OK. I'm looking at the PickLine output for the transfer lines (plus endcap only) for 10-October. Something is very wrong here. In each DCOPS, CCD number 1 has values for areabackground that are 0, while the rest are of order 340. The values for other areas printed out in this section seem also to be essentially meaningless. (In print(), _extensions is set true, apparently, even though the contents are useless.)
In any event, I drop this information from the .xls file and continue. I need to define a standard orientation for the DCOPS. Let the standard be such that the DCOPS vector is in the Plus direction.
Using the 10-October 0T data I generated this XLS worksheet
From that I generated this Pari script (I have to iterate once to get rid of the 0.E-25*s1h type of terms in CONST). That gives me this set of answers in the fit:
I calculated what the (uncalibrated) DCOPS CCD values ought to be in the standard orientation, and then calculated what the distance from the center of the DCOPS would be in the new coordinates: H (horizontal, = Rφ) and V (vertical = Radial).
At each transfer line 1-6 there are 2 slopes and 2 intercepts: snh with dnh and snv with dnv
I assume that YE+3 is fixed in position and rotation (I have to pick something), and use cnx and cny to represent the shift in YE+n. Since the DCOPS are all pretty much at the same radius (at 0T!) rotations can be represented by a shift in Rφ, which I label dHn.
The dH1 and dH2 have to be divided by the radius of the transfer DCOPS to find the angle. The radius being 7250mm, that gives dH1ang = -0.98mrad and dH2ang = -0.86mrad
From CMS-SG-UR-0124, disk centers and Z rotations: (error on position is 300 microns, on angle is 0.1 mrad)
|Type||YE+1||YE+2||YE+3||YE+1 - YE+3||YE+2 - YE+3|
|X (mm)||0.58||-0.15||0.59||-.01 c1x=-1.03 ± .05||-0.74 c2x=-1.08 ± .03|
|Y (mm)||-1.37||0.57||-0.04||-1.33 c1y=1.28 ± .05||0.61 c2y=2.07 ± .03|
|φ z (mrad)||-0.43||-0.46||0.18||-0.61 dH1→ -0.98 ± .01||-0.64 dH2→ -0.86 ± .004|
I think it fair to say that unless the errors are much larger than expected, these values are not consistent.
OK, who is right? What could have gone wrong?
I could have screwed up the model, or bollixed the data processing to give me the numbers. You can inspect this yourself in the Excel file linked above, and examine the Pari script. I'm fitting 30 variables using 47 points (one is missing), so the issue would be matrix stability rather than insufficient points.
The PG numbers are only reliable if none of the disks were moved before the measurements were taken. YE+3 would have to move first. But the before and after CRAFT measurements for YE+3 are similar, so there seems no chance of a bulk dislocation or rotation.
|s1h||-0.00011930 ± 0.000020704|
|s2h||0.0021423 ± 0.000023655|
|s3h||-0.00089929 ± 0.000020704|
|s4h||-0.00098290 ± 0.000020239|
|s5h||-0.00089273 ± 0.000020180|
|s6h||-0.00054225 ± 0.000020239|
|s1v||-0.0028544 ± 0.000016879|
|s2v||0.00080020 ± 0.000016667|
|s3v||-0.0018430 ± 0.000016879|
|s4v||-0.0026297 ± 0.000016879|
|s5v||-0.0021752 ± 0.000016667|
|s6v||-0.0029367 ± 0.000016879|
|d1h||-1.1968 ± 0.030912|
|d2h||0.56219 ± 0.031994|
|d3h||-0.44802 ± 0.030912|
|d4h||-1.0943 ± 0.030751|
|d5h||0.53755 ± 0.030731|
|d6h||0.35138 ± 0.030751|
|d1v||-1.4769 ± 0.029525|
|d2v||-0.56200 ± 0.029462|
|d3v||-1.3783 ± 0.029525|
|d4v||-1.4879 ± 0.029525|
|d5v||-1.7963 ± 0.029462|
|d6v||-1.0348 ± 0.029525|
|c1x||-1.0337 ± 0.052488|
|c2x||-1.0850 ± 0.027695|
|c1y||1.2830 ± 0.051012|
|c2y||2.0705 ± 0.027695|
|dH1||-7.1116 ± 0.052601|
|dH2||-6.2475 ± 0.027695|
These are taken from the square root of the diagonal of the inverse of the matrix. The correlated error matrix is too big to show here, but if you want to see it. The dH1 and dH2 are strongly correlated, as are c1x and c2x, and c1y and c2y; and in about the same way. The scaled correlation matrix shows quite a few (not unexpected) correlations.
Ack. Should have checked earlier. The matrix is almost (roundoff errors) singular. The original matrix has determinant E100, which makes dealing with the inverse tricky.
Modified 08-April-2009 at 10:17
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