#################################################################################
# The Institute for the Design of Advanced Energy Systems Integrated Platform
# Framework (IDAES IP) was produced under the DOE Institute for the
# Design of Advanced Energy Systems (IDAES).
#
# Copyright (c) 2018-2024 by the software owners: The Regents of the
# University of California, through Lawrence Berkeley National Laboratory,
# National Technology & Engineering Solutions of Sandia, LLC, Carnegie Mellon
# University, West Virginia University Research Corporation, et al.
# All rights reserved. Please see the files COPYRIGHT.md and LICENSE.md
# for full copyright and license information.
#################################################################################
"""
This module contains utilities to provide variable and expression scaling
factors by providing an expression to calculate them via a suffix.
The main purpose of this code is to use the calculate_scaling_factors function
to calculate scaling factors to be used with the Pyomo scaling transformation or
with solvers. A user can provide a scaling_expression suffix to calculate scale
factors from existing variable scaling factors. This allows scaling factors from
a small set of fundamental variables to be propagated to the rest of the model.
The scaling_expression suffix contains Pyomo expressions with model variables.
The expressions can be evaluated with variable scaling factors in place of
variables to calculate additional scaling factors.
"""
__author__ = "John Eslick, Tim Bartholomew, Robert Parker, Andrew Lee"
import math
import sys
import scipy.sparse.linalg as spla
import scipy.linalg as la
import pyomo.environ as pyo
from pyomo.core.base.var import VarData
from pyomo.core.base.param import ParamData
from pyomo.core.expr.visitor import identify_variables
from pyomo.network import Arc
from pyomo.contrib.pynumero.interfaces.pyomo_nlp import PyomoNLP
from pyomo.contrib.pynumero.asl import AmplInterface
from pyomo.common.modeling import unique_component_name
from pyomo.core.base.constraint import ConstraintData
from pyomo.common.collections import ComponentMap, ComponentSet
from pyomo.dae import DerivativeVar
from pyomo.dae.flatten import slice_component_along_sets
from pyomo.util.calc_var_value import calculate_variable_from_constraint
from pyomo.core import expr as EXPR
from pyomo.common.numeric_types import native_types
from pyomo.core.base.units_container import _PyomoUnit
import idaes.logger as idaeslog
_log = idaeslog.getLogger(__name__)
def __none_left_mult(x, y):
"""PRIVATE FUNCTION, If x is None return None, else return x * y"""
if x is not None:
return x * y
return None
def __scale_constraint(c, v):
"""PRIVATE FUNCTION, scale Constraint c to value v"""
if c.equality:
c.set_value((c.lower * v, c.body * v))
else:
c.set_value(
(__none_left_mult(c.lower, v), c.body * v, __none_left_mult(c.upper, v))
)
def scale_arc_constraints(blk):
"""Find Arc constraints in a block and its subblocks. Then scale them based
on the minimum scaling factor of the variables in the constraint.
Args:
blk: Block in which to look for Arc constraints to scale.
Returns:
None
"""
for arc in blk.component_data_objects(Arc, descend_into=True):
arc_block = arc.expanded_block
if arc_block is None: # arc not expanded or port empty?
_log.warning(
f"{arc} has no constraints. Has the Arc expansion transform "
"been applied?"
)
continue
warning = (
"Automatic scaling for arc constraints is supported for "
"only the Equality rule. Variable {name} on Port {port} was "
"created with a different rule, so the corresponding constraint "
"on {arc_name} will not be scaled."
)
port1 = arc.ports[0]
port2 = arc.ports[1]
for name in port1.vars.keys():
if not port1.is_equality(name):
_log.warning(
warning.format(name=name, port=port1.name, arc_name=arc.name)
)
continue
if not port2.is_equality(name):
_log.warning(
warning.format(name=name, port=port2.name, arc_name=arc.name)
)
continue
con = getattr(arc_block, name + "_equality")
for i, c in con.items():
if i is None:
sf = min_scaling_factor([port1.vars[name], port2.vars[name]])
else:
sf = min_scaling_factor([port1.vars[name][i], port2.vars[name][i]])
constraint_scaling_transform(c, sf)
[docs]
def map_scaling_factor(components, default=1, warning=False, func=min, hint=None):
"""Map get_scaling_factor to an iterable of Pyomo components, and call func
on the result. This could be use, for example, to get the minimum or
maximum scaling factor of a set of components.
Args:
components: Iterable yielding Pyomo components
default: The default value used when a scaling factor is missing. The
default is default=1.
warning: Log a warning for missing scaling factors
func: The function to call on the resulting iterable of scaling factors.
The default is min().
hint: Paired with warning=True, this is a string to indicate where the
missing scaling factor was being accessed, to easier diagnose issues.
Returns:
The result of func on the set of scaling factors
"""
return func(
map(
lambda x: get_scaling_factor(
x, default=default, warning=warning, hint=hint
),
components,
)
)
[docs]
def min_scaling_factor(components, default=1, warning=True, hint=None):
"""Map get_scaling_factor to an iterable of Pyomo components, and get the
minimum scaling factor.
Args:
iter: Iterable yielding Pyomo components
default: The default value used when a scaling factor is missing. If
None, this will raise an exception when scaling factors are missing.
The default is default=1.
warning: Log a warning for missing scaling factors
hint: Paired with warning=True, this is a string to indicate where the
missing scaling factor was being accessed, to easier diagnose issues.
Returns:
Minimum scaling factor of the components in iter
"""
return map_scaling_factor(
components, default=default, warning=warning, func=min, hint=hint
)
[docs]
def propagate_indexed_component_scaling_factors(
blk, typ=None, overwrite=False, descend_into=True
):
"""Use the parent component scaling factor to set all component data object
scaling factors.
Args:
blk: The block on which to search for components
typ: Component type(s) (default=(Var, Constraint, Expression, Param))
overwrite: if a data object already has a scaling factor should it be
overwrittten (default=False)
descend_into: descend into child blocks (default=True)
"""
if typ is None:
typ = (pyo.Var, pyo.Constraint, pyo.Expression)
for c in blk.component_objects(typ, descend_into=descend_into):
if get_scaling_factor(c) is not None and c.is_indexed():
for cdat in c.values():
if overwrite or get_scaling_factor(cdat) is None:
set_scaling_factor(cdat, get_scaling_factor(c))
def calculate_scaling_factors(blk):
"""Look for calculate_scaling_factors methods and run them. This uses a
recursive function to execute the subblock calculate_scaling_factors
methods first.
