def solve_nonlinear(self, inputs, outputs):
"""
Use numpy to solve Ax=b for x.
Parameters
----------
inputs : Vector
unscaled, dimensional input variables read via inputs[key]
outputs : Vector
unscaled, dimensional output variables read via outputs[key]
"""
# lu factorization for use with solve_linear
self._lup = linalg.lu_factor(inputs['A'])
outputs['x'] = linalg.lu_solve(self._lup, inputs['b'])
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