Advanced¶
Take advanced to mean without graphical interface, without prejudice to people who prefer touching mice to keyboards. The program was mainly developed for online analysis during experiments to get an idea if the setup and sample etc are OK. Other programs exist which might to a better job (eg GRAINDEX [link]) and you should consider trying for serious data analysis. Notably [Grainspotter] reads ImageD11 gve files and tends to make a better indexing. Nevertheless, the free nature of ImageD11 and convenience of the python language could tempt you to process large volumes of data using the functions in the program. Currently the indexing module is the most easily accessible for script writers. The other modules should be separated from the gui very soon. edit?]#Using_the_indexing_module_interactively?
Using the indexing module interactively
An example interactive session is given here. A trial orientation is generated from one g-vector file and then used to index another:
fable4:~/id11/lab6grains % /bliss/users/blissadm/bin/python
Python 2.4 (#3, Mar 11 2005, 10:10:40)
[GCC 3.3 20030226 (prerelease) (SuSE Linux)] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> from ImageD11 import indexing
>>> myindexingobject = indexing.indexer()
>>> dir(myindexingobject) # Gives a list of commands/properties
['__doc__', '__init__', '__module__', 'assigntorings', 'cosine_tol',
'coverage', 'ds_tol', 'find', 'friedelpairs', 'getind', 'gv', 'hkl_tol',
'max_grains', 'minpks', 'readgvfile', 'refine', 'ring_1', 'ring_2',
'saveindexing', 'saveubis', 'score', 'scores', 'scorethem', 'ubis',
'uniqueness', 'unitcell', 'wavelength']
>>> # Read in some filtered peaks (only the strong ones)
>>> myindexingobject.readgvfile("filt.gve")
Got wavelength from gv file of 0.3333
Read your gv file containing (112, 3)
>>> myindexingobject.assigntorings()
Maximum d-spacing considered 0.991615
Ring assignment array shape (112,)
Ring ( h, k, l) Mult total indexed to_index
Ring 0 ( -1, 0, 0) 6 11 0 11
Ring 1 ( -1, -1, 0) 12 39 0 39
Ring 2 ( -1, -1, -1) 8 17 0 17
Ring 3 ( -2, 0, 0) 6 13 0 13
Ring 4 ( -2, -1, 0) 24 13 0 13
Ring 5 ( -2, -1, -1) 24 4 0 4
Ring 6 ( -2, -2, 0) 12 2 0 2
Ring 7 ( -3, 0, 0) 30 8 0 8
Ring 8 ( -3, -1, 0) 24 3 0 3
Ring 9 ( -3, -1, -1) 24 1 0 1
Ring 10 ( -2, -2, -2) 8 0 0 0
Ring 11 ( -3, -2, 0) 24 0 0 0
Ring 12 ( -3, -2, -1) 48 0 0 0
Ring 13 ( -4, 0, 0) 6 0 0 0
Using only those peaks which are assigned to rings for scoring trial matrices
Shape of scoring matrix (111, 3)
>>> # Choose which rings to use for generating trial orientations
>>> print myindexingobject.ring_1
1
>>> print myindexingobject.ring_2
2
>>> myindexingobject.ring_1=0
>>> myindexingobject.ring_2=0
>>> print myindexingobject.ring_1, myindexingobject.ring_2
0 0
>>> # Find the trial orientations or grains
>>> myindexingobject.find()
hkls of rings being used for indexing
Ring 1: [(-1, 0, 0), (0, -1, 0), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)]
Ring 2: [(-1, 0, 0), (0, -1, 0), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 0)]
Possible angles and cosines between peaks in rings:
90.0 6.12303176911e-17
Number of peaks in ring 1: 11
Number of peaks in ring 2: 11
Minimum number of peaks to identify a grain 10
Percent done 90.909% ... potential hits 10
Number of trial orientations generated 10
Time taken 0.00019097328186
>>> # Test those orientations against the data
>>> myindexingobject.scorethem()
Scoring 10 potential orientations
Tested 9 Found 2 Rejected 0 as not being unique
Number of orientations with more than 10 peaks is 2
Time taken 0.00936889648438
UBI for best fitting
[[ 2.58780454 -3.00470196 1.24755448]
[-1.09995311 0.69776998 3.94961316]
[-3.05800078 -2.78861403 -0.35888152]]
Indexes 42 peaks, with <drlv2>= 0.00370687876058
That was the best thing I found so far
Number of peaks assigned to rings but not indexed = 11
>>> # Look at the orientations found:
>>> for u in myindexingobject.ubis: print u
...
[[ 2.59661965 -2.99631727 1.24883939]
[-1.09621729 0.69589138 3.94892308]
[-3.05545818 -2.79602729 -0.35546775]]
[[ 0.16666909 -3.31769292 2.49901696]
[-1.36226123 2.31902622 3.16959182]
[-3.92382675 -0.94603473 -0.9942598 ]]
>>> # see what the refined cell parameters are
>>> indexing.ubitocellpars(myindexingobject.ubis[0])
(4.156916, 4.156915999, 4.156916, 90.0, 89.9999,89.9999)
>>> indexing.ubitocellpars(myindexingobject.ubis[1])
(4.156916, 4.15691600, 4.1569159,90.00, 89.9999, 89.9999)
>>> # These look a bit too good to be true...?
Got an orientation now - test it on another dataset (could be another rotation or a different detector etc).
>>> # Anyway, apply these to another dataset with weak peaks in it too (peak.gve)...
