"""Define the EQConstraintComp class."""
from numbers import Number
import numpy as np
from openmdao.core.explicitcomponent import ExplicitComponent
from openmdao.utils import cs_safe
from openmdao.utils.array_utils import shape_to_len
[docs]class EQConstraintComp(ExplicitComponent):
"""
A component that computes the difference between two inputs to test for equality.
Parameters
----------
name : str
The name of the output variable to be created.
eq_units : str or None
Units for the left-hand-side and right-hand-side of the difference equation.
lhs_name : str or None
Optional name for the LHS variable associated with the difference equation.
If None, the default will be used: 'lhs:{name}'.
rhs_name : str or None
Optional name for the RHS variable associated with the difference equation.
If None, the default will be used: 'rhs:{name}'.
rhs_val : int, float, or np.array
Default value for the RHS of the given output. Must be compatible
with the shape (optionally) given by the val or shape option in kwargs.
use_mult : bool
Specifies whether the LHS multiplier is to be used. If True, then an additional
input `mult_name` is created, with the default value given by `mult_val`, that
multiplies lhs. Default is False.
mult_name : str or None
Optional name for the LHS multiplier variable associated with the output
variable. If None, the default will be used: 'mult:{name}'.
mult_val : int, float, or np.array
Default value for the LHS multiplier of the given output. Must be compatible
with the shape (optionally) given by the val or shape option in kwargs.
normalize : bool
Specifies whether or not the resulting output should be normalized by the RHS. When
the RHS value is between [-2, 2], the normalization value is a quadratic function that
is close to one but still provides a C1 continuous function. When this option is True,
the user-provided ref/ref0 scaler/adder options below are typically unnecessary.
add_constraint : bool
Specifies whether to add an equality constraint.
ref : float or ndarray, optional
Value of response variable that scales to 1.0 in the driver. This option is only
meaningful when add_constraint=True.
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver. This option is only
meaningful when add_constraint=True.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder
is first in precedence. This option is only meaningful when add_constraint=True.
scaler : float or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler
is second in precedence. This option is only meaningful when add_constraint=True.
**kwargs : dict
Additional arguments to be passed for the creation of the output variable.
(see `add_output` method).
Attributes
----------
_output_vars : dict
Cache the data provided during `add_eq_output`
so everything can be saved until setup is called.
"""
[docs] def __init__(self, name=None, eq_units=None, lhs_name=None, rhs_name=None, rhs_val=0.0,
use_mult=False, mult_name=None, mult_val=1.0, normalize=True, add_constraint=False,
ref=None, ref0=None, adder=None, scaler=None, **kwargs):
r"""
Initialize an EQConstraintComp, optionally add an output constraint to the model.
The EQConstraintComp allows for the creation of one or more output variables and
computes the values for those variables based on the following equation:
.. math::
name_{output} = \frac{name_{mult} \times name_{lhs} - name_{rhs} }{f_{norm}(name_{rhs})}
Where :math:`name_{lhs}` represents the left-hand-side of the equality,
:math:`name_{rhs}` represents the right-hand-side, and :math:`name_{mult}`
is an optional multiplier on the left hand side. If use_mult is True then
the default value of the multiplier is 1. The optional normalization function
:math:`f_{norm}` is computed as:
.. math::
f_{norm}(name_{rhs}) =
\begin{cases}
\left| name_{rhs} \right|, & \text{if normalize and } \left| name_{rhs} \right| \geq 2 \\
0.25 name_{rhs}^2 + 1, & \text{if normalize and } \left| name_{rhs} \right| < 2 \\
1, & \text{if not normalize}
\end{cases}
New output variables are created by calling `add_eq_output`.
"""
super().__init__()
self._output_vars = {}
if name is not None:
self.add_eq_output(name, eq_units, lhs_name, rhs_name, rhs_val,
use_mult, mult_name, mult_val, normalize, add_constraint, ref, ref0,
adder, scaler, **kwargs)
self._no_check_partials = True
[docs] def compute(self, inputs, outputs):
"""
Calculate the output for each equality constraint.
