r'\lplxPutLink'
lplxtailargs = ''
if el.link_type == 'URI':
hrstart = r"""\href{{{tgt}}}""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-ref':
hrstart = r"""\hyperref[{{{tgt}}}]""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-cite':
hrstart = r"""\hyperlink{{cite.{tgt}}}""".format(tgt=_makeltxsafe(el.link_target))
lplxtailargs = '{{{hrstart}}}{{}}'.format(hrstart=hrstart)
elif el.link_type == 'latex-box':
lplxcmd, lplxtailargs = _make_latexbox_from_url(el.link_target, el)
else:
logger.warning("Ignoring link with unsupported link_type: %r", el)
continue
# s += (
# r"\put({x},{y})".format(x=el.link_bbox[0], y=el.link_bbox[1]) +
# "{" + s2 + "}\n"
# )
s += (
r"{lplxcmd}{{{x:.8g}}}{{{y:.8g}}}{{{w:.8g}}}{{{h:.8g}}}{lplxtailargs}"
.format(lplxcmd=lplxcmd, x=x, y=y, w=w, h=h, lplxtailargs=lplxtailargs)
+ r"%" + "\n"
)
s += r"""}}%""" + "\n"
return s
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|
43,137 | ltxpdflinks._extractor | PdfGraphicLinksExtractor | null | class PdfGraphicLinksExtractor:
def __init__(self, fname):
super().__init__()
self.fname = fname
def extractGraphicLinks(self, pageno=None):
if pageno is None:
pageno = 0
with open(self.fname, 'rb') as f:
pdf = PyPDF2.PdfFileReader(f)
page = pdf.getPage(pageno).getObject()
page_size = (page.mediaBox.getWidth(), page.mediaBox.getHeight())
page_bottomleft = page.mediaBox.lowerLeft
extracted_list = []
if '/Annots' in page:
for annot in page['/Annots']:
annot = annot.getObject()
extracted = self._extract_annot_link(annot,
shift_rect_origin=page_bottomleft)
if extracted is not None:
logger.debug("Extracted link: %r", extracted)
extracted_list.append(extracted)
return ExtractedGraphicLinks(self.fname, page_size, extracted_list)
def _extract_annot_link(self, annot, *, shift_rect_origin=(0,0)):
if '/Subtype' not in annot or annot['/Subtype'].getObject() != '/Link':
logger.debug("Found annotation, not a link: %r", annot)
return None
if '/A' not in annot:
return None
annot_A = annot['/A'].getObject()
if '/S' not in annot_A or annot_A['/S'].getObject() != '/URI':
logger.warning("Link action %r has supported type (/S!=/URI)", annot_A)
return None
if '/URI' not in annot_A:
logger.warning("Link action %r does not have URI", annot_A)
return None
URI = annot_A['/URI'].getObject()
if '/Rect' not in annot:
logger.warning("Can't get annotation's bounding box (/Rect): %r", annot)
return None
else:
(x0,y0,x1,y1) = annot['/Rect'].getObject()
x = x0 - shift_rect_origin[0]
y = y0 - shift_rect_origin[1]
w = x1 - x0
h = y1 - y0
return ExtractedLink(link_bbox=(x,y,w,h), link_type='URI', link_target=URI)
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|
43,138 | ltxpdflinks._extractor | __init__ | null | def __init__(self, fname):
super().__init__()
self.fname = fname
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|
43,139 | ltxpdflinks._extractor | _extract_annot_link | null | def _extract_annot_link(self, annot, *, shift_rect_origin=(0,0)):
if '/Subtype' not in annot or annot['/Subtype'].getObject() != '/Link':
logger.debug("Found annotation, not a link: %r", annot)
return None
if '/A' not in annot:
return None
annot_A = annot['/A'].getObject()
if '/S' not in annot_A or annot_A['/S'].getObject() != '/URI':
logger.warning("Link action %r has supported type (/S!=/URI)", annot_A)
return None
if '/URI' not in annot_A:
logger.warning("Link action %r does not have URI", annot_A)
return None
URI = annot_A['/URI'].getObject()
if '/Rect' not in annot:
logger.warning("Can't get annotation's bounding box (/Rect): %r", annot)
return None
else:
(x0,y0,x1,y1) = annot['/Rect'].getObject()
x = x0 - shift_rect_origin[0]
y = y0 - shift_rect_origin[1]
w = x1 - x0
h = y1 - y0
return ExtractedLink(link_bbox=(x,y,w,h), link_type='URI', link_target=URI)
| (self, annot, *, shift_rect_origin=(0, 0)) | [
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|
43,140 | ltxpdflinks._extractor | extractGraphicLinks | null | def extractGraphicLinks(self, pageno=None):
if pageno is None:
pageno = 0
with open(self.fname, 'rb') as f:
pdf = PyPDF2.PdfFileReader(f)
page = pdf.getPage(pageno).getObject()
page_size = (page.mediaBox.getWidth(), page.mediaBox.getHeight())
page_bottomleft = page.mediaBox.lowerLeft
extracted_list = []
if '/Annots' in page:
for annot in page['/Annots']:
annot = annot.getObject()
extracted = self._extract_annot_link(annot,
shift_rect_origin=page_bottomleft)
if extracted is not None:
logger.debug("Extracted link: %r", extracted)
extracted_list.append(extracted)
return ExtractedGraphicLinks(self.fname, page_size, extracted_list)
| (self, pageno=None) | [
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|
43,145 | salesforce_api.client | Client | null | class Client:
def __init__(self,
connection: Connection = None,
domain: str = None,
username: str = None,
password: str = None,
security_token: str = None,
password_and_security_token: str = None,
client_id: str = None,
client_secret: str = None,
access_token: str = None,
session: requests.Session = None,
is_sandbox=False,
api_version: str = None):
self.connection = connection if connection else login.magic(
domain=domain,
username=username,
password=password,
security_token=security_token,
password_and_security_token=password_and_security_token,
client_id=client_id,
client_secret=client_secret,
access_token=access_token,
session=misc_utils.get_session(session),
is_sandbox=is_sandbox,
api_version=api_version
)
self._setup_services()
def _setup_services(self):
self.basic = basic.Basic(self.connection)
self.sobjects = sobjects.SObjects(self.connection)
self.tooling = tooling.Tooling(self.connection)
self.deploy = deploy.Deploy(self.connection)
self.retrieve = retrieve.Retrieve(self.connection)
self.bulk = bulk.Client(self.connection)
self.bulk_v1 = bulk.v1.Client(self.connection)
self.bulk_v2 = bulk.v2.Client(self.connection)
| (connection: salesforce_api.core.Connection = None, domain: str = None, username: str = None, password: str = None, security_token: str = None, password_and_security_token: str = None, client_id: str = None, client_secret: str = None, access_token: str = None, session: requests.sessions.Session = None, is_sandbox=False, api_version: str = None) | [
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|
43,146 | salesforce_api.client | __init__ | null | def __init__(self,
connection: Connection = None,
domain: str = None,
username: str = None,
password: str = None,
security_token: str = None,
password_and_security_token: str = None,
client_id: str = None,
client_secret: str = None,
access_token: str = None,
session: requests.Session = None,
is_sandbox=False,
api_version: str = None):
self.connection = connection if connection else login.magic(
domain=domain,
username=username,
password=password,
security_token=security_token,
password_and_security_token=password_and_security_token,
client_id=client_id,
client_secret=client_secret,
access_token=access_token,
session=misc_utils.get_session(session),
is_sandbox=is_sandbox,
api_version=api_version
)
self._setup_services()
| (self, connection: Optional[salesforce_api.core.Connection] = None, domain: Optional[str] = None, username: Optional[str] = None, password: Optional[str] = None, security_token: Optional[str] = None, password_and_security_token: Optional[str] = None, client_id: Optional[str] = None, client_secret: Optional[str] = None, access_token: Optional[str] = None, session: Optional[requests.sessions.Session] = None, is_sandbox=False, api_version: Optional[str] = None) | [
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|
43,147 | salesforce_api.client | _setup_services | null | def _setup_services(self):
self.basic = basic.Basic(self.connection)
self.sobjects = sobjects.SObjects(self.connection)
self.tooling = tooling.Tooling(self.connection)
self.deploy = deploy.Deploy(self.connection)
self.retrieve = retrieve.Retrieve(self.connection)
self.bulk = bulk.Client(self.connection)
self.bulk_v1 = bulk.v1.Client(self.connection)
self.bulk_v2 = bulk.v2.Client(self.connection)
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|
43,157 | fast_poisson_solver.data | Data | null | class Data:
def __init__(self, cases, domain_x=None, domain_y=None, grid_num=32, noise_std=0, shuffle=False,
initial_shuffle=False, batchsize=-1, batchsize_bc=-1,
use_torch=False, device='cpu', precision=torch.float32, random_coords=False, seed=0):
if domain_y is None:
domain_y = [0, 1]
if domain_x is None:
domain_x = [0, 1]
self.y = None
self.x = None
self.y_grid = None
self.x_grid = None
self.domain_x = domain_x
self.domain_y = domain_y
self.grid_num = grid_num
self.cases = cases
self.noise_std = noise_std
self.num_cases = len(cases)
self.shuffle = shuffle
self.initial_shuffle = initial_shuffle
self.batchsize = batchsize if batchsize > 0 else self.grid_num ** 2
self.batchsize_bc = batchsize_bc if batchsize_bc > 0 else 4 * self.grid_num + 4
self.batch_number = 0
self.number_of_batches = np.ceil(self.grid_num ** 2 / self.batchsize).astype(int)
self.use_torch = use_torch
self.device = device
self.random_coords = random_coords
self.seed = seed
self.precision = precision
assert 0 <= self.domain_y[0] <= 1 and 0 <= self.domain_y[1] <= 1, \
"Both elements of domain_y should lie within the interval [0, 1] inclusive"
assert self.domain_y[1] > self.domain_y[0], \
"The second element of domain_y should be larger than the first element"
assert 0 <= self.domain_x[0] <= 1 and 0 <= self.domain_x[1] <= 1, \
"Both elements of domain_x should lie within the interval [0, 1] inclusive"
assert self.domain_x[1] > self.domain_x[0], \
"The second element of domain_y should be larger than the first element"
x_domain_length = self.domain_x[1] - self.domain_x[0]
y_domain_length = self.domain_y[1] - self.domain_y[0]
if x_domain_length > y_domain_length:
self.x_grid_num = self.grid_num
self.y_grid_num = int(self.grid_num * y_domain_length / x_domain_length)
elif x_domain_length < y_domain_length:
self.x_grid_num = int(self.grid_num * x_domain_length / y_domain_length)
self.y_grid_num = self.grid_num
else:
self.x_grid_num = self.grid_num
self.y_grid_num = self.grid_num
np.random.seed(self.seed)
torch.manual_seed(self.seed)
# self.indices = [np.random.choice(self.grid_num**2, self.batchsize, replace=False) for _ in range(self.num_cases)]
# self.indices = np.arange(self.grid_num ** 2)
self.indices = np.arange(self.x_grid_num * self.y_grid_num)
# self.indices_bc = np.arange(4 * self.grid_num + 4)
self.indices_bc = np.arange(2 * self.x_grid_num + 2 * self.y_grid_num + 4)
if self.initial_shuffle:
self.indices = np.random.permutation(self.indices)
self.indices_bc = np.random.permutation(self.indices_bc)
self.generate_boundary_coords()
if not random_coords:
self.generate_grid()
else:
self.generate_random_coords()
self.calculate_cases()
if self.use_torch:
self.to_torch_tensors()
else:
self.x_grid = self.x_grid.reshape(-1, 1)
self.y_grid = self.x_grid.reshape(-1, 1)
self.x_bc = self.x_grid.reshape(-1, 1)
self.y_bc = self.x_grid.reshape(-1, 1)
def get_infos(self):
data = {
'domain_x': self.domain_x,
'domain_y': self.domain_y,
'grid_num': self.grid_num,
'num_cases': self.num_cases,
'shuffle': self.shuffle,
'initial_shuffle': self.initial_shuffle,
'batchsize': self.batchsize,
'batchsize_bc': self.batchsize_bc,
'use_torch': self.use_torch,
'device': self.device,
'seed': self.seed,
'precision': str(self.precision),
'cases': self.cases,
}
return data
def to_torch_tensors(self):
self.out = torch.from_numpy(self.out).to(self.device).to(self.precision)
self.x_grid = torch.from_numpy(self.x_grid).unsqueeze(1).to(self.device).to(self.precision)
self.y_grid = torch.from_numpy(self.y_grid).unsqueeze(1).to(self.device).to(self.precision)
self.bc = torch.from_numpy(self.bc).to(self.device).to(self.precision)
self.x_bc = torch.from_numpy(self.x_bc).unsqueeze(1).to(self.device).to(self.precision)
self.y_bc = torch.from_numpy(self.y_bc).unsqueeze(1).to(self.device).to(self.precision)
self.indices = torch.from_numpy(self.indices).long().to(self.device)
self.indices_bc = torch.from_numpy(self.indices_bc).long().to(self.device)
def __iter__(self):
return self
def __next__(self):
if self.batch_number < self.number_of_batches:
out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call = self.__call__(self.batch_number)
self.batch_number += 1
return out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call
else:
self.batch_number = 0
raise StopIteration
def __call__(self, batch_number):
if batch_number == 0 and self.shuffle:
self.shuffle_epoch()
min_batch = batch_number * self.batchsize
max_batch = min((min_batch + self.batchsize, self.grid_num ** 2))
max_batch = min((min_batch + self.batchsize, self.x_grid_num * self.y_grid_num))
batchsize_i = max_batch - min_batch
min_batch_bc = batch_number * self.batchsize_bc
# max_batch_bc = min((min_batch_bc + self.batchsize_bc, 4 * self.grid_num + 4))
max_batch_bc = min((min_batch_bc + self.batchsize_bc, 2 * self.x_grid_num + 2 * self.y_grid_num + 4))
batchsize_i_bc = max_batch_bc - min_batch_bc
indices_call = self.indices[min_batch: max_batch]
if self.use_torch:
out_call = torch.zeros(size=(batchsize_i, self.num_cases), device=self.device, dtype=self.precision)
else:
out_call = np.zeros((batchsize_i, self.num_cases))
x_call = self.x_grid[indices_call]
y_call = self.y_grid[indices_call]
for i, out_i in enumerate(self.out.T):
out_call[:, i] = out_i[indices_call]
indices_call_bc = self.indices_bc[min_batch_bc: max_batch_bc]
if self.use_torch:
bc_call = torch.zeros(size=(batchsize_i_bc, self.num_cases), device=self.device, dtype=self.precision)
else:
bc_call = np.zeros((batchsize_i_bc, self.num_cases))
x_bc_call = self.x_bc[indices_call_bc]
y_bc_call = self.y_bc[indices_call_bc]
for i, bc_i in enumerate(self.bc.T):
bc_call[:, i] = bc_i[indices_call_bc]
return out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call
def shuffle_epoch(self):
if self.use_torch:
self.indices = torch.randperm(self.indices.shape[0])
