"""Definition of the Cross Product Component."""
import numpy as np
from openmdao.core.explicitcomponent import ExplicitComponent
[docs]
class CrossProductComp(ExplicitComponent):
"""
Compute a vectorized cross product.
math::
c = np.cross(a, b)
where a is of shape (vec_size, 3)
b is of shape (vec_size, 3)
c is of shape (vec_size, 3)
if vec_size > 1 and
where a is of shape (3,)
b is of shape (3,)
c is of shape (3,)
otherwise.
Parameters
----------
**kwargs : dict of keyword arguments
Keyword arguments that will be mapped into the Component options.
Attributes
----------
_products : list
Cache the data provided during `add_product`
so everything can be saved until setup is called.
"""
[docs]
def __init__(self, **kwargs):
"""
Initialize the Cross Product component.
"""
super().__init__(**kwargs)
self._products = []
opt = self.options
self.add_product(c_name=opt['c_name'], a_name=opt['a_name'], b_name=opt['b_name'],
c_units=opt['c_units'], a_units=opt['a_units'], b_units=opt['b_units'],
vec_size=opt['vec_size'])
self._no_check_partials = True
[docs]
def initialize(self):
"""
Declare options.
"""
self.options.declare('vec_size', types=int, default=1,
desc='The number of points at which the cross product is computed')
self.options.declare('a_name', types=str, default='a',
desc='The variable name for vector a.')
self.options.declare('b_name', types=str, default='b',
desc='The variable name for vector b.')
self.options.declare('c_name', types=str, default='c',
desc='The variable name for vector c.')
self.options.declare('a_units', types=str, default=None, allow_none=True,
desc='The units for vector a.')
self.options.declare('b_units', types=str, default=None, allow_none=True,
desc='The units for vector b.')
self.options.declare('c_units', types=str, default=None, allow_none=True,
desc='The units for vector c.')
self._k = np.array([[0, 0, 0, -1, 0, 1],
[0, 1, 0, 0, -1, 0],
[-1, 0, 1, 0, 0, 0]], dtype=float)
self._minus_k = -self._k
[docs]
def add_product(self, c_name, a_name='a', b_name='b',
c_units=None, a_units=None, b_units=None,
vec_size=1):
"""
Add a new output product to the cross product component.
Parameters
----------
c_name : str
The name of the vector product output.
a_name : str
The name of the first vector input.
b_name : str
The name of the second vector input.
c_units : str or None
The units of the output.
a_units : str or None
The units of input a.
b_units : str or None
The units of input b.
vec_size : int
The number of points at which the dot vector product
should be computed simultaneously. The shape of
the output is (vec_size,).
"""
self._products.append({
'a_name': a_name,
'b_name': b_name,
'c_name': c_name,
'a_units': a_units,
'b_units': b_units,
'c_units': c_units,
'vec_size': vec_size,
})
# add inputs and outputs for all products
if self._static_mode:
var_rel2meta = self._static_var_rel2meta
var_rel_names = self._static_var_rel_names
else:
var_rel2meta = self._var_rel2meta
var_rel_names = self._var_rel_names
shape = (vec_size, 3) if vec_size > 1 else (3,)
if c_name not in var_rel2meta:
self.add_output(name=c_name, val=np.ones(shape=shape), units=c_units)
elif c_name in var_rel_names['input']:
raise NameError(f"{self.msginfo}: '{c_name}' specified as an output, "
"but it has already been defined as an input.")
else:
raise NameError(f"{self.msginfo}: Multiple definition of output '{c_name}'.")
if a_name not in var_rel2meta:
self.add_input(name=a_name, shape=shape, units=a_units)
elif a_name in var_rel_names['output']:
raise NameError(f"{self.msginfo}: '{a_name}' specified as an input, "
"but it has already been defined as an output.")
else:
meta = var_rel2meta[a_name]
if a_units != meta['units']:
raise ValueError(f"{self.msginfo}: Conflicting units '{a_units}' specified "
f"for input '{a_name}', which has already been defined "
f"with units '{meta['units']}'.")
meta_shape = meta['shape']
if shape != meta_shape:
raise ValueError(f"{self.msginfo}: Conflicting vec_size={vec_size} specified "
f"for input '{a_name}', which has already been defined with "
f"vec_size={meta_shape[0] if len(meta_shape) > 1 else 1}.")
if b_name not in var_rel2meta:
self.add_input(name=b_name, shape=shape, units=b_units)
elif b_name in var_rel_names['output']:
raise NameError(f"{self.msginfo}: '{b_name}' specified as an input, "
"but it has already been defined as an output.")
else:
meta = var_rel2meta[b_name]
if b_units != meta['units']:
raise ValueError(f"{self.msginfo}: Conflicting units '{b_units}' specified "
f"for input '{b_name}', which has already been defined "
f"with units '{meta['units']}'.")
meta_shape = meta['shape']
if shape != meta_shape:
raise ValueError(f"{self.msginfo}: Conflicting vec_size={vec_size} specified "
f"for input '{b_name}', which has already been defined with "
f"vec_size={meta_shape[0] if len(meta_shape) > 1 else 1}.")
row_idxs = np.repeat(np.arange(vec_size * 3, dtype=int), 2)
col_idxs = np.empty((0,), dtype=int)
M = np.array([1, 2, 0, 2, 0, 1], dtype=int)
for i in range(vec_size):
col_idxs = np.concatenate((col_idxs, M + i * 3))
self.declare_partials(of=c_name, wrt=a_name, rows=row_idxs, cols=col_idxs)
self.declare_partials(of=c_name, wrt=b_name, rows=row_idxs, cols=col_idxs)
[docs]
def compute(self, inputs, outputs):
"""
Compute the cross product of inputs `a` and `b` using np.cross.
Parameters
----------
inputs : Vector
Unscaled, dimensional input variables read via inputs[key].
outputs : Vector
Unscaled, dimensional output variables read via outputs[key].
"""
for product in self._products:
a = inputs[product['a_name']]
b = inputs[product['b_name']]
outputs[product['c_name']] = np.cross(a, b)
[docs]
def compute_partials(self, inputs, partials):
"""
Compute the sparse partials for the cross product w.r.t. the inputs.
Parameters
----------
inputs : Vector
Unscaled, dimensional input variables read via inputs[key].
partials : Jacobian
Sub-jac components written to partials[output_name, input_name].
"""
for product in self._products:
a = inputs[product['a_name']]
b = inputs[product['b_name']]
# Use the following for sparse partials
partials[product['c_name'], product['a_name']] = \
np.einsum('...j,ji->...i', b, self._minus_k).ravel()
partials[product['c_name'], product['b_name']] = \
np.einsum('...j,ji->...i', a, self._k).ravel()