"""
def cs(blk2):
"""Recursive function for to do subblocks first"""
for b in blk2.component_data_objects(pyo.Block, descend_into=False):
cs(b)
if hasattr(blk2, "calculate_scaling_factors"):
blk2.calculate_scaling_factors()
# Call recursive function to run calculate_scaling_factors on blocks from
# the bottom up.
cs(blk)
# If a scale factor is set for an indexed component, propagate it to the
# component data if a scale factor hasn't already been explicitly set
propagate_indexed_component_scaling_factors(blk)
# Use the variable scaling factors to scale the arc constraints.
scale_arc_constraints(blk)
[docs]
def set_scaling_factor(c, v, data_objects=True, overwrite=True):
"""Set a scaling factor for a model component. This function creates the
scaling_factor suffix if needed.
Args:
c: component to supply scaling factor for
v: scaling factor
data_objects: set scaling factors for indexed data objects (default=True)
overwrite: whether to overwrite an existing scaling factor
Returns:
None
"""
if isinstance(c, (float, int)):
# property packages can return 0 for material balance terms on components
# doesn't exist. This handles the case where you get a constant 0 and
# need its scale factor to scale the mass balance.
return 1
try:
suf = c.parent_block().scaling_factor
except AttributeError:
c.parent_block().scaling_factor = pyo.Suffix(direction=pyo.Suffix.EXPORT)
suf = c.parent_block().scaling_factor
if not overwrite:
try:
tmp = suf[c] # pylint: disable=unused-variable
# Able to access suffix value for c, so return without setting scaling factor
return
except KeyError:
# No value exists yet for c, go ahead and set it
pass
suf[c] = v
if data_objects and c.is_indexed():
for cdat in c.values():
if not overwrite:
try:
tmp = suf[cdat]
continue
except KeyError:
pass
suf[cdat] = v
[docs]
def get_scaling_factor(c, default=None, warning=False, exception=False, hint=None):
"""Get a component scale factor.
Args:
c: component
default: value to return if no scale factor exists (default=None)
warning: whether to log a warning if a scaling factor is not found
(default=False)
exception: whether to raise an Exception if a scaling factor is not
found (default=False)
hint: (str) a string to add to the warning or exception message to help
locate the source.
Returns:
scaling factor (float)
"""
try:
sf = c.parent_block().scaling_factor[c]
except (AttributeError, KeyError):
if not isinstance(c, (pyo.Param, ParamData)):
if hint is None:
h = ""
else:
h = f", {hint}"
if warning:
if hasattr(c, "is_component_type") and c.is_component_type():
_log.warning(f"Missing scaling factor for {c}{h}")
else:
_log.warning(f"Trying to get scaling factor for unnamed expr {h}")
if exception and default is None:
if hasattr(c, "is_component_type") and c.is_component_type():
_log.error(f"Missing scaling factor for {c}{h}")
else:
_log.error(f"Trying to get scaling factor for unnamed expr {h}")
raise
sf = default
else:
# Params can just use current value (as long it is not 0)
val = pyo.value(c)
if not val == 0:
sf = abs(1 / pyo.value(c))
else:
sf = 1
return sf
def set_and_get_scaling_factor(c, default, warning=False, exception=False, hint=None):
"""Checks whether a scaling factor exists for a component, sets the scaling factor
if it doesn't exist, then returns the scaling factor on the component (which is
the default value if it wasn't set originally).
Args:
c: component
default: default value to use for scaling factor of c if there is none
warning: whether to log a warning if a scaling factor is not found
(default=False)
exception: whether to raise an Exception if a scaling factor is not
found (default=False)
hint: (str) a string to add to the warning or exception message to help
locate the source.
Returns:
scaling factor (float)
"""
if c.is_indexed():
raise AttributeError(
f"Ambiguous which scaling factor to return for indexed component {c.name}."
)
sf = get_scaling_factor(c, warning=warning, exception=exception, hint=hint)
if sf is None:
sf = default
set_scaling_factor(c, sf, data_objects=False)
return sf
[docs]
def unset_scaling_factor(c, data_objects=True):
"""Delete a component scaling factor.
Args:
c: component
Returns:
None
"""
try:
del c.parent_block().scaling_factor[c]
except (AttributeError, KeyError):
pass # no scaling factor suffix, is fine
try:
if data_objects and c.is_indexed():
for cdat in c.values():
del cdat.parent_block().scaling_factor[cdat]
except (AttributeError, KeyError):
pass # no scaling factor suffix, is fine
def populate_default_scaling_factors(c):
"""
Method to set default scaling factors for a number of common quantities
based of typical values expressed in SI units. Values are converted to
those used by the property package using Pyomo's unit conversion tools.
"""
units = c.get_metadata().derived_units
si_scale = {
"temperature": (100 * pyo.units.K, "temperature"),
"pressure": (1e5 * pyo.units.Pa, "pressure"),
"dens_mol_phase": (100 * pyo.units.mol / pyo.units.m**3, "density_mole"),
"enth_mol": (1e4 * pyo.units.J / pyo.units.mol, "energy_mole"),
"entr_mol": (100 * pyo.units.J / pyo.units.mol / pyo.units.K, "entropy_mole"),
"fug_phase_comp": (1e4 * pyo.units.Pa, "pressure"),
"fug_coeff_phase_comp": (1 * pyo.units.dimensionless, None),
"gibbs_mol": (1e4 * pyo.units.J / pyo.units.mol, "energy_mole"),
"mole_frac_comp": (0.001 * pyo.units.dimensionless, None),
"mole_frac_phase_comp": (0.001 * pyo.units.dimensionless, None),
"mw": (1e-3 * pyo.units.kg / pyo.units.mol, "molecular_weight"),
"mw_comp": (1e-3 * pyo.units.kg / pyo.units.mol, "molecular_weight"),
"mw_phase": (1e-3 * pyo.units.kg / pyo.units.mol, "molecular_weight"),
}
for p, f in si_scale.items():
# If a default scaling factor exists, do not over write it
if p not in c.default_scaling_factor.keys():
if f[1] is not None:
v = pyo.units.convert(f[0], to_units=units[f[1]])
else:
v = f[0]
sf = 1 / (10 ** round(math.log10(pyo.value(v))))
c.set_default_scaling(p, sf)
def __set_constraint_transform_applied_scaling_factor(c, v):
"""PRIVATE FUNCTION Set the scaling factor used to transform a constraint.
