Matrix element LM plotting routines demo

28/11/19 v1, 07/02/20 updated Euler grouping,

Source notebook on Github.

Basic IO

[1]:

import sys
import os
import time
import numpy as np

# For module testing, include path to module here
modPath = r'D:\code\github\ePSproc'
# modPath = r'/home/femtolab/github/ePSproc/'
sys.path.append(modPath)
import epsproc as ep

* pyevtk not found, VTK export not available.

[2]:

# Load data from modPath\data
dataPath = os.path.join(modPath, 'data', 'photoionization')
dataFile = os.path.join(dataPath, 'n2_3sg_0.1-50.1eV_A2.inp.out')  # Set for sample N2 data for testing

# Scan data file
dataSet = ep.readMatEle(fileIn = dataFile)
dataXS = ep.readMatEle(fileIn = dataFile, recordType = 'CrossSection')  # XS info currently not set in NO2 sample file.

*** ePSproc readMatEle(): scanning files for DumpIdy segments.

*** Scanning file(s)
['D:\\code\\github\\ePSproc\\data\\photoionization\\n2_3sg_0.1-50.1eV_A2.inp.out']

*** Reading ePS output file:  D:\code\github\ePSproc\data\photoionization\n2_3sg_0.1-50.1eV_A2.inp.out
Expecting 51 energy points.
Expecting 2 symmetries.
Scanning CrossSection segments.
Expecting 102 DumpIdy segments.
Found 102 dumpIdy segments (sets of matrix elements).

Processing segments to Xarrays...
Processed 102 sets of DumpIdy file segments, (0 blank)
*** ePSproc readMatEle(): scanning files for CrossSection segments.

*** Scanning file(s)
['D:\\code\\github\\ePSproc\\data\\photoionization\\n2_3sg_0.1-50.1eV_A2.inp.out']

*** Reading ePS output file:  D:\code\github\ePSproc\data\photoionization\n2_3sg_0.1-50.1eV_A2.inp.out
Expecting 51 energy points.
Expecting 2 symmetries.
Scanning CrossSection segments.
Expecting 3 CrossSection segments.
Found 3 CrossSection segments (sets of results).
Processed 3 sets of CrossSection file segments, (0 blank)

[3]:

jobInfo = ep.headerFileParse(dataFile)
molInfo = ep.molInfoParse(dataFile)

*** Job info from file header.

 ePS n2, batch n2_3sg_0.1-50.1eV, orbital A2
 N2 X-state (3sg-1)
 E=0.1:1.0:50.1 (51 points)
 Fri Nov 30 08:47:52 EST 2018

*** Found orbitals
1   1 Ene =     -15.6719 Spin =Alpha Occup =   2.000000
2   2 Ene =     -15.6676 Spin =Alpha Occup =   2.000000
3   3 Ene =      -1.4948 Spin =Alpha Occup =   2.000000
4   4 Ene =      -0.7687 Spin =Alpha Occup =   2.000000
5   5 Ene =      -0.6373 Spin =Alpha Occup =   2.000000
6   6 Ene =      -0.6283 Spin =Alpha Occup =   2.000000
7   7 Ene =      -0.6283 Spin =Alpha Occup =   2.000000

*** Found atoms
Z =  7 ZS =  7 r =   0.0000000000   0.0000000000   0.5328050000
Z =  7 ZS =  7 r =   0.0000000000   0.0000000000  -0.5328050000

[4]:

ep.jobSummary(jobInfo, molInfo);


*** Job summary data
 ePS n2, batch n2_3sg_0.1-50.1eV, orbital A2
 N2 X-state (3sg-1)
 E=0.1:1.0:50.1 (51 points)
 Fri Nov 30 08:47:52 EST 2018

Electronic structure input: '/home/paul/ePS_stuff/n2/electronic_structure/n2_cc-pVQZ_geom.molden'
Initial state occ:               [2 2 2 2 2 4]
Final state occ:                 [2 2 2 2 1 4]
IPot (input vertical IP, eV):            15.58

*** Additional orbital info (SymProd)
Ionizing orb:                    [0 0 0 0 1 0]
Ionizing orb sym:                ['SG']
Orb energy (eV):                 [-17.34181631]
Orb energy (H):                  [-0.6373]
Orb energy (cm^-1):              [-139871.18257579]
Threshold wavelength (nm):       71.49435513338314

*** Molecular structure
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_5_1.png

Basic plotting

As shown in the basic demo notebook, basic plotting with Xarray functionality is a quick and easy way to plot matrix elements.

[5]:

# Plot matrix elements using Xarray functionality
daPlot = dataSet[0].sum('mu').sum('Sym').sel({'Type':'L'}).squeeze()
daPlot.pipe(np.abs).plot.line(x='Eke');
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_7_0.png

For more control, additional preprocessing with thresholding & selection can be used.

