Density Matrices notes + demo (ePSproc + PEMtk dev.)

30/08/21

In this notebook density matrices are considered & numerical routines demonstrated.

Density Matrices

The general density operator, for a mixture of indepent states \(|\psi_{n} \rangle\), can be defined as (Eqn. 2.8, Blum [1]):

\begin{equation} \hat{\rho}=\sum_{n}W_{n}|\psi_{n}\rangle\langle\psi_{n}| \end{equation}

Where \(W_{n}\) defines the (statistical) weighting of each state \(\psi_{n}\) in the mixture.

For a given basis set, \(|\phi_{m}\rangle\), the states can be expanded and the matrix elements of \(\boldsymbol{\rho}\) defined (Eqns. 2.9 - 2.11, Blum [1]):

\begin{equation} | \psi_{n} \rangle = \sum_{m'} a_{m'}^{(n)}| \phi_{m'}\rangle \end{equation}

\begin{equation} \hat{\rho}=\sum_{n}\sum_{mm'}W_{n}a_{m'}^{(n)}a_{m}^{(n)*}|\phi_{m'}\rangle\langle\phi_{m}| \end{equation}

And the matrix elements - the density matrix - given explicitly as:

\begin{equation} \boldsymbol{\rho}_{i,j}=\langle\phi_{i}|\hat{\rho}|\phi_{j}\rangle=\sum_{n}W_{n}a_{i}^{(n)}a_{j}^{(n)*} \end{equation}

For all pairs of basis states \((i,j)\). This defines the density matrix in the \(\{|\phi_n\rangle\}\) representation (basis space).

The expectation value of an operator \(\hat{Q}\) can then be found as (Eqn. 2.18, Blum [1]):

\begin{eqnarray} \langle \hat{Q}\rangle & = & \sum_{n}\sum_{mm'}W_{n}a_{m'}^{(n)}a_{m}^{(n)*}\langle\phi_{m}|\hat{Q}|\phi_{m'}\rangle\\ & = & \sum_{mm'}\langle\phi_{m'}|\hat{\rho}|\phi_{m}\rangle\langle\phi_{m}|\hat{Q}|\phi_{m'}\rangle\\ & = & \mathrm{tr}(\rho Q) \end{eqnarray}

For basic examples, in terms of \(|J,M\rangle\) states and alignment, see the Quantum Metrology with Photoelectrons notes.

Here, we’ll look at applying the formalism to photoionization, using ePSproc for the numerics…

[1] Blum, K. (2012). Density Matrix Theory and Applications (3rd Editio, Vol. 64). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-20561-3

Setup

import sys
import os
from pathlib import Path
import numpy as np
# import epsproc as ep
import xarray as xr

import matplotlib.pyplot as plt

from datetime import datetime as dt
timeString = dt.now()

import epsproc as ep

# Multijob class dev code
from epsproc.classes.multiJob import ePSmultiJob

* sparse not found, sparse matrix forms not available.
* natsort not found, some sorting functions not available.
* pyevtk not found, VTK export not available.

epDemoDataPath = Path(ep.__path__[0]).parent/'data'/'photoionization'/'n2_multiorb'

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

Load test data

# Class dev code
from epsproc.classes.multiJob import ePSmultiJob
from epsproc.classes.base import ePSbase

# Instantiate class object.
# Minimally this needs just the dataPath, if verbose = 1 is set then some useful output will also be printed.
data = ePSbase(epDemoDataPath, verbose = 1)

# ScanFiles() - this will look for data files on the path provided, and read from them.
data.scanFiles()

/home/paul/github/ePSproc/epsproc/IO.py:657: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['E', np.float(parseLineDigits(dumpSeg[3][2])[0]), 'eV'])
/home/paul/github/ePSproc/epsproc/IO.py:662: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['Lmax', np.int(parseLineDigits(dumpSeg[10][2])[0]), ''])
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/github/ePSproc/epsproc/IO.py:657: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['E', np.float(parseLineDigits(dumpSeg[3][2])[0]), 'eV'])
/home/paul/github/ePSproc/epsproc/IO.py:662: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  attribs.append(['Lmax', np.int(parseLineDigits(dumpSeg[10][2])[0]), ''])
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)

*** Job orb6 details
Key: orb6
Dir /home/paul/github/ePSproc/data/photoionization/n2_multiorb, 1 file(s).
{   'batch': 'ePS n2, batch n2_1pu_0.1-50.1eV, orbital A2',
    'event': ' N2 A-state (1piu-1)',
    'orbE': -17.09691397835426,
    'orbLabel': '1piu-1'}

*** Job orb5 details
Key: orb5
Dir /home/paul/github/ePSproc/data/photoionization/n2_multiorb, 1 file(s).
{   'batch': 'ePS n2, batch n2_3sg_0.1-50.1eV, orbital A2',
    'event': ' N2 X-state (3sg-1)',
    'orbE': -17.34181645456815,
    'orbLabel': '3sg-1'}

Density matrix functions - demo with photoionization matrix elements

As of ePSproc v1.3.1-dev commit f5e4019, density matrix routines are implemented in :py:func:epsproc.calc.density (functional forms only).

Note this currently requires Holoviews for plotting.

# Import routines
from epsproc.calc import density

Set data

The routines are not currently wrapped by the main data class, so we’ll just use a single sample dataset here.

# Set data from master class
k = 'orb5'  # N2 orb5 (SG) dataset
matE = data.data[k]['matE']
selDims = {'Type':'L'}
thres = 1e-2

# Check data with lmPlot()
ep.lmPlot(matE, selDims = selDims, thres = thres);

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)
/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:84: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  mask = np.zeros(data.shape, np.bool)
/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:282: PendingDeprecationWarning:
The label function will be deprecated in a future version. Use Tick.label1 instead.
  fontsize = tick.label.get_size()

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

/home/paul/github/ePSproc/epsproc/basicPlotters.py:762: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  if (item[0].dtype == np.float) or (item[0].name in ['Eke','Ehv','t','Euler']):

Calculate density matrix

The numerics essentially computer the outer product from the specified dimensions, as per the previous definition:

\begin{equation} \boldsymbol{\rho}_{i,j}=\langle\phi_{i}|\hat{\rho}|\phi_{j}\rangle=\sum_{n}W_{n}a_{i}^{(n)}a_{j}^{(n)*} \end{equation}

where \(a_{i}^{(n)}a_{j}^{(n)*}\) are the values along the specified dimensions/state vector/representation. These dimensions must be in data, but will be restacked as necessary to define the effective basis space. For instance, from the ionization matrix element data shown above, setting [l,m] would select the \(|\alpha\rangle = |l,m\rangle\) basis (equivalently LM, since the dimensions are already stacked in the ionization matrix elements). Setting ['LM','mu'] would set the \(|\alpha\rangle = |l,m,\mu\rangle\) as the basis vector and so forth, where \(|\alpha\rangle\) is used as a generic state vector denoting all required quantum numbers.

Note, however, that this selection is purely based on the numerics, which computes the outer product \(|\alpha\rangle\langle\alpha'|\) to form the density matrix, hence does not guarantee a well-formed density matrix in the strictest sense (depending on the basis set), although will always present a basis state correlation matrix of sorts.