This is used to keep track of scaling transformations that have been applied
to constraints.
Args:
c: component to supply scaling factor for
v: scaling factor
Returns:
None
"""
try:
c.parent_block().constraint_transformed_scaling_factor[c] = v
except AttributeError:
c.parent_block().constraint_transformed_scaling_factor = pyo.Suffix(
direction=pyo.Suffix.LOCAL
)
c.parent_block().constraint_transformed_scaling_factor[c] = v
def __unset_constraint_transform_applied_scaling_factor(c):
"""PRIVATE FUNCTION: Delete the recorded scale factor that has been used
to transform constraint c. This is used when undoing a constraint
transformation.
"""
try:
del c.parent_block().constraint_transformed_scaling_factor[c]
except AttributeError:
pass # no scaling factor suffix, is fine
except KeyError:
pass # no scaling factor is fine
[docs]
def unscaled_variables_generator(blk, descend_into=True, include_fixed=False):
"""Generator for unscaled variables
Args:
block
Yields:
variables with no scale factor
"""
for v in blk.component_data_objects(pyo.Var, descend_into=descend_into):
if v.fixed and not include_fixed:
continue
if get_scaling_factor(v) is None:
yield v
def list_unscaled_variables(
blk: pyo.Block, descend_into: bool = True, include_fixed: bool = False
):
"""
Return a list of variables which do not have a scaling factor assigned
Args:
blk: block to check for unscaled variables
descend_into: bool indicating whether to check variables in sub-blocks
include_fixed: bool indicating whether to include fixed Vars in list
Returns:
list of unscaled variable data objects
"""
return [c for c in unscaled_variables_generator(blk, descend_into, include_fixed)]
[docs]
def unscaled_constraints_generator(blk, descend_into=True):
"""Generator for unscaled constraints
Args:
block
Yields:
constraints with no scale factor
"""
for c in blk.component_data_objects(
pyo.Constraint, active=True, descend_into=descend_into
):
if (
get_scaling_factor(c) is None
and get_constraint_transform_applied_scaling_factor(c) is None
):
yield c
def list_unscaled_constraints(blk: pyo.Block, descend_into: bool = True):
"""
Return a list of constraints which do not have a scaling factor assigned
Args:
blk: block to check for unscaled constraints
descend_into: bool indicating whether to check constraints in sub-blocks
Returns:
list of unscaled constraint data objects
"""
return [c for c in unscaled_constraints_generator(blk, descend_into)]
def constraints_with_scale_factor_generator(blk, descend_into=True):
"""Generator for constraints scaled by a scaling factor, may or not have
been transformed.
Args:
block
Yields:
constraint with a scale factor, scale factor
"""
for c in blk.component_data_objects(
pyo.Constraint, active=True, descend_into=descend_into
):
s = get_scaling_factor(c)
if s is not None:
yield c, s
[docs]
def badly_scaled_var_generator(
blk, large=1e4, small=1e-3, zero=1e-10, descend_into=True, include_fixed=False
):
"""This provides a rough check for variables with poor scaling based on
their current scale factors and values. For each potentially poorly scaled
variable it returns the var and its current scaled value.
Note that while this method is a reasonable heuristic for non-negative
variables like (absolute) temperature and pressure, molar flows, etc., it
can be misleading for variables like enthalpies and fluxes.
Args:
blk: pyomo block
large: Magnitude that is considered to be too large
small: Magnitude that is considered to be too small
zero: Magnitude that is considered to be zero, variables with a value of
zero are okay, and not reported.
Yields:
variable data object, current absolute value of scaled value
"""
for v in blk.component_data_objects(pyo.Var, descend_into=descend_into):
if v.fixed and not include_fixed:
continue
val = pyo.value(v, exception=False)
if val is None:
continue
sf = get_scaling_factor(v, default=1)
sv = abs(val * sf) # scaled value
if sv > large:
yield v, sv
elif sv < zero:
continue
elif sv < small:
yield v, sv
def list_badly_scaled_variables(
blk,
large: float = 1e4,
small: float = 1e-3,
zero: float = 1e-10,
descend_into: bool = True,
include_fixed: bool = False,
):
"""Return a list of variables with poor scaling based on
their current scale factors and values. For each potentially poorly scaled
variable it returns the var and its current scaled value.
Note that while this method is a reasonable heuristic for non-negative
variables like (absolute) temperature and pressure, molar flows, etc., it
can be misleading for variables like enthalpies and fluxes.
Args:
blk: pyomo block
large: Magnitude that is considered to be too large
small: Magnitude that is considered to be too small
zero: Magnitude that is considered to be zero, variables with a value of
zero are okay, and not reported.
descend_into: bool indicating whether to check constraints in sub-blocks
include_fixed: bool indicating whether to include fixed Vars in list
Returns:
list of tuples containing (variable data object, current absolute value of scaled value)
"""
return [
c
for c in badly_scaled_var_generator(
blk, large, small, zero, descend_into, include_fixed
)
]
[docs]
def constraint_autoscale_large_jac(
m,
ignore_constraint_scaling=False,
ignore_variable_scaling=False,
max_grad=100,
min_scale=1e-6,
no_scale=False,
equality_constraints_only=False,
):
"""Automatically scale constraints based on the Jacobian. This function
imitates Ipopt's default constraint scaling. This scales constraints down
to avoid extremely large values in the Jacobian. This function also returns
the unscaled and scaled Jacobian matrixes and the Pynumero NLP which can be
used to identify the constraints and variables corresponding to the rows and
comlumns.
Args:
m: model to scale
ignore_constraint_scaling: ignore existing constraint scaling
ignore_variable_scaling: ignore existing variable scaling
max_grad: maximum value in Jacobian after scaling, subject to minimum
scaling factor restriction.
min_scale: minimum scaling factor allowed, keeps constraints from being
scaled too much.
no_scale: just calculate the Jacobian and scaled Jacobian, don't scale
anything
equality_constraints_only: Include only the equality constraints in the
Jacobian
Returns:
unscaled Jacobian CSR from, scaled Jacobian CSR from, Pynumero NLP
"""
# Pynumero requires an objective, but I don't, so let's see if we have one
n_obj = 0
for c in m.component_data_objects(pyo.Objective, active=True):
n_obj += 1
# Add an objective if there isn't one
if n_obj == 0:
dummy_objective_name = unique_component_name(m, "objective")
setattr(m, dummy_objective_name, pyo.Objective(expr=0))
# Create NLP and calculate the objective
if not AmplInterface.available():
raise RuntimeError("Pynumero not available.")