self.indices_bc = torch.randperm(self.indices_bc.shape[0])
else:
self.indices = np.random.permutation(self.indices)
self.indices_bc = np.random.permutation(self.indices_bc)
def generate_grid(self):
# x = np.linspace(self.domain_x[0], self.domain_x[1], self.grid_num + 2)[1:-1]
x = np.linspace(self.domain_x[0], self.domain_x[1], self.x_grid_num + 2)[1:-1]
y = np.linspace(self.domain_y[0], self.domain_y[1], self.y_grid_num + 2)[1:-1]
x, y = np.meshgrid(x, y)
self.x_grid = x.flatten()
self.y_grid = y.flatten()
def generate_random_coords(self):
engine = qmc.Sobol(d=2, scramble=True, seed=self.seed) # d=2 for 2D points
sample = engine.random(int(self.grid_num ** 2))
self.x_grid, self.y_grid = np.hsplit(sample, 2)
self.y_grid = self.y_grid.flatten()
self.x_grid = self.x_grid.flatten()
def generate_boundary_coords(self):
# x_grid = np.linspace(self.domain_x[0], self.domain_x[1], self.grid_num + 2)
x_grid = np.linspace(self | (cases, domain_x=None, domain_y=None, grid_num=32, noise_std=0, shuffle=False, initial_shuffle=False, batchsize=-1, batchsize_bc=-1, use_torch=False, device='cpu', precision=torch.float32, random_coords=False, seed=0) | [
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|
43,158 | fast_poisson_solver.data | __call__ | null | def __call__(self, batch_number):
if batch_number == 0 and self.shuffle:
self.shuffle_epoch()
min_batch = batch_number * self.batchsize
max_batch = min((min_batch + self.batchsize, self.grid_num ** 2))
max_batch = min((min_batch + self.batchsize, self.x_grid_num * self.y_grid_num))
batchsize_i = max_batch - min_batch
min_batch_bc = batch_number * self.batchsize_bc
# max_batch_bc = min((min_batch_bc + self.batchsize_bc, 4 * self.grid_num + 4))
max_batch_bc = min((min_batch_bc + self.batchsize_bc, 2 * self.x_grid_num + 2 * self.y_grid_num + 4))
batchsize_i_bc = max_batch_bc - min_batch_bc
indices_call = self.indices[min_batch: max_batch]
if self.use_torch:
out_call = torch.zeros(size=(batchsize_i, self.num_cases), device=self.device, dtype=self.precision)
else:
out_call = np.zeros((batchsize_i, self.num_cases))
x_call = self.x_grid[indices_call]
y_call = self.y_grid[indices_call]
for i, out_i in enumerate(self.out.T):
out_call[:, i] = out_i[indices_call]
indices_call_bc = self.indices_bc[min_batch_bc: max_batch_bc]
if self.use_torch:
bc_call = torch.zeros(size=(batchsize_i_bc, self.num_cases), device=self.device, dtype=self.precision)
else:
bc_call = np.zeros((batchsize_i_bc, self.num_cases))
x_bc_call = self.x_bc[indices_call_bc]
y_bc_call = self.y_bc[indices_call_bc]
for i, bc_i in enumerate(self.bc.T):
bc_call[:, i] = bc_i[indices_call_bc]
return out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call
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|
43,159 | fast_poisson_solver.data | __init__ | null | def __init__(self, cases, domain_x=None, domain_y=None, grid_num=32, noise_std=0, shuffle=False,
initial_shuffle=False, batchsize=-1, batchsize_bc=-1,
use_torch=False, device='cpu', precision=torch.float32, random_coords=False, seed=0):
if domain_y is None:
domain_y = [0, 1]
if domain_x is None:
domain_x = [0, 1]
self.y = None
self.x = None
self.y_grid = None
self.x_grid = None
self.domain_x = domain_x
self.domain_y = domain_y
self.grid_num = grid_num
self.cases = cases
self.noise_std = noise_std
self.num_cases = len(cases)
self.shuffle = shuffle
self.initial_shuffle = initial_shuffle
self.batchsize = batchsize if batchsize > 0 else self.grid_num ** 2
self.batchsize_bc = batchsize_bc if batchsize_bc > 0 else 4 * self.grid_num + 4
self.batch_number = 0
self.number_of_batches = np.ceil(self.grid_num ** 2 / self.batchsize).astype(int)
self.use_torch = use_torch
self.device = device
self.random_coords = random_coords
self.seed = seed
self.precision = precision
assert 0 <= self.domain_y[0] <= 1 and 0 <= self.domain_y[1] <= 1, \
"Both elements of domain_y should lie within the interval [0, 1] inclusive"
assert self.domain_y[1] > self.domain_y[0], \
"The second element of domain_y should be larger than the first element"
assert 0 <= self.domain_x[0] <= 1 and 0 <= self.domain_x[1] <= 1, \
"Both elements of domain_x should lie within the interval [0, 1] inclusive"
assert self.domain_x[1] > self.domain_x[0], \
"The second element of domain_y should be larger than the first element"
x_domain_length = self.domain_x[1] - self.domain_x[0]
y_domain_length = self.domain_y[1] - self.domain_y[0]
if x_domain_length > y_domain_length:
self.x_grid_num = self.grid_num
self.y_grid_num = int(self.grid_num * y_domain_length / x_domain_length)
elif x_domain_length < y_domain_length:
self.x_grid_num = int(self.grid_num * x_domain_length / y_domain_length)
self.y_grid_num = self.grid_num
else:
self.x_grid_num = self.grid_num
self.y_grid_num = self.grid_num
np.random.seed(self.seed)
torch.manual_seed(self.seed)
# self.indices = [np.random.choice(self.grid_num**2, self.batchsize, replace=False) for _ in range(self.num_cases)]
# self.indices = np.arange(self.grid_num ** 2)
self.indices = np.arange(self.x_grid_num * self.y_grid_num)
# self.indices_bc = np.arange(4 * self.grid_num + 4)
self.indices_bc = np.arange(2 * self.x_grid_num + 2 * self.y_grid_num + 4)
if self.initial_shuffle:
self.indices = np.random.permutation(self.indices)
self.indices_bc = np.random.permutation(self.indices_bc)
self.generate_boundary_coords()
if not random_coords:
self.generate_grid()
else:
self.generate_random_coords()
self.calculate_cases()
if self.use_torch:
self.to_torch_tensors()
else:
self.x_grid = self.x_grid.reshape(-1, 1)
self.y_grid = self.x_grid.reshape(-1, 1)
self.x_bc = self.x_grid.reshape(-1, 1)
self.y_bc = self.x_grid.reshape(-1, 1)
| (self, cases, domain_x=None, domain_y=None, grid_num=32, noise_std=0, shuffle=False, initial_shuffle=False, batchsize=-1, batchsize_bc=-1, use_torch=False, device='cpu', precision=torch.float32, random_coords=False, seed=0) | [
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|
43,161 | fast_poisson_solver.data | __next__ | null | def __next__(self):
if self.batch_number < self.number_of_batches:
out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call = self.__call__(self.batch_number)
self.batch_number += 1
return out_call, x_call, y_call, bc_call, x_bc_call, y_bc_call
else:
self.batch_number = 0
raise StopIteration
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|
43,162 | fast_poisson_solver.data | calculate_cases | null | def calculate_cases(self):
self.out = np.zeros((len(self.x_grid), len(self.cases)))
self.bc = np.zeros((len(self.x_bc), len(self.cases)))
for i, case in enumerate(self.cases):
if case['b_val'] == 'random':
self.bc[:, i] = np.ones_like(self.x_bc) * np.random.uniform(-10, 10)
else:
np.random.uniform(-10, 10) # to make sure the random seed is not affected
self.bc[:, i] = np.ones_like(self.x_bc) * case['b_val']
# if case['name'] == 'sinsin':
# self.out[:, i] = sf.sinsin(self.x_grid, self.y_grid, case['param'])
if case['name'] == 'sin':
self.out[:, i] = sf.sincos(self.x_grid, self.y_grid, case['param'])
elif case['name'] == 'exp':
self.out[:, i] = sf.exp(self.x_grid, self.y_grid, case['param'])
elif case['name'] == 'perlin':
self.out[:, i] = sf.perlin(self.x_grid, self.y_grid, case['param'])
# elif case['name'] == 'rectangle':
# self.out[:, i] = sf.rectangle(self.x_grid, self.y_grid, case['param'])
# elif case['name'] == 'circle':
# self.out[:, i] = sf.circle(self.x_grid, self.y_grid, case['param'])
elif case['name'] == 'geo':
self.out[:, i] = sf.rectangle_circle(self.x_grid, self.y_grid, case['param'], grid_num=self.grid_num)
else:
raise ValueError('Unknown case')
if self.noise_std > 0:
self.out[:, i] *= np.random.normal(1, self.noise_std, len(self.x_grid))
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|
43,163 | fast_poisson_solver.data | generate_boundary_coords | null | def generate_boundary_coords(self):
# x_grid = np.linspace(self.domain_x[0], self.domain_x[1], self.grid_num + 2)
x_grid = np.linspace(self.domain_x[0], self.domain_x[1], self.x_grid_num + 2)
y_grid = np.linspace(self.domain_y[0], self.domain_y[1], self.y_grid_num + 2)[1:-1]
lower_x = np.ones_like(y_grid) * self.domain_x[0]
lower_y = np.ones_like(x_grid) * self.domain_y[0]
upper_x = np.ones_like(y_grid) * self.domain_x[1]
upper_y = np.ones_like(x_grid) * self.domain_y[1]
self.x_bc = np.concatenate([x_grid, x_grid, lower_x, upper_x]).flatten()
self.y_bc = np.concatenate([lower_y, upper_y, y_grid, y_grid]).flatten()
| (self) | [
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|
43,164 | fast_poisson_solver.data | generate_grid | null | def generate_grid(self):
# x = np.linspace(self.domain_x[0], self.domain_x[1], self.grid_num + 2)[1:-1]
x = np.linspace(self.domain_x[0], self.domain_x[1], self.x_grid_num + 2)[1:-1]
y = np.linspace(self.domain_y[0], self.domain_y[1], self.y_grid_num + 2)[1:-1]
x, y = np.meshgrid(x, y)
self.x_grid = x.flatten()
self.y_grid = y.flatten()
| (self) | [
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|
43,165 | fast_poisson_solver.data | generate_random_coords | null | def generate_random_coords(self):
engine = qmc.Sobol(d=2, scramble=True, seed=self.seed) # d=2 for 2D points
sample = engine.random(int(self.grid_num ** 2))
self.x_grid, self.y_grid = np.hsplit(sample, 2)
self.y_grid = self.y_grid.flatten()
self.x_grid = self.x_grid.flatten()
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|
43,166 | fast_poisson_solver.data | get_infos | null | def get_infos(self):
data = {
'domain_x': self.domain_x,
'domain_y': self.domain_y,
'grid_num': self.grid_num,
'num_cases': self.num_cases,
'shuffle': self.shuffle,
'initial_shuffle': self.initial_shuffle,
'batchsize': self.batchsize,
'batchsize_bc': self.batchsize_bc,
'use_torch': self.use_torch,
'device': self.device,
'seed': self.seed,
'precision': str(self.precision),
'cases': self.cases,
}
return data
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|
43,167 | fast_poisson_solver.data | plot_functions | null | def plot_functions(self):
f, x, y, *_ = self.__call__(0)
if self.use_torch:
f = f.float().cpu().detach().numpy()
x = x.float().cpu().detach().numpy()
y = y.float().cpu().detach().numpy()
xy = np.array([x, y]).T
ind = np.lexsort((xy[:, 1], xy[:, 0]))
f = f[ind]
x = x[ind]
y = y[ind]
def plot(fig, ax, x, y, v, title):
x = x.reshape(self.grid_num, self.grid_num)
y = y.reshape(self.grid_num, self.grid_num)
v = v.reshape(self.grid_num, self.grid_num)
c = ax.contourf(x, y, v, 100, cmap='jet')
# c = ax.scatter(x, y, c=v, s=1)
ax.set_title(title)
ax.set_xlabel('x')
ax.set_ylabel('y')
fig.colorbar(c, ax=ax)
plots_x = np.min((self.num_cases, 4))
plots_y = int(np.ceil(self.num_cases / plots_x))
fig, axs = plt.subplots(plots_y, plots_x, figsize=(plots_x * 4, plots_y * 4), dpi=100, tight_layout=True)
if self.num_cases == 1:
plot(fig, axs, x, y, f[:, 0], self.cases[0]['name'])
else:
i = 0
for ax in axs.flatten():
if i < self.num_cases:
plot(fig, ax, x, y, f[:, i], self.cases[i]['name'])
else:
ax.axis('off')
i += 1
plt.savefig(os.path.join('..', 'images', 'functions.png'))
plt.close()
| (self) | [
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|
43,168 | fast_poisson_solver.data | shuffle_epoch | null | def shuffle_epoch(self):
if self.use_torch:
self.indices = torch.randperm(self.indices.shape[0])
self.indices_bc = torch.randperm(self.indices_bc.shape[0])
else:
self.indices = np.random.permutation(self.indices)
self.indices_bc = np.random.permutation(self.indices_bc)
| (self) | [
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|
43,169 | fast_poisson_solver.data | to_torch_tensors | null | def to_torch_tensors(self):
self.out = torch.from_numpy(self.out).to(self.device).to(self.precision)
self.x_grid = torch.from_numpy(self.x_grid).unsqueeze(1).to(self.device).to(self.precision)
self.y_grid = torch.from_numpy(self.y_grid).unsqueeze(1).to(self.device).to(self.precision)
self.bc = torch.from_numpy(self.bc).to(self.device).to(self.precision)
self.x_bc = torch.from_numpy(self.x_bc).unsqueeze(1).to(self.device).to(self.precision)
self.y_bc = torch.from_numpy(self.y_bc).unsqueeze(1).to(self.device).to(self.precision)
self.indices = torch.from_numpy(self.indices).long().to(self.device)
self.indices_bc = torch.from_numpy(self.indices_bc).long().to(self.device)
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|
43,170 | matplotlib.cm | ScalarMappable |
A mixin class to map scalar data to RGBA.
The ScalarMappable applies data normalization before returning RGBA colors
from the given colormap.
| class ScalarMappable:
"""
A mixin class to map scalar data to RGBA.
The ScalarMappable applies data normalization before returning RGBA colors
from the given colormap.
"""
def __init__(self, norm=None, cmap=None):
"""
Parameters
----------
norm : `.Normalize` (or subclass thereof) or str or None
The normalizing object which scales data, typically into the
interval ``[0, 1]``.
If a `str`, a `.Normalize` subclass is dynamically generated based
on the scale with the corresponding name.
If *None*, *norm* defaults to a *colors.Normalize* object which
initializes its scaling based on the first data processed.
cmap : str or `~matplotlib.colors.Colormap`
The colormap used to map normalized data values to RGBA colors.
"""
self._A = None
self._norm = None # So that the setter knows we're initializing.
self.set_norm(norm) # The Normalize instance of this ScalarMappable.
self.cmap = None # So that the setter knows we're initializing.
self.set_cmap(cmap) # The Colormap instance of this ScalarMappable.
#: The last colorbar associated with this ScalarMappable. May be None.
self.colorbar = None
self.callbacks = cbook.CallbackRegistry(signals=["changed"])
def _scale_norm(self, norm, vmin, vmax):
"""
Helper for initial scaling.
Used by public functions that create a ScalarMappable and support
parameters *vmin*, *vmax* and *norm*. This makes sure that a *norm*
will take precedence over *vmin*, *vmax*.
Note that this method does not set the norm.