# Compose density matrix

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = ['LM', 'mu']

# Calculate
daOut, *_ = density.densityCalc(matE, denDims = denDims, selDims = selDims, thres = thres)  # OK

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

# The output is an Xarray, with a square density matrix in the specified dims (alpha, alpha'), where the latter is labelled '_p'.
# Other dims will be automatically stacked (unless otherwise specified).
daOut

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/formatting.py:142: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  elif isinstance(x, (float, np.float)):

xarray.DataArray

'n2_3sg_0.1-50.1eV_A2.inp.out'

• Eke: 51
• Sym: 2
• l,m,mu: 9
• l,m,mu_p: 9

• (nan+nanj) (nan+nanj) ... (nan+nanj) (0.016421425862763843+0j)

  array([[[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  7.49604313+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 3.5560421 +0.j        ,         nan       +nanj,
             3.5560421 +0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 3.5560421 +0.j        ,         nan       +nanj,
             3.5560421 +0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]]],
  
  
         [[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  7.21492971+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 3.18485339+0.j        ,         nan       +nanj,
             3.18485339+0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 3.18485339+0.j        ,         nan       +nanj,
             3.18485339+0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]]],
  
  
         [[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  6.99261027+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 2.85754449+0.j        ,         nan       +nanj,
             2.85754449+0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 2.85754449+0.j        ,         nan       +nanj,
             2.85754449+0.j        , ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]]],
  
  
         ...,
  
  
         [[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  0.20562441+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
            -0.05319034+0.03310486j,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj, -0.05319034-0.03310486j,
                    nan       +nanj, ...,         nan       +nanj,
             0.0190889 +0.j        ,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 0.69781281+0.j        ,         nan       +nanj,
             0.69781281+0.j        , ..., -0.08672737+0.06366807j,
                    nan       +nanj, -0.08672737+0.06366807j],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 0.69781281+0.j        ,         nan       +nanj,
             0.69781281+0.j        , ..., -0.08672737+0.06366807j,
                    nan       +nanj, -0.08672737+0.06366807j],
           ...,
           [-0.08672737-0.06366807j,         nan       +nanj,
            -0.08672737-0.06366807j, ...,  0.01658791+0.j        ,
                    nan       +nanj,  0.01658791+0.j        ],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [-0.08672737-0.06366807j,         nan       +nanj,
            -0.08672737-0.06366807j, ...,  0.01658791+0.j        ,
                    nan       +nanj,  0.01658791+0.j        ]]],
  
  
         [[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  0.20739913+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
            -0.05638744+0.03137371j,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj, -0.05638744-0.03137371j,
                    nan       +nanj, ...,         nan       +nanj,
             0.02007652+0.j        ,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 0.68271263+0.j        ,         nan       +nanj,
             0.68271263+0.j        , ..., -0.08574537+0.06258809j,
                    nan       +nanj, -0.08574537+0.06258809j],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 0.68271263+0.j        ,         nan       +nanj,
             0.68271263+0.j        , ..., -0.08574537+0.06258809j,
                    nan       +nanj, -0.08574537+0.06258809j],
           ...,
           [-0.08574537-0.06258809j,         nan       +nanj,
            -0.08574537-0.06258809j, ...,  0.016507  +0.j        ,
                    nan       +nanj,  0.016507  +0.j        ],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [-0.08574537-0.06258809j,         nan       +nanj,
            -0.08574537-0.06258809j, ...,  0.016507  +0.j        ,
                    nan       +nanj,  0.016507  +0.j        ]]],
  
  
         [[[        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj,  0.20915604+0.j        ,
                    nan       +nanj, ...,         nan       +nanj,
            -0.05944301+0.02948374j,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           ...,
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [        nan       +nanj, -0.05944301-0.02948374j,
                    nan       +nanj, ...,         nan       +nanj,
             0.02105014+0.j        ,         nan       +nanj],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj]],
  
          [[ 0.66738586+0.j        ,         nan       +nanj,
             0.66738586+0.j        , ..., -0.08467309+0.06156213j,
                    nan       +nanj, -0.08467309+0.06156213j],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [ 0.66738586+0.j        ,         nan       +nanj,
             0.66738586+0.j        , ..., -0.08467309+0.06156213j,
                    nan       +nanj, -0.08467309+0.06156213j],
           ...,
           [-0.08467309-0.06156213j,         nan       +nanj,
            -0.08467309-0.06156213j, ...,  0.01642143+0.j        ,
                    nan       +nanj,  0.01642143+0.j        ],
           [        nan       +nanj,         nan       +nanj,
                    nan       +nanj, ...,         nan       +nanj,
                    nan       +nanj,         nan       +nanj],
           [-0.08467309-0.06156213j,         nan       +nanj,
            -0.08467309-0.06156213j, ...,  0.01642143+0.j        ,
                    nan       +nanj,  0.01642143+0.j        ]]]])

• Coordinates: (8)
  • Ehv
    (Eke)
    float64
    17.4 18.4 19.4 ... 65.4 66.4 67.4

    array([17.4, 18.4, 19.4, 20.4, 21.4, 22.4, 23.4, 24.4, 25.4, 26.4, 27.4,
           28.4, 29.4, 30.4, 31.4, 32.4, 33.4, 34.4, 35.4, 36.4, 37.4, 38.4,
           39.4, 40.4, 41.4, 42.4, 43.4, 44.4, 45.4, 46.4, 47.4, 48.4, 49.4,
           50.4, 51.4, 52.4, 53.4, 54.4, 55.4, 56.4, 57.4, 58.4, 59.4, 60.4,
           61.4, 62.4, 63.4, 64.4, 65.4, 66.4, 67.4])

  • it
    ()
    int64
    1

    array(1)

  • Eke
    (Eke)
    float64
    0.1 1.1 2.1 3.1 ... 48.1 49.1 50.1

    array([ 0.1,  1.1,  2.1,  3.1,  4.1,  5.1,  6.1,  7.1,  8.1,  9.1, 10.1, 11.1,
           12.1, 13.1, 14.1, 15.1, 16.1, 17.1, 18.1, 19.1, 20.1, 21.1, 22.1, 23.1,
           24.1, 25.1, 26.1, 27.1, 28.1, 29.1, 30.1, 31.1, 32.1, 33.1, 34.1, 35.1,
           36.1, 37.1, 38.1, 39.1, 40.1, 41.1, 42.1, 43.1, 44.1, 45.1, 46.1, 47.1,
           48.1, 49.1, 50.1])

  • Type
    ()
    <U1
    'L'

    array('L', dtype='<U1')

  • Sym
    (Sym)
    MultiIndex
    (Cont, Targ, Total)

    array([('SU', 'SG', 'SU'), ('PU', 'SG', 'PU')], dtype=object)

  • Cont
    (Sym)
    object
    'SU' 'PU'

    array(['SU', 'PU'], dtype=object)

  • Targ
    (Sym)
    object
    'SG' 'SG'

    array(['SG', 'SG'], dtype=object)

  • Total
    (Sym)
    object
    'SU' 'PU'

    array(['SU', 'PU'], dtype=object)