nlp = PyomoNLP(m)
if equality_constraints_only:
jac = nlp.evaluate_jacobian_eq().tocsr()
else:
jac = nlp.evaluate_jacobian().tocsr()
# Get lists of variables and constraints to translate Jacobian indexes
# save them on the NLP for later, since generating them seems to take a while
if equality_constraints_only:
nlp.clist = clist = nlp.get_pyomo_equality_constraints()
else:
nlp.clist = clist = nlp.get_pyomo_constraints()
nlp.vlist = vlist = nlp.get_pyomo_variables()
# Create a scaled Jacobian to account for variable scaling, for now ignore
# constraint scaling
jac_scaled = jac.copy()
for i, c in enumerate(clist):
for j in jac_scaled[i].indices:
v = vlist[j]
if ignore_variable_scaling:
sv = 1
else:
sv = get_scaling_factor(v, default=1)
jac_scaled[i, j] = jac_scaled[i, j] / sv
# calculate constraint scale factors
for i, c in enumerate(clist):
sc = get_scaling_factor(c, default=1)
if not no_scale:
if ignore_constraint_scaling or get_scaling_factor(c) is None:
sc = 1
row = jac_scaled[i]
for d in row.indices:
row[0, d] = abs(row[0, d])
mg = row.max()
if mg > max_grad:
sc = max(min_scale, max_grad / mg)
set_scaling_factor(c, sc)
for j in jac_scaled[i].indices:
# update the scaled jacobian
jac_scaled[i, j] = jac_scaled[i, j] * sc
# delete dummy objective
if n_obj == 0:
delattr(m, dummy_objective_name)
return jac, jac_scaled, nlp
[docs]
def get_jacobian(m, scaled=True, equality_constraints_only=False):
"""
Get the Jacobian matrix at the current model values. This function also
returns the Pynumero NLP which can be used to identify the constraints and
variables corresponding to the rows and columns.
Args:
m: model to get Jacobian from
scaled: if True return scaled Jacobian, else get unscaled
equality_constraints_only: Only include equality constraints in the
Jacobian calculated and scaled
Returns:
Jacobian matrix in Scipy CSR format, Pynumero nlp
"""
jac, jac_scaled, nlp = constraint_autoscale_large_jac(
m, no_scale=True, equality_constraints_only=equality_constraints_only
)
if scaled:
return jac_scaled, nlp
else:
return jac, nlp
def extreme_jacobian_entries(
m=None, scaled=True, large=1e4, small=1e-4, zero=1e-10, jac=None, nlp=None
):
"""
Show very large and very small Jacobian entries.
Args:
m: model
scaled: if true use scaled Jacobian
large: >= to this value is considered large
small: <= to this and >= zero is considered small
Returns:
(list of tuples), Jacobian entry, Constraint, Variable
"""
if jac is None or nlp is None:
jac, nlp = get_jacobian(m, scaled)
el = []
for i, c in enumerate(nlp.clist):
for j in jac[i].indices:
v = nlp.vlist[j]
e = abs(jac[i, j])
if (e <= small and e > zero) or e >= large:
el.append((e, c, v))
return el
[docs]
def extreme_jacobian_rows(
m=None, scaled=True, large=1e4, small=1e-4, jac=None, nlp=None
):
"""
Show very large and very small Jacobian rows. Typically indicates a badly-
scaled constraint.
Args:
m: model
scaled: if true use scaled Jacobian
large: >= to this value is considered large
small: <= to this is considered small
Returns:
(list of tuples), Row norm, Constraint
"""
# Need both jac for the linear algebra and nlp for constraint names
if jac is None or nlp is None:
jac, nlp = get_jacobian(m, scaled)
el = []
for i, c in enumerate(nlp.clist):
norm = 0
# Calculate L2 norm
for j in jac[i].indices:
norm += jac[i, j] ** 2
norm = norm**0.5
if norm <= small or norm >= large:
el.append((norm, c))
return el
[docs]
def extreme_jacobian_columns(
m=None, scaled=True, large=1e4, small=1e-4, jac=None, nlp=None
):
"""
Show very large and very small Jacobian columns. A more reliable indicator
of a badly-scaled variable than badly_scaled_var_generator.
Args:
m: model
scaled: if true use scaled Jacobian
large: >= to this value is considered large
small: <= to this is considered small
Returns:
(list of tuples), Column norm, Variable
"""
# Need both jac for the linear algebra and nlp for variable names
if jac is None or nlp is None:
jac, nlp = get_jacobian(m, scaled)
jac = jac.tocsc()
el = []
for j, v in enumerate(nlp.vlist):
norm = 0
# Calculate L2 norm
for i in jac.getcol(j).indices:
norm += jac[i, j] ** 2
norm = norm**0.5
if norm <= small or norm >= large:
el.append((norm, v))
return el
[docs]
def jacobian_cond(m=None, scaled=True, order=None, pinv=False, jac=None):
"""
Get the condition number of the scaled or unscaled Jacobian matrix of a model.
Args:
m: calculate the condition number of the Jacobian from this model.
scaled: if True use scaled Jacobian, else use unscaled
order: norm order, None = Frobenius, see scipy.sparse.linalg.norm for more
pinv: Use pseudoinverse, works for non-square matrices
jac: (optional) previously calculated Jacobian
Returns:
(float) Condition number
"""
if jac is None:
jac, _ = get_jacobian(m, scaled)
jac = jac.tocsc()
if jac.shape[0] != jac.shape[1] and not pinv:
_log.warning("Nonsquare Jacobian using pseudo inverse")
pinv = True
if not pinv:
jac_inv = spla.inv(jac)
return spla.norm(jac, order) * spla.norm(jac_inv, order)
else:
jac_inv = la.pinv(jac.toarray())
return spla.norm(jac, order) * la.norm(jac_inv, order)
def scale_time_discretization_equations(blk, time_set, time_scaling_factor):
"""
Scales time discretization equations generated via a Pyomo discretization
transformation. Also scales continuity equations for collocation methods
of discretization that require them.
Args:
blk: Block whose time discretization equations are being scaled
time_set: Time set object. For an IDAES flowsheet object fs, this is fs.time.
time_scaling_factor: Scaling factor to use for time
Returns:
None
"""
tname = time_set.local_name
# Copy and pasted from solvers.petsc.find_discretization_equations then modified
for var in blk.component_objects(pyo.Var):
if isinstance(var, DerivativeVar):
cont_set_set = ComponentSet(var.get_continuousset_list())
if time_set in cont_set_set:
if len(cont_set_set) > 1:
_log.warning(
"IDAES presently does not support automatically scaling discretization equations for "
f"second order or higher derivatives like {var.name} that are differentiated at least once with "
"respect to time. Please scale the corresponding discretization equation yourself."