"""
if vmin is not None or vmax is not None:
self.set_clim(vmin, vmax)
if isinstance(norm, colors.Normalize):
raise ValueError(
"Passing a Normalize instance simultaneously with "
"vmin/vmax is not supported. Please pass vmin/vmax "
"directly to the norm when creating it.")
# always resolve the autoscaling so we have concrete limits
# rather than deferring to draw time.
self.autoscale_None()
def to_rgba(self, x, alpha=None, bytes=False, norm=True):
"""
Return a normalized RGBA array corresponding to *x*.
In the normal case, *x* is a 1D or 2D sequence of scalars, and
the corresponding `~numpy.ndarray` of RGBA values will be returned,
based on the norm and colormap set for this ScalarMappable.
There is one special case, for handling images that are already
RGB or RGBA, such as might have been read from an image file.
If *x* is an `~numpy.ndarray` with 3 dimensions,
and the last dimension is either 3 or 4, then it will be
treated as an RGB or RGBA array, and no mapping will be done.
The array can be `~numpy.uint8`, or it can be floats with
values in the 0-1 range; otherwise a ValueError will be raised.
If it is a masked array, any masked elements will be set to 0 alpha.
If the last dimension is 3, the *alpha* kwarg (defaulting to 1)
will be used to fill in the transparency. If the last dimension
is 4, the *alpha* kwarg is ignored; it does not
replace the preexisting alpha. A ValueError will be raised
if the third dimension is other than 3 or 4.
In either case, if *bytes* is *False* (default), the RGBA
array will be floats in the 0-1 range; if it is *True*,
the returned RGBA array will be `~numpy.uint8` in the 0 to 255 range.
If norm is False, no normalization of the input data is
performed, and it is assumed to be in the range (0-1).
"""
# First check for special case, image input:
try:
if x.ndim == 3:
if x.shape[2] == 3:
if alpha is None:
alpha = 1
if x.dtype == np.uint8:
alpha = np.uint8(alpha * 255)
m, n = x.shape[:2]
xx = np.empty(shape=(m, n, 4), dtype=x.dtype)
xx[:, :, :3] = x
xx[:, :, 3] = alpha
elif x.shape[2] == 4:
xx = x
else:
raise ValueError("Third dimension must be 3 or 4")
if xx.dtype.kind == 'f':
if norm and (xx.max() > 1 or xx.min() < 0):
raise ValueError("Floating point image RGB values "
"must be in the 0..1 range.")
if bytes:
xx = (xx * 255).astype(np.uint8)
elif xx.dtype == np.uint8:
if not bytes:
xx = xx.astype(np.float32) / 255
else:
raise ValueError("Image RGB array must be uint8 or "
"floating point; found %s" % xx.dtype)
# Account for any masked entries in the original array
# If any of R, G, B, or A are masked for an entry, we set alpha to 0
if np.ma.is_masked(x):
xx[np.any(np.ma.getmaskarray(x), axis=2), 3] = 0
return xx
except AttributeError:
# e.g., x is not an ndarray; so try mapping it
pass
# This is the normal case, mapping a scalar array:
x = ma.asarray(x)
if norm:
x = self.norm(x)
rgba = self.cmap(x, alpha=alpha, bytes=bytes)
return rgba
def set_array(self, A):
"""
Set the value array from array-like *A*.
Parameters
----------
A : array-like or None
The values that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the value array *A*.
"""
if A is None:
self._A = None
return
A = cbook.safe_masked_invalid(A, copy=True)
if not np.can_cast(A.dtype, float, "same_kind"):
raise TypeError(f"Image data of dtype {A.dtype} cannot be "
"converted to float")
self._A = A
def get_array(self):
"""
Return the array of values, that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the array.
"""
return self._A
def get_cmap(self):
"""Return the `.Colormap` instance."""
return self.cmap
def get_clim(self):
"""
Return the values (min, max) that are mapped to the colormap limits.
"""
return self.norm.vmin, self.norm.vmax
def set_clim(self, vmin=None, vmax=None):
"""
Set the norm limits for image scaling.
Parameters
----------
vmin, vmax : float
The limits.
The limits may also be passed as a tuple (*vmin*, *vmax*) as a
single positional argument.
.. ACCEPTS: (vmin: float, vmax: float)
"""
# If the norm's limits are updated self.changed() will be called
# through the callbacks attached to the norm
if vmax is None:
try:
vmin, vmax = vmin
except (TypeError, ValueError):
pass
if vmin is not None:
self.norm.vmin = colors._sanitize_extrema(vmin)
if vmax is not None:
self.norm.vmax = colors._sanitize_extrema(vmax)
def get_alpha(self):
"""
Returns
-------
float
Always returns 1.
"""
# This method is intended to be overridden by Artist sub-classes
return 1.
def set_cmap(self, cmap):
"""
Set the colormap for luminance data.
Parameters
----------
cmap : `.Colormap` or str or None
"""
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|
43,171 | matplotlib.cm | __init__ |
Parameters
----------
norm : `.Normalize` (or subclass thereof) or str or None
The normalizing object which scales data, typically into the
interval ``[0, 1]``.
If a `str`, a `.Normalize` subclass is dynamically generated based
on the scale with the corresponding name.
If *None*, *norm* defaults to a *colors.Normalize* object which
initializes its scaling based on the first data processed.
cmap : str or `~matplotlib.colors.Colormap`
The colormap used to map normalized data values to RGBA colors.
| def __init__(self, norm=None, cmap=None):
"""
Parameters
----------
norm : `.Normalize` (or subclass thereof) or str or None
The normalizing object which scales data, typically into the
interval ``[0, 1]``.
If a `str`, a `.Normalize` subclass is dynamically generated based
on the scale with the corresponding name.
If *None*, *norm* defaults to a *colors.Normalize* object which
initializes its scaling based on the first data processed.
cmap : str or `~matplotlib.colors.Colormap`
The colormap used to map normalized data values to RGBA colors.
"""
self._A = None
self._norm = None # So that the setter knows we're initializing.
self.set_norm(norm) # The Normalize instance of this ScalarMappable.
self.cmap = None # So that the setter knows we're initializing.
self.set_cmap(cmap) # The Colormap instance of this ScalarMappable.
#: The last colorbar associated with this ScalarMappable. May be None.
self.colorbar = None
self.callbacks = cbook.CallbackRegistry(signals=["changed"])
| (self, norm=None, cmap=None) | [
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|
43,172 | matplotlib.cm | _scale_norm |
Helper for initial scaling.
Used by public functions that create a ScalarMappable and support
parameters *vmin*, *vmax* and *norm*. This makes sure that a *norm*
will take precedence over *vmin*, *vmax*.
Note that this method does not set the norm.
| def _scale_norm(self, norm, vmin, vmax):
"""
Helper for initial scaling.
Used by public functions that create a ScalarMappable and support
parameters *vmin*, *vmax* and *norm*. This makes sure that a *norm*
will take precedence over *vmin*, *vmax*.
Note that this method does not set the norm.
"""
if vmin is not None or vmax is not None:
self.set_clim(vmin, vmax)
if isinstance(norm, colors.Normalize):
raise ValueError(
"Passing a Normalize instance simultaneously with "
"vmin/vmax is not supported. Please pass vmin/vmax "
"directly to the norm when creating it.")
# always resolve the autoscaling so we have concrete limits
# rather than deferring to draw time.
self.autoscale_None()
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|
43,173 | matplotlib.cm | autoscale |
Autoscale the scalar limits on the norm instance using the
current array
| def autoscale(self):
"""
Autoscale the scalar limits on the norm instance using the
current array
"""
if self._A is None:
raise TypeError('You must first set_array for mappable')
# If the norm's limits are updated self.changed() will be called
# through the callbacks attached to the norm
self.norm.autoscale(self._A)
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|
43,174 | matplotlib.cm | autoscale_None |
Autoscale the scalar limits on the norm instance using the
current array, changing only limits that are None
| def autoscale_None(self):
"""
Autoscale the scalar limits on the norm instance using the
current array, changing only limits that are None
"""
if self._A is None:
raise TypeError('You must first set_array for mappable')
# If the norm's limits are updated self.changed() will be called
# through the callbacks attached to the norm
self.norm.autoscale_None(self._A)
| (self) | [
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|
43,175 | matplotlib.cm | changed |
Call this whenever the mappable is changed to notify all the
callbackSM listeners to the 'changed' signal.
| def changed(self):
"""
Call this whenever the mappable is changed to notify all the
callbackSM listeners to the 'changed' signal.
"""
self.callbacks.process('changed', self)
self.stale = True
| (self) | [
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|
43,176 | matplotlib.cm | get_alpha |
Returns
-------
float
Always returns 1.
| def get_alpha(self):
"""
Returns
-------
float
Always returns 1.
"""
# This method is intended to be overridden by Artist sub-classes
return 1.
| (self) | [
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|
43,177 | matplotlib.cm | get_array |
Return the array of values, that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the array.
| def get_array(self):
"""
Return the array of values, that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the array.
"""
return self._A
| (self) | [
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|
43,178 | matplotlib.cm | get_clim |
Return the values (min, max) that are mapped to the colormap limits.
| def get_clim(self):
"""
Return the values (min, max) that are mapped to the colormap limits.
"""
return self.norm.vmin, self.norm.vmax
| (self) | [
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|
43,179 | matplotlib.cm | get_cmap | Return the `.Colormap` instance. | def get_cmap(self):
"""Return the `.Colormap` instance."""
return self.cmap
| (self) | [
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|
43,180 | matplotlib.cm | set_array |
Set the value array from array-like *A*.
Parameters
----------
A : array-like or None
The values that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the value array *A*.
| def set_array(self, A):
"""
Set the value array from array-like *A*.
Parameters
----------
A : array-like or None
The values that are mapped to colors.
The base class `.ScalarMappable` does not make any assumptions on
the dimensionality and shape of the value array *A*.
"""
if A is None:
self._A = None
return
A = cbook.safe_masked_invalid(A, copy=True)
if not np.can_cast(A.dtype, float, "same_kind"):
raise TypeError(f"Image data of dtype {A.dtype} cannot be "
"converted to float")
self._A = A
| (self, A) | [
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|
43,181 | matplotlib.cm | set_clim |
Set the norm limits for image scaling.
Parameters
----------
vmin, vmax : float
The limits.
The limits may also be passed as a tuple (*vmin*, *vmax*) as a
single positional argument.
.. ACCEPTS: (vmin: float, vmax: float)
| def set_clim(self, vmin=None, vmax=None):
"""
Set the norm limits for image scaling.
Parameters
----------
vmin, vmax : float
The limits.
The limits may also be passed as a tuple (*vmin*, *vmax*) as a
single positional argument.
.. ACCEPTS: (vmin: float, vmax: float)
"""
# If the norm's limits are updated self.changed() will be called
# through the callbacks attached to the norm
if vmax is None:
try:
vmin, vmax = vmin
except (TypeError, ValueError):
pass
if vmin is not None:
self.norm.vmin = colors._sanitize_extrema(vmin)
if vmax is not None:
self.norm.vmax = colors._sanitize_extrema(vmax)
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|
43,182 | matplotlib.cm | set_cmap |
Set the colormap for luminance data.
Parameters
----------
cmap : `.Colormap` or str or None
| def set_cmap(self, cmap):
"""
Set the colormap for luminance data.
Parameters
----------
cmap : `.Colormap` or str or None
"""
in_init = self.cmap is None
self.cmap = _ensure_cmap(cmap)
if not in_init:
self.changed() # Things are not set up properly yet.
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|
43,183 | matplotlib.cm | set_norm |
Set the normalization instance.
Parameters
----------
norm : `.Normalize` or str or None
Notes
-----
If there are any colorbars using the mappable for this norm, setting
the norm of the mappable will reset the norm, locator, and formatters
on the colorbar to default.
| def set_norm(self, norm):
"""
Set the normalization instance.
Parameters
----------
norm : `.Normalize` or str or None
Notes
-----
If there are any colorbars using the mappable for this norm, setting
the norm of the mappable will reset the norm, locator, and formatters
on the colorbar to default.
"""
self.norm = norm
| (self, norm) | [
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|
43,184 | matplotlib.cm | to_rgba |
Return a normalized RGBA array corresponding to *x*.
In the normal case, *x* is a 1D or 2D sequence of scalars, and
the corresponding `~numpy.ndarray` of RGBA values will be returned,
based on the norm and colormap set for this ScalarMappable.
There is one special case, for handling images that are already
RGB or RGBA, such as might have been read from an image file.
If *x* is an `~numpy.ndarray` with 3 dimensions,
and the last dimension is either 3 or 4, then it will be
treated as an RGB or RGBA array, and no mapping will be done.
The array can be `~numpy.uint8`, or it can be floats with
values in the 0-1 range; otherwise a ValueError will be raised.
If it is a masked array, any masked elements will be set to 0 alpha.
If the last dimension is 3, the *alpha* kwarg (defaulting to 1)
will be used to fill in the transparency. If the last dimension
is 4, the *alpha* kwarg is ignored; it does not
replace the preexisting alpha. A ValueError will be raised
if the third dimension is other than 3 or 4.
In either case, if *bytes* is *False* (default), the RGBA
array will be floats in the 0-1 range; if it is *True*,
the returned RGBA array will be `~numpy.uint8` in the 0 to 255 range.
If norm is False, no normalization of the input data is
performed, and it is assumed to be in the range (0-1).
| def to_rgba(self, x, alpha=None, bytes=False, norm=True):
"""
Return a normalized RGBA array corresponding to *x*.
In the normal case, *x* is a 1D or 2D sequence of scalars, and
the corresponding `~numpy.ndarray` of RGBA values will be returned,
based on the norm and colormap set for this ScalarMappable.
There is one special case, for handling images that are already
RGB or RGBA, such as might have been read from an image file.
If *x* is an `~numpy.ndarray` with 3 dimensions,
and the last dimension is either 3 or 4, then it will be
treated as an RGB or RGBA array, and no mapping will be done.
The array can be `~numpy.uint8`, or it can be floats with
values in the 0-1 range; otherwise a ValueError will be raised.
If it is a masked array, any masked elements will be set to 0 alpha.
If the last dimension is 3, the *alpha* kwarg (defaulting to 1)
will be used to fill in the transparency. If the last dimension
is 4, the *alpha* kwarg is ignored; it does not
replace the preexisting alpha. A ValueError will be raised
if the third dimension is other than 3 or 4.
In either case, if *bytes* is *False* (default), the RGBA
array will be floats in the 0-1 range; if it is *True*,
the returned RGBA array will be `~numpy.uint8` in the 0 to 255 range.
If norm is False, no normalization of the input data is
performed, and it is assumed to be in the range (0-1).