[6]:

selDims = {'Type':'L','Cont':'PU'}
daPlot = ep.matEleSelector(dataSet[0], thres=1e-2, inds = selDims, sq = True)
daPlot.pipe(np.abs).sum('mu').plot.line(x='Eke');
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_9_0.png

… or faceting …

[7]:

# Plot with faceting on symmetry
daPlot = ep.matEleSelector(dataSet[0], thres=1e-2, dims = 'Eke', sq = True).sum('mu').squeeze()
daPlot.pipe(np.abs).plot.line(x='Eke', col='Sym', row='Type');
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_11_0.png

Plotting maps with lmPlot

For complex multidimensional cases line plots get busy, quickly. A nice alternative is provided by Seaborn’s Clustermap, which produces a 2D map of values (i.e. a heatmap or image), with additional dimensional information as a side-bar. This is now implemented in ep.lmPlot().

[8]:

# Plot with sensible defaults - all dims
daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0])

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_14_1.png

In order to use Seaborn, the data is converted from a multidimensional Xarray to a 2D Pandas array. This displays nicely in Jupyter, so is also handy for inspecting values.

[9]:

daPlotpd

[9]:
Eke 0.1 1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 ... 41.1 42.1 43.1 44.1 45.1 46.1 47.1 48.1 49.1 50.1
l m mu Cont Targ Total it Type
1 -1 1 PU SG PU 1 L 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550 5.546815 5.238038 4.958515 4.707928 ... 4.042680 4.036124 4.026955 4.015319 4.001367 3.985246 3.967107 3.947097 3.925361 3.902040
V 8.900023 8.224738 7.627702 7.095200 6.617558 6.187859 5.801034 5.453317 5.141863 4.864476 ... 3.819254 3.808920 3.796564 3.782339 3.766394 3.748875 3.729921 3.709668 3.688240 3.665757
0 0 SU SG SU 1 L 11.823354 11.429458 11.111935 10.849149 10.627257 10.437825 10.275304 10.134910 10.010680 9.893534 ... 2.013047 2.027855 2.044452 2.062457 2.081542 2.101424 2.121856 2.142623 2.163536 2.184431
V 12.883046 12.311423 11.824577 11.410811 11.061133 10.768451 10.526367 10.328033 10.164873 10.025049 ... 1.911386 1.913114 1.917096 1.922952 1.930353 1.939023 1.948722 1.959246 1.970418 1.982089
1 -1 PU SG PU 1 L 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550 5.546815 5.238038 4.958515 4.707928 ... 4.042680 4.036124 4.026955 4.015319 4.001367 3.985246 3.967107 3.947097 3.925361 3.902040
V 8.900023 8.224738 7.627702 7.095200 6.617558 6.187859 5.801034 5.453317 5.141863 4.864476 ... 3.819254 3.808920 3.796564 3.782339 3.766394 3.748875 3.729921 3.709668 3.688240 3.665757
3 -1 1 PU SG PU 1 L 2.620714 3.416440 4.071325 4.629875 5.118714 5.553100 5.941282 6.287526 6.594077 6.862346 ... 5.148526 5.002561 4.857925 4.714821 4.573432 4.433917 4.296420 4.161067 4.027969 3.897223
V 2.484140 3.291182 3.949586 4.494447 4.953052 5.345025 5.683818 5.978440 6.234936 6.457456 ... 4.636261 4.495796 4.357692 4.222128 4.089249 3.959168 3.831972 3.707721 3.586455 3.468196
0 0 SU SG SU 1 L 3.513428 4.719556 5.785863 6.766306 7.695465 8.593950 9.472654 10.335015 11.177359 11.987428 ... 0.992670 1.058092 1.127714 1.198394 1.268089 1.335497 1.399805 1.460528 1.517392 1.570263
V 3.682143 4.976274 6.086735 7.067816 7.963633 8.806609 9.618839 10.413320 11.194093 11.954877 ... 0.902085 0.948535 1.001878 1.058275 1.115154 1.170855 1.224342 1.274995 1.322471 1.366606
1 -1 PU SG PU 1 L 2.620714 3.416440 4.071325 4.629875 5.118714 5.553100 5.941282 6.287526 6.594077 6.862346 ... 5.148526 5.002561 4.857925 4.714821 4.573432 4.433917 4.296420 4.161067 4.027969 3.897223
V 2.484140 3.291182 3.949586 4.494447 4.953052 5.345025 5.683818 5.978440 6.234936 6.457456 ... 4.636261 4.495796 4.357692 4.222128 4.089249 3.959168 3.831972 3.707721 3.586455 3.468196
5 -1 1 PU SG PU 1 L 0.003993 0.013835 0.021033 0.026999 0.033004 0.039974 0.048709 0.059861 0.073792 0.090524 ... 0.590336 0.593791 0.596895 0.599690 0.602218 0.604516 0.606620 0.608561 0.610372 0.612081
V 0.002819 0.010751 0.017869 0.026216 0.036675 0.049162 0.063460 0.079409 0.096872 0.115674 ... 0.525880 0.528078 0.530057 0.531856 0.533511 0.535057 0.536522 0.537936 0.539322 0.540704
0 0 SU SG SU 1 L 0.006473 0.021244 0.032261 0.041993 0.052580 0.065454 0.081763 0.102433 0.127951 0.158158 ... 0.498452 0.521782 0.544691 0.567177 0.589239 0.610871 0.632070 0.652828 0.673139 0.692996
V 0.005091 0.017458 0.027707 0.039802 0.055471 0.074663 0.097135 0.122785 0.151483 0.182848 ... 0.407791 0.428275 0.448349 0.468019 0.487292 0.506174 0.524672 0.542791 0.560539 0.577920
1 -1 PU SG PU 1 L 0.003993 0.013835 0.021033 0.026999 0.033004 0.039974 0.048709 0.059861 0.073792 0.090524 ... 0.590336 0.593791 0.596895 0.599690 0.602218 0.604516 0.606620 0.608561 0.610372 0.612081
V 0.002819 0.010751 0.017869 0.026216 0.036675 0.049162 0.063460 0.079409 0.096872 0.115674 ... 0.525880 0.528078 0.530057 0.531856 0.533511 0.535057 0.536522 0.537936 0.539322 0.540704
7 -1 1 PU SG PU 1 L 0.000024 0.000158 0.000305 0.000394 0.000405 0.000362 0.000320 0.000354 0.000491 0.000707 ... 0.031990 0.033121 0.034251 0.035381 0.036513 0.037648 0.038786 0.039930 0.041080 0.042237
V 0.000025 0.000150 0.000266 0.000318 0.000325 0.000356 0.000461 0.000630 0.000840 0.001086 ... 0.022021 0.022759 0.023500 0.024244 0.024994 0.025749 0.026511 0.027280 0.028058 0.028846
0 0 SU SG SU 1 L 0.000020 0.000145 0.000292 0.000373 0.000355 0.000266 0.000224 0.000373 0.000628 0.000955 ... 0.040133 0.042184 0.044257 0.046351 0.048466 0.050598 0.052748 0.054914 0.057094 0.059287
V 0.000022 0.000137 0.000240 0.000265 0.000252 0.000340 0.000552 0.000822 0.001123 0.001465 ... 0.023763 0.025165 0.026594 0.028051 0.029534 0.031041 0.032572 0.034127 0.035704 0.037303
1 -1 PU SG PU 1 L 0.000024 0.000158 0.000305 0.000394 0.000405 0.000362 0.000320 0.000354 0.000491 0.000707 ... 0.031990 0.033121 0.034251 0.035381 0.036513 0.037648 0.038786 0.039930 0.041080 0.042237
V 0.000025 0.000150 0.000266 0.000318 0.000325 0.000356 0.000461 0.000630 0.000840 0.001086 ... 0.022021 0.022759 0.023500 0.024244 0.024994 0.025749 0.026511 0.027280 0.028058 0.028846