>>> another_indexing_object = indexing.indexer()
>>> another_indexing_object.readgvfile("peak.gve")
Got wavelength from gv file of 0.3333
Read your gv file containing (1734, 3)
>>> another_indexing_object.assigntorings()
Maximum d-spacing considered 1.177329
Ring assignment array shape (1734,)
Ring ( h, k, l) Mult total indexed to_index
Ring 0 ( -1, 0, 0) 6 71 0 71
Ring 1 ( -1, -1, 0) 12 160 0 160
Ring 2 ( -1, -1, -1) 8 88 0 88
Ring 3 ( -2, 0, 0) 6 65 0 65
Ring 4 ( -2, -1, 0) 24 203 0 203
Ring 5 ( -2, -1, -1) 24 143 0 143
Ring 6 ( -2, -2, 0) 12 76 0 76
Ring 7 ( -3, 0, 0) 30 191 0 191
Ring 8 ( -3, -1, 0) 24 149 0 149
Ring 9 ( -3, -1, -1) 24 127 0 127
Ring 10 ( -2, -2, -2) 8 25 0 25
Ring 11 ( -3, -2, 0) 24 95 0 95
Ring 12 ( -3, -2, -1) 48 142 0 142
Ring 13 ( -4, 0, 0) 6 13 0 13
Ring 14 ( -4, -1, 0) 48 67 0 67
Ring 15 ( -4, -1, -1) 36 47 0 47
Ring 16 ( -3, -3, -1) 24 17 0 17
Ring 17 ( -4, -2, 0) 24 13 0 13
Ring 18 ( -4, -2, -1) 48 27 0 27
Ring 19 ( -3, -3, -2) 24 5 0 5
Using only those peaks which are assigned to rings for scoring trial matrices
Shape of scoring matrix (1724, 3)
>>> another_indexing_object.hkl_tol=0.1 # Make a bigger tolerance in case grain rotates
>>> test_orientation = myindexingobject.ubis[0]
>>> print test_orientation
[[ 2.59661965 -2.99631727 1.24883939]
[-1.09621729 0.69589138 3.94892308]
[-3.05545818 -2.79602729 -0.35546775]]
>>> new_orientation = another_indexing_object.refine(test_orientation)
>>> print new_orientation
[[ 2.58919314 -3.00117096 1.24689206]
[-1.09852789 0.69658936 3.95070245]
[-3.05916685 -2.79050878 -0.3580728 ]]
>>> indexing.ubitocellpars(new_orientation)
(4.1552001238, 4.1593328915, 4.15615895,89.993, 89.975, 90.029)
>>> # These look like they were really refined. Maybe some peaks are
>>> # used that should not be due to the hkl_tol of 0.1 (a bit big)
>>> indexed_peaks = another_indexing_object.getind(new_orientation,tol=0.05)
>>> print indexed_peaks.shape
(339,)
>>> # So 339 peaks seem to be indexed with the peak.gve dataset and tol=0.05
>>> # Have a look at the hkls generated by the UBI matrix
>>> for k in indexed_peaks:
... print matrixmultiply(new_orientation,another_indexing_object.gv[k])
...
[ 0.10168799 -0.9761811 0.13347752]
[ 9.13527496e-04 1.97985539e-04 -9.97830257e-01]
[ 9.97934113e-01 7.92302450e-04 3.49838267e-03]
[ 0.99452548 -0.06653118 -0.05044758]
[ -3.98020413e-04 -9.99843377e-01 1.47886732e-04]
...<many lines snipped>..
>>> # etc
Transformations and peak merging without the gui¶
Use the history from the Tk gui...
Separating_U_from_UBI¶
Seems to come up a lot for some people? UBI is inverse of (UB), so (UB)^{-1}=B^{-1}U^{-1}, but U^{-1} is also transpose(U), so inevitably it gets flipped, even if you know what “B” is. There is now a ubitocellpars routine in (svn) indexing.py, which you can use to construct a “B” matrix according to some convention. “B” is chosen as a Cholesky factor of the product (UBI).(UBI)^T (=g, the metric tensor). Since you are free to chose “B” however you like (x along a, y along b*, z orthogonal etc) then you also chose “U” however you like (eg x along a*, y along b, z orthogonal). Take a triclinic or hexagonal unit cell instead of cubic and you see the mess. So perhaps this is not the “U” you want - please correct it - or add some sort of “U” labelling:
import Numeric as n
import LinearAlgebra as l
def getU(ubi):
# start by getting metric tensor
g=n.matrixmultiply(ubi,n.transpose(ubi))
# one convention for B is a Cholesky factor of g (triangular)
bi=l.cholesky_decomposition(g)
# get inverse to separate this from u
b = l.inverse(bi)
# ubi = (UB)^{-1} = B^{-1} U^{-1}
# ... premultiply B.B^{-1}.U^{-1}
ui=n.matrixmultiply(b,ubi)
# transpose is inverse - roughly 50% chance I got this wrong
# ... or C/fortran array ordering confuses as well
u=n.transpose(ui)
return u
>>> ubi
[[2.59661965, -2.99631727, 1.24883939],
[-1.0962173, 0.695891380, 3.94892308],
[-3.0554582, -2.79602729, -0.35546775]]
>>> getU(ubi)
array([[ 0.6246505 , -0.26370927, -0.73503005],
[-0.72080294, 0.16740569, -0.67262059],
[ 0.3004245 , 0.94996461, -0.08551237]])