# tensorplay.autograd.functional.hvp

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

# tensorplay.autograd.functional.hvp

tensorplay.autograd.functional.hvp(func, inputs, v=None, create_graph=False, strict=False)[[source]](../_modules/tensorplay/autograd/functional.html#hvp)

Compute the dot product between the scalar function’s Hessian and a vector v at a specified point.

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 .

- v ([tuple](https://docs.python.org/3/library/stdtypes.html#tuple) of Tensors or Tensor ) – The vector for which the Hessian vector product is computed. Must be the same size as the input of func . This argument is optional when func ’s input contains a single element and (if it is not provided) will be set as a Tensor containing a single 1 .

- create_graph ([bool](https://docs.python.org/3/library/functions.html#bool) , optional ) – If True , both the output and result will be computed in a differentiable way. 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 hvp for said inputs, which is the expected mathematical value. Defaults to False .

Returns:

tuple with:

func_output (tuple of Tensors or Tensor): output of func(inputs)

hvp (tuple of Tensors or Tensor): result of the dot product with
the same shape as the inputs.

Return type:

output ([tuple](https://docs.python.org/3/library/stdtypes.html#tuple))

Example

```
>>> def pow_reducer(x):
...     return x.pow(3).sum()
>>> inputs = tensorplay.rand(2, 2)
>>> v = tensorplay.ones(2, 2)
>>> output = hvp(pow_reducer, inputs, v)
>>> output[0]
tensor(0.1448)
>>> output[1]
tensor([[2.0239, 1.6456],
        [2.4988, 1.4310]])
```

Note

This function is significantly slower than vhp due to backward mode AD constraints.
If your function is twice continuously differentiable, then hvp = vhp.t(). So if you
know that your function satisfies this condition, you should use vhp instead that is
much faster with the current implementation.