# Providing an Initial Guess for Implicit States in a Group

# Providing an Initial Guess for Implicit States in a Group¶

In the documentation for ImplicitComponent,
you saw that you can provide an initial guess for implicit states within the
component using it’s *guess_nonlinear* method.

`Group`

also provides a *guess_nonlinear* method in which you can supply
the starting value for implicit state variables in any of it’s subsystems.

The following example demonstrates the capability of setting the initial guess
value at the group level, using the input from one component to compute the guess
for another. In this case, a `Discipline`

group solves a system of equations
using a BalanceComp. It answers the question:
“What is \(x\) such that \(x^2\) is equal to twice our input value”.

Given our knowledge of the relationship between the two equations, we can supply an initial guess for the implicit state variable, \(x\), that makes it unnecessary for the solver to iterate.

```
import numpy as np
import openmdao.api as om
class Discipline(om.Group):
def setup(self):
self.add_subsystem('comp0', om.ExecComp('y=x**2'))
self.add_subsystem('comp1', om.ExecComp('z=2*external_input'),
promotes_inputs=['external_input'])
self.add_subsystem('balance', om.BalanceComp('x', lhs_name='y', rhs_name='z'),
promotes_outputs=['x'])
self.connect('comp0.y', 'balance.y')
self.connect('comp1.z', 'balance.z')
self.connect('x', 'comp0.x')
self.nonlinear_solver = om.NewtonSolver(iprint=2, solve_subsystems=True)
self.linear_solver = om.DirectSolver()
def guess_nonlinear(self, inputs, outputs, residuals):
# Check residuals
if np.abs(residuals['x']) > 1.0E-2:
# inputs are addressed using full path name, regardless of promotion
external_input = inputs['comp1.external_input']
# balance drives x**2 = 2*external_input
x_guess = (2*external_input)**.5
# outputs are addressed by the their promoted names
outputs['x'] = x_guess # perfect guess should converge in 0 iterations
p = om.Problem()
p.model.add_subsystem('discipline', Discipline(), promotes_inputs=['external_input'])
p.setup()
p.set_val('external_input', 1.)
p.run_model()
print(p.model.nonlinear_solver._iter_count)
print(p.get_val('discipline.x'))
```

```
==========
discipline
==========
NL: Newton 0 ; 0.5 1
NL: Newton 1 ; 0.125 0.25
NL: Newton 2 ; 0.00347222222 0.00694444444
NL: Newton 3 ; 3.00365244e-06 6.00730488e-06
NL: Newton 4 ; 2.25530705e-12 4.5106141e-12
NL: Newton Converged
0
[1.41421356]
```