"""
# First check for special case, image input:
try:
if x.ndim == 3:
if x.shape[2] == 3:
if alpha is None:
alpha = 1
if x.dtype == np.uint8:
alpha = np.uint8(alpha * 255)
m, n = x.shape[:2]
xx = np.empty(shape=(m, n, 4), dtype=x.dtype)
xx[:, :, :3] = x
xx[:, :, 3] = alpha
elif x.shape[2] == 4:
xx = x
else:
raise ValueError("Third dimension must be 3 or 4")
if xx.dtype.kind == 'f':
if norm and (xx.max() > 1 or xx.min() < 0):
raise ValueError("Floating point image RGB values "
"must be in the 0..1 range.")
if bytes:
xx = (xx * 255).astype(np.uint8)
elif xx.dtype == np.uint8:
if not bytes:
xx = xx.astype(np.float32) / 255
else:
raise ValueError("Image RGB array must be uint8 or "
"floating point; found %s" % xx.dtype)
# Account for any masked entries in the original array
# If any of R, G, B, or A are masked for an entry, we set alpha to 0
if np.ma.is_masked(x):
xx[np.any(np.ma.getmaskarray(x), axis=2), 3] = 0
return xx
except AttributeError:
# e.g., x is not an ndarray; so try mapping it
pass
# This is the normal case, mapping a scalar array:
x = ma.asarray(x)
if norm:
x = self.norm(x)
rgba = self.cmap(x, alpha=alpha, bytes=bytes)
return rgba
| (self, x, alpha=None, bytes=False, norm=True) | [
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|
43,185 | fast_poisson_solver.solver | Solver |
This class represents the main solver used for fast Poisson equation solving.
It is a key component of the `fast_poisson_solver` package.
Parameters
----------
device : str, optional
Specifies the device where the computations will be performed.
This should be a valid PyTorch device string such as 'cuda' for GPU processing or 'cpu' for CPU processing.
Default is 'cuda'.
precision : torch.dtype, optional
This determines the precision of the computation.
This should be a valid PyTorch data type such as torch.float32 or torch.float64.
Default is torch.float32.
verbose : bool, optional
When set to True, enables the printing of detailed logs during computation.
Default is False.
use_weights : bool, optional
Determines whether the network uses pre-trained weights or random weights.
If True, the network uses pre-trained weights. Default is True.
compile_model : bool, optional
Specifies whether the network model is compiled for faster inference.
If False, the model won't be compiled. Default is True.
lambdas_pde : list of float, optional
A list that weights the influence of the PDE part in the loss term.
If None, default weight 1e-12 will be used. Default is None.
seed : int, optional
This parameter sets the seed for generating random numbers,
which helps in achieving deterministic results. Default is 0.
| class Solver:
"""
This class represents the main solver used for fast Poisson equation solving.
It is a key component of the `fast_poisson_solver` package.
Parameters
----------
device : str, optional
Specifies the device where the computations will be performed.
This should be a valid PyTorch device string such as 'cuda' for GPU processing or 'cpu' for CPU processing.
Default is 'cuda'.
precision : torch.dtype, optional
This determines the precision of the computation.
This should be a valid PyTorch data type such as torch.float32 or torch.float64.
Default is torch.float32.
verbose : bool, optional
When set to True, enables the printing of detailed logs during computation.
Default is False.
use_weights : bool, optional
Determines whether the network uses pre-trained weights or random weights.
If True, the network uses pre-trained weights. Default is True.
compile_model : bool, optional
Specifies whether the network model is compiled for faster inference.
If False, the model won't be compiled. Default is True.
lambdas_pde : list of float, optional
A list that weights the influence of the PDE part in the loss term.
If None, default weight 1e-12 will be used. Default is None.
seed : int, optional
This parameter sets the seed for generating random numbers,
which helps in achieving deterministic results. Default is 0.
"""
def __init__(self, device='cuda', precision=torch.float32, verbose=False,
use_weights=True, compile_model=True, lambdas_pde=None, seed=0):
if torch.cuda.is_available():
torch.backends.cuda.matmul.allow_tf32 = False
torch.backends.cudnn.allow_tf32 = False
if lambdas_pde is None:
lambdas_pde = [2 ** -12]
self.path = os.path.join('resources', 'final.pt')
self.verbose = verbose
self.precision = precision
self.device = device if torch.cuda.is_available() else 'cpu'
self.use_weights = use_weights
self.compile_model = compile_model
self.lambdas_pde = lambdas_pde
self.seed = seed
random.seed(self.seed)
np.random.seed(self.seed)
torch.manual_seed(self.seed)
self.n_lambdas = len(self.lambdas_pde)
# The losses for all the different values of lambda are put in those arrays
self.Ls = np.zeros(self.n_lambdas)
self.Ls_pde = np.zeros(self.n_lambdas)
self.Ls_bc = np.zeros(self.n_lambdas)
if self.path.endswith('.pt'):
self.weights_input = True
self.weights_path = pkg_resources.resource_stream(__name__, self.path)
self.path = os.path.join(*os.path.split(self.path)[:1])
else:
self.weights_input = False
# Path to the where the pre-computed data_utils will be saved.
self.precompute_path = 'precomputed-resources'
if not os.path.isdir(self.precompute_path):
os.makedirs(self.precompute_path)
self.precompute_file = os.path.join(self.precompute_path, 'default.pkl')
self.load_data()
self.build_model()
def load_data(self):
def tuple_constructor(loader, node):
return tuple(loader.construct_sequence(node))
yaml.SafeLoader.add_constructor('tag:yaml.org,2002:python/tuple', tuple_constructor)
path = pkg_resources.resource_stream(__name__, os.path.join(self.path, 'infos.yaml'))
self.infos = yaml.safe_load(path)
if 'out' not in self.infos['model']:
self.infos['model']['out'] = self.infos['data_utils']['num_cases']
if 'width' not in self.infos['model']:
if 'network_width' in self.infos['model']:
self.infos['model']['width'] = self.infos['model']['network_width']
if 'depth' not in self.infos['model']:
if 'network_depth' in self.infos['model']:
self.infos['model']['depth'] = self.infos['model']['network_depth'] - 1
# self.infos['model']['width'] = 800
# self.infos['model']['depth'] = 8
def build_model(self):
self.model = PINN(self.infos['model']).to(self.device)
if self.use_weights:
state_dict = torch.load(self.weights_path, map_location=self.device)
is_data_parallel = any('module' in key for key in state_dict.keys())
is_compiled = any('_orig_mod' in key for key in state_dict.keys())
if is_data_parallel:
state_dict = {key.replace("module.", ""): value for key, value in state_dict.items()}
if is_compiled:
state_dict = {key.replace("_orig_mod.", ""): value for key, value in state_dict.items()}
self.model.load_state_dict(state_dict)
self.model.to(self.precision)
if self.compile_model:
try:
self.model = torch.compile(self.model)
except Exception as e:
print(e)
print('Compiling did not work but do not worry, it will work without it.')
print('You need pytorch 2.0 for compiling and Linux.')
def evaluate_network_pde(self):
self.x_pde.requires_grad = True
self.y_pde.requires_grad = True
self.H = self.model.h(self.x_pde, self.y_pde)
self.DH = calculate_laplace(self.H, self.x_pde, self.y_pde).detach().to(self.precision)
self.DHtDH = torch.matmul(self.DH.t(), self.DH)
self.Dht = self.DH.t()
self.x_pde.requires_grad = False
self.y_pde.requires_grad = False
self.H = self.H.detach()
def evaluate_network_bc(self):
with torch.no_grad():
self.H_bc = self.model.h(self.x_bc, self.y_bc).to(self.precision)
self.Ht_bc = self.H_bc.t()
ones_Hbc = torch.ones(self.H_bc.shape[0], 1, device=self.device).to(self.precision)
self.Ht_bc_ones = (self.Ht_bc @ ones_Hbc).t()
def load_precomputed_data(self):
with open(self.precompute_file, 'rb') as f:
self.LHSs, self.RHSs, self.H, self.DH, self.Dht, self.DHtDH, self.H_bc, self.Ht_bc, self.Ht_bc_ones, self.NdO, self.NO = format_input(
pickle.load(f), self.precision, self.device, reshape=False)
if self.verbose > 0:
print('Pre-Computed data_utils loaded from storage.')
def precompute_LHS_RHS(self):
self.NO = self.DH.shape[0]
self.NdO = self.H_bc.shape[0]
M = torch.eye(self.NdO, device=self.device, dtype=self.precision) - \
torch.ones(self.NdO, device=self.device, dtype=self.precision) / self.NdO
lambdas = torch.tensor(self.lambdas_pde, device=self.device, dtype=self.precision).view(-1, 1, 1)
self.LHSs = lambdas / self.NO * self.DHtDH + \
1 / self.NdO * torch.matmul(self.Ht_bc, torch.matmul(M, self.H_bc))
self.RHSs = lambdas / self.NO * self.Dht
if self.verbose > 0:
print('Pre-Computed data_utils calculated.')
def save_precomputed_data(self):
with open(self.precompute_file, 'wb') as file:
pickle.dump(
[self.LHSs, self.RHSs, self.H, self.DH, self.Dht, self.DHtDH, self.H_bc, self.Ht_bc, self.Ht_bc_ones, self.NdO, self.NO],
file)
if self.verbose > 0:
print('Pre-Computed stored.')
def precompute(self, x_pde, y_pde, x_bc, y_bc, name=None, save=False, load=False):
"""
This method is used for precomputing of the data based on the given coordinates.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
name : str, optiona | (device='cuda', precision=torch.float32, verbose=False, use_weights=True, compile_model=True, lambdas_pde=None, seed=0) | [
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|
43,186 | fast_poisson_solver.solver | __init__ | null | def __init__(self, device='cuda', precision=torch.float32, verbose=False,
use_weights=True, compile_model=True, lambdas_pde=None, seed=0):
if torch.cuda.is_available():
torch.backends.cuda.matmul.allow_tf32 = False
torch.backends.cudnn.allow_tf32 = False
if lambdas_pde is None:
lambdas_pde = [2 ** -12]
self.path = os.path.join('resources', 'final.pt')
self.verbose = verbose
self.precision = precision
self.device = device if torch.cuda.is_available() else 'cpu'
self.use_weights = use_weights
self.compile_model = compile_model
self.lambdas_pde = lambdas_pde
self.seed = seed
random.seed(self.seed)
np.random.seed(self.seed)
torch.manual_seed(self.seed)
self.n_lambdas = len(self.lambdas_pde)
# The losses for all the different values of lambda are put in those arrays
self.Ls = np.zeros(self.n_lambdas)
self.Ls_pde = np.zeros(self.n_lambdas)
self.Ls_bc = np.zeros(self.n_lambdas)
if self.path.endswith('.pt'):
self.weights_input = True
self.weights_path = pkg_resources.resource_stream(__name__, self.path)
self.path = os.path.join(*os.path.split(self.path)[:1])
else:
self.weights_input = False
# Path to the where the pre-computed data_utils will be saved.
self.precompute_path = 'precomputed-resources'
if not os.path.isdir(self.precompute_path):
os.makedirs(self.precompute_path)
self.precompute_file = os.path.join(self.precompute_path, 'default.pkl')
self.load_data()
self.build_model()
| (self, device='cuda', precision=torch.float32, verbose=False, use_weights=True, compile_model=True, lambdas_pde=None, seed=0) | [
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|
43,187 | fast_poisson_solver.solver | build_model | null | def build_model(self):
self.model = PINN(self.infos['model']).to(self.device)
if self.use_weights:
state_dict = torch.load(self.weights_path, map_location=self.device)
is_data_parallel = any('module' in key for key in state_dict.keys())
is_compiled = any('_orig_mod' in key for key in state_dict.keys())
if is_data_parallel:
state_dict = {key.replace("module.", ""): value for key, value in state_dict.items()}
if is_compiled:
state_dict = {key.replace("_orig_mod.", ""): value for key, value in state_dict.items()}
self.model.load_state_dict(state_dict)
self.model.to(self.precision)
if self.compile_model:
try:
self.model = torch.compile(self.model)
except Exception as e:
print(e)
print('Compiling did not work but do not worry, it will work without it.')
print('You need pytorch 2.0 for compiling and Linux.')
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|
43,188 | fast_poisson_solver.solver | evaluate_network_bc | null | def evaluate_network_bc(self):
with torch.no_grad():
self.H_bc = self.model.h(self.x_bc, self.y_bc).to(self.precision)
self.Ht_bc = self.H_bc.t()
ones_Hbc = torch.ones(self.H_bc.shape[0], 1, device=self.device).to(self.precision)
self.Ht_bc_ones = (self.Ht_bc @ ones_Hbc).t()
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|
43,189 | fast_poisson_solver.solver | evaluate_network_pde | null | def evaluate_network_pde(self):
self.x_pde.requires_grad = True
self.y_pde.requires_grad = True
self.H = self.model.h(self.x_pde, self.y_pde)
self.DH = calculate_laplace(self.H, self.x_pde, self.y_pde).detach().to(self.precision)
self.DHtDH = torch.matmul(self.DH.t(), self.DH)
self.Dht = self.DH.t()
self.x_pde.requires_grad = False
self.y_pde.requires_grad = False
self.H = self.H.detach()
| (self) | [
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|
43,190 | fast_poisson_solver.solver | load_data | null | def load_data(self):
def tuple_constructor(loader, node):
return tuple(loader.construct_sequence(node))
yaml.SafeLoader.add_constructor('tag:yaml.org,2002:python/tuple', tuple_constructor)
path = pkg_resources.resource_stream(__name__, os.path.join(self.path, 'infos.yaml'))
self.infos = yaml.safe_load(path)
if 'out' not in self.infos['model']:
self.infos['model']['out'] = self.infos['data_utils']['num_cases']
if 'width' not in self.infos['model']:
if 'network_width' in self.infos['model']:
self.infos['model']['width'] = self.infos['model']['network_width']
if 'depth' not in self.infos['model']:
if 'network_depth' in self.infos['model']:
self.infos['model']['depth'] = self.infos['model']['network_depth'] - 1
# self.infos['model']['width'] = 800
# self.infos['model']['depth'] = 8
| (self) | [
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]
|
43,191 | fast_poisson_solver.solver | load_precomputed_data | null | def load_precomputed_data(self):
with open(self.precompute_file, 'rb') as f:
self.LHSs, self.RHSs, self.H, self.DH, self.Dht, self.DHtDH, self.H_bc, self.Ht_bc, self.Ht_bc_ones, self.NdO, self.NO = format_input(
pickle.load(f), self.precision, self.device, reshape=False)
if self.verbose > 0:
print('Pre-Computed data_utils loaded from storage.')
| (self) | [
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|
43,192 | fast_poisson_solver.solver | precompute |
This method is used for precomputing of the data based on the given coordinates.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
name : str, optional
Name used for saving or loading the precomputed data.
If no name is provided, the default name will be used. Default is None.
save : bool, optional
Specifies whether the precomputed data should be saved.
If True, the data will be saved using the provided `name`. Default is True.
load : bool, optional
Specifies whether the precomputed data with the provided `name` should be loaded.
If True, the method will attempt to load the data with the given name. Default is True.
| def precompute(self, x_pde, y_pde, x_bc, y_bc, name=None, save=False, load=False):
"""
This method is used for precomputing of the data based on the given coordinates.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the partial differential equation (PDE).
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
name : str, optional
Name used for saving or loading the precomputed data.
If no name is provided, the default name will be used. Default is None.
save : bool, optional
Specifies whether the precomputed data should be saved.
If True, the data will be saved using the provided `name`. Default is True.
load : bool, optional
Specifies whether the precomputed data with the provided `name` should be loaded.
If True, the method will attempt to load the data with the given name. Default is True.