  • SF
    (Eke)
    complex128
    (2.1560627+3.741674j) ... (4.4127053+1.8281945j)

    array([2.1560627+3.741674j , 2.2237521+3.6277801j, 2.2894411+3.5236912j,
           2.3532973+3.4280768j, 2.4154658+3.3398459j, 2.476074 +3.2580947j,
           2.5352337+3.1820671j, 2.5930439+3.1111249j, 2.6495932+3.0447254j,
           2.7049605+2.9824035j, 2.759217 +2.9237583j, 2.812427 +2.8684419j,
           2.8646489+2.816151j , 2.9159356+2.7666193j, 2.9663357+2.7196125j,
           3.0158937+2.6749231j, 3.0646504+2.6323667j, 3.1126435+2.5917789j,
           3.1599077+2.5530124j, 3.2064753+2.5159351j, 3.2523762+2.4804276j,
           3.2976383+2.4463822j, 3.3422875+2.4137013j, 3.386348 +2.3822961j,
           3.4298425+2.3520857j, 3.4727924+2.3229962j, 3.5152175+2.29496j  ,
           3.5571367+2.267915j , 3.5985676+2.2418041j, 3.6395269+2.2165748j,
           3.6800303+2.1921786j, 3.7200928+2.1685705j, 3.7597284+2.1457091j,
           3.7989505+2.1235559j, 3.8377718+2.1020749j, 3.8762043+2.0812328j,
           3.9142594+2.0609987j, 3.9519481+2.0413435j, 3.9892808+2.0222401j,
           4.0262673+2.0036632j, 4.0629171+1.985589j , 4.0992393+1.9679953j,
           4.1352425+1.9508611j, 4.1709348+1.9341668j, 4.2063244+1.9178938j,
           4.2414186+1.9020249j, 4.2762249+1.8865434j, 4.3107501+1.8714338j,
           4.345001 +1.8566817j, 4.378984 +1.8422729j, 4.4127053+1.8281945j])

  • l,m,mu
    (l,m,mu)
    MultiIndex
    (l, m, mu)

    array([(1, -1, 1), (1, 0, 0), (1, 1, -1), (3, -1, 1), (3, 0, 0), (3, 1, -1),
           (5, -1, 1), (5, 0, 0), (5, 1, -1)], dtype=object)

  • l
    (l,m,mu)
    int64
    1 1 1 3 3 3 5 5 5

    array([1, 1, 1, 3, 3, 3, 5, 5, 5])

  • m
    (l,m,mu)
    int64
    -1 0 1 -1 0 1 -1 0 1

    array([-1,  0,  1, -1,  0,  1, -1,  0,  1])

  • mu
    (l,m,mu)
    int64
    1 0 -1 1 0 -1 1 0 -1

    array([ 1,  0, -1,  1,  0, -1,  1,  0, -1])

  • l,m,mu_p
    (l,m,mu_p)
    MultiIndex
    (l_p, m_p, mu_p)

    array([(1, -1, 1), (1, 0, 0), (1, 1, -1), (3, -1, 1), (3, 0, 0), (3, 1, -1),
           (5, -1, 1), (5, 0, 0), (5, 1, -1)], dtype=object)

  • l_p
    (l,m,mu_p)
    int64
    1 1 1 3 3 3 5 5 5

    array([1, 1, 1, 3, 3, 3, 5, 5, 5])

  • m_p
    (l,m,mu_p)
    int64
    -1 0 1 -1 0 1 -1 0 1

    array([-1,  0,  1, -1,  0,  1, -1,  0,  1])

  • mu_p
    (l,m,mu_p)
    int64
    1 0 -1 1 0 -1 1 0 -1

    array([ 1,  0, -1,  1,  0, -1,  1,  0, -1])

• Attributes: (15)

  E :

  0.1

  Ehv :

  15.68

  SF :

  (2.1560627+3.741674j)

  Lmax :

  11

  Cont :

  SU

  Targ :

  SG

  Total :

  SU

  QNs :

  ['m', 'l', 'mu', 'ip', 'it', 'Value']

  dataType :

  Density Matrix

  file :

  n2_3sg_0.1-50.1eV_A2.inp.out

  fileBase :

  /home/paul/github/ePSproc/data/photoionization/n2_multiorb

  fileList :

  n2_3sg_0.1-50.1eV_A2.inp.out

  jobLabel :

  3sg-1

  density :

  {'denSettings': {'da': <xarray.DataArray 'n2_3sg_0.1-50.1eV_A2.inp.out' (LM: 18, Eke: 51, Sym: 2, mu: 3, it: 1, Type: 2)> array([[[[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-1.7757076e+00+6.3474768e-01j, -1.9403462e+00+6.9465999e-01j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ 1.1629411e+00-1.3536696e+00j, 1.2585400e+00-1.4670488e+00j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-6.7206736e-01-1.5510867e+00j, -7.2345845e-01-1.6647964e+00j]]]], ..., [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-4.3564182e-01-7.1276154e-01j, -4.2509554e-01-6.6006094e-01j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-4.3153069e-01-7.0462323e-01j, -4.2061423e-01-6.5253773e-01j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-4.2731653e-01-6.9626607e-01j, -4.1606509e-01-6.4490113e-01j]]]]], [[[[[ nan +nanj, nan +nanj]], [[ 2.7363206e+00-9.2696864e-02j, 2.9815816e+00-1.0062913e-01j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-2.3170597e+00+1.3587362e+00j, -2.4961077e+00+1.4631580e+00j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ 1.6888467e-01+2.6389559e+00j, 1.7928455e-01+2.8082277e+00j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], ..., [[[[ nan +nanj, nan +nanj]], [[-1.3280743e-01+4.3357421e-01j, -1.1225816e-01+3.9916386e-01j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-1.4907960e-01+4.3031896e-01j, -1.2699346e-01+3.9484078e-01j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-1.6461802e-01+4.2668132e-01j, -1.4097903e-01+3.9029174e-01j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]]], [[[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-1.7757076e+00+6.3474768e-01j, -1.9403462e+00+6.9465999e-01j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ 1.1629411e+00-1.3536696e+00j, 1.2585400e+00-1.4670488e+00j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-6.7206736e-01-1.5510867e+00j, -7.2345845e-01-1.6647964e+00j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], ..., [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-4.3564182e-01-7.1276154e-01j, -4.2509554e-01-6.6006094e-01j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-4.3153069e-01-7.0462323e-01j, -4.2061423e-01-6.5253773e-01j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-4.2731653e-01-6.9626607e-01j, -4.1606509e-01-6.4490113e-01j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]]], ..., [[[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[-2.2166421e-08+1.4897224e-08j, -2.2462645e-08+1.5296980e-08j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ 1.4168322e-07-1.0108773e-07j, 1.4358297e-07-1.0257807e-07j]]]], ..., [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ 9.1652969e-06-3.8486844e-06j, 5.8206861e-06-1.9595570e-06j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ 9.0395586e-06-4.2857498e-06j, 5.5904864e-06-2.2352132e-06j]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ 8.9213389e-06-4.6971505e-06j, 5.3667894e-06-2.4842580e-06j]]]]], [[[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ 3.4737547e-08-1.5180966e-08j, 3.7068537e-08-1.6190679e-08j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-2.2552182e-07+1.1579025e-07j, -2.3947258e-07+1.2304319e-07j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], ..., [[[[ nan +nanj, nan +nanj]], [[-5.3579641e-06+1.5190377e-06j, -1.5411234e-06-3.5035308e-07j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-5.7787135e-06+1.7595393e-06j, -1.7745738e-06-2.9031071e-07j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[-6.1975055e-06+2.0338273e-06j, -2.0070606e-06-2.0324783e-07j]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]]], [[[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[-2.2166421e-08+1.4897224e-08j, -2.2462645e-08+1.5296980e-08j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ 1.4168322e-07-1.0108773e-07j, 1.4358297e-07-1.0257807e-07j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], ..., [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ 9.1652969e-06-3.8486844e-06j, 5.8206861e-06-1.9595570e-06j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ 9.0395586e-06-4.2857498e-06j, 5.5904864e-06-2.2352132e-06j]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]], [[[[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]], [[[ 8.9213389e-06-4.6971505e-06j, nan +nanj]], [[ nan +nanj, nan +nanj]], [[ nan +nanj, nan +nanj]]]]]]) Coordinates: Ehv (Eke) float64 17.4 18.4 19.4 20.4 21.4 ... 63.4 64.4 65.4 66.4 67.4 * mu (mu) int64 -1 0 1 * LM (LM) MultiIndex - l (LM) int64 1 1 1 3 3 3 5 5 5 7 7 7 9 9 9 11 11 11 - m (LM) int64 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 -1 0 1 * it (it) int64 1 * 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 * Type (Type) object 'L' 'V' * Sym (Sym) MultiIndex - Cont (Sym) object 'SU' 'PU' - Targ (Sym) object 'SG' 'SG' - Total (Sym) object 'SU' 'PU' SF (Eke) complex128 (2.1560627+3.741674j) ... (4.4127053+1.8281945j) Attributes: E: 0.1 Ehv: 15.68 SF: (2.1560627+3.741674j) Lmax: 11 Cont: SU Targ: SG Total: SU QNs: ['m', 'l', 'mu', 'ip', 'it', 'Value'] dataType: matE file: n2_3sg_0.1-50.1eV_A2.inp.out fileBase: /home/paul/github/ePSproc/data/photoionization/n2_multiorb fileList: n2_3sg_0.1-50.1eV_A2.inp.out jobLabel: 3sg-1, 'denDims': ['LM', 'mu'], 'sumDims': None, 'keepDims': None, 'selDims': {'Type': 'L'}, 'thres': 0.01, 'squeeze': True, 'keepNaNs': False}, 'sumTot': [], 'denDims': None, 'kdims': ['l,m,mu', 'l,m,mu_p']}

