URL:
<http://gna.org/bugs/?22557>
Summary: Monte-Carlo simulations for R1rho dispersion
analysis, does not include randomization of R1.
Project: relax
Submitted by: tlinnet
Submitted on: Mon 01 Sep 2014 10:28:33 AM UTC
Category: relax's source code
Specific analysis category: None
Priority: 6
Severity: 4 - Important
Status: None
Assigned to: None
Originator Name:
Originator Email:
Open/Closed: Open
Release: Branches
Discussion Lock: Any
Operating System: All systems
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Details:
Please see:
http://thread.gmane.org/gmane.science.nmr.relax.devel/6969
The Monte-Carlo simulations only randomize data for R1rho prime.
It does not randomize for R1.
This is a bug.
It would then be possible to compare to error estimation from Co-variance
matrix.
Example DPL94:
One would first get the error for R1_ex, and then for Rex.
R1rho = R1_ex + Rex = R1 * cos(theta)**2 + (R1rho_p + ( (phi_ex * kex) /
(kex**2 + we**2) ) ) * sin(theta)**2.
Get the error from the covariance of R1_ex, and then for Rex.
J1: of R1 * cos(theta)**2
J2: of (R1rho_p + ( (phi_ex * kex) / (kex**2 + we**2) ) ) * sin(theta)**2.
Then Covar of J1, Covar of J2.
Then
STD(DPL94) = sqrt(diag(cov_J1)) + sqrt(diag(cov_J2))
This follows for standard rule of error propagation.
This error should approx correspond to the error for 10.000 Monte-Carlo
simulations.
My statements here should be checked thoroughly before implementation.
There is maybe a shortcut:
"Uncertainty in a Function of Several Variables"
Page 75, An Introduction to Error Analysis
http://www.uscibooks.com/taylornb.htm
std(q) = sqrt ( (dq/dx *std(x))**2 + (dq/dz *std(z))**2 )
where x, z are R1 and R1rho_prime, and q is DPL94.
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[bug #22557] Monte-Carlo simulations for R1rho dispersion analysis, does not include randomization of R1.