def covariance_to_internal_jacobian(external_values, constr):
r"""Jacobian of ``covariance_to_internal``.
For reference see docstring of ``jacobian_covariance_from_internal``. In
comparison to that function, however, here we want to differentiate the
reverse graph
external --> cov --> cholesky --> internal
Again use the vectors :math:`c` and :math:`x` to denote the external and
internal values, respectively. To solve for the jacobian we make use of the
identity
.. math::
\frac{\mathrm{d}x}{\mathrm{d}c} = (\frac{\mathrm{d}c}{\mathrm{d}x})^{-1}
Args:
external_values (np.ndarray): Row-wise half-vectorized covariance matrix
Returns:
deriv: The Jacobian matrix.
"""
cov = cov_params_to_matrix(external_values)
chol = robust_cholesky(cov)
internal = chol[np.tril_indices(len(chol))]
deriv = covariance_from_internal_jacobian(internal, constr=None)
deriv = np.linalg.pinv(deriv)
return deriv
def check_constraints_are_satisfied(pc, params):
"""Check that params satisfies all constraints.
This should be called before the more specialized constraints are rewritten to
linear constraints in order to get better error messages!
We let the checks pass if all "values" are np.nan. This way `process_constraints`
can be used on empty params DataFrames which is useful to construct templates for
start parameters that can be filled out by the user.
Args:
pc (list): List of constraints with processed selectors.
params (pd.DataFrame): See :ref:`params`
Raises:
ValueError if constraints are not satisfied.
"""
if params["value"].notnull().any():
for constr in pc:
typ = constr["type"]
subset = params.iloc[constr["index"]]["value"]
msg = f"{{}}:\n{subset.to_frame()}"
if typ == "covariance":
cov = cov_params_to_matrix(subset)
e, v = np.linalg.eigh(cov)
if not np.all(e > -1e-8):
raise ValueError(
msg.format("Invalid covariance parameters."))
elif typ == "sdcorr":
cov = sdcorr_params_to_matrix(subset)
dim = len(cov)
if (subset.iloc[:dim] < 0).any():
raise ValueError(
msg.format("Invalid standard deviations."))
if ((subset.iloc[dim:] < -1) | (subset.iloc[dim:] > 1)).any():
raise ValueError(msg.format("Invalid correlations."))
e, v = np.linalg.eigh(cov)
if not np.all(e > -1e-8):
raise ValueError(msg.format("Invalid sdcorr parameters."))
elif typ == "probability":
if not np.isclose(subset.sum(), 1, rtol=0.01):
raise ValueError(
msg.format("Probabilities do not sum to 1"))
if np.any(subset < 0):
raise ValueError(msg.format("Negative Probability."))
if np.any(subset > 1):
raise ValueError(msg.format("Probability larger than 1."))
elif typ == "increasing":
if np.any(np.diff(subset) < 0):
raise ValueError(
msg.format("Increasing constraint violated."))
elif typ == "decreasing":
if np.any(np.diff(subset) > 0):
raise ValueError(
msg.format("Decreasing constraint violated"))
elif typ == "linear":
# using sr.dot is important in case weights are a series in wrong order
wsum = subset.dot(constr["weights"])
if "lower_bound" in constr and wsum < constr["lower_bound"]:
raise ValueError(
msg.format(
"Lower bound of linear constraint is violated"))
elif "upper_bound" in constr and wsum > constr["upper_bound"]:
raise ValueError(
msg.format(
"Upper bound of linear constraint violated"))
elif "value" in constr and not np.isclose(
wsum, constr["value"]):
raise ValueError(
msg.format(
"Equality condition of linear constraint violated")
)
elif typ == "equality":
if len(subset.unique()) != 1:
raise ValueError(
msg.format("Equality constraint violated."))
def check_constraints_are_satisfied(flat_constraints, param_values,
param_names):
"""Check that params satisfies all constraints.
This should be called before the more specialized constraints are rewritten to
linear constraints in order to get better error messages!
We let the checks pass if all "values" are np.nan. This way `process_constraints`
can be used on empty params DataFrames which is useful to construct templates for
start parameters that can be filled out by the user.
Args:
pc (list): List of constraints with processed selectors.
params (pd.DataFrame): See :ref:`params`
Raises:
ValueError if constraints are not satisfied.
"""
# skip check if all parameters are NaN
if not np.isfinite(param_values).any():
return
for constr in flat_constraints:
typ = constr["type"]
subset = param_values[constr["index"]]
_msg = partial(_get_message, constr, param_names)
if typ == "covariance":
cov = cov_params_to_matrix(subset)
e, _ = np.linalg.eigh(cov)
if not np.all(e > -1e-8):
raise InvalidParamsError(_msg())
elif typ == "sdcorr":
cov = sdcorr_params_to_matrix(subset)
e, _ = np.linalg.eigh(cov)
if not np.all(e > -1e-8):
raise InvalidParamsError(_msg())
elif typ == "probability":
if not np.isclose(subset.sum(), 1, rtol=0.01):
explanation = "Probabilities do not sum to 1."
raise InvalidParamsError(_msg(explanation))
if np.any(subset < 0):
explanation = "There are negative Probabilities."
raise InvalidParamsError(_msg(explanation))
if np.any(subset > 1):
explanation = "There are probabilities larger than 1."
raise InvalidParamsError(_msg(explanation))
elif typ == "fixed":
if "value" in constr and not np.allclose(subset, constr["value"]):
explanation = (
"Fixing parameters to different values than their start values "
"was allowed in earlier versions of estimagic but is "
"forbidden now. ")
raise InvalidParamsError(_msg(explanation))
elif typ == "increasing":
if np.any(np.diff(subset) < 0):
raise InvalidParamsError(_msg())
elif typ == "decreasing":
if np.any(np.diff(subset) > 0):
InvalidParamsError(_msg())
elif typ == "linear":
wsum = subset.dot(constr["weights"])
if "lower_bound" in constr and wsum < constr["lower_bound"]:
explanation = "Lower bound of linear constraint is violated."
raise InvalidParamsError(_msg(explanation))
elif "upper_bound" in constr and wsum > constr["upper_bound"]:
explanation = "Upper bound of linear constraint violated"
raise InvalidParamsError(_msg(explanation))
elif "value" in constr and not np.isclose(wsum, constr["value"]):
explanation = "Equality condition of linear constraint violated"
raise InvalidParamsError(_msg(explanation))
elif typ == "equality":
if len(set(subset.tolist())) > 1:
raise InvalidParamsError(_msg())
def covariance_to_internal(external_values, constr):
"""Do a cholesky reparametrization."""
cov = cov_params_to_matrix(external_values)
chol = robust_cholesky(cov)
return chol[np.tril_indices(len(cov))]
def test_cov_params_to_matrix():
params = np.array([1, 0.1, 2, 0.2, 0.22, 3])
expected = np.array([[1, 0.1, 0.2], [0.1, 2, 0.22], [0.2, 0.22, 3]])
calculated = cov_params_to_matrix(params)
aaae(calculated, expected)