  kdims :

  ['l,m,mu', 'l,m,mu_p']

Plotting density matrices

This is handled by the matPlot() routine. This uses Holoviews to compose a full-dimensional plot, as a set of matrices in the key dimensions \([\alpha,\alpha']\), and stacked in other dimensions. The plots are interactive + widgets for control, or can be pushed to a layout with Holoviews functionality.

# Plot full matrix
# This is interactive (with Holoviews), with the widgets allowing selection of other (stacked) dimensions.
# Plot types [real, imag, abs] are also set.
# Note this may take a while for data with a large number of dimensions.
density.matPlot(daOut)

Set plot kdims to ['l,m,mu', 'l,m,mu_p']; pass kdims = [dim1,dim2] for more control.

WARNING:param.HeatMapPlot04138: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

# For more control, the Xarray and/or Holoviews object can be manipulated prior to plotting

hvmap = density.matPlot(daOut.sum('Sym').sel(Eke=slice(5,50,20)))  # Sum & slice data prior to plot
                                                                    # Note that summation may replace NaNs with zeros.
hvmap.layout('Eke').cols(1)  # Layout results by Eke, single column layout

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
WARNING:param.HeatMapPlot1146619: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.
WARNING:param.HeatMapPlot1146640: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

Set plot kdims to ['l,m,mu', 'l,m,mu_p']; pass kdims = [dim1,dim2] for more control.

WARNING:param.HeatMapPlot1146661: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

TODO:

• Cmapping & dynamic map range control.
• NaN replacement issues?
• Normalisation.

Density matrices from other data types

As defined above, an approximate density/correlation matrix can be composed from any Xarray. Strictly speaking, this may not always provide a well-formed density matrix, but will always provide a correlation matrix which may be interesting/informative for a given case.

Here we’ll look at some other data-types, using the AF-BLM routine (strictly speaking, this defines a set of geometric tensors, which may have a direct relation with the corresponding density matrix - this will be explored below, here we’ll just do the numerics). For an more details of the AF-BLM routine see the theory notes and the basis set exploration page.

# Calculate AFPADs with full basis set return
# The default case will compute LF-BLM parameters
BetasNormX, basis = ep.afblmXprod(matE, selDims=selDims, basisReturn='Full', symSum=False)

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/dataarray.py:1954: PendingDeprecationWarning: dropping variables using `drop` will be deprecated; using drop_vars is encouraged.
  ds = self._to_temp_dataset().drop(labels, dim, errors=errors)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__and__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__and__.  Use index.intersection(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/dataarray.py:1954: PendingDeprecationWarning: dropping variables using `drop` will be deprecated; using drop_vars is encouraged.
  ds = self._to_temp_dataset().drop(labels, dim, errors=errors)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__and__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__and__.  Use index.intersection(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__or__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__or__.  Use index.union(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__and__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__and__.  Use index.intersection(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/dataarray.py:1954: PendingDeprecationWarning: dropping variables using `drop` will be deprecated; using drop_vars is encouraged.
  ds = self._to_temp_dataset().drop(labels, dim, errors=errors)

# Basis set arrays
basis.keys()

dict_keys(['QNs', 'EPRX', 'lambdaTerm', 'BLMtable', 'BLMtableResort', 'AFterm', 'AKQS', 'polProd', 'phaseConvention', 'BLMRenorm'])

# Compose density matrix

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = 'BLM'

# Calculate
daOut, *_ = density.densityCalc(BetasNormX, denDims = denDims, selDims = selDims, thres = thres)  # OK

daOut.name = 'BLMplot' # Set name - note this can't be the same as a dimension!

# Plot
hvmap = density.matPlot(daOut.sel(Eke=slice(5,50,20)))  # Sum & slice data prior to plot
                                                                    # Note that summation may replace NaNs with zeros.
hvmap

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

Set plot kdims to ['BLM', 'BLM_p']; pass kdims = [dim1,dim2] for more control.

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)
WARNING:param.HeatMapPlot1148235: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)

Not very interesting so far/in this case… but what about some of the basis tensors?

# Available basis arrays
basis.keys()

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

dict_keys(['QNs', 'EPRX', 'lambdaTerm', 'BLMtable', 'BLMtableResort', 'AFterm', 'AKQS', 'polProd', 'phaseConvention', 'BLMRenorm'])

# Compose density matrix

termName = 'AFterm'
daIn = basis[termName]  # Set data

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = ['P','R']

# Calculate + sum over other terms
daOut, *_ = density.densityCalc(daIn, denDims = denDims, selDims = selDims, thres = thres, sumDims=True)  # OK

daOut.name = termName # Set name - note this can't be the same as a dimension!