24 rows × 51 columns

[10]:

# With slicing by index (dims, energy)
daPlotpd.iloc[0:6, 0:6]

[10]:
Eke 0.1 1.1 2.1 3.1 4.1 5.1
l m mu Cont Targ Total it Type
1 -1 1 PU SG PU 1 L 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550
V 8.900023 8.224738 7.627702 7.095200 6.617558 6.187859
0 0 SU SG SU 1 L 11.823354 11.429458 11.111935 10.849149 10.627257 10.437825
V 12.883046 12.311423 11.824577 11.410811 11.061133 10.768451
1 -1 PU SG PU 1 L 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550
V 8.900023 8.224738 7.627702 7.095200 6.617558 6.187859

Examples…

Various settings can be passed for more control over the plot.

Example with - Selection on Type = L - Thresholding type by % of max value - Log10 scaling - Extended figure size

[11]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'},
                                               plotDims = ('l','m','mu','Cont','Targ','Total','it'),
                                               thresType='pc', thres = 0.01, figsize = (15,10), logFlag = True)

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_20_1.png 
[12]:

daPlot.unstack().stack(plotDim = ('l','m','mu','Cont','Targ','Total'))

[12]:

<xarray.DataArray 'n2_3sg_0.1-50.1eV_A2.inp.out' (Eke: 51, it: 1, plotDim: 108)>
array([[[nan, nan, ..., nan, nan]],

       [[nan, nan, ..., nan, nan]],

       ...,

       [[nan, nan, ..., nan, nan]],

       [[nan, nan, ..., nan, nan]]])
Coordinates:
  * it       (it) int64 1
    Type     <U1 'L'
  * Eke      (Eke) float64 0.1 1.1 2.1 3.1 4.1 5.1 ... 46.1 47.1 48.1 49.1 50.1
    Ehv      (Eke) float64 15.68 16.68 17.68 18.68 ... 62.68 63.68 64.68 65.68
    SF       (Eke) complex128 (2.1560627+3.741674j) ... (4.4127053+1.8281945j)
  * plotDim  (plotDim) MultiIndex
  - l        (plotDim) int64 1 1 1 1 1 1 1 1 1 1 1 1 ... 5 5 5 5 5 5 5 5 5 5 5 5
  - m        (plotDim) int64 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ... 1 1 1 1 1 1 1 1 1
  - mu       (plotDim) int64 -1 -1 -1 -1 0 0 0 0 1 1 1 ... -1 -1 0 0 0 0 1 1 1 1
  - Cont     (plotDim) object 'PU' 'PU' 'SU' 'SU' 'PU' ... 'PU' 'PU' 'SU' 'SU'
  - Targ     (plotDim) object 'SG' 'SG' 'SG' 'SG' 'SG' ... 'SG' 'SG' 'SG' 'SG'
  - Total    (plotDim) object 'PU' 'SU' 'PU' 'SU' 'PU' ... 'PU' 'SU' 'PU' 'SU'
Attributes:
    Lmax:          11
    Targ:          SG
    QNs:           ['m', 'l', 'mu', 'ip', 'it', 'Value']
    dataType:      matE
    file:          n2_3sg_0.1-50.1eV_A2.inp.out
    fileBase:      D:\code\github\ePSproc\data\photoionization
    pType:         a
    pTypeDetails:  {'Type': 'abs', 'Formula': 'np.abs(dataPlot)', 'Exec': <fu...

