Example using test1.smr data set¶
Input Commands¶
Start the program from the data directory in the source tree.
We’ll use UNIX shell redirection to get everything in a text file:
cd src/jldesmear/data
python ../api/traditional.py < test1.inp > test1.out
The program will print a header:
<<< SAS data desmearing, by Pete R. Jemian
<<< Based on the iterative technique of JA Lake and PR Jemian.
<<< P.R.Jemian,; Ph.D. thesis, Northwestern University (1990).
<<< J.A. Lake; ACTA CRYST 23 (1967) 191-194.
<<<
<<< $Id$
<<< desmear using the same FORTRAN & C command line interface
<<<
Then, the program will ask some questions about the input data.
Here, the test data is test1.smr:
<<< What is the input data file name? <''=Quit> <> ==>
>>> test1.smr
Name the (new) file name to write the results. If it exists,
it will be overwritten without further comment.
Here, we choose the name test1.out:
<<< What is the output data file name? <> ==>
>>> test1.out
The slit length is the term l_o and has the same units as X:
<<< What is the slit length (x-axis units)? <1.0> ==>
>>> .08
To complete the smearing integral at highest X, it is necessary
to extrapolate beyond the range of measured data.
Choose the functional form that best represents the data at
highest X. Fit coefficients will be evaluated for each
desmearing iteration over the range X_start <= X <= X_max:
<<< Extrapolation forms to avoid truncation-error.
<<< constant = flat background, I(q) = B
<<< linear = linear, I(q) = b + q * m
<<< powerlaw = power law, I(q) = b * q^m
<<< Porod = Porod law, I(q) = Cp + Bkg / q^4
<<<
Choose the linear form (although constant would work with this data as well):
<<< Which form? <constant> ==>
>>> linear
This is X-start as noted above: .08:
<<< What X to begin evaluating extrapolation (x-axis units)? <1.0> ==>
>>> .08
Accept the solution after 20 iterations this time:
<<< How many iteration(s)? (10000 = infinite) <10000> ==>
>>> 20
This question is largely historical. The fast method
is always the best choice. The others were implementations of either
Jansson or Halsey & Blass. They converge more slowly by far.
That said, you are free to re-determine this for yourself.
Press the [return] key to accept the default suggestion:
<<< Weighting methods for iterative corrections:
<<< Correction = weight * (MeasuredI - SmearedI)
<<< constant: weight = 1.0
<<< fast: weight = CorrectedI / SmearedI
<<< ChiSqr: weight = 2*SQRT(ChiSqr(0) / ChiSqr(i))
<<<
<<< Which method? <fast> ==>
>>>
Program output to console¶
Now the program starts the work of desmearing. The first step shows
an awful chi-square statistic. This will improve with subsequent iterations.
The plot is standardized residual vs. data point number. There are
========== bars indicated at +1 and -1; these merge together
on the first plot.:
Input file: test1.smr
-/|\ ...
