Я удивлен выводом метода check_partial_derivatives()
, примененного к проблеме, показанной в моем предыдущем вопросе: Оптимизация параболоидов, требующая масштабирования. Когда я добавляю вызов к этому методу:
from __future__ import print_function import sys from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer class Paraboloid(Component): def __init__(self): super(Paraboloid, self).__init__() self.add_param('x', val=0.0) self.add_param('y', val=0.0) self.add_output('f_xy', val=0.0) def solve_nonlinear(self, params, unknowns, resids): x = params['x'] y = params['y'] #unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0 unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3. def linearize(self, params, unknowns, resids): """ Jacobian for our paraboloid.""" x = params['x'] y = params['y'] J = {} #J['f_xy', 'x'] = 2.0*x - 6.0 + y #J['f_xy', 'y'] = 2.0*y + 8.0 + x J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x return J if __name__ == "__main__": top = Problem() root = top.root = Group() #root.fd_options['force_fd'] = True root.add('p1', IndepVarComp('x', 3.0)) root.add('p2', IndepVarComp('y', -4.0)) root.add('p', Paraboloid()) root.connect('p1.x', 'p.x') root.connect('p2.y', 'p.y') top.driver = ScipyOptimizer() top.driver.options['optimizer'] = 'SLSQP' top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=1000.) top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=0.001) top.driver.add_objective('p.f_xy') top.setup() top.check_partial_derivatives() # added line top.run() print('\n') print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
Получаю следующий результат:
Partial Derivatives Check ---------------- Component: 'p' ---------------- p: 'f_xy' wrt 'x' Forward Magnitude : 6.000000e+03 Reverse Magnitude : 6.000000e+03 Fd Magnitude : 2.199400e+07 Absolute Error (Jfor - Jfd) : 2.200000e+07 Absolute Error (Jrev - Jfd) : 2.200000e+07 Absolute Error (Jfor - Jrev): 0.000000e+00 Relative Error (Jfor - Jfd) : 1.000273e+00 Relative Error (Jrev - Jfd) : 1.000273e+00 Relative Error (Jfor - Jrev): 0.000000e+00 Raw Forward Derivative (Jfor) [[-6000.]] Raw Reverse Derivative (Jrev) [[-6000.]] Raw FD Derivative (Jfor) [[ 21994001.]] - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - p: 'f_xy' wrt 'y' Forward Magnitude : 8.000000e-02 Reverse Magnitude : 8.000000e-02 Fd Magnitude : 2.200000e+07 Absolute Error (Jfor - Jfd) : 2.200000e+07 Absolute Error (Jrev - Jfd) : 2.200000e+07 Absolute Error (Jfor - Jrev): 0.000000e+00 Relative Error (Jfor - Jfd) : 1.000000e+00 Relative Error (Jrev - Jfd) : 1.000000e+00 Relative Error (Jfor - Jrev): 0.000000e+00 Raw Forward Derivative (Jfor) [[ 0.08]] Raw Reverse Derivative (Jrev) [[ 0.08]] Raw FD Derivative (Jfor) [[ 22000000.08]] Optimization terminated successfully. (Exit mode 0) Current function value: [-27.33333333] Iterations: 4 Function evaluations: 6 Gradient evaluations: 4 Optimization Complete ----------------------------------- Minimum of -27.333333 found at (0.006667, -733.333333)
Оптимизация верна (т. Е. Почти наверняка доказывает правильность производных), но результат check_partial_derivatives
не показывает согласованных результатов между методами fd и прямым / обратным ходом.