Example with - Selection on Type = L - Sum over mu - Thresholding type by % of max value - Log10 scaling - Extended figure size

[13]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'}, sumDims = ['mu'],
                                               plotDims = ('l','m','Cont','Targ','Total'),
                                               thresType='pc', thres = 0.01, figsize = (15,10), logFlag = True)

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_23_1.png

Example with - Selection on Type = L - Sum over mu and Sym - Thresholding type by % of max value - Log10 scaling - Extended figure size

[14]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'}, sumDims = ['mu', 'Sym'],
                                               plotDims = ('l','m'),
                                               thresType='pc', thres = 0.01, figsize = (15,10), logFlag = True)

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn

No handles with labels found to put in legend.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_25_2.png

Example with - Changing the ordering of plotDims, here with ‘m’ as the main index.

[15]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'}, sumDims = ['Sym'],
                                               plotDims = ('m','l','mu'),
                                               thresType='pc', thres = 0.01, figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn

No handles with labels found to put in legend.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_27_2.png

Example with - Ordering by symmetry group.

[16]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'},
                                               plotDims = ('Total','Cont','Targ','l','m','mu'),
                                               thresType='pc', thres = 0.01, figsize = (15,10), logFlag = True)

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_29_1.png

Example with - Unwrapped phase plot

[17]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'},
                                               plotDims = ('l','m','mu','Cont','Targ','Total'),
                                               thres = 0.5, figsize = (15,10),
                                               pType = 'phaseUW')

C:\Program Files (x86)\Microsoft Visual Studio\Shared\Anaconda3_64\envs\ePSdev\lib\site-packages\numpy\lib\function_base.py:1519: RuntimeWarning:

invalid value encountered in remainder

C:\Program Files (x86)\Microsoft Visual Studio\Shared\Anaconda3_64\envs\ePSdev\lib\site-packages\numpy\lib\function_base.py:1520: RuntimeWarning:

invalid value encountered in greater

C:\Program Files (x86)\Microsoft Visual Studio\Shared\Anaconda3_64\envs\ePSdev\lib\site-packages\numpy\lib\function_base.py:1522: RuntimeWarning:

invalid value encountered in less


Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=phaseUW, thres=0.5, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_31_2.png

Further analysis examples

Summations

  • Sum over Eke, plot by l.
[18]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'}, xDim = 'LM', sumDims = 'Eke',
                                               plotDims = ('Total','Cont','Targ','m','mu'),
                                               thresType='pc', thres = 0.01, figsize = (15,10),
                                               cmap = 'Greens')

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_34_1.png 
[19]:

daPlotpd

[19]:
l 1 3 5 7 9 11
Total Cont Targ m mu
PU PU SG -1 -1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 207.905550 212.622228 17.570951 0.779478 0.020871 0.000572
0 -1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
1 -1 207.905550 212.622228 17.570951 0.779478 0.020871 0.000572
1 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
SU SU SG -1 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
0 0 220.297545 95.032282 13.737638 0.950270 0.026699 0.000313
1 0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000

Correlations

[20]:

ep.snsMatMod.clustermap(daPlotpd.corr())

[20]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229ffcb6908>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_37_1.png
  • Sum over symetries, plot by Eke.
[21]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'}, sumDims = ['mu', 'Sym'],
                                               plotDims = ('l','m'),
                                               thresType='pc', thres = 0.01, figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.08224737585639882, with Seaborn

No handles with labels found to put in legend.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_39_2.png 
[22]:

# Display values for first 10 Ekes
daPlotpd.iloc[:,0:11]

[22]:
Eke 0.1 1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 10.1
l m
1 -1 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550 5.546815 5.238038 4.958515 4.707928 4.486077
0 11.823354 11.429458 11.111935 10.849149 10.627257 10.437825 10.275304 10.134910 10.010680 9.893534 9.769350
1 8.143443 7.593716 7.103404 6.660060 6.255712 5.885550 5.546815 5.238038 4.958515 4.707928 4.486077
3 -1 2.620714 3.416440 4.071325 4.629875 5.118714 5.553100 5.941282 6.287526 6.594077 6.862346 7.093572
0 3.513428 4.719556 5.785863 6.766306 7.695465 8.593950 9.472654 10.335015 11.177359 11.987428 12.741400
1 2.620714 3.416440 4.071325 4.629875 5.118714 5.553100 5.941282 6.287526 6.594077 6.862346 7.093572
5 -1 0.003993 0.013835 0.021033 0.026999 0.033004 0.039974 0.048709 0.059861 0.073792 0.090524 0.109801
0 0.006473 0.021244 0.032261 0.041993 0.052580 0.065454 0.081763 0.102433 0.127951 0.158158 0.192134
1 0.003993 0.013835 0.021033 0.026999 0.033004 0.039974 0.048709 0.059861 0.073792 0.090524 0.109801
  • Correlations…
[23]:

