Developers Corner

XRStools.roifinder_and_gui Module

XRStools.xrs_utilities Module

XRStools.xrs_utilities.Chi(chi, degrees=True)

rotation around (1,0,0), pos sense

XRStools.xrs_utilities.HRcorrect(pzprofile, occupation, q)

Returns the first order correction to filled 1s, 2s, and 2p Compton profiles.

Implementation after Holm and Ribberfors (citation …).

Args:

• pzprofile (np.array): Compton profile (e.g. tabulated from Biggs) to be corrected (2D matrix).

• occupation (list): electron configuration.

• q (float or np.array): momentum transfer in [a.u.].

Returns:

asymmetry (np.array): asymmetries to be added to the raw profiles (normalized to the number of electrons on pz scale)

XRStools.xrs_utilities.NNMFcost(x, A, F, C, F_up, C_up, n, k, m)

NNMFcost Returns cost and gradient for NNMF with constraints.

XRStools.xrs_utilities.NNMFcost_der(x, A, F, C, F_up, C_up, n, k, m)

XRStools.xrs_utilities.NNMFcost_old(x, A, W, H, W_up, H_up)

NNMFcost Returns cost and gradient for NNMF with constraints.

XRStools.xrs_utilities.Omega(omega, degrees=True)

rotation around (0,0,1), pos sense

XRStools.xrs_utilities.Phi(phi, degrees=True)

rotation around (0,1,0), neg sense

XRStools.xrs_utilities.Rx(chi, degrees=True)

Rx Rotation matrix for vector rotations around the [1,0,0]-direction.

Args:

• chi (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.Ry(phi, degrees=True)

Ry Rotation matrix for vector rotations around the [0,1,0]-direction.

Args:

• phi (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.Rz(omega, degrees=True)

Rz Rotation matrix for vector rotations around the [0,0,1]-direction.

Args:

• omega (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.TTsolver1D(el_energy, hkl=[6, 6, 0], crystal='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0, chitable_prefix='/home/christoph/sources/XRStools/data/chitables/chitable_')

TTsolver Solves the Takagi-Taupin equation for a bent crystal.

This function is based on a Matlab implementation by S. Huotari of M. Krisch’s Fortran programs.

Args:

• el_energy (float): Fixed nominal (working) energy in keV.

• hkl (array): Reflection order vector, e.g. [6, 6, 0]

• crystal (str): Crystal used (can be silicon ‘Si’ or ‘Ge’)

• R (float): Crystal bending radius in m.

• dev (np.array): Deviation parameter (in arc. seconds) for which the reflectivity curve should be calculated.

• alpha (float): Crystal assymetry angle.

Returns:

• refl (np.array): Reflectivity curve.

• e (np.array): Deviation from Bragg angle in meV.

• dev (np.array): Deviation from Bragg angle in microrad.

XRStools.xrs_utilities.absCorrection(mu1, mu2, alpha, beta, samthick, geometry='transmission')

absCorrection

Calculates absorption correction for given mu1 and mu2. Multiply the measured spectrum with this correction factor. This is a translation of Keijo Hamalainen’s Matlab function (KH 30.05.96).

Args

• mu1 : np.array Absorption coefficient for the incident energy in [1/cm].

• mu2 : np.array Absorption coefficient for the scattered energy in [1/cm].

• alpha : float Incident angle relative to plane normal in [deg].

• beta : float Exit angle relative to plane normal [deg].

• samthick : float Sample thickness in [cm].

• geometry : string, optional Key word for different sample geometries (‘transmission’, ‘reflection’, ‘sphere’). If geometry is set to ‘sphere’, no angular dependence is assumed.

Returns

• ac : np.array Absorption correction factor. Multiply this with your measured spectrum.

XRStools.xrs_utilities.abscorr2(mu1, mu2, alpha, beta, samthick)

Calculates absorption correction for given mu1 and mu2. Multiply the measured spectrum with this correction factor.

This is a translation of Keijo Hamalainen’s Matlab function (KH 30.05.96).

Args:

• mu1 (np.array): absorption coefficient for the incident energy in [1/cm].

• mu2 (np.array): absorption coefficient for the scattered energy in [1/cm].