standardized residuals, ChiSqr = 1.29823e+07, iteration=0
x: min=1 step=3.45833 max=250
y: min=-545.836 step=24.8717 max=1.34169
-------------------------------------------------------------------------
| + |
|==============================================+++++++++++++++++++++++++++|
|+ ++ |
| ++ |
| ++ |
|+ + ++ |
|++ + ++ |
| + ++ |
| +++ ++ |
| +++ + |
| ++ + |
| ++ ++ |
| + + |
| ++ +++ ++ |
| ++ +++++ + |
| ++++++++++++ + |
| + |
| + |
| + |
| + |
| + |
| + |
| + |
-------------------------------------------------------------------------
After the next iteration, the chi-squared statistic has improved by an order of magnitude but the plot still does not different:
standardized residuals, ChiSqr = 1.36804e+06, iteration=1
x: min=1 step=3.45833 max=250
y: min=-206.354 step=9.44611 max=1.46073
-------------------------------------------------------------------------
| + |
|================================================+++++++++++++++++++++++++|
|+ ++ |
| ++ |
|+ + |
| + + + |
| +++ ++ |
| +++++ ++ |
| +++ ++ |
| ++ +++++ ++ |
| ++ +++++++ ++ |
| +++++++++++ + |
| + + |
| + |
| + |
| ++ |
| + |
| + |
| + |
| + |
| + |
| + |
| + |
-------------------------------------------------------------------------
Skipping forward a few iterations, we see some real progress:
standardized residuals, ChiSqr = 566.385, iteration=5
x: min=1 step=3.45833 max=250
y: min=-3.97891 step=0.499962 max=7.02024
-------------------------------------------------------------------------
| + |
| + |
| |
| |
| |
| |
| |
| + + + |
| + + +++ |
| + ++++ |
|+ + ++++ + |
|++ + ++ |
| + + ++ ++ + |
|=======+===+=+=++=++=+==============+=============+===+===+======+====== |
| + ++ +++ + ++ +++++++ + + + ++ + ++++++++++++++++|
|+ +++ + + ++ +++++ + ++++++++++ + + ++++ + ++++++++++++++++ |
|+ + + ++ + + ++ + + + + ++ +++ +++++ ++ + |
|========+===================++=====+==========+=+++=====+=============== |
| + + +++ |
| + |
| + + |
| ++ |
| ++ |
-------------------------------------------------------------------------
After about 10 iterations or so, it seems convergence has been achieved. The chi-squared statistic has dropped and the plot looks more randomly-arranged about 0.:
standardized residuals, ChiSqr = 103.479, iteration=11
x: min=1 step=3.45833 max=250
y: min=-2.89125 step=0.349475 max=4.7972
-------------------------------------------------------------------------
| + |
| + |
| |
| |
| |
| + |
| + |
| |
| |
| |
|+ |
|=+====+================================================================= |
| + ++ + + + + + + + |
| + + + + ++ ++ + + ++ ++ +++ ++ + + |
|+ +++ ++++++++++++ ++ +++++ ++++++++++++++ ++++ ++++ +++++++++++++++++|
| + ++ +++ ++ ++++ +++++++++ ++ ++++++++ +++++ ++ ++ ++ + ++++ |
|++ + + + + ++ + + + + |
|====++=+================================================================ |
|+ + |
| |
| + |
| |
| + |
-------------------------------------------------------------------------
Finally, after 20 iterations (numbered 0 .. 19):
standardized residuals, ChiSqr = 46.9362, iteration=19
x: min=1 step=3.45833 max=250
y: min=-2.94353 step=0.264922 max=2.88475
-------------------------------------------------------------------------
| + |
| |
| + |
| |
| + |
| + |
| |
|+ |
|==+===================================================================== |
| + ++ |
| + + ++ + + + ++ + + + ++++ +++ ++ +|
| + +++ ++++++ ++ + ++ ++++++++++++++++++++++++++++++++++ +++++++++++++ |
| ++ + ++++++ ++++ + +++++++++ + ++ ++++++++++++++++ +++++ + ++ + ++ ++ |
|++ + + ++ + + |
|+ + |
|======+================================================================= |
| + ++ |
| |
| |
| |
| |
| |
| + |
-------------------------------------------------------------------------
The result is accepted and the data are saved to the output file:
Saving data in file: test1.out
SAS log-log plot, final, S=input, D=desmeared
x: min=-7.898 step=0.0889226 max=-1.49558
y: min=3.0786 step=0.637599 max=17.1058
-------------------------------------------------------------------------
|D |
|DDDDDD |
|D DDDDDDDD |
| DDDDD |
| DDD |
| DDD |
| DDD |
| DD |
|SSSSS DDD |
| SSSSSSS DD |
| SSSSS DDD |
| SSSS DD |
| SSSS DDD |
| SSS DD |
| SSS DDD |
| SSS DDD |
| SSS DDD |
| SSSS DDD |
| SSS DD |
| SSSS DDDD |
| SSSSS DDDD |
| SSSSSDDDDDDDDDD D DD DDDDDD |
| D DDDDDSSDDDDDDDDDDDDDD|
-------------------------------------------------------------------------