# Eke correlations
ep.snsMatMod.clustermap(daPlotpd.iloc[:,0:11].corr())

[23]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229ffc27d68>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_42_1.png 
[24]:

# (l,m) correlations
ep.snsMatMod.clustermap(daPlotpd.iloc[:,0:11].T.corr())

[24]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229f9b9c9e8>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_43_1.png

Phase correlations

  • Full phases and correlations…
[25]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(dataSet[0], selDims = {'Type':'L'},
                                               plotDims = ('l','m','mu','Cont','Targ','Total'),
                                               thres = 0.5, figsize = (15,10),
                                               pType = 'phase')

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=phase, thres=0.5, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_45_1.png 
[26]:

# ep.snsMatMod.clustermap(daPlotpd.iloc[:,0:11].corr())
ep.snsMatMod.clustermap(daPlotpd.corr())

[26]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229fc665e48>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_46_1.png 
[27]:

# ep.snsMatMod.clustermap(daPlotpd.iloc[:,0:11].T.corr())
ep.snsMatMod.clustermap(daPlotpd.T.corr())

[27]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229ffe65f60>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_47_1.png

For \(\beta_{L,M}\)

The same functionality can be applied to plotting \(\beta_{L,M}\) paramters…

(For calculation details, see :math:beta_{L,M}` calculations demo notebook <https://github.com/phockett/ePSproc/blob/master/epsproc/tests/ePSproc_BLM_calc_demo_Sept2019.ipynb>`__.)

[28]:

daIn = dataSet[0].copy()
BLMXeN2 = ep.mfblm(daIn, selDims = {'Type':'L'}, thres = 1e-2, verbose = 0)   # Run for all Eke

[29]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(BLMXeN2, SFflag = True,
                                               plotDims = ('l','m'), sumDims = ('Euler'),
                                               figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn

No handles with labels found to put in legend.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_51_2.png
  • \(\beta_{L,M}\) correlations over Eke
[30]:

ep.snsMatMod.clustermap(daPlotpd.corr())

[30]:

<epsproc._sns_matrixMod.ClusterGrid at 0x22983bfd2b0>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_53_1.png

For the \(\beta_{L,M}\) case, the SFflag controls whether normalised or unnormalised values are plotted. In the former case, the cross-section (\(\beta_{0,0}\)) is divided out, hence \(\beta_{0,0}\) = 1.

[31]:

daPlot, daPlotpd, legendList, gFig = ep.lmPlot(BLMXeN2, SFflag = False,
                                               plotDims = ('l','m'),
                                               figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn

No handles with labels found to put in legend.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_55_2.png 
[32]:

ep.snsMatMod.clustermap(daPlotpd.T.corr())

[32]:

<epsproc._sns_matrixMod.ClusterGrid at 0x229ffa9ceb8>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_56_1.png

As a function of Euler angle…

[33]:

# Set pol geoms - these correspond to (z,x,y) in molecular frame (relative to principle/symmetry axis)
# pRot = [0, 0, np.pi/2]
# tRot = [0, np.pi/2, np.pi/2]
# cRot = [0, 0, 0]
# eAngs = np.array([pRot, tRot, cRot]).T   # List form to use later, rows per set of angles

eAngs = ep.setPolGeoms()  # Functionalised form, returns Xarray of pol geoms, defaults to (z,x,y)

[34]:

thres = 1e-2
# Calculate for each pol geom
# Run for all Eke, selected gauge only; round angles for display purposes only (to be fixed!)
BLMeuler = ep.mfblmEuler(daIn, selDims = {'Type':'L'}, eAngs = eAngs, thres = thres, verbose = 0)
BLMeulerLabel = BLMeuler.drop('Euler').swap_dims({'Euler':'Labels'})  # Swap values and labels for plotting, otherwise will be plotted vs. Euler angles

Cross-sections…

[35]:

# Check XS values
BLMeulerLabel.XS.real.plot.line(x='Eke');
# BLMeuler.XS.sum('Euler').real.plot.line(x='Eke');  # Add sum over Euler angles sets
BLMeulerLabel.XS.sum('Labels').real.plot.line(x='Eke');  # Add sum over Euler angles sets

C:\Program Files (x86)\Microsoft Visual Studio\Shared\Anaconda3_64\envs\ePSdev\lib\site-packages\xarray\plot\plot.py:76: FutureWarning:

This DataArray contains multi-dimensional coordinates. In the future, these coordinates will be transposed as well unless you specify transpose_coords=False.
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_61_1.png 
[36]:

# Check XS from ePS file GetCRO outputs
# This is for each symmetry group, averaged over all angles (i.e. unaligned LF) - see ePS manaul, https://www.chem.tamu.edu/rgroup/lucchese/ePolyScat.E3.manual/GetCro.html
# Hence should be similar to (x,y,z) MF orientations, but not identical
dataXS[0].sel({'XC':'SIGMA', 'Type':'L'}).plot.line(x='Eke');
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_62_0.png

