结合Theano中的标量和矢量来计算Hessian

我正在尝试使用Theano来计算关于向量以及几个标量的函数的粗糙度(编辑:也就是说,我基本上希望附加到我正在计算粗麻布的向量的标量) .这是一个最小的例子:

import theano
import theano.tensor as T
A = T.vector('A')
b,c = T.scalars('b','c')
y = T.sum(A)*b*c

我的第一次尝试是:

hy = T.hessian(y,[A,b,c])

哪个失败了 AssertionError: tensor.hessian expects a (list of) 1 dimensional variable as 'wrt'

我的第二次尝试是将A,b和c与:

wrt = T.concatenate([A,T.stack(b,c)])
hy = T.hessian(y,[wrt])

哪个失败了 DisconnectedInputError: grad method was asked to compute the gradient with respect to a variable that is not part of the computational graph of the cost, or is used only by a non-differentiable operator: Join.0

在这种情况下计算粗麻线的正确方法是什么？

更新:为了澄清我在寻找什么,假设A是2元素向量.然后黑森州将是:

[[d2y/d2A1, d2y/dA1dA2, d2y/dA1dB, d2y/dA1dC],
[d2y/dA2dA1, d2y/d2A2, d2y/dA2dB, d2y/dA2dC],
[d2y/dBdA1, d2y/dBdA2, d2y/d2B, d2y/dABdC],
[d2y/dCdA1, d2y/dCdA2, d2y/dCdB, d2y/d2C]]

对于示例函数y应该是:

[[0, 0, C, B],
[0, 0, C, B],
[C, C, 0, A1+A2],
[B, B, A1+A2, 0]]

所以,如果我们要定义一个函数:

f = theano.function([A,b,c], hy)

那么,假设我们可以hy成功计算,我们会期望输出:

f([1,1], 4, 5) = 
    [[0, 0, 5, 4],
    [0, 0, 5, 4],
    [5, 5, 0, 2],
    [4, 4, 2, 0]]

在我的实际应用中,A有25个元素y,而且更复杂,但想法是一样的.