Math::Symbolic::Custom::ErrorPropagation - Calculate Gaussian Error Propagation
use Math::Symbolic qw/parse_from_string/; use Math::Symbolic::Custom::ErrorPropagation; # Force is mass times acceleration. my $force = parse_from_string('m*a'); # The measurements of the acceleration and the mass are prone to # statistical errors. (Hence have variances themselves.) # Thus, the variance in the force is: my $variance = $force->apply_error_propagation('a', 'm'); print $variance; # prints: # ( # ((sigma_a ^ 2) * ((partial_derivative(m * a, a)) ^ 2)) + # ((sigma_m ^ 2) * ((partial_derivative(m * a, m)) ^ 2)) # ) ^ 0.5
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.
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 ) ) = sqrt( sum_over_i=1_to_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.
Please send feedback, bug reports, and support requests to one of the contributors or the Math::Symbolic mailing list.
List of contributors:
Steffen M�ller, symbolic-module at steffen-mueller dot net
New versions of this module can be found on http://steffen-mueller.net or CPAN.