Simple Explicit Expressions

In this example, we define multiple expressions and register their outputs. Note that the outputs need not be registered in the order in which they are defined, nor do they necessarily appear in the n2 diagram in the order in which they are registered. This is due to the fact that omtools automatically rearranges expressions so that the Component objects do not have any unnecessary feedbacks.

from openmdao.api import Problem
from openmdao.api import ScipyKrylov, NewtonSolver, NonlinearBlockGS
from omtools.api import Group, ImplicitComponent
import omtools.api as ot
import numpy as np


class ExampleBinaryOperations(Group):
    def setup(self):
        # declare inputs with default values
        x1 = self.declare_input('x1', val=2)
        x2 = self.declare_input('x2', val=3)
        x3 = self.declare_input('x3', val=np.arange(7))

        # Expressions with multiple binary operations
        y1 = -2 * x1**2 + 4 * x2 + 3
        self.register_output('y1', y1)

        # Elementwise addition
        y2 = x2 + x1

        # Elementwise subtraction
        y3 = x2 - x1

        # Elementwise multitplication
        y4 = x1 * x2

        # Elementwise division
        y5 = x1 / x2
        y6 = x1 / 3
        y7 = 2 / x2

        # Elementwise Power
        y8 = x2**2
        y9 = x1**2

        self.register_output('y2', y2)
        self.register_output('y3', y3)
        self.register_output('y4', y4)
        self.register_output('y5', y5)
        self.register_output('y6', y6)
        self.register_output('y7', y7)
        self.register_output('y8', y8)
        self.register_output('y9', y9)

        # Adding other expressions
        self.register_output('y10', y1 + y7)

        # Array with scalar power
        y11 = x3**2
        self.register_output('y11', y11)

        # Array with array of powers
        y12 = x3**(2 * np.ones(7))
        self.register_output('y12', y12)


prob = Problem()
prob.model = ExampleBinaryOperations()
prob.setup(force_alloc_complex=True)
prob.run_model()

print('y1', prob['y1'].shape)
print(prob['y1'])
print('y2', prob['y2'].shape)
print(prob['y2'])
print('y3', prob['y3'].shape)
print(prob['y3'])
print('y4', prob['y4'].shape)
print(prob['y4'])
print('y5', prob['y5'].shape)
print(prob['y5'])
print('y6', prob['y6'].shape)
print(prob['y6'])
print('y7', prob['y7'].shape)
print(prob['y7'])
print('y8', prob['y8'].shape)
print(prob['y8'])
print('y9', prob['y9'].shape)
print(prob['y9'])
print('y10', prob['y10'].shape)
print(prob['y10'])
print('y11', prob['y11'].shape)
print(prob['y11'])
print('y12', prob['y12'].shape)
print(prob['y12'])

y1 (1,)
[7.]
y2 (1,)
[5.]
y3 (1,)
[1.]
y4 (1,)
[6.]
y5 (1,)
[0.66666667]
y6 (1,)
[0.66666667]
y7 (1,)
[0.66666667]
y8 (1,)
[9.]
y9 (1,)
[4.]
y10 (1,)
[7.66666667]
y11 (7,)
[ 0.  1.  4.  9. 16. 25. 36.]
y12 (7,)
[ 0.  1.  4.  9. 16. 25. 36.]

The Component objects added to the model are guaranteed to be connected such that there are no unnecessary feedbacks, regardless of the order in which each output is defined or registered. In this case, since there are no cycles, the n2 diagram is upper triangular.