)
continue
state_var = var.get_state_var()
parent_block = var.parent_block()
disc_eq = getattr(parent_block, var.local_name + "_disc_eq")
# Look for continuity equation, which exists only for collocation with certain sets of polynomials
try:
cont_eq = getattr(
parent_block, state_var.local_name + "_" + tname + "_cont_eq"
)
except AttributeError:
cont_eq = None
deriv_dict = dict(
(key, pyo.Reference(slc))
for key, slc in slice_component_along_sets(var, (time_set,))
)
state_dict = dict(
(key, pyo.Reference(slc))
for key, slc in slice_component_along_sets(state_var, (time_set,))
)
disc_dict = dict(
(key, pyo.Reference(slc))
for key, slc in slice_component_along_sets(disc_eq, (time_set,))
)
if cont_eq is not None:
cont_dict = dict(
(key, pyo.Reference(slc))
for key, slc in slice_component_along_sets(cont_eq, (time_set,))
)
for key, deriv in deriv_dict.items():
state = state_dict[key]
disc = disc_dict[key]
if cont_eq is not None:
cont = cont_dict[key]
for t in time_set:
s_state = get_scaling_factor(state[t], default=1, warning=True)
set_scaling_factor(
deriv[t], s_state / time_scaling_factor, overwrite=False
)
s_deriv = get_scaling_factor(deriv[t])
# Check time index to decide what constraints to scale
if cont_eq is None:
if t == time_set.first() or t == time_set.last():
try:
constraint_scaling_transform(
disc[t], s_deriv, overwrite=False
)
except KeyError:
# Discretization and continuity equations may or may not exist at the first or last time
# points depending on the method. Backwards skips first, forwards skips last, central skips
# both (which means the user needs to provide additional equations)
pass
else:
constraint_scaling_transform(
disc[t], s_deriv, overwrite=False
)
else:
# Lagrange-Legendre is a pain, because it has continuity equations on the edges of finite
# instead of discretization equations, but no intermediate continuity equations, so we have
# to look for both at every timepoint
try:
constraint_scaling_transform(
disc[t], s_deriv, overwrite=False
)
except KeyError:
if t != time_set.first():
constraint_scaling_transform(
cont[t], s_state, overwrite=False
)
class CacheVars(object):
"""
A class for saving the values of variables then reloading them,
usually after they have been used to perform some solve or calculation.
"""
def __init__(self, vardata_list):
self.vars = vardata_list
self.cache = [None for var in self.vars]
def __enter__(self):
for i, var in enumerate(self.vars):
self.cache[i] = var.value
return self
def __exit__(self, ex_type, ex_value, ex_traceback):
for i, var in enumerate(self.vars):
var.set_value(self.cache[i])
class FlattenedScalingAssignment(object):
"""
A class to assist in the calculation of scaling factors when a
variable-constraint assignment can be constructed, especially when
the variables and constraints are all indexed by some common set(s).
"""
def __init__(self, scaling_factor, varconlist=None, nominal_index=()):
"""
Args:
scaling_factor: A Pyomo scaling_factor Suffix that will hold all
the scaling factors calculated
varconlist: A list of variable, constraint tuples. These variables
and constraints should be indexed by the same sets,
so they may need to be references-to-slices along some
common sets.
nominal_index: The index of variables and constraints to access
when a calculation needs to be performed using
data objects.
"""
if varconlist is None:
varconlist = []
self.scaling_factor = scaling_factor
self.nominal_index = nominal_index
if nominal_index is None or nominal_index == ():
self.dim = 0
else:
try:
self.dim = len(nominal_index)
except TypeError:
self.dim = 1
varlist = []
conlist = []
for var, con in varconlist:
varlist.append(var)
conlist.append(con)
self.varlist = varlist
self.conlist = conlist
data_getter = self.get_representative_data_object
var_con_data_list = [
(data_getter(var), data_getter(con)) for var, con in varconlist
]
con_var_data_list = [
(data_getter(con), data_getter(var)) for var, con in varconlist
]
self.var2con = ComponentMap(var_con_data_list)
self.con2var = ComponentMap(con_var_data_list)
def get_representative_data_object(self, obj):
"""
Gets a data object from an object of the appropriate dimension
"""
if self.dim == 0:
# In this way, obj can be a data object and this class can be
# used even if the assignment is not between "flattened components"
return obj
else:
nominal_index = self.nominal_index
return obj[nominal_index]
def calculate_variable_scaling_factor(self, var, include_fixed=False):
"""
Calculates the scaling factor of a variable based on the
constraint assigned to it. Loads each variable in that constraint
with its nominal value (inverse of scaling factor), calculates
the value of the target variable from the constraint, then sets
its scaling factor to the inverse of the calculated value.
"""
vardata = self.get_representative_data_object(var)
condata = self.var2con[vardata]
scaling_factor = self.scaling_factor
in_constraint = list(
identify_variables(
condata.expr,
include_fixed=include_fixed,
)
)
source_vars = [v for v in in_constraint if v is not vardata]
nominal_source = [1 / scaling_factor[var] for var in source_vars]
with CacheVars(in_constraint):
for v, nom_val in zip(source_vars, nominal_source):
v.set_value(nom_val)
# This assumes that target var is initialized to a somewhat
# reasonable value
calculate_variable_from_constraint(vardata, condata)
nominal_target = vardata.value
if nominal_target == 0:
target_factor = 1.0
else:
target_factor = abs(1 / nominal_target)
if self.dim == 0:
scaling_factor[var] = target_factor
else:
for v in var.values():
scaling_factor[v] = target_factor
def set_constraint_scaling_factor(self, con):
"""
Sets the scaling factor of a constraint to that of its assigned variable
"""
condata = self.get_representative_data_object(con)
vardata = self.con2var[condata]
scaling_factor = self.scaling_factor
var_factor = scaling_factor[vardata]
if self.dim == 0:
scaling_factor[con] = var_factor
else:
for c in con.values():
scaling_factor[c] = var_factor
def set_derivative_factor_from_state(self, deriv, nominal_wrt=1.0):
"""
Sets the scaling factor for a DerivativeVar equal to the factor for
its state var at every index. This method needs access to the
get_state_var method, so deriv must be an actual DerivativeVar,
not a reference-to-slice.
