NAME

Math::Symbolic::Custom::ErrorPropagation - Calculate Gaussian Error Propagation

SYNOPSIS

  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

DESCRIPTION

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.

$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 ) ) =
    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.

AUTHOR

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

SEE ALSO

New versions of this module can be found on http://steffen-mueller.net or CPAN.

Math::Symbolic

Math::Symbolic::Custom, Math::Symbolic::Custom::Base,