\(\beta_{L,M}\) parameters…

[37]:

# Plot (normalised) BLM results - basic with Xarray (note Seaborn style may now be applied, since lmPlot() sets this globally)
BLMplot = ep.matEleSelector(BLMeulerLabel, thres=thres, dims = 'Eke')
BLMplot.real.squeeze().plot.line(x='Eke', col='Labels');
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_64_0.png 
[38]:

# Plot resutls - 2D maps with Xarray, faceted on Euler angle sets
# Set BLM index for y-axis
BLMplot['BLMind'] = ('BLM',np.arange(0, BLMplot.BLM.size))
# Plot
BLMplot.real.squeeze().plot(x='Eke', y='BLMind', col='Labels', size = 5);
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_65_0.png 
[39]:

# Plot results with lmPlot()
daPlot, daPlotpd, legendList, gFig = ep.lmPlot(BLMeuler, SFflag = False, eulerGroup = True,
                                               plotDims = ('l','m','Labels'),
                                               figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_66_1.png 
[40]:

daPlotpd

[40]:
Eke 0.1 1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 ... 41.1 42.1 43.1 44.1 45.1 46.1 47.1 48.1 49.1 50.1
l m Labels
0 0 z 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 ... 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
x 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 ... 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
y 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 ... 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
2 0 z 0.785011 0.293449 0.111540 0.049561 0.056243 0.104724 0.178871 0.268287 0.365983 0.467176 ... 0.320748 0.389800 0.463637 0.538792 0.612895 0.684425 0.752480 0.816588 0.876568 0.932425
x 0.272486 0.637673 0.773735 0.812507 0.791447 0.732312 0.649701 0.553911 0.452233 0.349699 ... 0.764359 0.761156 0.756929 0.751725 0.745586 0.738551 0.730656 0.721932 0.712410 0.702118
y 0.272486 0.637673 0.773735 0.812507 0.791447 0.732312 0.649701 0.553911 0.452233 0.349699 ... 0.764359 0.761156 0.756929 0.751725 0.745586 0.738551 0.730656 0.721932 0.712410 0.702118
-2 x 0.512057 0.586600 0.614373 0.622288 0.617989 0.605918 0.589055 0.569502 0.548747 0.527818 ... 0.300411 0.301065 0.301928 0.302990 0.304243 0.305679 0.307291 0.309072 0.311015 0.313116
y 0.512057 0.586600 0.614373 0.622288 0.617989 0.605918 0.589055 0.569502 0.548747 0.527818 ... 0.300411 0.301065 0.301928 0.302990 0.304243 0.305679 0.307291 0.309072 0.311015 0.313116
2 x 0.512057 0.586600 0.614373 0.622288 0.617989 0.605918 0.589055 0.569502 0.548747 0.527818 ... 0.300411 0.301065 0.301928 0.302990 0.304243 0.305679 0.307291 0.309072 0.311015 0.313116
y 0.512057 0.586600 0.614373 0.622288 0.617989 0.605918 0.589055 0.569502 0.548747 0.527818 ... 0.300411 0.301065 0.301928 0.302990 0.304243 0.305679 0.307291 0.309072 0.311015 0.313116
4 0 z 0.040440 0.474638 0.598502 0.603911 0.543444 0.444731 0.324406 0.193160 0.058087 0.076090 ... 0.405478 0.321374 0.231758 0.140971 0.051947 0.033463 0.114184 0.189684 0.259784 0.324538
x 0.059137 0.269489 0.430702 0.519099 0.560386 0.569288 0.555695 0.526731 0.487676 0.442441 ... 0.434418 0.441791 0.448488 0.454535 0.459955 0.464771 0.469002 0.472664 0.475772 0.478341
y 0.059137 0.269489 0.430702 0.519099 0.560386 0.569288 0.555695 0.526731 0.487676 0.442441 ... 0.434418 0.441791 0.448488 0.454535 0.459955 0.464771 0.469002 0.472664 0.475772 0.478341
-2 x 0.080476 0.152557 0.251643 0.293304 0.298915 0.280822 0.247316 0.204290 0.155991 0.105436 ... 0.565731 0.566930 0.567553 0.567625 0.567169 0.566205 0.564751 0.562825 0.560441 0.557615
y 0.080476 0.152557 0.251643 0.293304 0.298915 0.280822 0.247316 0.204290 0.155991 0.105436 ... 0.565731 0.566930 0.567553 0.567625 0.567169 0.566205 0.564751 0.562825 0.560441 0.557615
2 x 0.080476 0.152557 0.251643 0.293304 0.298915 0.280822 0.247316 0.204290 0.155991 0.105436 ... 0.565731 0.566930 0.567553 0.567625 0.567169 0.566205 0.564751 0.562825 0.560441 0.557615
y 0.080476 0.152557 0.251643 0.293304 0.298915 0.280822 0.247316 0.204290 0.155991 0.105436 ... 0.565731 0.566930 0.567553 0.567625 0.567169 0.566205 0.564751 0.562825 0.560441 0.557615
6 0 z 0.068194 0.122431 0.179261 0.235361 0.289105 0.339558 0.386124 0.428443 0.466366 0.499925 ... 0.164395 0.179851 0.196062 0.212134 0.227491 0.241791 0.254860 0.266630 0.277105 0.286334
x 0.059156 0.106111 0.155866 0.205371 0.252784 0.296866 0.336789 0.372096 0.402658 0.428609 ... 0.389928 0.381806 0.373613 0.365354 0.357037 0.348667 0.340251 0.331793 0.323301 0.314781
y 0.059156 0.106111 0.155866 0.205371 0.252784 0.296866 0.336789 0.372096 0.402658 0.428609 ... 0.389928 0.381806 0.373613 0.365354 0.357037 0.348667 0.340251 0.331793 0.323301 0.314781
-2 x 0.040411 0.072488 0.106477 0.140295 0.172685 0.202798 0.230071 0.254190 0.275068 0.292796 ... 0.266372 0.260823 0.255226 0.249585 0.243903 0.238185 0.232435 0.226658 0.220857 0.215037
y 0.040411 0.072488 0.106477 0.140295 0.172685 0.202798 0.230071 0.254190 0.275068 0.292796 ... 0.266372 0.260823 0.255226 0.249585 0.243903 0.238185 0.232435 0.226658 0.220857 0.215037
2 x 0.040411 0.072488 0.106477 0.140295 0.172685 0.202798 0.230071 0.254190 0.275068 0.292796 ... 0.266372 0.260823 0.255226 0.249585 0.243903 0.238185 0.232435 0.226658 0.220857 0.215037
y 0.040411 0.072488 0.106477 0.140295 0.172685 0.202798 0.230071 0.254190 0.275068 0.292796 ... 0.266372 0.260823 0.255226 0.249585 0.243903 0.238185 0.232435 0.226658 0.220857 0.215037

