mescla.uncertainty.propagation.genereux_sigma¶

mescla.uncertainty.propagation.genereux_sigma(c_sample, c_1, c_2, sd_sample, sd_1, sd_2)[source]¶

Standard deviation of the two-component mixing fraction f1.

With \(f_1 = (C_s - C_2)/(C_1 - C_2)\), first-order Gaussian propagation gives

\[\sigma_{f_1}^2 = \left[\frac{C_s - C_2}{(C_1 - C_2)^2}\sigma_{C_1}\right]^2 + \left[\frac{C_s - C_1}{(C_1 - C_2)^2}\sigma_{C_2}\right]^2 + \left[\frac{1}{C_1 - C_2}\sigma_{C_s}\right]^2\]

Parameters:

c_sample (float or array_like) – Tracer concentration in the mixture(s).
c_1 (float) – Tracer concentration in each end-member.
c_2 (float) – Tracer concentration in each end-member.
sd_sample (float) – Corresponding standard deviations.
sd_1 (float) – Corresponding standard deviations.
sd_2 (float) – Corresponding standard deviations.

Returns:

float or ndarray

Return type:

ndarray | float

Examples

Doubling the end-member contrast halves the uncertainty:

>>> round(genereux_sigma(50.0, 100.0, 0.0, 1.0, 5.0, 5.0), 4)
0.0367
>>> round(genereux_sigma(100.0, 200.0, 0.0, 1.0, 5.0, 5.0), 4)
0.0184