• alpha (float): incident angle relative to plane normal in [deg].

• beta (float): exit angle relative to plane normal [deg] (for transmission geometry use beta < 0).

• samthick (float): sample thickness in [cm].

Returns:

• ac (np.array): absorption correction factor. Multiply this with your measured spectrum.

XRStools.xrs_utilities.addch(xold, yold, n, n0=0, errors=None)

# ADDCH Adds contents of given adjacent channels together # # [x2,y2] = addch(x,y,n,n0) # x = original x-scale (row or column vector) # y = original y-values (row or column vector) # n = number of channels to be summed up # n0 = offset for adding, default is 0 # x2 = new x-scale # y2 = new y-values # # KH 17.09.1990 # Modified 29.05.1995 to include offset

XRStools.xrs_utilities.bidiag_reduction(A)

function [U,B,V]=bidiag_reduction(A) % [U B V]=bidiag_reduction(A) % Algorithm 6.5-1 in Golub & Van Loan, Matrix Computations % Johns Hopkins University Press % Finds an upper bidiagonal matrix B so that A=U*B*V’ % with U,V orthogonal. A is an m x n matrix

XRStools.xrs_utilities.bootstrapCNNMF(A, F_ini, C_ini, F_up, C_up, Niter)

bootstrapCNNMF Constrained non-negative matrix factorization with bootstrapping for error estimates.

XRStools.xrs_utilities.bootstrapCNNMF_old(A, k, Aerr, F_ini, C_ini, F_up, C_up, Niter=100)

bootstrapCNNMF Constrained non-negative matrix factorization with bootstrapping for error estimates.

XRStools.xrs_utilities.bragg(hkl, e, xtal='Si')

% BRAGG Calculates Bragg angle for given reflection in RAD % output=bangle(hkl,e,xtal) % hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; % e=energy in keV % xtal=’Si’, ‘Ge’, etc. (check dspace.m) or d0 (Si default) % % KH 28.09.93 %

class XRStools.xrs_utilities.bragg_refl(crystal, hkl, alpha=0.0)

Bases: object

Dynamical theory of diffraction.

get_chi(energy, crystal=None, hkl=None)

get_nff(nff_path=None)

get_polarization_factor(tth, case='sigma')

Calculate polarization factor.

get_reflectivity(energy, delta_theta, case='sigma')

get_reflectivity_bent(energy, delta_theta, R)

XRStools.xrs_utilities.braggd(hkl, e, xtal='Si')

# BRAGGD Calculates Bragg angle for given reflection in deg # Call BRAGG.M # output=bangle(hkl,e,xtal) # hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; # e=energy in keV # xtal=’Si’, ‘Ge’, etc. (check dspace.m) or d0 (Si default) # # KH 28.09.93

XRStools.xrs_utilities.cNNMF_chris(A, W_fixed, W_free, maxIter=100, verbose=True)

XRStools.xrs_utilities.cixsUBfind(x, G, Q_sample, wi, wo, lambdai, lambdao)

cixsUBfind

XRStools.xrs_utilities.cixsUBgetAngles_primo(Q)

XRStools.xrs_utilities.cixsUBgetAngles_secondo(Q)

XRStools.xrs_utilities.cixsUBgetAngles_terzo(Q)

XRStools.xrs_utilities.cixsUBgetQ_primo(tthv, tthh, psi)

returns the Q0 given the detector position (tthv, tth) and th crystal orientation. This orientation is calculated considering :

the Bragg condition and the rotation around the G vector :

this rotation is defined by psi which is a rotation around G

XRStools.xrs_utilities.cixsUBgetQ_secondo(tthv, tthh, psi)

XRStools.xrs_utilities.cixsUBgetQ_terzo(tthv, tthh, psi)

XRStools.xrs_utilities.cixs_primo(tthv, tthh, psi, anal_braggd=86.5)

cixs_primo

XRStools.xrs_utilities.cixs_secondo(tthv, tthh, psi, anal_braggd=86.5)

cixs_secondo

XRStools.xrs_utilities.cixs_terzo(tthv, tthh, psi, anal_braggd=86.5)

cixs_terzo

XRStools.xrs_utilities.compute_matrix_elements(R1, R2, k, r)

XRStools.xrs_utilities.con2mat(x, W, H, W_up, H_up)

XRStools.xrs_utilities.constrained_mf(A, W_ini, W_up, coeff_ini, coeff_up, maxIter=1000, tol=1e-08, maxIter_power=1000)

cfactorizeOffDiaMatrix constrained version of factorizeOffDiaMatrix Returns main components from an off-diagonal Matrix (energy-loss x angular-departure).