24 rows × 51 columns

  • Look at correlations over all (l,m,Euler)
[41]:

ep.snsMatMod.clustermap(daPlotpd.T.corr())

[41]:

<epsproc._sns_matrixMod.ClusterGrid at 0x2298740d6a0>
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_69_1.png
  • Replot with sorting by Euler sets
[42]:

# Plot results with lmPlot(), ordering by Euler sets
daPlot, daPlotpd, legendList, gFig = ep.lmPlot(BLMeuler, SFflag = False, eulerGroup = True,
                                               plotDims = ('Labels','l','m'),
                                               figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_71_1.png

… and including cross-section …

[43]:

# Plot results with lmPlot(), ordering by Euler sets + use XS
# NOTE - this currently plots with unstacked Euler angles (P,T,C) - should change to treat these as a stacked set.
daPlot, daPlotpd, legendList, gFig = ep.lmPlot(BLMeuler, SFflag = True,
                                               plotDims = ('Labels','l','m'),
                                               figsize = (15,10))

Plotting data n2_3sg_0.1-50.1eV_A2.inp.out, pType=a, thres=0.01, with Seaborn
../_images/demos_ePSproc_demo_matE_plotting_Feb2020_73_1.png 
[44]:

daPlotpd

[44]:
Eke 0.1 1.1 2.1 3.1 4.1 5.1 6.1 7.1 8.1 9.1 ... 41.1 42.1 43.1 44.1 45.1 46.1 47.1 48.1 49.1 50.1
Labels l m
z 0 0 9.938070 10.137061 10.536345 11.091344 11.782562 12.601551 13.542177 14.594115 15.735898 16.925624 ... 0.312529 0.322779 0.334491 0.347201 0.360532 0.374177 0.387879 0.401433 0.414667 0.427443
2 0 7.801490 2.974707 1.175228 0.549695 0.662683 1.319691 2.422303 3.915404 5.759074 7.907254 ... 0.100243 0.125819 0.155082 0.187069 0.220969 0.256096 0.291871 0.327805 0.363484 0.398559
4 0 0.401896 4.811433 6.306021 6.698186 6.403164 5.604304 4.393168 2.819004 0.914053 1.287878 ... 0.126724 0.103733 0.077521 0.048945 0.018729 0.012521 0.044290 0.076145 0.107724 0.138722
6 0 0.677715 1.241087 1.888756 2.610470 3.406393 4.278957 5.228955 6.252740 7.338681 8.461538 ... 0.051378 0.058052 0.065581 0.073653 0.082018 0.090473 0.098855 0.107034 0.114906 0.122391
x 0 0 4.780633 4.596718 4.500082 4.463496 4.471544 4.513611 4.580735 4.664598 4.757434 4.852244 ... 2.658339 2.549036 2.442990 2.340289 2.240996 2.145147 2.052760 1.963831 1.878342 1.796260
2 0 1.302658 2.931201 3.481869 3.626621 3.538992 3.305371 2.976108 2.583773 2.151469 1.696826 ... 2.031927 1.940213 1.849169 1.759253 1.670856 1.584301 1.499861 1.417752 1.338150 1.261186
-2 2.447955 2.696434 2.764731 2.777579 2.763365 2.734878 2.698305 2.656499 2.610629 2.561100 ... 0.798595 0.767426 0.737607 0.709085 0.681808 0.655727 0.630795 0.606965 0.584193 0.562438
2 2.447955 2.696434 2.764731 2.777579 2.763365 2.734878 2.698305 2.656499 2.610629 2.561100 ... 0.798595 0.767426 0.737607 0.709085 0.681808 0.655727 0.630795 0.606965 0.584193 0.562438
4 0 0.282713 1.238766 1.938195 2.316998 2.505790 2.569545 2.545493 2.456989 2.320085 2.146831 ... 1.154830 1.126141 1.095651 1.063742 1.030758 0.997002 0.962748 0.928232 0.893663 0.859225