"""
t0 = time.perf_counter()
if name is not None:
self.precompute_file = os.path.join(self.precompute_path, name + f'.pkl')
self.x_pde, self.y_pde, self.x_bc, self.y_bc = format_input([x_pde, y_pde, x_bc, y_bc],
self.precision, self.device)
self.x_tot = torch.cat([self.x_pde, self.x_bc], dim=0)
self.y_tot = torch.cat([self.y_pde, self.y_bc], dim=0)
assert torch.min(self.x_tot) >= 0 and torch.max(
self.x_tot) <= 1, 'x coordinates should be in [0, 1]. Please rescale.'
assert torch.min(self.y_tot) >= 0 and torch.max(
self.y_tot) <= 1, 'y coordinates should be in [0, 1]. Please rescale.'
if load and os.path.isfile(self.precompute_file):
self.load_precomputed_data()
else:
self.evaluate_network_pde()
self.evaluate_network_bc()
self.precompute_LHS_RHS()
if save:
self.save_precomputed_data()
# First time running torch.linalg.solve() is very slow, so we run it once here to get rid of the delay
torch.linalg.solve(
torch.rand(self.LHSs[0].shape).to(self.device).to(self.precision),
torch.rand(self.LHSs[0].shape[0], 1).to(self.device).to(self.precision))
t3 = time.perf_counter()
if self.verbose > 0:
print('\nPre-Computing Successful:', t3 - t0, 'seconds')
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|
43,193 | fast_poisson_solver.solver | precompute_LHS_RHS | null | def precompute_LHS_RHS(self):
self.NO = self.DH.shape[0]
self.NdO = self.H_bc.shape[0]
M = torch.eye(self.NdO, device=self.device, dtype=self.precision) - \
torch.ones(self.NdO, device=self.device, dtype=self.precision) / self.NdO
lambdas = torch.tensor(self.lambdas_pde, device=self.device, dtype=self.precision).view(-1, 1, 1)
self.LHSs = lambdas / self.NO * self.DHtDH + \
1 / self.NdO * torch.matmul(self.Ht_bc, torch.matmul(M, self.H_bc))
self.RHSs = lambdas / self.NO * self.Dht
if self.verbose > 0:
print('Pre-Computed data_utils calculated.')
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|
43,194 | fast_poisson_solver.solver | save_precomputed_data | null | def save_precomputed_data(self):
with open(self.precompute_file, 'wb') as file:
pickle.dump(
[self.LHSs, self.RHSs, self.H, self.DH, self.Dht, self.DHtDH, self.H_bc, self.Ht_bc, self.Ht_bc_ones, self.NdO, self.NO],
file)
if self.verbose > 0:
print('Pre-Computed stored.')
| (self) | [
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|
43,195 | fast_poisson_solver.solver | solve |
This method is used to solve the PDE with the provided source function and boundary condition.
Parameters
----------
f : tensor/array/list
The source function for the PDE.
bc : tensor/array/list
The boundary condition for the PDE.
Returns
-------
tuple
The tuple contains the following elements:
u_pred : tensor
The complete solution of the PDE.
u_pde_pred : tensor
The solution of the PDE inside the domain.
u_bc_pred : tensor
The solution for the boundary condition.
f_pred : tensor
The predicted source function.
runtime : float
The time it took the method to run in seconds.
| def solve(self, f, bc):
"""
This method is used to solve the PDE with the provided source function and boundary condition.
Parameters
----------
f : tensor/array/list
The source function for the PDE.
bc : tensor/array/list
The boundary condition for the PDE.
Returns
-------
tuple
The tuple contains the following elements:
u_pred : tensor
The complete solution of the PDE.
u_pde_pred : tensor
The solution of the PDE inside the domain.
u_bc_pred : tensor
The solution for the boundary condition.
f_pred : tensor
The predicted source function.
runtime : float
The time it took the method to run in seconds.
"""
self.f, self.bc = format_input([f, bc], self.precision, self.device)
w_outs = []
biases = np.empty(len(self.lambdas_pde))
t0 = time.perf_counter()
RHSs = torch.matmul(self.RHSs, self.f)
self.bct_ones = torch.sum(self.bc).reshape(1, 1)
for i, l in enumerate(self.lambdas_pde):
self.w_out = torch.linalg.solve(self.LHSs[i], RHSs[i])
self.bias = - 1 / self.NdO * (self.Ht_bc_ones @ self.w_out - self.bct_ones)
# Just calculates the loss if multiple lambdas are provided to find the best one.
if self.n_lambdas > 1:
u_pred_bc = torch.matmul(self.H_bc, self.w_out) + self.bias
f_pred = torch.matmul(self.DH, self.w_out)
self.Ls_pde[i] = torch.mean((f_pred - self.f) ** 2).item()
self.Ls_bc[i] = torch.mean((u_pred_bc - self.bc) ** 2).item()
self.Ls[i] = self.Ls_pde[i] + self.Ls_bc[i]
w_outs.append(self.w_out)
biases[i] = self.bias
if self.n_lambdas > 1:
minimum = np.argmin(self.Ls)
self.lambda_pde = self.lambdas_pde[minimum]
self.w_out = w_outs[minimum]
self.bias = biases[minimum]
else:
self.lambda_pde = self.lambdas_pde[0]
self.u_pde_pred = torch.add(torch.matmul(self.H, self.w_out), self.bias)
self.f_pred = torch.matmul(self.DH, self.w_out)
self.u_bc_pred = torch.matmul(self.H_bc, self.w_out) + self.bias
self.u_pred = torch.cat([self.u_pde_pred, self.u_bc_pred])
t1 = time.perf_counter()
if self.verbose > 0:
print('\nRun Successful:', t1 - t0, 'seconds\n')
return self.u_pred, self.u_pde_pred, self.u_bc_pred, self.f_pred, t1 - t0
| (self, f, bc) | [
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|
43,196 | fast_poisson_solver.analyze | analyze |
Analyze the performance of a Poisson equation solver by comparing predictions with true or numerical values.
This function calculates various error metrics including Mean Squared Error (MSE), Root Mean Squared Error (RMSE),
Mean Absolute Error (MAE), Relative Mean Absolute Error (rMSE), Structural Similarity Index (SSIM),
Peak Signal-to-Noise Ratio (PSNR), and R-Squared (R2) for each of the source term (f), solution (u), and
boundary condition (bc) predictions.
The predicted source term 'f_pred' and boundary condition 'u_bc_pred' are compared with the true source term 'f'
and true boundary condition 'u_bc'. If provided, the predicted solution 'u_pred' is compared with the numerical
solution 'u_num'.
Parameters
----------
f_pred : array-like
The predicted source term by the solver. Can be a list, numpy array or PyTorch tensor.
f : array-like
The true source term of the Poisson equation. Can be a list, numpy array or PyTorch tensor.
u_bc_pred : array-like
The predicted solution for the boundary condition. Can be a list, numpy array or PyTorch tensor.
u_bc : array-like
The true boundary condition. Can be a list, numpy array or PyTorch tensor.
u_pred : array-like, optional
The predicted solution of the Poisson equation. Can be a list, numpy array or PyTorch tensor (default is None).
u_num : array-like, optional
The numerical solution of the Poisson equation. Can be a list, numpy array or PyTorch tensor (default is None).
normalize : bool, optional
If True, normalize the input arrays before calculating the error metrics (default is True).
Returns
-------
dict
A dictionary containing the calculated error metrics for the corresponding part of the Poisson equation.
'u'
A dictionary containing the error metrics for the predicted solution 'u_pred' compared to the numerical
solution 'u_num' (only if 'u_num' and 'u_pred' are provided).
'f'
A dictionary containing the error metrics for the predicted source term 'f_pred' compared to the true
source term 'f'.
'bc'
A dictionary containing the error metrics for the predicted boundary condition 'u_bc_pred' compared to the
true boundary condition 'u_bc'.
| def analyze(f_pred, f, u_bc_pred, u_bc, u_pred=None, u_num=None, normalize=True):
"""
Analyze the performance of a Poisson equation solver by comparing predictions with true or numerical values.
This function calculates various error metrics including Mean Squared Error (MSE), Root Mean Squared Error (RMSE),
Mean Absolute Error (MAE), Relative Mean Absolute Error (rMSE), Structural Similarity Index (SSIM),
Peak Signal-to-Noise Ratio (PSNR), and R-Squared (R2) for each of the source term (f), solution (u), and
boundary condition (bc) predictions.
The predicted source term 'f_pred' and boundary condition 'u_bc_pred' are compared with the true source term 'f'
and true boundary condition 'u_bc'. If provided, the predicted solution 'u_pred' is compared with the numerical
solution 'u_num'.
Parameters
----------
f_pred : array-like
The predicted source term by the solver. Can be a list, numpy array or PyTorch tensor.
f : array-like
The true source term of the Poisson equation. Can be a list, numpy array or PyTorch tensor.
u_bc_pred : array-like
The predicted solution for the boundary condition. Can be a list, numpy array or PyTorch tensor.
u_bc : array-like
The true boundary condition. Can be a list, numpy array or PyTorch tensor.
u_pred : array-like, optional
The predicted solution of the Poisson equation. Can be a list, numpy array or PyTorch tensor (default is None).
u_num : array-like, optional
The numerical solution of the Poisson equation. Can be a list, numpy array or PyTorch tensor (default is None).
normalize : bool, optional
If True, normalize the input arrays before calculating the error metrics (default is True).
Returns
-------
dict
A dictionary containing the calculated error metrics for the corresponding part of the Poisson equation.
'u'
A dictionary containing the error metrics for the predicted solution 'u_pred' compared to the numerical
solution 'u_num' (only if 'u_num' and 'u_pred' are provided).
'f'
A dictionary containing the error metrics for the predicted source term 'f_pred' compared to the true
source term 'f'.
'bc'
A dictionary containing the error metrics for the predicted boundary condition 'u_bc_pred' compared to the
true boundary condition 'u_bc'.
"""
if u_num is None or u_pred is None:
u_num = [0]
u_pred = [0]
u_comparison = False
else:
u_comparison = True
f, f_pred, u_pred, u_bc_pred, u_num, u_bc = format_input([f, f_pred, u_pred, u_bc_pred, u_num, u_bc], as_array=True)
f, f_pred, u_pred, u_bc_pred, u_num, u_bc = [v.reshape(-1) for v in [f, f_pred, u_pred, u_bc_pred, u_num, u_bc]]
if normalize:
bv = u_bc[0]
else:
bv = 0
def analyze_struct(image1, image2, bv):
image1_ = image1 - bv
image2_ = image2 - bv
maximum = np.max(image1_)
minimum = np.min(image1_)
if len(np.unique(image1_)) != 1 and normalize:
image1_ = (image1_ - minimum) / (maximum - minimum)
image2_ = (image2_ - minimum) / (maximum - minimum)
range = 1
else:
range = np.min((maximum - minimum, 1e-8))
ssim_value = ssim(image1_, image2_, data_range=range + 1e-8, multichannel=False, gaussian_weights=True)
psnr_value = psnr(image1_, image2_, data_range=range)
r2 = r2_score(image1_.reshape(-1), image2_.reshape(-1))
return ssim_value, psnr_value, r2
def analyze_standard(image1, image2, bv):
image1_ = image1 - bv
image2_ = image2 - bv
maximum = np.max(image1_)
minimum = np.min(image1_)
if len(np.unique(image1_)) != 1 and normalize:
image1_ = (image1_ - minimum) / (maximum - minimum)
image2_ = (image2_ - minimum) / (maximum - minimum)
mse = np.mean((image1_ - image2_) ** 2)
rmse = np.sqrt(mse)
mae = np.mean(np.abs(image1_ - image2_))
mae_r = np.mean(np.abs(image1_ - image2_)) / np.max((np.mean(np.abs(image1_)), 1e-6))
return mse, rmse, mae, mae_r
res = {}
if u_comparison:
ssim_value_u, psnr_value_u, r2_u = analyze_struct(u_num, u_pred, bv)
mse_u, rmse_u, mae_u, mae_r_u = analyze_standard(u_num, u_pred, bv)
res['u'] = {
'MSE': mse_u,
'RMSE': rmse_u,
'MAE': mae_u,
'rMAE': mae_r_u,
'SSIM': ssim_value_u,
'PSNR': psnr_value_u,
'R2': r2_u
}
ssim_value_f, psnr_valuie_f, r2_f = analyze_struct(f, f_pred, 0)
mse_f, rmse_f, mae_f, mae_r_f = analyze_standard(f, f_pred, 0)
res['f'] = {
'MSE': mse_f,
'RMSE': rmse_f,
'MAE': mae_f,
'rMAE': mae_r_f,
'SSIM': ssim_value_f,
'PSNR': psnr_valuie_f,
'R2': r2_f
}
mse_u_bc, rmse_u_bc, mae_u_bc, mae_r_bc = analyze_standard(u_bc, u_bc_pred, bv)
res['bc'] = {
'MSE': mse_u_bc,
'RMSE': rmse_u_bc,
'MAE': mae_u_bc,
'rMAE': mae_r_bc
}
return res
| (f_pred, f, u_bc_pred, u_bc, u_pred=None, u_num=None, normalize=True) | [
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|
43,197 | fast_poisson_solver.utils | bicubic_interpolate |
Performs bicubic interpolation of a two-dimensional field.
The function performs bicubic interpolation of a field, which is defined by its values `v_base` at points
`(x_pde_base, y_pde_base)` for the domain and `(x_bc_base, y_bc_base)` for the boundary. Interpolation is done
at new points `(x_pde_new, y_pde_new)` for the domain and `(x_bc_new, y_bc_new)` for the boundary.
Interpolation can be done only inside the domain, excluding the boundary, depending on the `domain` parameter.
Parameters
----------
x_pde_base : tensor/array/list
x-coordinates of the PDE base points.
y_pde_base : tensor/array/list
y-coordinates of the PDE base points.
x_bc_base : tensor/array/list
x-coordinates of the boundary base points.
y_bc_base : tensor/array/list
y-coordinates of the boundary base points.
v_base : tensor/array/list
Values of the field at the base points.
x_pde_new : tensor/array/list
x-coordinates of the new PDE points for interpolation.
y_pde_new : tensor/array/list
y-coordinates of the new PDE points for interpolation.
x_bc_new : tensor/array/list
x-coordinates of the new boundary points for interpolation.
y_bc_new : tensor/array/list
y-coordinates of the new boundary points for interpolation.
domain : bool, optional
If True, the interpolation is done only inside the domain, not on the boundary. Defaults to False.
Returns
-------
tensor/array/list
The interpolated field values at the new points.
| def bicubic_interpolate(x_pde_base, y_pde_base, x_bc_base, y_bc_base, v_base, x_pde_new, y_pde_new, x_bc_new, y_bc_new,
domain=False):
"""
Performs bicubic interpolation of a two-dimensional field.
The function performs bicubic interpolation of a field, which is defined by its values `v_base` at points
`(x_pde_base, y_pde_base)` for the domain and `(x_bc_base, y_bc_base)` for the boundary. Interpolation is done
at new points `(x_pde_new, y_pde_new)` for the domain and `(x_bc_new, y_bc_new)` for the boundary.
Interpolation can be done only inside the domain, excluding the boundary, depending on the `domain` parameter.
Parameters
----------
x_pde_base : tensor/array/list
x-coordinates of the PDE base points.
y_pde_base : tensor/array/list
y-coordinates of the PDE base points.
x_bc_base : tensor/array/list
x-coordinates of the boundary base points.
y_bc_base : tensor/array/list
y-coordinates of the boundary base points.
v_base : tensor/array/list
Values of the field at the base points.
x_pde_new : tensor/array/list
x-coordinates of the new PDE points for interpolation.
y_pde_new : tensor/array/list
y-coordinates of the new PDE points for interpolation.
x_bc_new : tensor/array/list
x-coordinates of the new boundary points for interpolation.
y_bc_new : tensor/array/list
y-coordinates of the new boundary points for interpolation.
domain : bool, optional
If True, the interpolation is done only inside the domain, not on the boundary. Defaults to False.