Parameters
----------
inputs : Vector
Unscaled, dimensional input variables read via inputs[key].
outputs : Vector
Unscaled, dimensional output variables read via outputs[key].
"""
for name, options in self._output_vars.items():
lhs = inputs[options['lhs_name']]
rhs = inputs[options['rhs_name']]
# set dtype to rhs.dtype to prevent
# "Casting complex values to real discards the imaginary part" warning.
_scale_factor = np.ones((rhs.shape), dtype=rhs.dtype)
# Compute scaling factors
# scale factor that normalizes by the rhs, except near 0
if options['normalize']:
# Indices where the rhs is near zero or not near zero
idxs_nz = np.where(cs_safe.abs(rhs) < 2)
idxs_nnz = np.where(cs_safe.abs(rhs) >= 2)
_scale_factor[idxs_nnz] = 1.0 / cs_safe.abs(rhs[idxs_nnz])
_scale_factor[idxs_nz] = 1.0 / (.25 * rhs[idxs_nz] ** 2 + 1)
if options['use_mult']:
outputs[name] = (inputs[options['mult_name']] * lhs - rhs) * _scale_factor
else:
outputs[name] = (lhs - rhs) * _scale_factor
[docs] def compute_partials(self, inputs, partials):
"""
Compute sub-jacobian parts. The model is assumed to be in an unscaled state.
Parameters
----------
inputs : Vector
Unscaled, dimensional input variables read via inputs[key].
partials : Jacobian
Sub-jac components written to partials[output_name, input_name].
"""
for name, options in self._output_vars.items():
lhs_name = options['lhs_name']
rhs_name = options['rhs_name']
lhs = inputs[lhs_name]
rhs = inputs[rhs_name]
_scale_factor = np.ones((rhs.shape))
_dscale_drhs = np.zeros((rhs.shape))
if options['normalize']:
# Indices where the rhs is near zero or not near zero
idxs_nz = np.where(cs_safe.abs(rhs) < 2)
idxs_nnz = np.where(cs_safe.abs(rhs) >= 2)
# scale factor that normalizes by the rhs, except near 0
_scale_factor[idxs_nnz] = 1.0 / cs_safe.abs(rhs[idxs_nnz])
_scale_factor[idxs_nz] = 1.0 / (.25 * rhs[idxs_nz] ** 2 + 1)
_dscale_drhs[idxs_nnz] = -np.sign(rhs[idxs_nnz]) / rhs[idxs_nnz]**2
_dscale_drhs[idxs_nz] = -.5 * rhs[idxs_nz] / (.25 * rhs[idxs_nz] ** 2 + 1) ** 2
if options['use_mult']:
mult_name = options['mult_name']
mult = inputs[mult_name]
# Partials of output wrt mult
deriv = lhs * _scale_factor
partials[name, mult_name] = deriv.flatten()
else:
mult = 1.0
# Partials of output wrt rhs
deriv = (mult * lhs - rhs) * _dscale_drhs - _scale_factor
partials[name, rhs_name] = deriv.flatten()
# Partials of output wrt lhs
deriv = mult * _scale_factor
partials[name, lhs_name] = deriv.flatten()
[docs] def add_eq_output(self, name, eq_units=None, lhs_name=None, rhs_name=None, rhs_val=0.0,
use_mult=False, mult_name=None, mult_val=1.0, normalize=True,
add_constraint=False, ref=None, ref0=None, adder=None, scaler=None,
linear=False, indices=None, cache_linear_solution=False,
flat_indices=False, alias=None, **kwargs):
"""
Add a new output variable computed via the difference equation.
This will create new inputs `lhs:name`, `rhs:name`, and `mult:name` that will
define the left and right sides of the difference equation, and a
multiplier for the left-hand-side.
