# Simple coupled example edit


```python
'''
Simple coupled example edit:
'''
import csdl_alpha as csdl
import numpy as np

import time as time
start = time.time()
recorder = csdl.build_new_recorder(inline = True)
recorder.start()

x1 = csdl.ImplicitVariable(name='x1', value=1.5)
x2 = csdl.ImplicitVariable(name='x2', value=3.5)
a = csdl.Variable(name='a', value=10.0)

residual_1 = x1-(csdl.sqrt(a-x1*x2))
residual_2 = x2-(csdl.sqrt((57-x2)/(3*x1)))
print('residual_1:', residual_1.value)
print('residual_2:', residual_2.value)

residual_1.name = 'residual_1'
residual_2.name = 'residual_2'

# sum of solved states
sum_states = x1 + x2
sum_states.name = 'states_sum'

# apply coupling:
# x_update = x-residual_1/(-csdl.square(y)-3.0*x*x)
# y_update = y-residual_2/(2.0*y)

# ONE SOLVER COUPLING:
# solver = csdl.nonlinear_solvers.GaussSeidel('gs_xy')
# solver.add_state(x1, residual_1)
# solver.add_state(x2, residual_2)
# solver.run()

# NESTED (x) SOLVER COUPLING:
solver = csdl.nonlinear_solvers.GaussSeidel('gs_x')
solver.add_state(x1, residual_1)
solver.run()

solver = csdl.nonlinear_solvers.GaussSeidel('gs_y')
solver.add_state(x2, residual_2)
solver.run()

# NESTED (y) SOLVER COUPLING:
# solver = csdl.nonlinear_solvers.GaussSeidel('gs_y')
# solver.add_state(y, residual_2, state_update=y_update)
# solver.run()

# solver = csdl.nonlinear_solvers.GaussSeidel('gs_x')
# solver.add_state(x, residual_1, state_update=x_update)
# solver.run()


print('x1 Value:', x1.value)
print('x2 Value:', x2.value)
print('param Value:', a.value)

# A solution: 
x_sol = (np.sqrt(5)-1)/2
y_sol = np.sqrt((-1+np.sqrt(5))/2)
print('an x solution:', x_sol)
print('a y solution:', y_sol)

recorder.active_graph.visualize('FINAL_top_level')

```