Returns
-------
tensor/array/list
The interpolated field values at the new points.
"""
x_pde_base, y_pde_base, x_bc_base, y_bc_base, v_base, x_pde_new, y_pde_new, x_bc_new, y_bc_new = format_input(
[x_pde_base, y_pde_base, x_bc_base, y_bc_base, v_base, x_pde_new, y_pde_new, x_bc_new, y_bc_new],
precision=v_base.dtype, device='cpu', as_array=True, reshape=True)
if domain:
x_base = x_pde_base.reshape(-1)
y_base = y_pde_base.reshape(-1)
x_new = x_pde_new.reshape(-1)
y_new = y_pde_new.reshape(-1)
else:
x_base = np.concatenate([x_pde_base, x_bc_base]).reshape(-1)
y_base = np.concatenate([y_pde_base, y_bc_base]).reshape(-1)
x_new = np.concatenate([x_pde_new, x_bc_new]).reshape(-1)
y_new = np.concatenate([y_pde_new, y_bc_new]).reshape(-1)
coordinates_base = np.array([x_base, y_base]).T
coordinates_new = np.array([x_new, y_new]).T
v_new = griddata(coordinates_base, v_base.reshape(-1), coordinates_new, method='cubic')
return v_new
| (x_pde_base, y_pde_base, x_bc_base, y_bc_base, v_base, x_pde_new, y_pde_new, x_bc_new, y_bc_new, domain=False) | [
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|
43,202 | fast_poisson_solver.utils | format_input | null | def format_input(v, precision=torch.float32, device='cpu', as_array=False, reshape=True):
if isinstance(device, str):
device = torch.device(device)
for i in range(len(v)):
if isinstance(v[i], list):
v[i] = torch.tensor(v[i], dtype=precision, device=device)
elif isinstance(v[i], np.ndarray):
v[i] = torch.tensor(v[i], dtype=precision, device=device)
elif isinstance(v[i], int) or isinstance(v[i], float):
continue
else:
v[i] = v[i].to(precision).to(device)
if reshape:
v = [v_i.reshape(-1, 1) for v_i in v]
if as_array:
v = [v_i.detach().cpu().numpy() for v_i in v]
return v
| (v, precision=torch.float32, device='cpu', as_array=False, reshape=True) | [
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|
43,203 | fast_poisson_solver.utils | minmax | null | def minmax(v1, v2=None):
if v2 is None:
v2 = v1
vmin = min((np.min(v1), np.min(v2)))
vmax = max((np.max(v1), np.max(v2)))
return vmin, vmax
| (v1, v2=None) | [
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|
43,206 | fast_poisson_solver.numeric_solver | numeric_solve |
This function numerically solves the partial differential equation (PDE) using the provided source function,
PDE coordinates, boundary condition, and boundary condition coordinates. It uses the precision specified,
measures the time taken for the operation if requested, and controls the verbosity of the output.
Parameters
----------
f : tensor/array/list
The source function for the PDE.
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
u_bc : tensor/array/list
The boundary condition for the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
precision : torch.dtype, optional
The precision to be used for the numeric solver. Default is torch.float32.
verbose : int, optional
Controls the verbosity of the output. If 0, only the solution 'u' is returned. If greater than 0,
both the solution 'u' and runtime 'delta t' are returned. Default is 1.
Returns
-------
tuple
u : tensor
The complete numeric solution of the PDE.
t : float
The runtime, i.e., the time it took the method to run in seconds.
References
----------
Zaman, M.A. "Numerical Solution of the Poisson Equation Using Finite Difference Matrix Operators",
Electronics 2022, 11, 2365. https://doi.org/10.3390/electronics11152365
See also: https://github.com/zaman13/Poisson-solver-2D
| def numeric_solve(f, x_pde, y_pde, u_bc, x_bc, y_bc, precision=torch.float32, verbose=0):
"""
This function numerically solves the partial differential equation (PDE) using the provided source function,
PDE coordinates, boundary condition, and boundary condition coordinates. It uses the precision specified,
measures the time taken for the operation if requested, and controls the verbosity of the output.
Parameters
----------
f : tensor/array/list
The source function for the PDE.
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
u_bc : tensor/array/list
The boundary condition for the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
precision : torch.dtype, optional
The precision to be used for the numeric solver. Default is torch.float32.
verbose : int, optional
Controls the verbosity of the output. If 0, only the solution 'u' is returned. If greater than 0,
both the solution 'u' and runtime 'delta t' are returned. Default is 1.
Returns
-------
tuple
u : tensor
The complete numeric solution of the PDE.
t : float
The runtime, i.e., the time it took the method to run in seconds.
References
----------
Zaman, M.A. "Numerical Solution of the Poisson Equation Using Finite Difference Matrix Operators",
Electronics 2022, 11, 2365. https://doi.org/10.3390/electronics11152365
See also: https://github.com/zaman13/Poisson-solver-2D
"""
f, x_pde, y_pde, u_bc, x_bc, y_bc = format_input([f, x_pde, y_pde, u_bc, x_bc, y_bc],
precision=precision, device="cpu", as_array=True)
dtype_map = {
torch.float32: np.float32,
torch.float64: np.float64,
# add more mappings as needed
}
precision = dtype_map.get(precision, None)
x = np.concatenate([x_pde, x_bc], axis=0)
y = np.concatenate([y_pde, y_bc], axis=0)
x_unique = np.unique(x)
y_unique = np.unique(y)
Nx = len(x_unique)
Ny = len(y_unique)
dx = x_unique[1] - x_unique[0]
dy = y_unique[1] - y_unique[0]
Dx_2d, Dy_2d, D2x_2d, D2y_2d = Diff_mat_2D(Nx, Ny)
Dx_2d = Dx_2d.astype(precision)
Dy_2d = Dy_2d.astype(precision)
D2x_2d = D2x_2d.astype(precision)
D2y_2d = D2y_2d.astype(precision)
# Construction of the system matrix and adjust the right hand vector for boundary conditions
I_sp = sp.eye(Nx * Ny).tocsr().astype(precision)
L_sys = D2x_2d / dx ** 2 + D2y_2d / dy ** 2
BD = I_sp # .tolil() # Dirichlet boundary operator
BNx = Dx_2d # .tolil() # Neumann boundary operator for x component
BNy = Dy_2d # .tolil() # Neumann boundary operator for y component
t0_run = time.perf_counter()
xy = np.concatenate([x.reshape(-1, 1), y.reshape(-1, 1)], 1)
ind = np.lexsort((xy[:, 0], xy[:, 1]))
reverse_ind = np.argsort(ind)
b_ind = [np.argwhere(ind >= len(x_pde)).reshape(-1)]
f = np.concatenate([f, u_bc], axis=0)
f = f[ind]
b_type = [0]
b_val = [u_bc[0]]
N_B = len(b_val)
# Selectively replace the rows of the system matrix that correspond to
# boundary value points. We replace these rows with
# those of the boundary operator
for m in range(N_B):
# print(f[b_ind[m]], b_val[m] )
# f[b_ind[m]] = b_val[m] # Insert boundary values at the outer boundary points
if b_type[m] == 0:
L_sys[b_ind[m], :] = BD[b_ind[m], :]
elif b_type[m] == 1:
L_sys[b_ind[m], :] = BNx[b_ind[m], :]
elif b_type[m] == 2:
L_sys[b_ind[m], :] = BNy[b_ind[m], :]
u = spsolve(L_sys, f)
u = u[reverse_ind] # reorder the solution to the original order
u = u.astype(precision)
end = time.perf_counter()
dt = end - t0_run
if verbose > 0:
print(f"Time Numeric Solver: {dt:.6f} s")
return u, dt
| (f, x_pde, y_pde, u_bc, x_bc, y_bc, precision=torch.float32, verbose=0) | [
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|
43,209 | fast_poisson_solver.plotter | plot |
This function is used to plot the predicted Machine Learning solution of the PDE,
the true source function, and the predicted source function.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
show_points: bool, optional
Whether to show the points used to train the model. Default is False.
| def plot(x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, grid=False, save=False, save_path=None, name=None, show=True,
show_points=False):
"""
This function is used to plot the predicted Machine Learning solution of the PDE,
the true source function, and the predicted source function.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
show_points: bool, optional
Whether to show the points used to train the model. Default is False.
"""
u_pred, f, f_pred, x, y, x_bc, y_bc = format_input([u_pred, f, f_pred, x_pde, y_pde, x_bc, y_bc],
precision=torch.float64, device="cpu", as_array=True)
x_tot = np.concatenate([x, x_bc])
y_tot = np.concatenate([y, y_bc])
if grid:
x_tot, y_tot, u_pred = process_grid_data(x_tot, y_tot, u_pred)
x, y, f, f_pred = process_grid_data(x, y, f, f_pred)
vmin_u, vmax_u = minmax(u_pred)
vmin_f, vmax_f = minmax(f_pred, f)
fig, axs = plt.subplots(2, 3, figsize=(10, 8), dpi=400, tight_layout=True, sharey='row', sharex='col')
axs[0][0].text(-0.15, 0.5, 'Potential', ha='center', va='center', rotation='vertical', fontsize=16,
fontweight='bold')
axs[1][0].text(-0.15, 0.5, 'Source Function', ha='center', va='center', rotation='vertical', fontsize=16,
fontweight='bold')
plot_subplot(axs[0][1], x_tot, y_tot, u_pred, 'Machine Learning', vmin_u, vmax_u, cb_pad=0.03, grid=grid)
plot_subplot(axs[1][0], x, y, f, '', vmin_f, vmax_f, cb_pad=0.08, grid=grid, show_points=show_points)
plot_subplot(axs[1][1], x, y, f_pred, '', vmin_f, vmax_f, cb_pad=0.08, grid=grid)
plot_subplot(axs[1][2], x, y, (f_pred - f), '', cb_pad=0.08, cb_ztick=True, grid=grid)
axs[0][0].set_ylabel('y', labelpad=-10, fontsize=14)
axs[1][0].set_ylabel('y', labelpad=-10, fontsize=14)
axs[1][0].set_xlabel('x', labelpad=-15, fontsize=14)
axs[1][1].set_xlabel('x', labelpad=-15, fontsize=14)
axs[1][2].set_xlabel('x', labelpad=-15, fontsize=14)
if save:
if not os.path.isdir(save_path):
os.makedirs(save_path, exist_ok=True)
plt.savefig(os.path.join(save_path, name + '.pdf'), bbox_inches="tight")
plt.savefig(os.path.join(save_path, name + '.png'), bbox_inches="tight")
if show:
plt.show()
plt.close()
| (x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, grid=False, save=False, save_path=None, name=None, show=True, show_points=False) | [
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|
43,210 | fast_poisson_solver.plotter | plot_comparison |
This function is used to plot and compare the numeric solution, the predicted Machine Learning solution,
and the residual between the two. It also shows the true source function, the predicted source function,
and the residual between these two.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
u_num : tensor/array/list
The numeric solution of the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
show_points: bool, optional
Whether to show the points of the data. Default is False.
| def plot_comparison(x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, u_num,
grid=False, save=False, save_path=None, name=None, show=True,
show_points=False):
"""
This function is used to plot and compare the numeric solution, the predicted Machine Learning solution,
and the residual between the two. It also shows the true source function, the predicted source function,
and the residual between these two.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
u_num : tensor/array/list
The numeric solution of the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
show_points: bool, optional
Whether to show the points of the data. Default is False.
"""
u_pred, u_num, f, f_pred, x, y, x_bc, y_bc = format_input([u_pred, u_num, f, f_pred, x_pde, y_pde, x_bc, y_bc],
precision=torch.float64, device="cpu", as_array=True)
x_tot = np.concatenate([x, x_bc])
y_tot = np.concatenate([y, y_bc])
if grid:
x_tot, y_tot, u_num, u_pred = process_grid_data(x_tot, y_tot, u_num, u_pred)
x, y, f, f_pred = process_grid_data(x, y, f, f_pred)
vmin_u, vmax_u = minmax(u_pred, u_num)
vmin_f, vmax_f = minmax(f_pred, f)
fig, axs = plt.subplots(2, 3, figsize=(10, 8), dpi=400, tight_layout=True, sharey='row', sharex='col')
axs[0][0].text(-0.15, 0.5, 'Potential', ha='center', va='center', rotation='vertical', fontsize=16,
fontweight='bold')
axs[1][0].text(-0.15, 0.5, 'Source Function', ha='center', va='center', rotation='vertical', fontsize=16,
fontweight='bold')
plot_subplot(axs[0][0], x_tot, y_tot, u_num, 'Numeric', vmin_u, vmax_u, cb_pad=0.03, grid=grid)
plot_subplot(axs[0][1], x_tot, y_tot, u_pred, 'Machine Learning', vmin_u, vmax_u, cb_pad=0.03, grid=grid)
plot_subplot(axs[0][2], x_tot, y_tot, (u_pred - u_num), 'Residual', cb_pad=0.03, cb_ztick=True, grid=grid)
plot_subplot(axs[1][0], x, y, f, '', vmin_f, vmax_f, cb_pad=0.08, grid=grid, show_points=show_points)
plot_subplot(axs[1][1], x, y, f_pred, '', vmin_f, vmax_f, cb_pad=0.08, grid=grid)
plot_subplot(axs[1][2], x, y, (f_pred - f), '', cb_pad=0.08, cb_ztick=True, grid=grid)
axs[0][0].set_ylabel('y', labelpad=-10, fontsize=14)
axs[1][0].set_ylabel('y', labelpad=-10, fontsize=14)
axs[1][0].set_xlabel('x', labelpad=-15, fontsize=14)
axs[1][1].set_xlabel('x', labelpad=-15, fontsize=14)
axs[1][2].set_xlabel('x', labelpad=-15, fontsize=14)
if save:
if not os.path.isdir(save_path):
os.makedirs(save_path, exist_ok=True)
plt.savefig(os.path.join(save_path, name + '.pdf'), bbox_inches="tight")
plt.savefig(os.path.join(save_path, name + '.png'), bbox_inches="tight")
if show:
plt.show()
plt.close()
# np.save(os.path.join(save_path, name + '_residual.npy'), (u_pred - u_num).reshape(solver.grid_size, solver.grid_size))
| (x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, u_num, grid=False, save=False, save_path=None, name=None, show=True, show_points=False) | [
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|
43,211 | fast_poisson_solver.plotter | plot_side_by_side |
This function is used to plot and compare the numeric solution, the predicted Machine Learning solution,
and the residual between the two. It also shows the true source function, the predicted source function,
and the residual between these two.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
u_num : tensor/array/list
The numeric solution of the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
| def plot_side_by_side(x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, u_num,
grid=False, save=False, save_path=None, name=None, show=True):
"""
This function is used to plot and compare the numeric solution, the predicted Machine Learning solution,
and the residual between the two. It also shows the true source function, the predicted source function,
and the residual between these two.