-2 0.384727 0.701263 1.132412 1.309163 1.336610 1.267522 1.132891 0.952932 0.742118 0.511599 ... 1.503904 1.445124 1.386526 1.328407 1.271023 1.214593 1.159298 1.105293 1.052700 1.001621
2 0.384727 0.701263 1.132412 1.309163 1.336610 1.267522 1.132891 0.952932 0.742118 0.511599 ... 1.503904 1.445124 1.386526 1.328407 1.271023 1.214593 1.159298 1.105293 1.052700 1.001621
6 0 0.282804 0.487763 0.701410 0.916675 1.130337 1.339937 1.542742 1.735677 1.915618 2.079715 ... 1.036562 0.973238 0.912732 0.855035 0.800119 0.747943 0.698453 0.651586 0.607271 0.565429
-2 0.193192 0.333205 0.479155 0.626208 0.772167 0.915352 1.053893 1.185693 1.308616 1.420716 ... 0.708106 0.664848 0.623515 0.584100 0.546585 0.510942 0.477134 0.445118 0.414845 0.386261
2 0.193192 0.333205 0.479155 0.626208 0.772167 0.915352 1.053893 1.185693 1.308616 1.420716 ... 0.708106 0.664848 0.623515 0.584100 0.546585 0.510942 0.477134 0.445118 0.414845 0.386261
y 0 0 4.780633 4.596718 4.500082 4.463496 4.471544 4.513611 4.580735 4.664598 4.757434 4.852244 ... 2.658339 2.549036 2.442990 2.340289 2.240996 2.145147 2.052760 1.963831 1.878342 1.796260
2 0 1.302658 2.931201 3.481869 3.626621 3.538992 3.305371 2.976108 2.583773 2.151469 1.696826 ... 2.031927 1.940213 1.849169 1.759253 1.670856 1.584301 1.499861 1.417752 1.338150 1.261186
-2 2.447955 2.696434 2.764731 2.777579 2.763365 2.734878 2.698305 2.656499 2.610629 2.561100 ... 0.798595 0.767426 0.737607 0.709085 0.681808 0.655727 0.630795 0.606965 0.584193 0.562438
2 2.447955 2.696434 2.764731 2.777579 2.763365 2.734878 2.698305 2.656499 2.610629 2.561100 ... 0.798595 0.767426 0.737607 0.709085 0.681808 0.655727 0.630795 0.606965 0.584193 0.562438
4 0 0.282713 1.238766 1.938195 2.316998 2.505790 2.569545 2.545493 2.456989 2.320085 2.146831 ... 1.154830 1.126141 1.095651 1.063742 1.030758 0.997002 0.962748 0.928232 0.893663 0.859225
-2 0.384727 0.701263 1.132412 1.309163 1.336610 1.267522 1.132891 0.952932 0.742118 0.511599 ... 1.503904 1.445124 1.386526 1.328407 1.271023 1.214593 1.159298 1.105293 1.052700 1.001621
2 0.384727 0.701263 1.132412 1.309163 1.336610 1.267522 1.132891 0.952932 0.742118 0.511599 ... 1.503904 1.445124 1.386526 1.328407 1.271023 1.214593 1.159298 1.105293 1.052700 1.001621
6 0 0.282804 0.487763 0.701410 0.916675 1.130337 1.339937 1.542742 1.735677 1.915618 2.079715 ... 1.036562 0.973238 0.912732 0.855035 0.800119 0.747943 0.698453 0.651586 0.607271 0.565429
-2 0.193192 0.333205 0.479155 0.626208 0.772167 0.915352 1.053893 1.185693 1.308616 1.420716 ... 0.708106 0.664848 0.623515 0.584100 0.546585 0.510942 0.477134 0.445118 0.414845 0.386261
2 0.193192 0.333205 0.479155 0.626208 0.772167 0.915352 1.053893 1.185693 1.308616 1.420716 ... 0.708106 0.664848 0.623515 0.584100 0.546585 0.510942 0.477134 0.445118 0.414845 0.386261

24 rows × 51 columns

Version info

[45]:

%load_ext version_information

[46]:

%version_information epsproc, xarray

[46]:
SoftwareVersion
Python3.7.3 64bit [MSC v.1915 64 bit (AMD64)]
IPython7.7.0
OSWindows 10 10.0.17763 SP0
epsproc1.2.4
xarray0.12.3
Fri Feb 07 12:13:28 2020 Eastern Standard Time
[ ]: