copapy.jacobian

copapy.jacobian(x, y)

Returns the Jacobian dx/dy where x and y might be a scalar, a list of scalars, a vector or a tensor. The result has the shape x.shape + y.shape. It is calculated with one reverse-mode pass of grad per element of x.

Overloads:

• x (value[Any]), y (value[Any]) → value[float] | float

• x (value[Any]), y (vector[Any]) → vector[float]

• x (value[Any]), y (quaternion) → quaternion

• x (vector[Any] | tensor[Any] | quaternion), y (value[Any] | vector[Any] | tensor[Any] | quaternion) → tensor[float]

• x (Any), y (tensor[Any]) → tensor[float]

• x (Sequence[Any]), y (Sequence[value[Any]]) → list[list[value[float] | float]]

• x (Sequence[Any]), y (value[Any]) → list[value[float] | float]

For a scalar x the result is the same as of grad(x, y). The result is a list of lists if x and y are lists and otherwise a tensor. Arrays are not supported, an array can be used as tensor by cp.tensor(arr).

Parameters:

• x (Any) – Value to return derivative of

• y (value[Any] | Sequence[value[Any]] | vector[Any] | tensor[Any] | quaternion) – Value(s) to derive in respect to

Returns:

Derivative of x with the dimensions of x and y