Parameters
----------
x_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
y_pde : tensor/array/list
Coordinates that lie inside the domain and define the behavior of the PDE.
x_bc : tensor/array/list
Coordinates of the boundary condition.
y_bc : tensor/array/list
Coordinates of the boundary condition.
u_pred : tensor/array/list
The predicted solution of the PDE using Machine Learning.
f : tensor/array/list
The true source function for the PDE.
f_pred : tensor/array/list
The predicted source function for the PDE.
u_num : tensor/array/list
The numeric solution of the PDE.
grid : bool, optional
If True, the data is arranged into a grid and plotted as an image.
If False, tricontourf is used to create a contour plot. Default is False.
save : bool, optional
Whether to save the image. The image is saved in both .pdf and .png formats. Default is False.
save_path : str, optional
Path where the image will be saved. Used only if `save` is True. Default is None.
name : str, optional
Name of the image file. Used only if `save` is True. Default is None.
show : bool, optional
Whether to display the plot. Default is False.
"""
u_pred, u_num, f, f_pred, x, y, x_bc, y_bc = format_input([u_pred, u_num, f, f_pred, x_pde, y_pde, x_bc, y_bc],
precision=torch.float64, device="cpu", as_array=True)
x_tot = np.concatenate([x, x_bc])
y_tot = np.concatenate([y, y_bc])
if grid:
x_tot, y_tot, u_num, u_pred = process_grid_data(x_tot, y_tot, u_num, u_pred)
x, y, f, f_pred = process_grid_data(x, y, f, f_pred)
vmin_u, vmax_u = minmax(u_pred, u_num)
vmin_f, vmax_f = minmax(f_pred, f)
fig, ax = plt.subplots(1, 2, figsize=(10, 8), dpi=400, tight_layout=True, sharey='row', sharex='col')
ax[0].tricontourf(x_tot.reshape(-1), y_tot.reshape(-1), u_num.reshape(-1), 200, cmap='jet', vmin=vmin_u,
vmax=vmax_u)
ax[1].tricontourf(x_tot.reshape(-1), y_tot.reshape(-1), u_pred.reshape(-1), 200, cmap='jet', vmin=vmin_u,
vmax=vmax_u)
font_name = "Calibri" if "Calibri" in fm.findSystemFonts(fontpaths=None, fontext='ttf') else None
ax[0].set_title('Numeric (5s)', fontsize=30, fontweight='bold', fontname=font_name, pad=20)
ax[1].set_title('Ours (0.003s)', fontsize=30, fontweight='bold', fontname=font_name, pad=20)
ax[0].set_aspect('equal', adjustable='box')
ax[1].set_aspect('equal', adjustable='box')
ax[0].axis('off')
ax[1].axis('off')
plt.text(1, -0.06, '400x400 Grid', ha='right', va='bottom', transform=plt.gca().transAxes)
if save:
if not os.path.isdir(save_path):
os.makedirs(save_path, exist_ok=True)
plt.savefig(os.path.join(save_path, name + '.pdf'), bbox_inches="tight")
plt.savefig(os.path.join(save_path, name + '.png'), bbox_inches="tight")
if show:
plt.show()
plt.close()
# np.save(os.path.join(save_path, name + '_residual.npy'), (u_pred - u_num).reshape(solver.grid_size, solver.grid_size))
| (x_pde, y_pde, x_bc, y_bc, u_pred, f, f_pred, u_num, grid=False, save=False, save_path=None, name=None, show=True) | [
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|
43,212 | fast_poisson_solver.plotter | plot_subplot | null | def plot_subplot(ax, x, y, v, title, vmin=None, vmax=None, cb_pad=0.018, cb_ztick=False, grid=False, show_points=False):
if vmin is None:
vmin = min((np.min(v), 0))
if vmax is None:
vmax = max((np.max(v), 0))
if grid:
c = ax.imshow(v, cmap='jet', vmin=vmin, vmax=vmax, extent=(0, 1, 0, 1), origin='lower')
else:
c = ax.tricontourf(x.reshape(-1), y.reshape(-1), v.reshape(-1), 100, cmap='jet', vmin=vmin,
vmax=vmax) # , extent=(0, 1, 0, 1))
if show_points:
ax.scatter(x, y, s=1, c='black', marker='.', alpha=0.5)
if title != '':
ax.set_title(title, fontsize=16, pad=12, fontweight='bold')
# ax.set_xlim(0, 1)
# ax.set_ylim(0, 1)
ax.set_aspect('equal', adjustable='box')
ax.set_xticks((0, 1), labels=('0', '1'), fontsize=14)
ax.set_yticks((0, 1), labels=('0', '1'), fontsize=14)
for spine in ax.spines.values():
spine.set_visible(False)
cb = plt.colorbar(ScalarMappable(norm=c.norm, cmap=c.cmap), ax=ax, extendrect=True, pad=cb_pad,
location='bottom', shrink=0.8)
cb.outline.set_visible(False)
if cb_ztick:
cb.set_ticks([vmin, 0, vmax], labels=[f'{vmin:.4f}', '0', f'{vmax:.4f}'], fontsize=15)
else:
cb.set_ticks([vmin, vmax], labels=[f'{vmin:.4f}', f'{vmax:.4f}'], fontsize=15)
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|
43,215 | fast_poisson_solver.utils | process_grid_data | null | def process_grid_data(x, y, z1, z2=None):
x_num = len(np.unique(x))
y_num = len(np.unique(y))
if z2 is not None:
x, y, [z1, z2] = sort_ascend(x, y, [z1, z2])
z1 = z1.reshape(x_num, y_num)
z2 = z2.reshape(x_num, y_num)
return x, y, z1, z2
else:
x, y, [z1] = sort_ascend(x, y, [z1])
z1 = z1.reshape(x_num, y_num)
return x, y, z1
| (x, y, z1, z2=None) | [
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|
43,216 | skimage.metrics.simple_metrics | peak_signal_noise_ratio |
Compute the peak signal to noise ratio (PSNR) for an image.
Parameters
----------
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
Test image.
data_range : int, optional
The data range of the input image (distance between minimum and
maximum possible values). By default, this is estimated from the image
data-type.
Returns
-------
psnr : float
The PSNR metric.
Notes
-----
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_psnr`` to
``skimage.metrics.peak_signal_noise_ratio``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
| def peak_signal_noise_ratio(image_true, image_test, *, data_range=None):
"""
Compute the peak signal to noise ratio (PSNR) for an image.
Parameters
----------
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
Test image.
data_range : int, optional
The data range of the input image (distance between minimum and
maximum possible values). By default, this is estimated from the image
data-type.
Returns
-------
psnr : float
The PSNR metric.
Notes
-----
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_psnr`` to
``skimage.metrics.peak_signal_noise_ratio``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
"""
check_shape_equality(image_true, image_test)
if data_range is None:
if image_true.dtype != image_test.dtype:
warn(
"Inputs have mismatched dtype. Setting data_range based on "
"image_true."
)
dmin, dmax = dtype_range[image_true.dtype.type]
true_min, true_max = np.min(image_true), np.max(image_true)
if true_max > dmax or true_min < dmin:
raise ValueError(
"image_true has intensity values outside the range expected "
"for its data type. Please manually specify the data_range."
)
if true_min >= 0:
# most common case (255 for uint8, 1 for float)
data_range = dmax
else:
data_range = dmax - dmin
image_true, image_test = _as_floats(image_true, image_test)
err = mean_squared_error(image_true, image_test)
return 10 * np.log10((data_range**2) / err)
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|
43,217 | sklearn.metrics._regression | r2_score | :math:`R^2` (coefficient of determination) regression score function.
Best possible score is 1.0 and it can be negative (because the
model can be arbitrarily worse). In the general case when the true y is
non-constant, a constant model that always predicts the average y
disregarding the input features would get a :math:`R^2` score of 0.0.
In the particular case when ``y_true`` is constant, the :math:`R^2` score
is not finite: it is either ``NaN`` (perfect predictions) or ``-Inf``
(imperfect predictions). To prevent such non-finite numbers to pollute
higher-level experiments such as a grid search cross-validation, by default
these cases are replaced with 1.0 (perfect predictions) or 0.0 (imperfect
predictions) respectively. You can set ``force_finite`` to ``False`` to
prevent this fix from happening.
Note: when the prediction residuals have zero mean, the :math:`R^2` score
is identical to the
:func:`Explained Variance score <explained_variance_score>`.
Read more in the :ref:`User Guide <r2_score>`.
Parameters
----------
y_true : array-like of shape (n_samples,) or (n_samples, n_outputs)
Ground truth (correct) target values.
y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs)
Estimated target values.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
multioutput : {'raw_values', 'uniform_average', 'variance_weighted'}, array-like of shape (n_outputs,) or None, default='uniform_average'
Defines aggregating of multiple output scores.
Array-like value defines weights used to average scores.
Default is "uniform_average".
'raw_values' :
Returns a full set of scores in case of multioutput input.
'uniform_average' :
Scores of all outputs are averaged with uniform weight.
'variance_weighted' :
Scores of all outputs are averaged, weighted by the variances
of each individual output.
.. versionchanged:: 0.19
Default value of multioutput is 'uniform_average'.
force_finite : bool, default=True
Flag indicating if ``NaN`` and ``-Inf`` scores resulting from constant
data should be replaced with real numbers (``1.0`` if prediction is
perfect, ``0.0`` otherwise). Default is ``True``, a convenient setting
for hyperparameters' search procedures (e.g. grid search
cross-validation).
.. versionadded:: 1.1
Returns
-------
z : float or ndarray of floats
The :math:`R^2` score or ndarray of scores if 'multioutput' is
'raw_values'.
Notes
-----
This is not a symmetric function.
Unlike most other scores, :math:`R^2` score may be negative (it need not
actually be the square of a quantity R).
This metric is not well-defined for single samples and will return a NaN
value if n_samples is less than two.
References
----------
.. [1] `Wikipedia entry on the Coefficient of determination
<https://en.wikipedia.org/wiki/Coefficient_of_determination>`_
Examples
--------
>>> from sklearn.metrics import r2_score
>>> y_true = [3, -0.5, 2, 7]
>>> y_pred = [2.5, 0.0, 2, 8]
>>> r2_score(y_true, y_pred)
0.948...
>>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
>>> y_pred = [[0, 2], [-1, 2], [8, -5]]
>>> r2_score(y_true, y_pred,
... multioutput='variance_weighted')
0.938...
>>> y_true = [1, 2, 3]
>>> y_pred = [1, 2, 3]
>>> r2_score(y_true, y_pred)
1.0
>>> y_true = [1, 2, 3]
>>> y_pred = [2, 2, 2]
>>> r2_score(y_true, y_pred)
0.0
>>> y_true = [1, 2, 3]
>>> y_pred = [3, 2, 1]
>>> r2_score(y_true, y_pred)
-3.0
>>> y_true = [-2, -2, -2]
>>> y_pred = [-2, -2, -2]
>>> r2_score(y_true, y_pred)
1.0
>>> r2_score(y_true, y_pred, force_finite=False)
nan
>>> y_true = [-2, -2, -2]
>>> y_pred = [-2, -2, -2 + 1e-8]
>>> r2_score(y_true, y_pred)
0.0
>>> r2_score(y_true, y_pred, force_finite=False)
-inf
| def mean_absolute_error(
y_true, y_pred, *, sample_weight=None, multioutput="uniform_average"
):
"""Mean absolute error regression loss.
Read more in the :ref:`User Guide <mean_absolute_error>`.
Parameters
----------
y_true : array-like of shape (n_samples,) or (n_samples, n_outputs)
Ground truth (correct) target values.
y_pred : array-like of shape (n_samples,) or (n_samples, n_outputs)
Estimated target values.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
multioutput : {'raw_values', 'uniform_average'} or array-like of shape \
(n_outputs,), default='uniform_average'
Defines aggregating of multiple output values.
Array-like value defines weights used to average errors.
'raw_values' :
Returns a full set of errors in case of multioutput input.
'uniform_average' :
Errors of all outputs are averaged with uniform weight.
Returns
-------
loss : float or ndarray of floats
If multioutput is 'raw_values', then mean absolute error is returned
for each output separately.
If multioutput is 'uniform_average' or an ndarray of weights, then the
weighted average of all output errors is returned.
MAE output is non-negative floating point. The best value is 0.0.
Examples
--------
>>> from sklearn.metrics import mean_absolute_error
>>> y_true = [3, -0.5, 2, 7]
>>> y_pred = [2.5, 0.0, 2, 8]
>>> mean_absolute_error(y_true, y_pred)
0.5
>>> y_true = [[0.5, 1], [-1, 1], [7, -6]]
>>> y_pred = [[0, 2], [-1, 2], [8, -5]]
>>> mean_absolute_error(y_true, y_pred)
0.75
>>> mean_absolute_error(y_true, y_pred, multioutput='raw_values')
array([0.5, 1. ])
>>> mean_absolute_error(y_true, y_pred, multioutput=[0.3, 0.7])
0.85...
"""
y_type, y_true, y_pred, multioutput = _check_reg_targets(
y_true, y_pred, multioutput
)
check_consistent_length(y_true, y_pred, sample_weight)
output_errors = np.average(np.abs(y_pred - y_true), weights=sample_weight, axis=0)
if isinstance(multioutput, str):
if multioutput == "raw_values":
return output_errors
elif multioutput == "uniform_average":
# pass None as weights to np.average: uniform mean
multioutput = None
return np.average(output_errors, weights=multioutput)
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|
43,219 | skimage.metrics._structural_similarity | structural_similarity |
Compute the mean structural similarity index between two images.
Please pay attention to the `data_range` parameter with floating-point images.
Parameters
----------
im1, im2 : ndarray
Images. Any dimensionality with same shape.
win_size : int or None, optional
The side-length of the sliding window used in comparison. Must be an
odd value. If `gaussian_weights` is True, this is ignored and the
window size will depend on `sigma`.
gradient : bool, optional
If True, also return the gradient with respect to im2.
data_range : float, optional
The data range of the input image (difference between maximum and
minimum possible values). By default, this is estimated from the image
data type. This estimate may be wrong for floating-point image data.
Therefore it is recommended to always pass this scalar value explicitly
(see note below).
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
gaussian_weights : bool, optional
If True, each patch has its mean and variance spatially weighted by a
normalized Gaussian kernel of width sigma=1.5.
full : bool, optional
If True, also return the full structural similarity image.
Other Parameters
----------------
use_sample_covariance : bool
If True, normalize covariances by N-1 rather than, N where N is the
number of pixels within the sliding window.
K1 : float
Algorithm parameter, K1 (small constant, see [1]_).
K2 : float
Algorithm parameter, K2 (small constant, see [1]_).
sigma : float
Standard deviation for the Gaussian when `gaussian_weights` is True.
Returns
-------
mssim : float
The mean structural similarity index over the image.
grad : ndarray
The gradient of the structural similarity between im1 and im2 [2]_.
This is only returned if `gradient` is set to True.
S : ndarray
The full SSIM image. This is only returned if `full` is set to True.
Notes
-----
If `data_range` is not specified, the range is automatically guessed
based on the image data type. However for floating-point image data, this
estimate yields a result double the value of the desired range, as the
`dtype_range` in `skimage.util.dtype.py` has defined intervals from -1 to
+1. This yields an estimate of 2, instead of 1, which is most often
required when working with image data (as negative light intensities are
nonsensical). In case of working with YCbCr-like color data, note that
these ranges are different per channel (Cb and Cr have double the range
of Y), so one cannot calculate a channel-averaged SSIM with a single call
to this function, as identical ranges are assumed for each channel.