"""
scaling_factor = self.scaling_factor
state_var = deriv.get_state_var()
for index, dv in deriv.items():
state_data = state_var[index]
nominal_state = 1 / scaling_factor[state_data]
nominal_deriv = nominal_state / nominal_wrt
scaling_factor[dv] = 1 / nominal_deriv
# New functions
def set_scaling_from_default(
component,
missing: float = None,
overwrite: bool = False,
descend_into: bool = True,
components_to_scale: "List of Pyomo component types" = None,
):
"""
Set scaling factor(s) for given component from default scaling factor dictionary associated with the parent model.
This function accepts any type of Pyomo component as an input, and will attempt to apply scaling factors to all
attached types of components listed in 'components_to_scale' argument. A warning will be logged for any
component which does not have a default scaling factor assigned.
Args:
component: Pyomo component to apply scaling factors to.
missing: value to use if a component does not have a default scaling factor assigned (default=None).
overwrite: bool indicating whether to overwrite existing scaling factors (default=False).
descend_into: bool indicating whether to descend into child Blocks if component is a Block (default=True).
components_to_scale: list of Pyomo component types to apply scaling factors to if component is a Block (default=[Var]).
Returns:
None
"""
if components_to_scale is None:
components_to_scale = [pyo.Var]
if isinstance(component, pyo.Block):
for c in component.component_data_objects(
components_to_scale, descend_into=descend_into
):
set_scaling_from_default(c, missing=missing, overwrite=overwrite)
elif component.is_indexed():
for k in component.values():
set_scaling_from_default(k, missing=missing, overwrite=overwrite)
else:
if not overwrite:
# If there is already a scaling factor, we can end here
sf = get_scaling_factor(
component, default=None, warning=False, exception=False
)
if sf is not None:
return
parent = component.parent_block()
try:
dsf = parent.get_default_scaling(
component.parent_component().local_name, index=component.index()
)
except AttributeError:
dsf = None
_log.warning(
f"{component.name} block missing 'get_default_scaling()' method, no scaling factor assigned."
)
if dsf is not None:
set_scaling_factor(component, dsf, overwrite=overwrite)
elif missing is not None:
_log.warning(
f"No default scaling factor found for {component.name}, assigning value of {missing} instead."
)
set_scaling_factor(component, missing, overwrite=overwrite)
else:
_log.warning(
f"No default scaling factor found for {component.name}, no scaling factor assigned."
)
def set_variable_scaling_from_current_value(
component, descend_into: bool = True, overwrite: bool = False
):
"""
Set scaling factor for variables based on current value. Component argument can be either a Pyomo Var or Block.
In case of a Block, this function will attempt to scale all variables in the block using their current value,
Args:
component: component to scale
overwrite: bool indicating whether to overwrite existing scaling factors (default=False).
descend_into: bool indicating whether to descend into child Blocks if component is a Block (default=True).
Returns:
None
"""
if isinstance(component, pyo.Block):
for c in component.component_data_objects(pyo.Var, descend_into=descend_into):
set_variable_scaling_from_current_value(c, overwrite=overwrite)
elif component.is_indexed():
for k in component.values():
set_variable_scaling_from_current_value(k, overwrite=overwrite)
elif not isinstance(component, VarData):
raise TypeError(
f"Invalid component type {component.name} (type:{type(component)}). "
"component argument to set_variable_scaling_from_current_value must be "
"either a Pyomo Var or Block."
)
else:
if not overwrite:
# If there is already a scaling factor, we can end here
sf = get_scaling_factor(
component, default=None, warning=False, exception=False
)
if sf is not None:
return
try:
val = pyo.value(component)
if val == 0:
_log.warning(
f"Component {component.name} currently has a value of 0; no scaling factor assigned."
)
else:
set_scaling_factor(component, 1 / val, overwrite=overwrite)
except ValueError:
_log.warning(
f"Component {component.name} does not have a current value; no scaling factor assigned."
)
# TODO: Deprecate in favor of new walker
class NominalValueExtractionVisitor(EXPR.StreamBasedExpressionVisitor):
"""
Expression walker for collecting scaling factors in an expression and determining the
expected value of the expression using the scaling factors as nominal inputs.
Returns a list of expected values for each additive term in the expression.
In order to properly assess the expected value of terms within functions, the sign
of each term is maintained throughout thus returned values may be negative. Functions
using this walker should handle these appropriately.
"""
def __init__(self, warning: bool = True):
"""
Visitor class used to determine nominal values of all terms in an expression based on
scaling factors assigned to the associated variables. Do not use this class directly.
Args:
warning: bool indicating whether to log a warning when a
missing scaling factors is encountered (default=True)
Notes
-----
This class inherits from the :class:`StreamBasedExpressionVisitor` to implement
a walker that returns the nominal value corresponding to all additive terms in an
expression.
There are class attributes (dicts) that map the expression node type to the
particular method that should be called to return the nominal value of the node based
on the nominal value of its child arguments. This map is used in exitNode.
"""
super().__init__()
self.warning = warning
def _get_magnitude_base_type(self, node):
# Get scaling factor for node
sf = get_scaling_factor(node, default=1, warning=self.warning)
# Try to determine expected sign of node
if isinstance(node, pyo.Var):
ub = node.ub
lb = node.lb
domain = node.domain
# To avoid NoneType errors, assign dummy values in place of None
if ub is None:
# No upper bound, take a positive value
ub = 1000
if lb is None:
# No lower bound, take a negative value
lb = -1000
if lb >= 0 or domain in [
pyo.NonNegativeReals,
pyo.PositiveReals,
pyo.PositiveIntegers,
pyo.NonNegativeIntegers,
pyo.Boolean,
pyo.Binary,
]:
# Strictly positive
sign = 1
elif ub <= 0 or domain in [
pyo.NegativeReals,
pyo.NonPositiveReals,
pyo.NegativeIntegers,
pyo.NonPositiveIntegers,
]:
# Strictly negative
sign = -1
else:
# Unbounded, see if there is a current value
try:
value = pyo.value(node)
except ValueError:
value = None
if value is not None and value < 0:
# Assigned negative value, assume value will remain negative
sign = -1
else:
# Either a positive value or no value, assume positive
sign = 1
elif isinstance(node, pyo.Param):
domain = node.domain
if domain in [
pyo.NonNegativeReals,
pyo.PositiveReals,
pyo.PositiveIntegers,
pyo.NonNegativeIntegers,
pyo.Boolean,
pyo.Binary,
]:
# Strictly positive
sign = 1
elif domain in [
pyo.NegativeReals,
pyo.NonPositiveReals,
pyo.NegativeIntegers,
pyo.NonPositiveIntegers,
]:
# Strictly negative
sign = -1
else:
# Unbounded, see if there is a current value
try:
value = pyo.value(node)
except ValueError:
value = None
if value is not None and value < 0:
# Assigned negative value, assume value will remain negative
sign = -1
else:
# Either a positive value or no value, assume positive
sign = 1
else:
# No idea, assume positive
sign = 1
try:
return [sign / sf]
except ZeroDivisionError:
raise ValueError(
f"Found component {node.name} with scaling factor of 0. "
"Scaling factors should not be set to 0 as this results in "
"numerical failures."