XRStools.xrs_utilities.constrained_svd(M, U_ini, S_ini, VT_ini, U_up, max_iter=10000, verbose=False)

constrained_nnmf Approximate singular value decomposition with constraints.

function [U, S, V] = constrained_svd(M,U_ini,S_ini,V_ini,U_up,max_iter=10000,verbose=False)

XRStools.xrs_utilities.convertSplitEDF2EDF(foldername)

converts the old style EDF files (one image for horizontal and one image for vertical chambers) to the new style EDF (one single image).

Arg:

foldername (str): Path to folder with all the EDF-files to be

converted.

XRStools.xrs_utilities.convg(x, y, fwhm)

Convolution with Gaussian x = x-vector y = y-vector fwhm = fulll width at half maximum of the gaussian with which y is convoluted

XRStools.xrs_utilities.convtoprim(hklconv)

convtoprim converts diamond structure reciprocal lattice expressed in conventional lattice vectors to primitive one (Helsinki -> Palaiseau conversion) from S. Huotari

XRStools.xrs_utilities.cshift(w1, th)

cshift Calculates Compton peak position.

Args:

• w1 (float, array): Incident energy in [keV].

• th (float): Scattering angle in [deg].

Returns:

• w2 (foat, array): Energy of Compton peak in [keV].

Funktion adapted from Keijo Hamalainen.

XRStools.xrs_utilities.delE_JohannAberration(E, A, R, Theta)

Calculates the Johann aberration of a spherical analyzer crystal.

Args:

E (float): Working energy in [eV]. A (float): Analyzer aperture [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Johann abberation in [eV].

XRStools.xrs_utilities.delE_dicedAnalyzerIntrinsic(E, Dw, Theta)

Calculates the intrinsic energy resolution of a diced crystal analyzer.

Args:

E (float): Working energy in [eV]. Dw (float): Darwin width of the used reflection [microRad]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Intrinsic energy resolution of a perfect analyzer crystal.

XRStools.xrs_utilities.delE_offRowland(E, z, A, R, Theta)

Calculates the off-Rowland contribution of a spherical analyzer crystal.

Args:

E (float): Working energy in [eV]. z (float): Off-Rowland distance [mm]. A (float): Analyzer aperture [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Off-Rowland contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.delE_pixelSize(E, p, R, Theta)

Calculates the pixel size contribution to the resolution function of a diced analyzer crystal.

Args:

E (float): Working energy in [eV]. p (float): Pixel size in [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Pixel size contribution in [eV] to the energy resolution for a diced analyzer crystal.

XRStools.xrs_utilities.delE_sourceSize(E, s, R, Theta)

Calculates the source size contribution to the resolution function.

Args:

E (float): Working energy in [eV]. s (float): Source size in [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Source size contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.delE_stressedCrystal(E, t, v, R, Theta)

Calculates the stress induced contribution to the resulution function of a spherically bent crystal analyzer.

Args:

E (float): Working energy in [eV]. t (float): Absorption length in the analyzer material [mm]. v (float): Poisson ratio of the analyzer material. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Stress-induced contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.diode(current, energy, thickness=0.03)

diode Calculates the number of photons incident for a Si PIPS diode.

Args:

• current (float): Diode current in [pA].

• energy (float): Photon energy in [keV].

• thickness (float): Thickness of Si active layer in [cm].

Returns:

• flux (float): Number of photons per second.

Function adapted from Matlab function by S. Huotari.

