mailRe: Is theta = atan2(omega1, Delta_omega) of theta = atan2(Delta_omega, omega1)


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Posted by Troels Emtekær Linnet on July 28, 2014 - 11:47:
Hi Ed.

You are correct.

I got confused yesterday, and thought the theta angle was between
X, Z axis instead of the Z,X axis.

Best
Troels

2014-07-28 11:29 GMT+02:00 Edward d'Auvergne <edward@xxxxxxxxxxxxx>:
Hi Troels,

Do you have a literature reference where this is inverted?  Have a
look at Art Palmer's 2001 review:

  - Palmer, A. G. III, Kroenke, C. D. and Loria J. P. (2001)  Nuclear
Magnetic Resonance Methods for Quantifying Microsecond-to-Millisecond
Motions in Biological Macromolecules.  Methods Enzymol., 339, 204-238.
(http://dx.doi.org/10.1016/S0076-6879(01)39315-1).

Specifically at the top of page 216 where you can see:

tan(theta) = omega1 / Omega.

Therefore:

theta = arctan(omega1 / Omega).

So it should be correct in relax using the atan2() function.  Or am I
missing something?

Regards,

Edward






On 25 July 2014 19:45, Troels Emtekær Linnet <tlinnet@xxxxxxxxxxxxx> wrote:
Hi Edward.

I was stumpling over the expression
theta = atan2(omega1, Delta_omega)

in:
specific_analyses/relax_disp/data.py in return_offset_data().

atan2 requires:
math.atan2(y, x)
Return atan(y / x), in radians. The result is between -pi and pi. The
vector in the plane from the origin to point (x, y) makes this angle
with the positive X axis. The point of atan2() is that the signs of
both inputs are known to it, so it can compute the correct quadrant
for the angle. For example, atan(1) and atan2(1, 1) are both pi/4, but
atan2(-1, -1) is -3*pi/4.

But what is y, and x?

If I look at my own figure at:
http://wiki.nmr-relax.com/images/1/12/Fig1_Palmer_Massi_2006.png

I would say that y is Delta_omega, and x is omega1.

Have I done this wrong earlier?

Best
Troels

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