To match the implementation of Wang et al. [1]_, set `gaussian_weights`
to True, `sigma` to 1.5, `use_sample_covariance` to False, and
specify the `data_range` argument.
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_ssim`` to
``skimage.metrics.structural_similarity``.
References
----------
.. [1] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P.
(2004). Image quality assessment: From error visibility to
structural similarity. IEEE Transactions on Image Processing,
13, 600-612.
https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf,
:DOI:`10.1109/TIP.2003.819861`
.. [2] Avanaki, A. N. (2009). Exact global histogram specification
optimized for structural similarity. Optical Review, 16, 613-621.
:arxiv:`0901.0065`
:DOI:`10.1007/s10043-009-0119-z`
| def structural_similarity(
im1,
im2,
*,
win_size=None,
gradient=False,
data_range=None,
channel_axis=None,
gaussian_weights=False,
full=False,
**kwargs,
):
"""
Compute the mean structural similarity index between two images.
Please pay attention to the `data_range` parameter with floating-point images.
Parameters
----------
im1, im2 : ndarray
Images. Any dimensionality with same shape.
win_size : int or None, optional
The side-length of the sliding window used in comparison. Must be an
odd value. If `gaussian_weights` is True, this is ignored and the
window size will depend on `sigma`.
gradient : bool, optional
If True, also return the gradient with respect to im2.
data_range : float, optional
The data range of the input image (difference between maximum and
minimum possible values). By default, this is estimated from the image
data type. This estimate may be wrong for floating-point image data.
Therefore it is recommended to always pass this scalar value explicitly
(see note below).
channel_axis : int or None, optional
If None, the image is assumed to be a grayscale (single channel) image.
Otherwise, this parameter indicates which axis of the array corresponds
to channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
gaussian_weights : bool, optional
If True, each patch has its mean and variance spatially weighted by a
normalized Gaussian kernel of width sigma=1.5.
full : bool, optional
If True, also return the full structural similarity image.
Other Parameters
----------------
use_sample_covariance : bool
If True, normalize covariances by N-1 rather than, N where N is the
number of pixels within the sliding window.
K1 : float
Algorithm parameter, K1 (small constant, see [1]_).
K2 : float
Algorithm parameter, K2 (small constant, see [1]_).
sigma : float
Standard deviation for the Gaussian when `gaussian_weights` is True.
Returns
-------
mssim : float
The mean structural similarity index over the image.
grad : ndarray
The gradient of the structural similarity between im1 and im2 [2]_.
This is only returned if `gradient` is set to True.
S : ndarray
The full SSIM image. This is only returned if `full` is set to True.
Notes
-----
If `data_range` is not specified, the range is automatically guessed
based on the image data type. However for floating-point image data, this
estimate yields a result double the value of the desired range, as the
`dtype_range` in `skimage.util.dtype.py` has defined intervals from -1 to
+1. This yields an estimate of 2, instead of 1, which is most often
required when working with image data (as negative light intensities are
nonsensical). In case of working with YCbCr-like color data, note that
these ranges are different per channel (Cb and Cr have double the range
of Y), so one cannot calculate a channel-averaged SSIM with a single call
to this function, as identical ranges are assumed for each channel.
To match the implementation of Wang et al. [1]_, set `gaussian_weights`
to True, `sigma` to 1.5, `use_sample_covariance` to False, and
specify the `data_range` argument.
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_ssim`` to
``skimage.metrics.structural_similarity``.
References
----------
.. [1] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P.
(2004). Image quality assessment: From error visibility to
structural similarity. IEEE Transactions on Image Processing,
13, 600-612.
https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf,
:DOI:`10.1109/TIP.2003.819861`
.. [2] Avanaki, A. N. (2009). Exact global histogram specification
optimized for structural similarity. Optical Review, 16, 613-621.
:arxiv:`0901.0065`
:DOI:`10.1007/s10043-009-0119-z`
"""
check_shape_equality(im1, im2)
float_type = _supported_float_type(im1.dtype)
if channel_axis is not None:
# loop over channels
args = dict(
win_size=win_size,
gradient=gradient,
data_range=data_range,
channel_axis=None,
gaussian_weights=gaussian_weights,
full=full,
)
args.update(kwargs)
nch = im1.shape[channel_axis]
mssim = np.empty(nch, dtype=float_type)
if gradient:
G = np.empty(im1.shape, dtype=float_type)
if full:
S = np.empty(im1.shape, dtype=float_type)
channel_axis = channel_axis % im1.ndim
_at = functools.partial(utils.slice_at_axis, axis=channel_axis)
for ch in range(nch):
ch_result = structural_similarity(im1[_at(ch)], im2[_at(ch)], **args)
if gradient and full:
mssim[ch], G[_at(ch)], S[_at(ch)] = ch_result
elif gradient:
mssim[ch], G[_at(ch)] = ch_result
elif full:
mssim[ch], S[_at(ch)] = ch_result
else:
mssim[ch] = ch_result
mssim = mssim.mean()
if gradient and full:
return mssim, G, S
elif gradient:
return mssim, G
elif full:
return mssim, S
else:
return mssim
K1 = kwargs.pop('K1', 0.01)
K2 = kwargs.pop('K2', 0.03)
sigma = kwargs.pop('sigma', 1.5)
if K1 < 0:
raise ValueError("K1 must be positive")
if K2 < 0:
raise ValueError("K2 must be positive")
if sigma < 0:
raise ValueError("sigma must be positive")
use_sample_covariance = kwargs.pop('use_sample_covariance', True)
if gaussian_weights:
# Set to give an 11-tap filter with the default sigma of 1.5 to match
# Wang et. al. 2004.
truncate = 3.5
if win_size is None:
if gaussian_weights:
# set win_size used by crop to match the filter size
r = int(truncate * sigma + 0.5) # radius as in ndimage
win_size = 2 * r + 1
else:
win_size = 7 # backwards compatibility
if np.any((np.asarray(im1.shape) - win_size) < 0):
raise ValueError(
'win_size exceeds image extent. '
'Either ensure that your images are '
'at least 7x7; or pass win_size explicitly '
'in the function call, with an odd value '
'less than or equal to the smaller side of your '
'images. If your images are multichannel '
'(with color channels), set channel_axis to '
'the axis number corresponding to the channels.'
)
if not (win_size % 2 == 1):
raise ValueError('Window size must be odd.')
if data_range is None:
if np.issubdtype(im1.dtype, np.floating) or np.issubdtype(
im2.dtype, np.floating
):
raise ValueError(
'Since image dtype is floating point, you must specify '
'the data_range parameter. Please read the documentation '
'carefully (including the note). It is recommended that '
'you always specify the data_range anyway.'
)
if im1.dtype != im2.dtype:
warn(
"Inputs have mismatched dtypes. Setting data_range based on im1.dtype.",
stacklevel=2,
)
dmin, dmax = dtype_range[im1.dtype.type]
data_range = dmax - dmin
if np.issubdtype(im1.dtype, np.integer) and (im1.dtype != np.uint8):
warn(
"Setting data_range based on im1.dtype. "
+ f"data_range = {data_range:.0f}. "
+ "Please specify data_range explicitly to avoid mistakes.",
stacklevel=2,
)
ndim = im1.ndim
if gaussian_weights:
filter_func = gaussian
| (im1, im2, *, win_size=None, gradient=False, data_range=None, channel_axis=None, gaussian_weights=False, full=False, **kwargs) | [
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|
43,292 | plumage | get_path | Returns installation path of the theme.
Used in ``pelicanconf.py`` to dynamiccaly fetch theme location on the system.
| def get_path() -> str:
"""Returns installation path of the theme.
Used in ``pelicanconf.py`` to dynamiccaly fetch theme location on the system.
"""
return str(PLUMAGE_ROOT)
| () -> str | [
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|
43,294 | plumage.config | register_signals | null | def register_signals() -> None:
signals.initialized.connect(check_config)
signals.static_generator_finalized.connect(add_favicon_assets)
signals.content_written.connect(transform)
| () -> NoneType | [
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]
|
43,296 | mo_dots.datas | Data |
Please see https://github.com/klahnakoski/mo-dots/tree/dev/docs#data-replaces-pythons-dict
| class Data:
"""
Please see https://github.com/klahnakoski/mo-dots/tree/dev/docs#data-replaces-pythons-dict
"""
__slots__ = [SLOT]
def __init__(self, *args, **kwargs):
"""
CONSTRUCT DATA WITH GIVEN PROPERTY VALUES
"""
if args:
raise Exception("only keywords are allowed, not " + args[0].__class__.__name__)
_set(self, SLOT, kwargs)
def __bool__(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
return True
else:
return d != None
__nonzero__ = __bool__
def __contains__(self, item):
value = Data.__getitem__(self, item)
if is_data(value) or value:
return True
return False
def __iter__(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
yield from d.items()
else:
yield from d.__iter__()
def __getitem__(self, key):
if is_null(key):
return Null
if key == ".":
output = _get(self, SLOT)
if is_data(output):
return self
else:
return output
key = str(key)
d = _get(self, SLOT)
if key.find(".") >= 0:
seq = _split_field(key)
for n in seq:
if _get(d, CLASS) is NullType:
d = NullType(d, n) # OH DEAR, Null TREATS n AS PATH, NOT LITERAL
elif is_many(d):
d = [_getdefault(dd, n) for dd in d]
else:
d = _getdefault(d, n) # EVERYTHING ELSE TREATS n AS LITERAL
return to_data(d)
else:
o = d.get(key)
if is_null(o):
return NullType(d, key)
return to_data(o)
def __setitem__(self, key, value):
if key == "":
get_logger().error("key is empty string. Probably a bad idea")
if is_null(key):
return Null
if key == ".":
# SOMETHING TERRIBLE HAPPENS WHEN value IS NOT A Mapping;
# HOPEFULLY THE ONLY OTHER METHOD RUN ON self IS from_data()
v = from_data(value)
if is_many(v):
_set(self, CLASS, FlatList)
_set(self, SLOT, v)
return self
try:
d = _get(self, SLOT)
value = from_data(value)
if "." not in key:
if value is None:
d.pop(key, None)
else:
d[key] = value
return self
seq = _split_field(key)
for k in seq[:-1]:
d = _getdefault(d, k)
if is_null(value):
try:
d.pop(seq[-1], None)
except Exception as _:
pass
elif is_null(d):
d[literal_field(seq[-1])] = value
elif is_sequence(d):
for dd in d:
from_data(dd)[seq[-1]] = value
else:
d[seq[-1]] = value
return self
except Exception as e:
from mo_logs import Log
Log.error("can not set key={{key}}", key=key, cause=e)
def __getattr__(self, key):
d = _get(self, SLOT)
v = d.get(key)
t = _get(v, CLASS)
# OPTIMIZED to_data()
if t is dict:
return dict_to_data(v)
elif t in utils._null_types:
return NullType(d, key)
elif t is list:
return list_to_data(v)
elif t in generator_types:
return FlatList(list(from_data(vv) for vv in v))
else:
return v
def __setattr__(self, key, value):
d = _get(self, SLOT)
value = from_data(value)
if value is None:
d = _get(self, SLOT)
d.pop(key, None)
else:
d[key] = value
return self
def __add__(self, other):
return _iadd(_iadd({}, self), other)
def __radd__(self, other):
return _iadd(_iadd({}, other), self)
def __iadd__(self, other):
return _iadd(self, other)
def __or__(self, other):
"""
RECURSIVE COALESCE OF DATA PROPERTIES
"""
if not is_data(other):
get_logger().error("Expecting Data")
d = _get(self, SLOT)
output = Data(**d) # COPY
output.__ior__(other)
return output
def __ror__(self, other):
"""
RECURSIVE COALESCE OF DATA PROPERTIES
"""
if not is_data(other):
get_logger().error("Expecting Data")
return to_data(other).__or__(self)
def __ior__(self, other):
"""
RECURSIVE COALESCE OF DATA PROPERTIES
"""
d = _get(self, SLOT)
if not is_data(other):
if is_missing(d) or (isinstance(d, dict) and not d):
_set(self, SLOT, other)
return self
for ok, ov in other.items():
if is_null(ov):
continue
sv = to_data(d.get(ok))
if is_null(sv):
d[ok] = ov
elif is_data(sv):
d[ok] = sv | ov
return self
def __hash__(self):
d = _get(self, SLOT)
return hash_value(d)
def __eq__(self, other):
if self is other:
return True
d = _get(self, SLOT)
if _get(d, CLASS) is not dict:
return d == other
if not d and is_null(other):
return False
if not is_data(other):
return False
e = other
for k, v in d.items():
if e.get(k) != v:
return False
for k, v in e.items():
if d.get(k) != v:
return False
return True
def __ne__(self, other):
return not self.__eq__(other)
def get(self, key, default=Null):
v = self[key]
if _get(v, CLASS) == NullType:
if default is Null:
return NullType(self, key)
return default
return v
def items(self):
d = _get(self, SLOT)
return [(k, to_data(v)) for k, v in d.items() if v != None or is_data(v)]
def leaves(self, prefix=None):
"""
LIKE items() BUT RECURSIVE, AND ONLY FOR THE LEAVES (non dict) VALUES
"""
return leaves(self, prefix)
def iteritems(self):
# LOW LEVEL ITERATION, NO WRAPPING
d = _get(self, SLOT)
return ((k, to_data(v)) for k, v in d.items())
def pop(self, key, default=Null):
if is_null(key):
return Null
if key == ".":
raise NotImplemented()
key = str(key)
d = _get(self, SLOT)
if key.find(".") >= 0:
seq = _split_field(key)
for n in seq[:-1]:
if _get(d, CLASS) is NullType:
d = NullType(d, n) # OH DEAR, Null TREATS n AS PATH, NOT LITERAL
elif is_many(d):
d = [_getdefault(dd, n) for dd in d]
else:
d = _getdefault(d, n) # EVERYTHING ELSE TREATS n AS LITERAL
key = seq[-1]
o = d.get(key)
if is_null(o):
if default is Null:
return NullType(d, key)
return default
d[key] = None
return to_data(o)
def keys(self):
d = _get(self, SLOT)
return set(d.keys())
def values(self):
d = _get(self, SLOT)
return listwrap(list(d.values()))
def clear(self):
get_logger().error("clear() not supported")
def __len__(self):
d = _get(self, SLOT)
return dict.__len__(d)
def copy(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
return Data(**d)
else:
return copy(d)
def __copy__(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
return Data(**self)
else:
return copy(d)
def __deepcopy__(self, memo):
d = _get(self, SLOT)
return to_data(d | (*args, **kwargs) | [
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|
43,297 | mo_dots.datas | __add__ | null | def __add__(self, other):
return _iadd(_iadd({}, self), other)
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|
43,298 | mo_dots.datas | __bool__ | null | def __bool__(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
return True
else:
return d != None
| (self) | [
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|
43,299 | mo_dots.datas | __contains__ | null | def __contains__(self, item):
value = Data.__getitem__(self, item)
if is_data(value) or value:
return True
return False
| (self, item) | [
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|
43,300 | mo_dots.datas | __copy__ | null | def __copy__(self):
d = _get(self, SLOT)
if _get(d, CLASS) is dict:
return Data(**self)
else:
return copy(d)
| (self) | [
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|
43,301 | mo_dots.datas | __deepcopy__ | null | def __deepcopy__(self, memo):
d = _get(self, SLOT)
return to_data(deepcopy(d, memo))
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|
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