XRStools.xrs_utilities.dspace(hkl=[6, 6, 0], xtal='Si')

% DSPACE Gives d-spacing for given xtal % d=dspace(hkl,xtal) % hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; % xtal=’Si’,’Ge’,’LiF’,’InSb’,’C’,’Dia’,’Li’ (case insensitive) % if xtal is number this is user as a d0 % % KH 28.09.93 % SH 2005 %

class XRStools.xrs_utilities.dtxrd(hkl, energy, crystal='Si', asym_angle=0.0, angular_range=[- 0.0005, 0.0005], angular_step=1e-08)

Bases: object

class to hold all things dynamic theory of diffraction.

get_anomalous_absorption(energy=None)

get_eta(angular_range, angular_step=1e-08)

get_extinction_length(energy=None)

get_reflection_width()

get_reflectivity(angular_range=None, angular_step=None)

set_asymmetry(alpha)

negative alpha -> more grazing incidence

set_energy(energy)

set_hkl(hkl)

XRStools.xrs_utilities.dtxrd_anomalous_absorption(energy, hkl, alpha=0.0, crystal='Si', angular_range=array([- 0.0005]))

XRStools.xrs_utilities.dtxrd_extinction_length(energy, hkl, alpha=0.0, crystal='Si')

XRStools.xrs_utilities.dtxrd_reflectivity(energy, hkl, alpha=0.0, crystal='Si', angular_range=array([- 0.0005]))

XRStools.xrs_utilities.e2pz(w1, w2, th)

Calculates the momentum scale and the relativistic Compton cross section correction according to P. Holm, PRA 37, 3706 (1988).

This function is translated from Keijo Hamalainen’s Matlab implementation (KH 29.05.96).

Args:

• w1 (float or np.array): incident energy in [keV]

• w2 (float or np.array): scattered energy in [keV]

• th (float): scattering angle two theta in [deg]

returns:

• pz (float or np.array): momentum scale in [a.u.]

• cf (float or np.array): cross section correction factor such that: J(pz) = cf * d^2(sigma)/d(w2)*d(Omega) [barn/atom/keV/srad]

XRStools.xrs_utilities.edfread(filename)

reads edf-file with filename “filename” OUTPUT: data = 256x256 numpy array

XRStools.xrs_utilities.edfread_test(filename)

reads edf-file with filename “filename” OUTPUT: data = 256x256 numpy array

here is how i opened the HH data: data = np.fromfile(f,np.int32) image = np.reshape(data,(dim,dim))

XRStools.xrs_utilities.element(z)

Converts atomic number into string of the element symbol and vice versa.

Returns atomic number of given element, if z is a string of the element symbol or string of element symbol of given atomic number z.

Args:

• z (string or int): string of the element symbol or atomic number.

Returns:

• Z (string or int): string of the element symbol or atomic number.

XRStools.xrs_utilities.energy(d, ba)

% ENERGY Calculates energy corrresponing to Bragg angle for given d-spacing % function e=energy(dspace,bragg_angle) % % dspace for reflection % bragg_angle in DEG % % KH 28.09.93

XRStools.xrs_utilities.energy_monoangle(angle, d=1.6374176589984608)

% ENERGY Calculates energy corrresponing to Bragg angle for given d-spacing % function e=energy(dspace,bragg_angle) % % dspace for reflection (defaulf for Si(311) reflection) % bragg_angle in DEG % % KH 28.09.93 %

XRStools.xrs_utilities.fermi(rs)

fermi Calculates the plasmon energy (in eV), Fermi energy (in eV), Fermi momentum (in a.u.), and critical plasmon cut-off vector (in a.u.).

Args:

• rs (float): electron separation parameter

Returns:

• wp (float): plasmon energy (in eV)

• ef (float): Fermi energy (in eV)

• kf (float): Fermi momentum (in a.u.)

• kc (float): critical plasmon cut-off vector (in a.u.)

Based on Matlab function from A. Soininen.

XRStools.xrs_utilities.find_center_of_mass(x, y)

Returns the center of mass (first moment) for the given curve y(x)

XRStools.xrs_utilities.find_diag_angles(q, x0, U, B, Lab, beam_in, lambdai, lambdao, tol=1e-08, method='BFGS')

find_diag_angles Finds the FOURC spectrometer and sample angles for a desired q.

Args:

• q (array): Desired momentum transfer in Lab coordinates.

