lin_error_propagation Interface

public interface lin_error_propagation

Performs linear error (or uncertainties) propagation given the sensitivity coefficients and a covariance matrix. The following formula is applied:

$$\sigma^2_{y} = S \Sigma^{X} S^\intercal$$

Where:

• $y$ is the response whose uncertainty is to be calculated.
• $X$ is a set of input parameters to propagate their uncertainty to $y$.
• $S$ is the vector of sensitivity coefficients of $y$ with respect to the different parameters in $X$.
• $\Sigma^{x}$ is the covariance matrix of the parameters in $X$.

Syntax

y = lin_error_propagation(s,m)

Where:

• s = vector of rank 1 with real numbers containing the sensitivity coefficients.
• m = array of rank 2 containing the covariance matrix.
• y = real number of the same kind as s and m with the error or uncertainty propagated to this new variable.

Example

The following program calculates the linearly propagated error:

 PROGRAM lin_error_propagationExample
    USE FU_Statistics, ONLY: lin_error_propagation
    IMPLICIT NONE
    REAL, DIMENSION(3) :: s = [1., 2., 3.]
    REAL, DIMENSION(3,3) :: m = &
       RESHAPE((/0.5, 2., 3., 2., 5.4, 6., 3., 6., 3.3/),SHAPE(m))
    WRITE(*,*) lin_error_propagation(s, m)
 END PROGRAM lin_error_propagationExample

Module Procedures