This module extends the functionality of Math::Symbolic by offering
facilities to calculate the propagated variance of a function of
variables with variances themselves.
The module adds a method to all Math::Symbolic objects.
CW$ms_tree->apply_error_propagation( [list of variable names] )
This method does not modify the Math::Symbolic tree itself, but instead
calculates and returns its variance based on its variable dependencies which
are expected to be passed as arguments to this method in form of a list
of variable names.
The variance is returned as a Math::Symbolic tree itself. It is calculated
using the Gaussian error propagation formula for uncorrelated variances:
variance( f(x_1, x_2, ..., x_n ) ) =
variance(x_i)^2 * (df/dx_i)^2
In the above formula, the derivatives are partial derivatives and the
component variances variance(x_i) are represented as sigma_x_i in the
resulting formula. (The x_i is replaced by the variable name, though.)
Please refer to the SYNOPSIS for an example.