epsproc.geomFunc.geomUtils module

ePSproc utility functions for geometric terms and tensors.

26/02/20 v1

Code from ePSproc_MFBLM_Numba_dev_tests_120220.py

epsproc.geomFunc.geomUtils.genKQSterms(Kmin=0, Kmax=2, mFlag=True)[source]
epsproc.geomFunc.geomUtils.genKQStermsFromTensors(EPR, AKQS, uniqueFlag=True, phaseConvention='S')[source]

Generate all QNs for \(\Delta_{L,M}(K,Q,S)\) from existing tensors (Xarrays) \(E_{P,R}\) and \(A^K_{Q,S}\).

Cf. epsproc.geomFunc.genllpMatE(), code adapted from there.

Parameters:
  • matE (Xarray) – Xarray containing matrix elements, with QNs (l,m), as created by readMatEle()
  • uniqueFlag (bool, default = True) – Check for duplicates and remove (can occur with some forms of matrix elements).
  • mFlag (bool, optional, default = True) – m, mp take all passed values if mFlag=True, or =0 only if mFlag=False
  • phaseConvention (optional, str, default = 'S') – Set phase conventions with epsproc.geomCalc.setPhaseConventions(). To use preset phase conventions, pass existing dictionary. If matE.attrs[‘phaseCons’] is already set, this will be used instead of passed args.
Returns:

  • QNs1, QNs2 (two 2D np.arrays) – Values take all allowed combinations [‘P’,’K’,’L’,’R’,’Q’,’M’] and [‘P’,’K’,’L’,’Rp’,’S’,’S-Rp’] from supplied matE. Note phase conventions not applied to QN lists as yet.
  • To do
  • —–
  • - Implement output options (see dev. function w3jTable).
epsproc.geomFunc.geomUtils.genllL(Lmin=0, Lmax=10, mFlag=True)[source]

Generate quantum numbers for angular momentum contractions (l, lp, L)

Parameters:
  • Lmax (Lmin,) – Integer values for Lmin and Lmax respectively.
  • mFlag (bool, optional, default = True) – m, mp take all values -l…+l if mFlag=True, or =0 only if mFlag=False
Returns:

QNs – Values take all allowed combinations [‘l’,’lp’,’L’,’m’,’mp’,’M’] up to l=lp=Lmax, one set per row.
Return type:

2D np.array

Examples

>>> # Calculate up to Lmax = 2
>>> QNs = genllL(Lmax=2)
>>> # Use with w3jTable function to calculate Wigner 3j terms
>>> w3j = w3jTable(QNs = QNs)
  • Implement output options (see dev. function w3jTable).
epsproc.geomFunc.geomUtils.genllLList(Llist, uniqueFlag=True, mFlag=True)[source]

Generate quantum numbers for angular momentum contractions (l, lp, L) from a passed list, (m, mp, M)=0 or all allowed terms.

Parameters:
  • Llist (list) – Values [l, lp, L] to use for calculations.
  • uniqueFlag (bool, optional, default = True) – Drop duplicate [l,lp,L] sets from list.
  • mFlag (bool, optional, default = True) – m, mp take all values -l…+l if mFlag=True, or =0 only if mFlag=False
Returns:

QNs – Values take all allowed combinations [‘l’,’lp’,’L’,’m’,’mp’,’M’] up to l=lp=Lmax, one set per row.
Return type:

2D np.array

Examples

>>> # Set from an array
>>> QNs = genllLList(np.array([[1,1,2],[1,3,2],[1,1,2]]), mFlag = True)
>>> # Use with w3jTable function to calculate Wigner 3j terms
>>> w3j = w3jTable(QNs = QNs)
  • Implement output options (see dev. function w3jTable).
epsproc.geomFunc.geomUtils.genllpMatE(matE, uniqueFlag=True, mFlag=True, phaseConvention='S')[source]

Generate quantum numbers for angular momentum contractions (l, lp, L, m, mp, M) from sets of matrix elements.

Parameters:
  • matE (Xarray) – Xarray containing matrix elements, with QNs (l,m), as created by readMatEle()
  • uniqueFlag (bool, default = True) – Check for duplicates and remove (can occur with some forms of matrix elements).
  • mFlag (bool, optional, default = True) – m, mp take all passed values if mFlag=True, or =0 only if mFlag=False
  • phaseConvention (optional, str, default = 'S') – Set phase conventions with epsproc.geomCalc.setPhaseConventions(). To use preset phase conventions, pass existing dictionary. If matE.attrs[‘phaseCons’] is already set, this will be used instead of passed args.
Returns:

QNs – Values take all allowed combinations [‘l’,’lp’,’L’,’m’,’mp’,’M’] from supplied matE
Return type:

2D np.array

Examples

>>> # From demo matrix elements
>>> dataFile = os.path.join(dataPath, 'n2_3sg_0.1-50.1eV_A2.inp.out')  # Set for sample N2 data for testing
>>> # Scan data file
>>> dataSet = ep.readMatEle(fileIn = dataFile)
>>> QNs = genllpMatE(dataSet[0])
>>> # Use with w3jTable function to calculate Wigner 3j terms
>>> w3j = w3jTable(QNs = QNs)
  • Implement output options (see dev. function w3jTable).
epsproc.geomFunc.geomUtils.selQNsRow(QNs, QNmask, fields=None, verbose=1)[source]

Basic routine for selecting/filtering valid rows from an input array of QNs.

This is similar to methods used in Matlab version, but likely rather slow.

Parameters:
  • QNs (np.array) – Values to be filtered.
  • QNmask (list or np.array) – Values to be matched. Must be same dims as QNs, unless fields is also set. If set to None field will be skipped (i.e. match all values)
  • fields (list or np.array, optional, default = None) – Which fields to match in QNs.
  • verbose (int, optional, default = 1) – Print info to terminal.
Returns:

  • QNs[boolMask] (np.array of selected values.)
  • boolMask (np.array corresponding to selected values.)

Examples

>>> QNsMask, mask = selQNsRow(QNs,[None, None, None, 0, 0, 0], verbose = False)
>>> # With fields
>>> QNsMask, mask = selQNsRow(QNs,[0, 0, 0], fields = [3,4,5], verbose = False)