# Source code for openmdao.components.eq_constraint_comp

"""Define the EQConstraintComp class."""

from __future__ import print_function, division, absolute_import

from numbers import Number
from six import iteritems

import numpy as np

from openmdao.core.explicitcomponent import ExplicitComponent

[docs]class EQConstraintComp(ExplicitComponent):
"""
A component that computes the difference between two inputs to test for equality.

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,
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.

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.
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
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver. This option is only
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).
"""
super(EQConstraintComp, self).__init__()
self._output_vars = {}
if name is not None:
use_mult, mult_name, mult_val, normalize, add_constraint, ref, ref0,

def _post_configure(self):
"""
Define the independent variables, output variables, and partials.
"""
# set static mode to False because we are doing things that would normally be done in setup
self._static_mode = False

for name, options in iteritems(self._output_vars):

shape = meta['shape']

for s in ('lhs', 'rhs', 'mult'):
if options['{0}_name'.format(s)] is None:
options['{0}_name'.format(s)] = '{0}:{1}'.format(s, name)

val=np.ones(shape),
units=options['eq_units'])

val=options['rhs_val'] * np.ones(shape),
units=options['eq_units'])

if options['use_mult']:
val=options['mult_val'] * np.ones(shape),
units=None)

self._scale_factor = np.ones(shape)
self._dscale_drhs = np.ones(shape)

ar = np.arange(np.prod(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)

self._static_mode = True

super(EQConstraintComp, self)._post_configure()

[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]
"""
if inputs._under_complex_step:
self._scale_factor = self._scale_factor.astype(np.complex)
else:
self._scale_factor = self._scale_factor.real

for name, options in iteritems(self._output_vars):
lhs = inputs[options['lhs_name']]
rhs = inputs[options['rhs_name']]

# 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(np.abs(rhs) < 2)[0]
idxs_nnz = np.where(np.abs(rhs) >= 2)[0]

self._scale_factor[idxs_nnz] = 1.0 / np.abs(rhs[idxs_nnz])
self._scale_factor[idxs_nz] = 1.0 / (.25 * rhs[idxs_nz] ** 2 + 1)
else:
self._scale_factor[:] = 1.0

if options['use_mult']:
outputs[name] = (inputs[options['mult_name']] * lhs - rhs) * self._scale_factor
else:
outputs[name] = (lhs - rhs) * self._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]
"""
if inputs._under_complex_step:
self._dscale_drhs = self._dscale_drhs.astype(np.complex)
else:
self._dscale_drhs = self._dscale_drhs.real

for name, options in iteritems(self._output_vars):
lhs_name = options['lhs_name']
rhs_name = options['rhs_name']

lhs = inputs[lhs_name]
rhs = inputs[rhs_name]

if options['normalize']:
# Indices where the rhs is near zero or not near zero
idxs_nz = np.where(np.abs(rhs) < 2)[0]
idxs_nnz = np.where(np.abs(rhs) >= 2)[0]

# scale factor that normalizes by the rhs, except near 0
self._scale_factor[idxs_nnz] = 1.0 / np.abs(rhs[idxs_nnz])
self._scale_factor[idxs_nz] = 1.0 / (.25 * rhs[idxs_nz] ** 2 + 1)

self._dscale_drhs[idxs_nnz] = -np.sign(rhs[idxs_nnz]) / rhs[idxs_nnz]**2
self._dscale_drhs[idxs_nz] = -.5 * rhs[idxs_nz] / (.25 * rhs[idxs_nz] ** 2 + 1) ** 2
else:
self._scale_factor[:] = 1.0
self._dscale_drhs[:] = 0.0

if options['use_mult']:
mult_name = options['mult_name']
mult = inputs[mult_name]

# Partials of output wrt mult
deriv = lhs * self._scale_factor
partials[name, mult_name] = deriv.flatten()
else:
mult = 1.0

# Partials of output wrt rhs
deriv = (mult * lhs - rhs) * self._dscale_drhs - self._scale_factor
partials[name, rhs_name] = deriv.flatten()

# Partials of output wrt lhs
deriv = mult * self._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 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.
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
ref0 : float or ndarray, optional
Value of response variable that scales to 0.0 in the driver. This option is only
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).
"""
self._output_vars[name] = {'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,