klampt.math.autodiff.pytorch module

class klampt.math.autodiff.pytorch.ADModule

Bases: torch.autograd.function.Function

Converts a Klamp’t autodiff function call or function instance to a PyTorch Function. The class must be created with the terminal symbols corresponding to the PyTorch arguments to which this is called.

static backward(ctx, grad)

Defines a formula for differentiating the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by as many outputs did forward() return, and it should return as many tensors, as there were inputs to forward(). Each argument is the gradient w.r.t the given output, and each returned value should be the gradient w.r.t. the corresponding input.

The context can be used to retrieve tensors saved during the forward pass. It also has an attribute ctx.needs_input_grad as a tuple of booleans representing whether each input needs gradient. E.g., backward() will have ctx.needs_input_grad[0] = True if the first input to forward() needs gradient computated w.r.t. the output.

static check_derivatives_torch(func, terminals, h=1e-06, rtol=0.01, atol=0.001)

static forward(ctx, func, terminals, *args)

Performs the operation.

This function is to be overridden by all subclasses.

It must accept a context ctx as the first argument, followed by any number of arguments (tensors or other types).

The context can be used to store tensors that can be then retrieved during the backward pass.

class klampt.math.autodiff.pytorch.TorchModuleFunction(module)

Bases: klampt.math.autodiff.ad.ADFunctionInterface

Converts a PyTorch function to a Klamp’t autodiff function class.

derivative(arg, *args)

Returns the Jacobian of the function w.r.t. argument #arg.

Parameters

• arg (int) – A value from 0,…,self.n_args()-1 indicating that we wish to take \(df/dx_{arg}\).

• args (list of ndarrays) – arguments for the function.

Returns

A numpy array of shape (self.n_out(),self.n_in(arg)). Keep in mind that even if the argument or result is a scalar, this needs to be a 2D array.

If the derivative is not implemented, raise a NotImplementedError.

If the derivative is zero, can just return 0 (the integer) regardless of the size of the result.

Return type

ndarray

eval(*args)

Evaluates the application of the function to the given (instantiated) arguments.

Parameters

args (list) – a list of arguments, which are either ndarrays or scalars.

jvp(arg, darg, *args)

Performs a Jacobian-vector product for argument #arg.

Parameters

• arg (int) – A value from 0,…,self.n_args()-1 indicating that we wish to calculate df/dx_arg * darg.

• darg (ndarray) – the derivative of x_arg w.r.t some other parameter. Must have darg.shape = (self.n_in(arg),).

• args (list of ndarrays) – arguments for the function.

Returns

A numpy array of length self.n_out()

If the derivative is not implemented, raise a NotImplementedError.

Return type

ndarray

n_in(arg)

Returns the number of entries in argument #arg. If 1, this can either be a 1-D vector or a scalar. If -1, the function can accept a variable sized argument.

n_out()

Returns the number of entries in the output of the function. If -1, this can output a variable sized argument.

klampt.math.autodiff.pytorch.ad_to_torch(func, terminals=None)

Converts a Klamp’t autodiff function call or function instance to a PyTorch Function. If terminals is provided, this is the list of arguments that PyTorch will expect. Otherwise, the variables in the expression will be automatically determined by the forward traversal order.

klampt.math.autodiff.pytorch.torch_to_ad(module, args)

Converts a PyTorch function applied to args (list of scalars or numpy arrays) to a Klamp’t autodiff function call on those arguments.