# Plot
hvmap = density.matPlot(daOut)  # Sum & slice data prior to plot
                                                                    # Note that summation may replace NaNs with zeros.
hvmap

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
WARNING:param.HeatMapPlot1260001: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

{'L', 'M', 'Rp', 'S-Rp'} set() {'L', 'M', 'Rp', 'S-Rp'}
Set plot kdims to ['P,R', 'P,R_p']; pass kdims = [dim1,dim2] for more control.

In this case, the Xarray already contains all the tensor components, so this calculation is somewhat redundant, as we can see from a closer inspection…

basis[termName]

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/formatting.py:142: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  elif isinstance(x, (float, np.float)):

xarray.DataArray

• P: 3
• L: 3
• R: 3
• M: 3
• Rp: 5
• S-Rp: 5
• t: 1

• 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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• Coordinates: (7)
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    Index

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• Attributes: (0)

# Use lmPlot to show the full dimensionality
ep.lmPlot(basis[termName], xDim={'PR':denDims});

Set dataType (No dataType)
Plotting data (No filename), pType=a, thres=0.01, with Seaborn

/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:84: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  mask = np.zeros(data.shape, np.bool)
/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:282: PendingDeprecationWarning:
The label function will be deprecated in a future version. Use Tick.label1 instead.
  fontsize = tick.label.get_size()
/home/paul/github/ePSproc/epsproc/basicPlotters.py:762: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  if (item[0].dtype == np.float) or (item[0].name in ['Eke','Ehv','t','Euler']):

In this case, we could also compose the density matrix directly by passing the relevant dims to the plotting function (all other dims will be stacked)…

(Two issues - plotting may be slow for multi-dim case, and many combinations may be zero/uninteresting.)

# Plot
daIn.name = termName # Set name - note this can't be the same as a dimension!
hvmap = density.matPlot(daIn.squeeze(), kdims = ['R','Rp'])  # Sum & slice data prior to plot
                                                                    # Note that summation may replace NaNs with zeros.
hvmap

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
WARNING:param.HeatMapPlot4110618: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

# Compose density matrix

termName = 'lambdaTerm'  # 'AKQS' # Also needs fixing for single-value case?   # 'lambdaTerm'  # Needs fixing for singleton dim case!  # NOW OK if squeeze = False
daIn = basis[termName]  # Set data

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = ['mu','mup']   # 'ADM'  #
daIn.name = termName

# Calculate + sum over other terms
daOut, *_ = density.densityCalc(daIn, denDims = denDims, selDims = selDims, thres = thres)  #, squeeze = False)  #, sumDims=True)  # OK

daOut.name = termName # Set name - note this can't be the same as a dimension!

# Plot
hvmap = density.matPlot(daOut)  # Sum & slice data prior to plot
                                                                    # Note that summation may replace NaNs with zeros.
hvmap

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)

Set plot kdims to ['mup,mu', 'mup,mu_p']; pass kdims = [dim1,dim2] for more control.

WARNING:param.HeatMapPlot1194796: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/nputils.py:215: RuntimeWarning: All-NaN slice encountered
  result = getattr(npmodule, name)(values, axis=axis, **kwargs)

ep.util.misc.checkDims(daIn, refDims = denDims)

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

{'dataDims': ('ADM', 't'),
 'dataDimsUS': ('t', 'K', 'Q', 'S'),
 'refDims': ['ADM'],
 'shared': [],
 'extra': ['Q', 't', 'K', 'S'],
 'invalid': ['ADM'],
 'stacked': ['ADM'],
 'stackedMap': {'ADM': FrozenList(['K', 'Q', 'S'])},
 'stackedShared': ['ADM'],
 'stackedExtra': [],
 'stackedInvalid': [],
 'missing': []}

Density matrix from geometric tensors

As discussed here, photoionization can be defined in terms of a set of geometric tensors (state multipoles). These are intimately related to the density matrix, and can be thought of as a coupled basis equivalent.

For example, in the \(\{|JM\rangle\}\) representation (Eqn. 4.8 in Blum [1]):

\begin{equation} \hat{T}(J',J)_{KQ}=\sum_{M'M}(-1)^{J'-M'}(2K+1)^{1/2}\left(\begin{array}{ccc} J' & J & K\\ M' & -M & Q \end{array}\right)|J'M'\rangle\langle JM| \end{equation}

Where \(\hat{T}(J',J)_{KQ}\) are tensor operators. The corresponding matrix elements are (Eqn. 4.9 in Blum [1]):

\begin{equation} \langle J'M'|\hat{T}(J',J)_{KQ}|JM\rangle=(-1)^{J'-M'}(2K+1)^{1/2}\left(\begin{array}{ccc} J' & J & K\\ M' & -M & Q \end{array}\right) \end{equation}

The density matrix can be written in terms of the tensor operators (Eqn. 4.30 in Blum):

\begin{equation} \boldsymbol{\rho}=\sum_{KQ}\sum_{J'J}\left[\sum_{M'M}\langle J'M'|\hat{\rho}|JM\rangle(-1)^{J'-M'}(2K+1)^{1/2}\left(\begin{array}{ccc} J' & J & K\\ M' & -M & Q \end{array}\right)\right]\hat{T}(J',J)_{KQ} \end{equation}

And the state multipoles are defined as the term in square brackets (Eqn. 4.31 in Blum):

\begin{equation} \left\langle T(J',J)_{KQ}^{\dagger}\right\rangle =\sum_{M'M}\langle J'M'|\hat{\rho}|JM\rangle(-1)^{J'-M'}(2K+1)^{1/2}\left(\begin{array}{ccc} J' & J & K\\ M' & -M & -Q \end{array}\right) \end{equation}

And the inverse (Eqn. 4.34 in Blum):

\begin{equation} \langle J'M'|\hat{\rho}|JM\rangle=\sum_{KQ}(-1)^{J'-M'}(2K+1)^{1/2}\left(\begin{array}{ccc} J' & J & K\\ M' & -M & -Q \end{array}\right)\left\langle T(J',J)_{KQ}^{\dagger}\right\rangle \end{equation}

---

As discussed above, the AF-\(\beta_{LM}\) routines currently define a set of geometric tensors. These can be regarded & treated in general as state multipole type terms (although this is not strictly true in all cases) with appropriate summations. This means that the basis can be readily expressed in terms of mulitpoles or density matrices, and a few examples are given below.

(Note demos in previous section only plot existing tensors, but don’t convert definitions.)

TODO: update matPlot & consolidate dim-handling routines from densityCalc to provide easier plotting routines here (without manual restack etc.).

\(B_{L,M}\) term

The coupling of the partial wave pairs, \(|l,m\rangle\) and \(|l',m'\rangle\), into the observable set of \(\{L,M\}\) is defined by a tensor contraction with two 3j terms.

\begin{equation} B_{L,M}=(-1)^{m}\left(\frac{(2l+1)(2l'+1)(2L+1)}{4\pi}\right)^{1/2}\left(\begin{array}{ccc} l & l' & L\\ 0 & 0 & 0 \end{array}\right)\left(\begin{array}{ccc} l & l' & L\\ -m & m' & M \end{array}\right) \end{equation}

Note for the AF case \(B_{L,S-R'}(l,l',m,m')\) instead of \(B_{L,-M}(l,l',m,m')\) for MF case. This allows for all MF projections to contribute (rather than a single specified polarization geometry).