)
def _get_nominal_value_for_sum_subexpression(self, child_nominal_values):
return sum(i for i in child_nominal_values)
def _get_nominal_value_for_sum(self, node, child_nominal_values):
# For sums, collect all child values into a list
sf = []
for i in child_nominal_values:
for j in i:
sf.append(j)
return sf
def _get_nominal_value_for_product(self, node, child_nominal_values):
assert len(child_nominal_values) == 2
mag = []
for i in child_nominal_values[0]:
for j in child_nominal_values[1]:
mag.append(i * j)
return mag
def _get_nominal_value_for_division(self, node, child_nominal_values):
assert len(child_nominal_values) == 2
numerator = self._get_nominal_value_for_sum_subexpression(
child_nominal_values[0]
)
denominator = self._get_nominal_value_for_sum_subexpression(
child_nominal_values[1]
)
if denominator == 0:
# Assign a nominal value of 1 so that we can continue
denominator = 1
# Log a warning for the user
_log.debug(
"Nominal value of 0 found in denominator of division expression. "
"Assigning a value of 1. You should check you scaling factors and models to "
"ensure there are no values of 0 that can appear in these functions."
)
return [numerator / denominator]
def _get_nominal_value_for_power(self, node, child_nominal_values):
assert len(child_nominal_values) == 2
# Use the absolute value of the base term to avoid possible complex numbers
base = abs(
self._get_nominal_value_for_sum_subexpression(child_nominal_values[0])
)
exponent = self._get_nominal_value_for_sum_subexpression(
child_nominal_values[1]
)
return [base**exponent]
def _get_nominal_value_single_child(self, node, child_nominal_values):
assert len(child_nominal_values) == 1
return child_nominal_values[0]
def _get_nominal_value_abs(self, node, child_nominal_values):
assert len(child_nominal_values) == 1
return [abs(i) for i in child_nominal_values[0]]
def _get_nominal_value_negation(self, node, child_nominal_values):
assert len(child_nominal_values) == 1
return [-i for i in child_nominal_values[0]]
def _get_nominal_value_for_unary_function(self, node, child_nominal_values):
assert len(child_nominal_values) == 1
func_name = node.getname()
# TODO: Some of these need the absolute value of the nominal value (e.g. sqrt)
func_nominal = self._get_nominal_value_for_sum_subexpression(
child_nominal_values[0]
)
func = getattr(math, func_name)
try:
return [func(func_nominal)]
except ValueError:
raise ValueError(
f"Evaluation error occurred when getting nominal value in {func_name} "
f"expression with input {func_nominal}. You should check you scaling factors "
f"and model to address any numerical issues or scale this constraint manually."
)
def _get_nominal_value_expr_if(self, node, child_nominal_values):
assert len(child_nominal_values) == 3
return child_nominal_values[1] + child_nominal_values[2]
def _get_nominal_value_external_function(self, node, child_nominal_values):
# First, need to get expected magnitudes of input terms, which may be sub-expressions
input_mag = []
for i in child_nominal_values:
if isinstance(i[0], str):
# Sometimes external functions might have string arguments
# Check here, and return the string if true
input_mag.append(i[0])
else:
input_mag.append(self._get_nominal_value_for_sum_subexpression(i))
# Next, create a copy of the external function with expected magnitudes as inputs
newfunc = node.create_node_with_local_data(input_mag)
# Evaluate new function and return the absolute value
return [pyo.value(newfunc)]
node_type_method_map = {
EXPR.EqualityExpression: _get_nominal_value_for_sum,
EXPR.InequalityExpression: _get_nominal_value_for_sum,
EXPR.RangedExpression: _get_nominal_value_for_sum,
EXPR.SumExpression: _get_nominal_value_for_sum,
EXPR.NPV_SumExpression: _get_nominal_value_for_sum,
EXPR.ProductExpression: _get_nominal_value_for_product,
EXPR.MonomialTermExpression: _get_nominal_value_for_product,
EXPR.NPV_ProductExpression: _get_nominal_value_for_product,
EXPR.DivisionExpression: _get_nominal_value_for_division,
EXPR.NPV_DivisionExpression: _get_nominal_value_for_division,
EXPR.PowExpression: _get_nominal_value_for_power,
EXPR.NPV_PowExpression: _get_nominal_value_for_power,
EXPR.NegationExpression: _get_nominal_value_negation,
EXPR.NPV_NegationExpression: _get_nominal_value_negation,
EXPR.AbsExpression: _get_nominal_value_abs,
EXPR.NPV_AbsExpression: _get_nominal_value_abs,
EXPR.UnaryFunctionExpression: _get_nominal_value_for_unary_function,
EXPR.NPV_UnaryFunctionExpression: _get_nominal_value_for_unary_function,
EXPR.Expr_ifExpression: _get_nominal_value_expr_if,
EXPR.ExternalFunctionExpression: _get_nominal_value_external_function,
EXPR.NPV_ExternalFunctionExpression: _get_nominal_value_external_function,
EXPR.LinearExpression: _get_nominal_value_for_sum,
}
def exitNode(self, node, data):
"""Callback for :class:`pyomo.core.current.StreamBasedExpressionVisitor`. This
method is called when moving back up the tree in a depth first search."""
