# tensorplay.autograd.functional.hessian

Source: https://www.tensorplay.cn/docs/generated/tensorplay.autograd.functional.hessian.html

# tensorplay.autograd.functional.hessian

tensorplay.autograd.functional.hessian(func, inputs, create_graph=False, strict=False, vectorize=False, outer_jacobian_strategy='reverse-mode')[[source]](../_modules/tensorplay/autograd/functional.html#hessian)

Compute the Hessian of a given scalar function.

Parameters:

- func ( function ) – a Python function that takes Tensor inputs and returns a Tensor with a single element.

- inputs ([tuple](https://docs.python.org/3/library/stdtypes.html#tuple) of Tensors or Tensor ) – inputs to the function func .

- create_graph ([bool](https://docs.python.org/3/library/functions.html#bool) , optional ) – If True , the Hessian will be computed in a differentiable manner. Note that when strict is False , the result can not require gradients or be disconnected from the inputs. Defaults to False .

- strict ([bool](https://docs.python.org/3/library/functions.html#bool) , optional ) – If True , an error will be raised when we detect that there exists an input such that all the outputs are independent of it. If False , we return a Tensor of zeros as the hessian for said inputs, which is the expected mathematical value. Defaults to False .

- vectorize ([bool](https://docs.python.org/3/library/functions.html#bool) , optional ) – Not supported by this engine yet; passing True raises [NotImplementedError](https://docs.python.org/3/library/exceptions.html#NotImplementedError).

- outer_jacobian_strategy ([str](https://docs.python.org/3/library/stdtypes.html#str) , optional ) – Only "reverse-mode" is supported; forward-mode AD raises [NotImplementedError](https://docs.python.org/3/library/exceptions.html#NotImplementedError).

Returns:

if there is a single input,
this will be a single Tensor containing the Hessian for the input.
If it is a tuple, then the Hessian will be a tuple of tuples where
Hessian[i][j] will contain the Hessian of the ith input
and jth input with size the sum of the size of the ith input plus
the size of the jth input. Hessian[i][j] will have the same
dtype and device as the corresponding ith input.

Return type:

Hessian (Tensor or a tuple of [tuple](https://docs.python.org/3/library/stdtypes.html#tuple) of Tensors)

Example

```
>>> def pow_reducer(x):
...     return x.pow(3).sum()
>>> inputs = tensorplay.rand(2, 2)
>>> hessian(pow_reducer, inputs)
tensor([[[[5.2265, 0.0000],
          [0.0000, 0.0000]],
         [[0.0000, 4.8221],
          [0.0000, 0.0000]]],
        [[[0.0000, 0.0000],
          [1.9456, 0.0000]],
         [[0.0000, 0.0000],
          [0.0000, 3.2550]]]])
```