This term, with a subset of elements defined for the photoionization matrix elements set previously, is (currently, v1.3.0) given by the ‘BLMtableResort’ basis array.

basis['BLMtableResort']

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/formatting.py:142: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  elif isinstance(x, (float, np.float)):

xarray.DataArray

'w3jStacked'

• l: 4
• lp: 4
• L: 8
• m: 3
• mp: 3
• S-Rp: 5

• nan nan nan nan nan nan nan nan ... nan nan -0.2318 nan nan nan nan

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           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.20601291],
             [        nan,         nan,         nan,  0.0594708 ,
                      nan],
             [        nan,         nan,  0.12615663,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.0594708 ,
                      nan],
             [        nan,         nan,  0.16820883,         nan,
                      nan],
             [        nan, -0.0594708 ,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.12615663,         nan,
                      nan],
             [        nan,  0.0594708 ,         nan,         nan,
                      nan],
             [-0.20601291,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.1621931 ],
             [        nan,         nan,         nan,  0.09932258,
                      nan],
             [        nan,         nan,  0.02564498,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.09932258,
                      nan],
             [        nan,         nan,  0.15386989,         nan,
                      nan],
             [        nan, -0.09932258,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.02564498,         nan,
                      nan],
             [        nan,  0.09932258,         nan,         nan,
                      nan],
             [-0.1621931 ,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.09280237],
             [        nan,         nan,         nan, -0.16943318,
                      nan],
             [        nan,         nan,  0.22731846,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.2143179 ,
                      nan],
             [        nan,         nan,  0.2396147 ,         nan,
                      nan],
             [        nan, -0.2143179 ,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.22731846,         nan,
                      nan],
             [        nan, -0.16943318,         nan,         nan,
                      nan],
             [ 0.09280237,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.10633465],
             [        nan,         nan,         nan,  0.0095775 ,
                      nan],
             [        nan,         nan,  0.08601992,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.11508947,
                      nan],
             [        nan,         nan,  0.14837393,         nan,
                      nan],
             [        nan, -0.11508947,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.08601992,         nan,
                      nan],
             [        nan,  0.0095775 ,         nan,         nan,
                      nan],
             [-0.10633465,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.13808836],
             [        nan,         nan,         nan, -0.18267373,
                      nan],
             [        nan,         nan,  0.21833687,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22549735,
                      nan],
             [        nan,         nan,  0.23583077,         nan,
                      nan],
             [        nan, -0.22549735,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.21833687,         nan,
                      nan],
             [        nan, -0.18267373,         nan,         nan,
                      nan],
             [ 0.13808836,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.22991069],
             [        nan,         nan,         nan,  0.21285594,
                      nan],
             [        nan,         nan, -0.1898425 ,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22991069,
                      nan],
             [        nan,         nan,  0.23434667,         nan,
                      nan],
             [        nan, -0.22991069,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.1898425 ,         nan,
                      nan],
             [        nan,  0.21285594,         nan,         nan,
                      nan],
             [-0.22991069,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]]],
  
  
  
  
         [[[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.12028562],
             [        nan,         nan,         nan,  0.24057125,
                      nan],
             [        nan,         nan,  0.19018827,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,  0.15528807,
                      nan],
             [        nan,         nan,  0.245532  ,         nan,
                      nan],
             [        nan,  0.15528807,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.19018827,         nan,
                      nan],
             [        nan,  0.24057125,         nan,         nan,
                      nan],
             [ 0.12028562,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.09280237],
             [        nan,         nan,         nan,  0.2143179 ,
                      nan],
             [        nan,         nan,  0.22731846,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,  0.16943318,
                      nan],
             [        nan,         nan,  0.2396147 ,         nan,
                      nan],
             [        nan,  0.16943318,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.22731846,         nan,
                      nan],
             [        nan,  0.2143179 ,         nan,         nan,
                      nan],
             [ 0.09280237,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.10633465],
             [        nan,         nan,         nan,  0.11508947,
                      nan],
             [        nan,         nan,  0.08601992,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.0095775 ,
                      nan],
             [        nan,         nan,  0.14837393,         nan,
                      nan],
             [        nan, -0.0095775 ,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.08601992,         nan,
                      nan],
             [        nan,  0.11508947,         nan,         nan,
                      nan],
             [-0.10633465,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.19808933],
             [        nan,         nan,         nan,  0.036166  ,
                      nan],
             [        nan,         nan,  0.14556534,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.036166  ,
                      nan],
             [        nan,         nan,  0.16173926,         nan,
                      nan],
             [        nan, -0.036166  ,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.14556534,         nan,
                      nan],
             [        nan,  0.036166  ,         nan,         nan,
                      nan],
             [-0.19808933,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.13724032],
             [        nan,         nan,         nan,  0.05315295,
                      nan],
             [        nan,         nan,  0.0867984 ,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.05315295,
                      nan],
             [        nan,         nan,  0.1301976 ,         nan,
                      nan],
             [        nan, -0.05315295,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.0867984 ,         nan,
                      nan],
             [        nan,  0.05315295,         nan,         nan,
                      nan],
             [-0.13724032,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.23489031],
             [        nan,         nan,         nan,  0.22283651,
                      nan],
             [        nan,         nan, -0.19395429,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22283651,
                      nan],
             [        nan,         nan,  0.23274515,         nan,
                      nan],
             [        nan, -0.22283651,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.19395429,         nan,
                      nan],
             [        nan,  0.22283651,         nan,         nan,
                      nan],
             [-0.23489031,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.09481237],
             [        nan,         nan,         nan, -0.17737771,
                      nan],
             [        nan,         nan,  0.23224194,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.2077235 ,
                      nan],
             [        nan,         nan,  0.23797717,         nan,
                      nan],
             [        nan, -0.2077235 ,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.23224194,         nan,
                      nan],
             [        nan, -0.17737771,         nan,         nan,
                      nan],
             [ 0.09481237,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.09337991],
             [        nan,         nan,         nan, -0.01703862,
                      nan],
             [        nan,         nan,  0.11200777,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.09561096,
                      nan],
             [        nan,         nan,  0.13911977,         nan,
                      nan],
             [        nan, -0.09561096,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.11200777,         nan,
                      nan],
             [        nan, -0.01703862,         nan,         nan,
                      nan],
             [-0.09337991,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.13015569],
             [        nan,         nan,         nan,  0.09679569,
                      nan],
             [        nan,         nan, -0.03876058,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.11470498,
                      nan],
             [        nan,         nan,  0.1323926 ,         nan,
                      nan],
             [        nan, -0.11470498,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.03876058,         nan,
                      nan],
             [        nan,  0.09679569,         nan,         nan,
                      nan],
             [-0.13015569,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.23240488],
             [        nan,         nan,         nan,  0.22022851,
                      nan],
             [        nan,         nan, -0.19792311,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22566707,
                      nan],
             [        nan,         nan,  0.23178382,         nan,
                      nan],
             [        nan, -0.22566707,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.19792311,         nan,
                      nan],
             [        nan,  0.22022851,         nan,         nan,
                      nan],
             [-0.23240488,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]]],
  
