cached variable

[kunyuan]

Sometimes, a n-dimensional variable needs to be transformed before it could be used in the integrand. For example, the (r, theta, phi) spherical coordinates to (x, y, z). It will be more efficient for the variable to cache the transformed values if the integrand involves many variables.

One possible implementation is to add a cached array and add a transform function as the member of the variable struct. If the transform function is initialized, the variable will be transformed and saved to the cached array after every update.

[kunyuan]

It is better for the user to cache it in the user code