我正在尝试编写一个自定义的Theano
Op，它将在两个值之间的函数数字化集成。Op是PyMC3的自定义可能性，其中涉及一些积分的数值评估。我不能简单地使用@as_op装饰器，因为我需要使用HMC来执行MCMC步骤。任何帮助将不胜感激，因为这个问题似乎已经走到了好几次，但一直没有得到解决（如https://stackoverflow.com/questions/36853015/using-
theano-with-numerical-
integration
，Theano：实现一个积分函数）。

显然，一种解决方案是在Theano中编写一个数值积分器，但是当非常好的积分器已经可以使用（例如通过scipy.integrate）时，这似乎是在浪费精力。

为了将其作为一个最小的示例，让我们尝试在Op内部集成介于0和1之间的函数。下面的代码在Op之外集成了Theano函数，并根据我的测试产生了正确的结果。

import theano
import theano.tensor as tt
from scipy.integrate import quad

x = tt.dscalar('x')
y = x**4 # integrand
f = theano.function([x], y)

print f(0)
print f(1)

ans = integrate.quad(f, 0, 1)[0]

print ans

但是，尝试在Op内进行集成似乎要困难得多。我目前的最大努力是：

import numpy as np
import theano
import theano.tensor as tt
from scipy import integrate

class IntOp(theano.Op):
    __props__ = ()

    def make_node(self, x):
        x = tt.as_tensor_variable(x)
        return theano.Apply(self, [x], [x.type()])

    def perform(self, node, inputs, output_storage):
        x = inputs[0]
        z = output_storage[0]

        f_to_int = theano.function([x], x)
        z[0] = tt.as_tensor_variable(integrate.quad(f_to_int, 0, 1)[0])

    def infer_shape(self, node, i0_shapes):
        return i0_shapes

    def grad(self, inputs, output_grads):
        ans = integrate.quad(output_grads[0], 0, 1)[0]
        return [ans]

intOp = IntOp()

x = tt.dmatrix('x')
y = intOp(x)

f = theano.function([x], y)

inp = np.asarray([[2, 4], [6, 8]], dtype=theano.config.floatX)
out = f(inp)

print inp
print out

出现以下错误：

Traceback (most recent call last):
  File "stackoverflow.py", line 35, in <module>
    out = f(inp)
  File "/usr/local/lib/python2.7/dist-packages/theano/compile/function_module.py", line 871, in __call__
    storage_map=getattr(self.fn, 'storage_map', None))
  File "/usr/local/lib/python2.7/dist-packages/theano/gof/link.py", line 314, in raise_with_op
    reraise(exc_type, exc_value, exc_trace)
  File "/usr/local/lib/python2.7/dist-packages/theano/compile/function_module.py", line 859, in __call__
    outputs = self.fn()
  File "/usr/local/lib/python2.7/dist-packages/theano/gof/op.py", line 912, in rval
    r = p(n, [x[0] for x in i], o)
  File "stackoverflow.py", line 17, in perform
    f_to_int = theano.function([x], x)
  File "/usr/local/lib/python2.7/dist-packages/theano/compile/function.py", line 320, in function
    output_keys=output_keys)
  File "/usr/local/lib/python2.7/dist-packages/theano/compile/pfunc.py", line 390, in pfunc
    for p in params]
  File "/usr/local/lib/python2.7/dist-packages/theano/compile/pfunc.py", line 489, in _pfunc_param_to_in
    raise TypeError('Unknown parameter type: %s' % type(param))
TypeError: Unknown parameter type: <type 'numpy.ndarray'>
Apply node that caused the error: IntOp(x)
Toposort index: 0
Inputs types: [TensorType(float64, matrix)]
Inputs shapes: [(2, 2)]
Inputs strides: [(16, 8)]
Inputs values: [array([[ 2.,  4.],
       [ 6.,  8.]])]
Outputs clients: [['output']]

Backtrace when the node is created(use Theano flag traceback.limit=N to make it longer):
  File "stackoverflow.py", line 30, in <module>
    y = intOp(x)
  File "/usr/local/lib/python2.7/dist-packages/theano/gof/op.py", line 611, in __call__
    node = self.make_node(*inputs, **kwargs)
  File "stackoverflow.py", line 11, in make_node
    return theano.Apply(self, [x], [x.type()])

HINT: Use the Theano flag 'exception_verbosity=high' for a debugprint and storage map footprint of this apply node.

我对此感到惊讶，尤其是TypeError，因为我以为我已将output_storage变量转换为张量，但似乎在这里仍然相信它仍然是ndarray。