  
  
  
         [[[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.13808836],
             [        nan,         nan,         nan,  0.22549735,
                      nan],
             [        nan,         nan,  0.21833687,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,  0.18267373,
                      nan],
             [        nan,         nan,  0.23583077,         nan,
                      nan],
             [        nan,  0.18267373,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.21833687,         nan,
                      nan],
             [        nan,  0.22549735,         nan,         nan,
                      nan],
             [ 0.13808836,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.22991069],
             [        nan,         nan,         nan,  0.22991069,
                      nan],
             [        nan,         nan, -0.1898425 ,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.21285594,
                      nan],
             [        nan,         nan,  0.23434667,         nan,
                      nan],
             [        nan, -0.21285594,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.1898425 ,         nan,
                      nan],
             [        nan,  0.22991069,         nan,         nan,
                      nan],
             [-0.22991069,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
               0.09481237],
             [        nan,         nan,         nan,  0.2077235 ,
                      nan],
             [        nan,         nan,  0.23224194,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,  0.17737771,
                      nan],
             [        nan,         nan,  0.23797717,         nan,
                      nan],
             [        nan,  0.17737771,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.23224194,         nan,
                      nan],
             [        nan,  0.2077235 ,         nan,         nan,
                      nan],
             [ 0.09481237,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.09337991],
             [        nan,         nan,         nan,  0.09561096,
                      nan],
             [        nan,         nan,  0.11200777,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,  0.01703862,
                      nan],
             [        nan,         nan,  0.13911977,         nan,
                      nan],
             [        nan,  0.01703862,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.11200777,         nan,
                      nan],
             [        nan,  0.09561096,         nan,         nan,
                      nan],
             [-0.09337991,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.13015569],
             [        nan,         nan,         nan,  0.11470498,
                      nan],
             [        nan,         nan, -0.03876058,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.09679569,
                      nan],
             [        nan,         nan,  0.1323926 ,         nan,
                      nan],
             [        nan, -0.09679569,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.03876058,         nan,
                      nan],
             [        nan,  0.11470498,         nan,         nan,
                      nan],
             [-0.13015569,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.23240488],
             [        nan,         nan,         nan,  0.22566707,
                      nan],
             [        nan,         nan, -0.19792311,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22022851,
                      nan],
             [        nan,         nan,  0.23178382,         nan,
                      nan],
             [        nan, -0.22022851,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.19792311,         nan,
                      nan],
             [        nan,  0.22566707,         nan,         nan,
                      nan],
             [-0.23240488,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]]],
  
  
  
          [[[[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan]],
  
            [[        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.28209479,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan],
             [        nan,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.19575887],
             [        nan,         nan,         nan,  0.02615938,
                      nan],
             [        nan,         nan,  0.15127378,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.02615938,
                      nan],
             [        nan,         nan,  0.15983645,         nan,
                      nan],
             [        nan, -0.02615938,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.15127378,         nan,
                      nan],
             [        nan,  0.02615938,         nan,         nan,
                      nan],
             [-0.19575887,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.1314077 ],
             [        nan,         nan,         nan,  0.03725058,
                      nan],
             [        nan,         nan,  0.10240281,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.03725058,
                      nan],
             [        nan,         nan,  0.12466429,         nan,
                      nan],
             [        nan, -0.03725058,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.10240281,         nan,
                      nan],
             [        nan,  0.03725058,         nan,         nan,
                      nan],
             [-0.1314077 ,         nan,         nan,         nan,
                      nan]]],
  
  
           ...,
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.11029632],
             [        nan,         nan,         nan,  0.07658591,
                      nan],
             [        nan,         nan,  0.00195159,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.07658591,
                      nan],
             [        nan,         nan,  0.10928903,         nan,
                      nan],
             [        nan, -0.07658591,         nan,         nan,
                      nan]],
  
            [[        nan,         nan,  0.00195159,         nan,
                      nan],
             [        nan,  0.07658591,         nan,         nan,
                      nan],
             [-0.11029632,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.12948219],
             [        nan,         nan,         nan,  0.10736096,
                      nan],
             [        nan,         nan, -0.05054088,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.10736096,
                      nan],
             [        nan,         nan,  0.1286495 ,         nan,
                      nan],
             [        nan, -0.10736096,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.05054088,         nan,
                      nan],
             [        nan,  0.10736096,         nan,         nan,
                      nan],
             [-0.12948219,         nan,         nan,         nan,
                      nan]]],
  
  
           [[[        nan,         nan,         nan,         nan,
              -0.23181191],
             [        nan,         nan,         nan,  0.22337955,
                      nan],
             [        nan,         nan, -0.20186723,         nan,
                      nan]],
  
            [[        nan,         nan,         nan, -0.22337955,
                      nan],
             [        nan,         nan,  0.2307054 ,         nan,
                      nan],
             [        nan, -0.22337955,         nan,         nan,
                      nan]],
  
            [[        nan,         nan, -0.20186723,         nan,
                      nan],
             [        nan,  0.22337955,         nan,         nan,
                      nan],
             [-0.23181191,         nan,         nan,         nan,
                      nan]]]]]])

• Coordinates: (6)
  • L
    (L)
    int64
    0 2 4 6 8 10 12 14

    array([ 0,  2,  4,  6,  8, 10, 12, 14])

  • l
    (l)
    int64
    1 3 5 7

    array([1, 3, 5, 7])

  • lp
    (lp)
    int64
    1 3 5 7

    array([1, 3, 5, 7])

  • m
    (m)
    int64
    -1 0 1

    array([-1,  0,  1])

  • mp
    (mp)
    int64
    -1 0 1

    array([-1,  0,  1])

  • S-Rp
    (S-Rp)
    int64
    -2 -1 0 1 2

    array([-2, -1,  0,  1,  2])

• Attributes: (2)

  dataType :

  betaTerm

  phaseCons :

  {'phaseConvention': 'E', 'genMatEcons': {'negm': False}, 'EPR': {'Rphase': True, 'negR': True, 'negRlabel': False, 'negRcoordSwap': False}, 'lambdaCons': {'negMup': True, 'negRp': True, 'phaseNegR': True, 'conjFlag': True, 'RpPhase': True}, 'betaCons': {'negM': False, 'mPhase': True}, 'mfblmCons': {'negRcoordSwap': False, 'negMcoordSwap': False, 'Mphase': False, 'negmCoordSwap': False, 'mPhase': False, 'mupPhase': True, 'BLMmPhase': False}, 'afblmCons': {'negM': False, 'negQ': True, 'negS': True, 'llpPhase': True}, 'lfblmCGCons': {'negmp': False, 'negM': True, 'negmup': False, 'negMP': False}}

The lmPlot() routine can be used to show the full dimensionality…

# Plot BLM term with restack to standard LM terms
ep.lmPlot(basis['BLMtableResort'].rename({'S-Rp':'M'}).stack({'LM':['L','M']}), xDim={'LM':['L','M']});

Plotting data (No filename), pType=a, thres=0.01, with Seaborn

/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:84: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  mask = np.zeros(data.shape, np.bool)
/home/paul/github/ePSproc/epsproc/_sns_matrixMod.py:282: PendingDeprecationWarning:
The label function will be deprecated in a future version. Use Tick.label1 instead.
  fontsize = tick.label.get_size()
/home/paul/github/ePSproc/epsproc/basicPlotters.py:762: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  if (item[0].dtype == np.float) or (item[0].name in ['Eke','Ehv','t','Euler']):
No handles with labels found to put in legend.

