检查偏导数和有限差分错误

Question

关于我之前的问题，我看到你解决了一次与运行相关的问题。我想尝试，但我仍然对以下代码中显示的导数检查和有限差分有问题：

""" Unconstrained optimization of the scaled paraboloid component."""

from __future__ import print_function
import sys
import numpy as np

from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer

class Paraboloid(Component):

    def __init__(self):
        super(Paraboloid, self).__init__()

        self.add_param('X', val=np.array([0.0, 0.0]))
        self.add_output('f_xy', val=0.0)

    def solve_nonlinear(self, params, unknowns, resids):
        X = params['X']
        x = X[0]
        y = X[1]
        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']
        J = {}

        x = X[0]
        y = X[1]

        J['f_xy', 'X'] = np.array([[ 2000000.0*x - 6000.0 + 10.0*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    # Error if uncommented

    root.add('p1', IndepVarComp('X', np.array([3.0, -4.0])))
    root.add('p', Paraboloid())

    root.connect('p1.X', 'p.X')

    top.driver = ScipyOptimizer()
    top.driver.options['optimizer'] = 'SLSQP'

    top.driver.add_desvar('p1.X',
                          lower=np.array([-1000.0, -1000.0]),
                          upper=np.array([1000.0, 1000.0]),
                          scaler=np.array([1000., 0.001]))
    top.driver.add_objective('p.f_xy')


    top.setup()
    top.check_partial_derivatives()
    top.run()
    top.check_partial_derivatives()

    print('\n')
    print('Minimum of %f found at (%s)' % (top['p.f_xy'], top['p.X']))

第一次检查工作正常，但第二次 check_partial_derivatives 给出了 FD 的奇怪结果：

[...]
Partial Derivatives Check

----------------
Component: 'p'
----------------
  p: 'f_xy' wrt 'X'

    Forward Magnitude : 1.771706e-04
    Reverse Magnitude : 1.771706e-04
         Fd Magnitude : 9.998228e-01

    Absolute Error (Jfor - Jfd) : 1.000000e+00
    Absolute Error (Jrev - Jfd) : 1.000000e+00
    Absolute Error (Jfor - Jrev): 0.000000e+00

    Relative Error (Jfor - Jfd) : 1.000177e+00
    Relative Error (Jrev - Jfd) : 1.000177e+00
    Relative Error (Jfor - Jrev): 0.000000e+00

    Raw Forward Derivative (Jfor)

[[ -1.77170624e-04  -8.89040341e-10]]

    Raw Reverse Derivative (Jrev)

[[ -1.77170624e-04  -8.89040341e-10]]

    Raw FD Derivative (Jfd)

[[ 0.99982282  0.        ]]

Minimum of -27.333333 found at ([  6.66666658e-03  -7.33333333e+02])

并且（可能不相关）当我尝试设置 root.fd_options['force_fd'] = True（只是为了看看）时，我在第一次检查时出错：

Partial Derivatives Check

----------------
Component: 'p'
----------------
Traceback (most recent call last):
  File "C:\Program Files (x86)\Wing IDE 101 5.0\src\debug\tserver\_sandbox.py", line 59, in 
  File "d:\rlafage\OpenMDAO\OpenMDAO\openmdao\core\problem.py", line 1827, in check_partial_derivatives
    u_size = np.size(dunknowns[u_name])
  File "d:\rlafage\OpenMDAO\OpenMDAO\openmdao\core\vec_wrapper.py", line 398, in __getitem__
    return self._dat[name].get()
  File "d:\rlafage\OpenMDAO\OpenMDAO\openmdao\core\vec_wrapper.py", line 223, in _get_scalar
    return self.val[0]
IndexError: index 0 is out of bounds for axis 0 with size 0

我使用 OpenMDAO HEAD (d1e12d4)。

Answer 1

这只是有限差分的步长问题。 2nd FD 发生在不同的点（最佳点），并且在那个点它必须更敏感。

我试过中心差

top.root.p.fd_options['form'] = 'central'

并且得到了更好的结果。

----------------
Component: 'p'
----------------
p: 'f_xy' wrt 'X'

Forward Magnitude : 1.771706e-04
Reverse Magnitude : 1.771706e-04
     Fd Magnitude : 1.771738e-04

设置 'fd' 时出现的异常是一个真正的错误，与 des_var 上的缩放器相关是一个数组。感谢您的报告；我们会得到一个故事来修复它。

检查偏导数和有限差分错误

Check partial derivatives and finite differences error

openmdao