annotaed error propagation (a71bd7c8) · Commits · Zolnierczuk, Piotr / DrSPINE

.gitignore

+1 −0

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		@@ -6,6 +6,7 @@
		*.a
		*.h5
		.*.swp
		.DS_Store

		# work directory (for tmp development)
		work/*

sources/data_types.f90

+26 −6

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		@@ -299,8 +299,8 @@ module data_types
		!! calibration set of data may also be present
		!!
		type collection_item
		!> fqt = sqt/sq is the standard evaluation result of 2*amplitude/(up-down)/resolution
		!! this shall contain the standard NSE result representing @f$ F(Q,t) = S(Q,t)/S(Q,t=0) @f$.
		!> fqt = sqt/sq is the standard evaluation result of 2*amplitude/(up-down)/resolution.
		!! This shall contain the standard NSE result representing @f$ F(Q,t) = S(Q,t)/S(Q,t=0) @f$.
		!! @f[
		!! F(Q,t) = \frac{2 A(Q,t)}{U(Q,t)-D(Q,t)} \times {\cal{R}}(Q,t)^{-1}
		!! @f]
		@@ -310,17 +310,30 @@ module data_types
		!! @f[
		!! F_{n+1} = (1-w_n) \, F_n + w_n \Delta
		!! @f]
		!! with
		!! and @f$ \delta_n @f$ the (statistical error) of the current value of fqt
		!! @f[
		!! \delta_{n+1}^2 = (1-w_n)^2 \, \delta_{n}^2 + w_n^2 \delta^2
		!! @f]
		!! where
		!! @f[
		!! w_n = \delta_n^2 / ( \delta_n^2 + \delta^2 )
		!! @f]
		!! with @f$ \delta_n @f$ the (statistical error) of the current value of fqt
		!!
		!! Note that the these expressions for @f$F_{n+1}@f$ and @f$\delta_{n+1}@f$ are equivalent:
		!!
		!! @f[
		!! \delta_{n+1}^2 = (1-w_n)^2 \, \delta_{n}^2 + w_n^2 \delta^2
		!! F_{n+1} = (1-w_n) \, F_n + w_n \Delta =
		!! \left(\frac{F_{n}}{\delta_{n}^2} + \frac{\Delta}{\delta^2} \right) /
		!! \left(\frac{1}{\delta{n}^2} + \frac{1}{\delta^2} \right)
		!! @f]
		!! and
		!! @f[
		!! \delta_{n+1}^2 = (1-w_n)^2 \, \delta_{n}^2 + w_n^2 \delta^2 = w_n \delta^2 =
		!! \left(\frac{1}{\delta_{n}^2} + \frac{1}{\delta^2} \right)^{-1}
		!! @f]
		real(kind=DBL) :: fqt

		!> sqt/sq-variance the variance of valuec collected in this bin during filling the collection bins,
		!> sqt/sq-variance the variance of values collected in this bin during filling the collection bins,
		!! during filling the value shall accumulate @f$ \langle fqt^2 \rangle @f$.
		!! The final variance is then sqrt(fqt_var - fqt**2).
		!! when adding a new increment @f$ \Delta \pm \delta @f$ with statistical error @f$ \delta @f$
		@@ -1362,6 +1375,13 @@ CONTAINS
		sqt%tq_bin(it,iq)%fqt_var = (1.0_DBL-w) sqt%tq_bin(it,iq)%fqt_var + w ps_sample%fqtRes%value**2
		sqt%tq_bin(it,iq)%fqt_err2 = (1.0_DBL-w)*2 sqt%tq_bin(it,iq)%fqt_err2 + w*2 ps_sample%fqtRes%sigma2

		! -----------------------------------------------------------------------------------------------------------------
		! (paz) testing error propagation: these three expressions are equivalent
		! (1.0_DBL-w)*2 sqt%tq_bin(it,iq)%fqt_err2 + w*2 ps_sample%fqtRes%sigma2 =
		! w * ps_sample%fqtRes%sigma2 =
		! (1/sqt%tq_bin(it,iq)%fqt_err2 + 1/ps_sample%fqtRes%sigma2)**(-1)
		! -----------------------------------------------------------------------------------------------------------------

		sqt%tq_bin(it,iq)%fqt_tau = (1.0_DBL-w) sqt%tq_bin(it,iq)%fqt_tau + w tau ! ps_sample%tau
		sqt%tq_bin(it,iq)%fqt_tau_var = (1.0_DBL-w) sqt%tq_bin(it,iq)%fqt_tau_var + w tau2 ! ps_sample%tau2