# Solves the intersection of a line with a parabola
from __future__ import print_function
from openmdao.api import Component, Group, Problem, Newton, ScipyGMRES
[docs]class Line(Component):
"""Evaluates y = -2x + 4."""
def __init__(self):
super(Line, self).__init__()
self.add_param('x', 1.0)
self.add_output('y', 0.0)
# User can change these.
self.slope = -2.0
self.intercept = 4.0
[docs] def solve_nonlinear(self, params, unknowns, resids):
""" y = -2x + 4 """
x = params['x']
m = self.slope
b = self.intercept
unknowns['y'] = m*x + b
[docs] def linearize(self, params, unknowns, resids):
""" Jacobian for our line."""
m = self.slope
J = {}
J['y', 'x'] = m
return J
[docs]class Parabola(Component):
"""Evaluates y = 3x^2 - 5"""
def __init__(self):
super(Parabola, self).__init__()
self.add_param('x', 1.0)
self.add_output('y', 0.0)
# User can change these.
self.a = 3.0
self.b = 0.0
self.c = -5.0
[docs] def solve_nonlinear(self, params, unknowns, resids):
""" y = 3x^2 - 5 """
x = params['x']
a = self.a
b = self.b
c = self.c
unknowns['y'] = a*x**2 + b*x + c
[docs] def linearize(self, params, unknowns, resids):
""" Jacobian for our parabola."""
x = params['x']
a = self.a
b = self.b
J = {}
J['y', 'x'] = 2.0*a*x + b
return J
[docs]class Balance(Component):
"""Evaluates the residual y1-y2"""
def __init__(self):
super(Balance, self).__init__()
self.add_param('y1', 0.0)
self.add_param('y2', 0.0)
self.add_state('x', 5.0)
[docs] def solve_nonlinear(self, params, unknowns, resids):
"""This component does no calculation on its own. It mainly holds the
initial value of the state. An OpenMDAO solver outside of this
component varies it to drive the residual to zero."""
pass
[docs] def apply_nonlinear(self, params, unknowns, resids):
""" Report the residual y1-y2 """
y1 = params['y1']
y2 = params['y2']
resids['x'] = y1 - y2
[docs] def linearize(self, params, unknowns, resids):
""" Jacobian for our parabola."""
J = {}
J['x', 'y1'] = 1.0
J['x', 'y2'] = -1.0
return J
if __name__ == '__main__':
top = Problem()
root = top.root = Group()
root.add('line', Line())
root.add('parabola', Parabola())
root.add('bal', Balance())
root.connect('line.y', 'bal.y1')
root.connect('parabola.y', 'bal.y2')
root.connect('bal.x', 'line.x')
root.connect('bal.x', 'parabola.x')
root.nl_solver = Newton()
root.ln_solver = ScipyGMRES()
top.setup()
# Positive solution
top['bal.x'] = 7.0
root.list_states()
top.run()
print('Positive Solution x=%f, line.y=%f, parabola.y=%f' % (top['bal.x'], top['line.y'], top['parabola.y']))
# Negative solution
top['bal.x'] = -7.0
root.list_states()
top.run()
print('Negative Solution x=%f, line.y=%f, parabola.y=%f' % (top['bal.x'], top['line.y'], top['parabola.y']))