• x0 (list): Guesses for the angles (tthv, tthh, chi, phi, omega).

• U (array): 3x3 U-matrix Lab-to-sample transformation.

• B (array): 3x3 B-matrix reciprocal lattice to absolute units transformation.

• lambdai (float): Incident x-ray wavelength in Angstrom.

• lambdao (float): Scattered x-ray wavelength in Angstrom.

• tol (float): Toleranz for minimization (see scipy.optimize.minimize)

• method (str): Method for minimization (see scipy.optimize.minimize)

Returns:

• ans (array): tthv, tthh, phi, chi, omega

XRStools.xrs_utilities.fwhm(x, y)

finds full width at half maximum of the curve y vs. x returns f = FWHM x0 = position of the maximum

XRStools.xrs_utilities.gauss(x, x0, fwhm)

XRStools.xrs_utilities.get_UB_Q(tthv, tthh, phi, chi, omega, **kwargs)

get_UB_Q Returns the momentum transfer and scattering vectors for given FOURC spectrometer and sample angles. U-, B-matrices and incident/scattered wavelength are passed as keyword-arguments.

Args:

• tthv (float): Spectrometer vertical 2Theta angle.

• tthh (float): Spectrometer horizontal 2Theta angle.

• chi (float): Sample rotation around x-direction.

• phi (float): Sample rotation around y-direction.

• omega (float): Sample rotation around z-direction.

• kwargs (dict): Dictionary with key-word arguments:

  • kwargs[‘U’] (array): 3x3 U-matrix Lab-to-sample transformation.

  • kwargs[‘B’] (array): 3x3 B-matrix reciprocal lattice to absolute units transformation.

  • kwargs[‘lambdai’] (float): Incident x-ray wavelength in Angstrom.

  • kwargs[‘lambdao’] (float): Scattered x-ray wavelength in Angstrom.

Returns:

• Q_sample (array): Momentum transfer in sample coordinates.

• Ki_sample (array): Incident beam direction in sample coordinates.

• Ko_sample (array): Scattered beam direction in sample coordinates.

XRStools.xrs_utilities.get_gnuplot_rgb(start=None, end=None, length=None)

get_gnuplot_rgb Prints out a progression of RGB hex-keys to use in Gnuplot.

Args:

• start (array): RGB code to start from (must be numbers out of [0,1]).

• end (array): RGB code to end at (must be numbers out of [0,1]).

• length (int): How many colors to print out.

XRStools.xrs_utilities.get_num_of_MD_steps(time_ps, time_step)

Calculates the number of steps in an MD simulation for a desired time (in ps) and given step size (in a.u.)

Args:

time_ps (float): Desired time span (ps). time_step (float): Chosen time step (a.u.).

Returns:

The number of steps required to span the desired time span.

XRStools.xrs_utilities.getpenetrationdepth(energy, formulas, concentrations, densities)

returns the penetration depth of a mixture of chemical formulas with certain concentrations and densities

XRStools.xrs_utilities.gettransmission(energy, formulas, concentrations, densities, thickness)

returns the transmission through a sample composed of chemical formulas with certain densities mixed to certain concentrations, and a thickness

XRStools.xrs_utilities.hex2rgb(hex_val)

XRStools.xrs_utilities.hlike_Rwfn(n, l, r, Z)

hlike_Rwfn Returns an array with the radial part of a hydrogen-like wave function.

Args:

• n (integer): main quantum number n

• l (integer): orbitalquantum number l

• r (array): vector of radii on which the function should be evaluated

• Z (float): effective nuclear charge

XRStools.xrs_utilities.householder(b, k)

function H = householder(b, k) % H = householder(b, k) % Atkinson, Section 9.3, p. 611 % b is a column vector, k an index < length(b) % Constructs a matrix H that annihilates entries % in the product H*b below index k

% $Id: householder.m,v 1.1 2008-01-16 15:33:30 mike Exp $ % M. M. Sussman

XRStools.xrs_utilities.interpolate_M(xc, xi, yi, i0)

Linear interpolation scheme after Martin Sundermann that conserves the absolute number of counts.

ONLY WORKS FOR EQUALLY/EVENLY SPACED XC, XI!