# first check if the node is a leaf
nodetype = type(node)
if nodetype in native_types:
return [node]
node_func = self.node_type_method_map.get(nodetype, None)
if node_func is not None:
return node_func(self, node, data)
elif not node.is_expression_type():
# this is a leaf, but not a native type
if nodetype is _PyomoUnit:
return [1]
else:
return self._get_magnitude_base_type(node)
# might want to add other common types here
# not a leaf - check if it is a named expression
if (
hasattr(node, "is_named_expression_type")
and node.is_named_expression_type()
):
return self._get_nominal_value_single_child(node, data)
raise TypeError(
f"An unhandled expression node type: {str(nodetype)} was encountered while "
f"retrieving the scaling factor of expression {str(node)}"
)
def set_constraint_scaling_max_magnitude(
component, warning: bool = True, overwrite: bool = False, descend_into: bool = True
):
"""
Set scaling factors for constraints using maximum expected magnitude of additive terms in expression.
Scaling factor for constraints will be 1 / max(abs(nominal value)).
Args:
component: a Pyomo component to set constraint scaling factors for.
warning: bool indicating whether to log a warning if a missing variable scaling factor is
found (default=True).
overwrite: bool indicating whether to overwrite existing scaling factors (default=False).
descend_into: bool indicating whether function should descend into child Blocks
if component is a Pyomo Block (default=True).
Returns:
None
"""
def _set_sf_max_mag(c):
nominal = NominalValueExtractionVisitor(warning=warning).walk_expression(c.expr)
# 0 terms will never be the largest absolute magnitude, so we can ignore them
max_mag = max(abs(i) for i in nominal)
set_scaling_factor(c, max_mag, overwrite=overwrite)
if isinstance(component, pyo.Block):
# Iterate over all constraint datas and call this method on each
for c in component.component_data_objects(
pyo.Constraint, descend_into=descend_into
):
set_constraint_scaling_max_magnitude(
c, warning=warning, overwrite=overwrite
)
elif component.is_indexed():
for i in component:
_set_sf_max_mag(component[i])
else:
_set_sf_max_mag(component)
def set_constraint_scaling_min_magnitude(
component, warning: bool = True, overwrite: bool = False, descend_into: bool = True
):
"""
Set scaling factors for constraints using minimum expected magnitude of additive terms in expression.
Scaling factor for constraints will be 1 / min(abs(nominal value)).
Args:
component: a Pyomo component to set constraint scaling factors for.
warning: bool indicating whether to log a warning if a missing variable scaling factor is
found (default=True).
overwrite: bool indicating whether to overwrite existing scaling factors (default=False).
descend_into: bool indicating whether function should descend into child Blocks
if component is a Pyomo Block (default=True).
Returns:
None
"""
def _set_sf_min_mag(c):
nominal = NominalValueExtractionVisitor(warning=warning).walk_expression(c.expr)
# Ignore any 0 terms - we will assume they do not contribute to scaling
min_mag = min(abs(i) for i in [j for j in nominal if j != 0])
set_scaling_factor(c, min_mag, overwrite=overwrite)
if isinstance(component, pyo.Block):
# Iterate over all constraint datas and call this method on each
for c in component.component_data_objects(
pyo.Constraint, descend_into=descend_into
):
set_constraint_scaling_min_magnitude(
c, warning=warning, overwrite=overwrite
)
elif component.is_indexed():
for i in component:
_set_sf_min_mag(component[i])
else:
_set_sf_min_mag(component)
def set_constraint_scaling_harmonic_magnitude(
component, warning: bool = True, overwrite: bool = False, descend_into: bool = True
):
"""
Set scaling factors for constraints using the harmonic sum of the expected magnitude of
additive terms in expression. Scaling factor for constraints will be 1 / sum(1/abs(nominal value)).
Args:
component: a Pyomo component to set constraint scaling factors for.
warning: bool indicating whether to log a warning if a missing variable scaling factor is
found (default=True).
overwrite: bool indicating whether to overwrite existing scaling factors (default=False).
descend_into: bool indicating whether function should descend into child Blocks
if component is a Pyomo Block (default=True).
Returns:
None
"""
def _set_sf_har_mag(c):
nominal = NominalValueExtractionVisitor(warning=warning).walk_expression(c.expr)
# Ignore any 0 terms - we will assume they do not contribute to scaling
harm_sum = sum(1 / abs(i) for i in [j for j in nominal if j != 0])
set_scaling_factor(c, harm_sum, overwrite=overwrite)
if isinstance(component, pyo.Block):
# Iterate over all constraint datas and call this method on each
for c in component.component_data_objects(
pyo.Constraint, descend_into=descend_into
):
set_constraint_scaling_harmonic_magnitude(
c, warning=warning, overwrite=overwrite
)
elif component.is_indexed():
for i in component:
_set_sf_har_mag(component[i])
else:
_set_sf_har_mag(component)
def report_scaling_issues(
blk,
ostream: "Stream" = None,
prefix: str = "",
large: float = 1e4,
small: float = 1e-3,
zero: float = 1e-10,
descend_into: bool = True,
include_fixed: bool = False,
):
"""
Write a report on potential scaling issues to a stream.
Args:
blk: block to check for scaling issues
ostream: stream object to write results to (default=stdout)
prefix: string to prefix output with
large: Magnitude that is considered to be too large
small: Magnitude that is considered to be too small
zero: Magnitude that is considered to be zero, variables with a value of
zero are okay, and not reported.
descend_into: bool indicating whether to check constraints in sub-blocks
include_fixed: bool indicating whether to include fixed Vars in list
Returns:
None
"""
if ostream is None:
ostream = sys.stdout
# Write output
max_str_length = 84
tab = " " * 4
ostream.write("\n" + "=" * max_str_length + "\n")
ostream.write(f"{prefix}Potential Scaling Issues")
ostream.write("\n" * 2)
ostream.write(f"{prefix}{tab}Unscaled Variables")
ostream.write("\n" * 2)
for v in unscaled_variables_generator(blk, descend_into, include_fixed):
ostream.write(f"{prefix}{tab*2}{v.name}")
ostream.write("\n" * 2)
ostream.write(f"{prefix}{tab}Badly Scaled Variables")
ostream.write("\n" * 2)
for v in badly_scaled_var_generator(
blk, large, small, zero, descend_into, include_fixed
):
ostream.write(f"{prefix}{tab*2}{v[0].name}: {v[1]}")
ostream.write("\n" * 2)
ostream.write(f"{prefix}{tab}Unscaled Constraints")
ostream.write("\n" * 2)
for c in unscaled_constraints_generator(blk, descend_into):
ostream.write(f"{prefix}{tab * 2}{c.name}")
ostream.write("\n")
ostream.write("\n" + "=" * max_str_length + "\n")