Parameters
----------
name : str
The name of the output variable to be created.
eq_units : str or None
Units for the left-hand-side and right-hand-side of the difference equation.
lhs_name : str or None
Optional name for the LHS variable associated with the difference equation. If
None, the default will be used: 'lhs:{name}'.
rhs_name : str or None
Optional name for the RHS variable associated with the difference equation. If
None, the default will be used: 'rhs:{name}'.
rhs_val : int, float, or np.array
Default value for the RHS. Must be compatible with the shape (optionally)
given by the val or shape option in kwargs.
use_mult : bool
Specifies whether the LHS multiplier is to be used. If True, then an additional
input `mult_name` is created, with the default value given by `mult_val`, that
multiplies lhs. Default is False.
mult_name : str or None
Optional name for the LHS multiplier variable associated with the output
variable. If None, the default will be used: 'mult:{name}'.
mult_val : int, float, or np.array
Default value for the LHS multiplier. Must be compatible with the shape (optionally)
given by the val or shape option in kwargs.
normalize : bool
Specifies whether or not the resulting output should be normalized by a quadratic
function of the RHS. When this option is True, the user-provided ref/ref0 scaler/adder
options below are typically unnecessary.
add_constraint : bool
Specifies whether to add an equality constraint.
ref : float or ndarray, optional
Value of response variable that scales to 1.0 in the driver. This option is only
meaningful when add_constraint=True.
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver. This option is only
meaningful when add_constraint=True.
adder : float or ndarray, optional
Value to add to the model value to get the scaled value for the driver. adder
is first in precedence. This option is only meaningful when add_constraint=True.
scaler : float or ndarray, optional
Value to multiply the model value to get the scaled value for the driver. scaler
is second in precedence. This option is only meaningful when add_constraint=True.
linear : bool
Set to True if constraint is linear. Default is False.
indices : sequence of int, optional
If variable is an array, these indicate which entries are of
interest for this particular response. These may be positive or
negative integers.
cache_linear_solution : bool
If True, store the linear solution vectors for this variable so they can
be used to start the next linear solution with an initial guess equal to the
solution from the previous linear solve.
flat_indices : bool
If True, interpret specified indices as being indices into a flat source array.
alias : str
Alias for this response. Necessary when adding multiple constraints on different
indices or slices of a single variable.
**kwargs : dict
Additional arguments to be passed for the creation of the output variable.
(see `add_output` method).
"""
self._output_vars[name] = options = {'kwargs': kwargs,
'eq_units': eq_units,
'lhs_name': lhs_name,
'rhs_name': rhs_name,
'rhs_val': rhs_val,
'use_mult': use_mult,
'mult_name': mult_name,
'mult_val': mult_val,
'normalize': normalize,
'add_constraint': add_constraint,
'ref': ref,
'ref0': ref0,
'adder': adder,
'scaler': scaler}
meta = self.add_output(name, **options['kwargs'])
shape = meta['shape']
for s in ('lhs', 'rhs', 'mult'):
if options[f'{s}_name'] is None:
options[f'{s}_name'] = f'{s}:{name}'
self.add_input(options['lhs_name'],
val=np.ones(shape),
units=options['eq_units'])
self.add_input(options['rhs_name'],
val=options['rhs_val'] * np.ones(shape),
units=options['eq_units'])
if options['use_mult']:
self.add_input(options['mult_name'],
val=options['mult_val'] * np.ones(shape),
units=None)
ar = np.arange(shape_to_len(shape))
self.declare_partials(of=name, wrt=options['lhs_name'], rows=ar, cols=ar, val=1.0)
self.declare_partials(of=name, wrt=options['rhs_name'], rows=ar, cols=ar, val=1.0)
if options['use_mult']:
self.declare_partials(of=name, wrt=options['mult_name'], rows=ar, cols=ar, val=1.0)
if options['add_constraint']:
self.add_constraint(name, equals=0., ref0=options['ref0'], ref=options['ref'],
adder=options['adder'], scaler=options['scaler'],
linear=linear, indices=indices, flat_indices=flat_indices,
cache_linear_solution=cache_linear_solution, alias=alias)