The above shows, essentially, all the terms in the summation. By suitable summation we can look at the corresponding density matrix or state multipole.

# Compose density matrix

termName = 'BLMtableResort'  # 'AKQS' # Also needs fixing for single-value case?   # 'lambdaTerm'  # Needs fixing for singleton dim case!  # NOW OK if squeeze = False
daIn = basis[termName]  # Set data

# Reformat
daIn = daIn.rename({'S-Rp':'M'}).stack({'LM':['L','M'], 'lm':['l','m'], 'lmp':['lp','mp']})

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = ['lm','lmp']   # 'ADM'  #
daIn.name = termName

hvmap = density.matPlot(daIn.sum('LM').squeeze(), kdims = denDims)

hvmap

WARNING:param.HeatMapPlot7042169: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

# Plot tensor BLM (state multipole) term with restack to standard LM terms
hvmap = density.matPlot(daIn.sum(['lm','lmp']).unstack(), kdims = ['L','M'])
hvmap

WARNING:param.HeatMapPlot7042532: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

Lambda terms

https://epsproc.readthedocs.io/en/dev/methods/ePSproc_geom_methods_summary_190821-v1-tidy.html#:nbsphinx-math:Lambda-Term

# Compose density matrix

termName = 'lambdaTerm'  # 'AKQS' # Also needs fixing for single-value case?   # 'lambdaTerm'  # Needs fixing for singleton dim case!  # NOW OK if squeeze = False
daIn = basis[termName]  # Set data

# Set dimensions/state vector/representation
# These must be in original data, but will be restacked as necessary to define the effective basis space.
denDims = ['mu','mup']   # 'ADM'  #
daIn.name = termName

hvmap = density.matPlot(daIn.squeeze(), kdims = denDims)

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

hvmap

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
WARNING:param.HeatMapPlot7003395: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

# Try with explicity summation over tensor (K,Q) dims...
# hvmap = density.matPlot(daIn.sum(['P','Rp']).squeeze(), kdims = denDims)  # Sum over P,Rp
hvmap = density.matPlot(daIn.sum('Rp').squeeze(), kdims = denDims)  # Sum over Rp only
hvmap.layout('P').cols(1)

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
WARNING:param.HeatMapPlot7001209: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.
WARNING:param.HeatMapPlot7001230: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.
WARNING:param.HeatMapPlot7001251: Due to internal constraints, when aspect and width/height is set, the bokeh backend uses those values as frame_width/frame_height instead. This ensures the aspect is respected, but means that the plot might be slightly larger than anticipated. Set the frame_width/frame_height explicitly to suppress this warning.

# Full response function
# TODO: restacking + summation routine for general cases like this (with multiple existing dims).
basis['BLMtableResort'] * basis['polProd']

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/alignment.py:298: FutureWarning: Index.__and__ operating as a set operation is deprecated, in the future this will be a logical operation matching Series.__and__.  Use index.intersection(other) instead
  index = joiner(matching_indexes)
/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/xarray/core/formatting.py:142: DeprecationWarning: `np.float` is a deprecated alias for the builtin `float`. To silence this warning, use `float` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.float64` here.
Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations
  elif isinstance(x, (float, np.float)):

xarray.DataArray

• l: 4
• lp: 4
• L: 2
• m: 3
• mp: 3
• S-Rp: 5
• mu: 3
• mup: 3
• Labels: 1
• M: 1
• t: 1

• (nan+nanj) (nan+nanj) (nan+nanj) ... (nan+nanj) (nan+nanj) (nan+nanj)

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Versions

import scooby
scooby.Report(additional=['epsproc', 'holoviews', 'hvplot', 'xarray', 'matplotlib', 'bokeh'])

Mon Aug 30 19:14:10 2021 EDT
OS	Linux	CPU(s)	64	Machine	x86_64
Architecture	64bit	Environment	Jupyter
Python 3.7.10 (default, Feb 26 2021, 18:47:35) [GCC 7.3.0]
epsproc	1.3.1-dev	holoviews	1.14.2	hvplot	Could not import
xarray	0.15.0	matplotlib	3.3.4	bokeh	2.3.0
numpy	1.20.1	scipy	1.6.1	IPython	7.21.0
scooby	0.5.6

# Check current Git commit for local ePSproc version
from pathlib import Path
!git -C {Path(ep.__file__).parent} branch
!git -C {Path(ep.__file__).parent} log --format="%H" -n 1

* dev
  master
b2d5316e998fca42a50739aa1e3215fddceac725

/home/paul/anaconda3/envs/epsdev-xr15/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
  and should_run_async(code)

# Check current remote commits
!git ls-remote --heads git://github.com/phockett/ePSproc

b2d5316e998fca42a50739aa1e3215fddceac725        refs/heads/dev
d4f0da444112922a15d01fba074187fa4e632980        refs/heads/master
69cd89ce5bc0ad6d465a4bd8df6fba15d3fd1aee        refs/heads/numba-tests
ea30878c842f09d525fbf39fa269fa2302a13b57        refs/heads/revert-9-master

!hostname

jake

!conda env list

# conda environments:
#
base                     /home/paul/anaconda3
baseBK-250821            /home/paul/anaconda3/envs/baseBK-250821
baseBK-280321            /home/paul/anaconda3/envs/baseBK-280321
ePSproc-v1.2             /home/paul/anaconda3/envs/ePSproc-v1.2
ePSproc-v1.2-dev         /home/paul/anaconda3/envs/ePSproc-v1.2-dev
epsTestConda             /home/paul/anaconda3/envs/epsTestConda
epsTestPip               /home/paul/anaconda3/envs/epsTestPip
epsTestPypi              /home/paul/anaconda3/envs/epsTestPypi
epsTestSetup             /home/paul/anaconda3/envs/epsTestSetup
epsdev                   /home/paul/anaconda3/envs/epsdev
epsdev-040821            /home/paul/anaconda3/envs/epsdev-040821
epsdev-040821-YMLnb      /home/paul/anaconda3/envs/epsdev-040821-YMLnb
epsdev-xr13              /home/paul/anaconda3/envs/epsdev-xr13
epsdev-xr15           *  /home/paul/anaconda3/envs/epsdev-xr15
epsdev-xr17              /home/paul/anaconda3/envs/epsdev-xr17
epsdevTestYML            /home/paul/anaconda3/envs/epsdevTestYML
epsman                   /home/paul/anaconda3/envs/epsman
fibre-sim                /home/paul/anaconda3/envs/fibre-sim
frog                     /home/paul/anaconda3/envs/frog
matlab                   /home/paul/anaconda3/envs/matlab
tmo-dev                  /home/paul/anaconda3/envs/tmo-dev