[bug #22557] Monte-Carlo simulations for R1rho dispersion analysis, does not include randomization of R1.

[Edward d Auvergne]

Update of bug #22557 (project relax):

  Status:None => Postponed  


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[bug #22557] Monte-Carlo simulations for R1rho dispersion analysis, does not include randomization of R1.

[Troels E. Linnet]

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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