Args:

xc (np.array): The x-coordinates of the interpolated values. xi (np.array): The x-coordinates of the data points, must be increasing. yi (np.array): The y-coordinates of the data points, same length as xp. i0 (np.array): Normalization values for the data points, same length as xp.

Returns:

ic (np.array): The interpolated and normalized data points.

from scipy.interpolate import Rbf x = arange(20) d = zeros(len(x)) d[10] = 1 xc = arange(0.5,19.5) rbfi = Rbf(x, d) di = rbfi(xc)

XRStools.xrs_utilities.is_allowed_refl_fcc(H)

is_allowed_refl_fcc Check if given reflection is allowed for a FCC lattice.

Args:

• H (array, list, tuple): H=[h,k,l]

Returns:

• boolean

XRStools.xrs_utilities.lindhard_pol(q, w, rs=3.93, use_corr=False, lifetime=0.28)

lindhard_pol Calculates the Lindhard polarizability function (RPA) for certain q (a.u.), w (a.u.) and rs (a.u.).

Args:

• q (float): momentum transfer (in a.u.)

• w (float): energy (in a.u.)

• rs (float): electron parameter

• use_corr (boolean): if True, uses Bernardo’s calculation for n(k) instead of the Fermi function.

• lifetime (float): life time (default is 0.28 eV for Na).

Based on Matlab function by S. Huotari.

XRStools.xrs_utilities.makeprofile(element, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35.0, correctasym=None)

takes the profiles from ‘makepzprofile()’, converts them onto eloss scale and normalizes them to S(q,w) [1/eV] input: element = element symbol (e.g. ‘Si’, ‘Al’, etc.) filename = path and filename to tabulated profiles E0 = scattering energy [keV] tth = scattering angle [deg] returns: enscale = energy loss scale J = total CP C = only core contribution to CP V = only valence contribution to CP q = momentum transfer [a.u.]

XRStools.xrs_utilities.makeprofile_comp(formula, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35, correctasym=None)

returns the compton profile of a chemical compound with formula ‘formula’ input: formula = string of a chemical formula (e.g. ‘SiO2’, ‘Ba8Si46’, etc.) filename = path and filename to tabulated profiles E0 = scattering energy [keV] tth = scattering angle [deg] returns: eloss = energy loss scale J = total CP C = only core contribution to CP V = only valence contribution to CP q = momentum transfer [a.u.]

XRStools.xrs_utilities.makeprofile_compds(formulas, concentrations=None, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35.0, correctasym=None)

returns sum of compton profiles from a lost of chemical compounds weighted by the given concentration

XRStools.xrs_utilities.makepzprofile(element, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat')

constructs compton profiles of element ‘element’ on pz-scale (-100:100 a.u.) from the Biggs tables provided in ‘filename’

input:

• element = element symbol (e.g. ‘Si’, ‘Al’, etc.)

• filename = path and filename to tabulated profiles

returns:

• pzprofile = numpy array of the CP: * 1. column: pz-scale * 2. … n. columns: compton profile of nth shell * binden = binding energies of shells * occupation = number of electrons in the according shells

XRStools.xrs_utilities.mat2con(W, H, W_up, H_up)

XRStools.xrs_utilities.mat2vec(F, C, F_up, C_up, n, k, m)

class XRStools.xrs_utilities.maxipix_det(name, spot_arrangement)

Bases: object

Class to store some useful values from the detectors used. To be used for arranging the ROIs.

get_det_name()

get_pixel_range()

XRStools.xrs_utilities.momtrans_au(e1, e2, tth)

Calculates the momentum transfer in atomic units input: e1 = incident energy [keV] e2 = scattered energy [keV] tth = scattering angle [deg] returns: q = momentum transfer [a.u.] (corresponding to sin(th)/lambda)

XRStools.xrs_utilities.momtrans_inva(e1, e2, tth)

Calculates the momentum transfer in inverse angstrom input: e1 = incident energy [keV] e2 = scattered energy [keV] tth = scattering angle [deg] returns: q = momentum transfer [a.u.] (corresponding to sin(th)/lambda)

XRStools.xrs_utilities.mpr(energy, compound)

Calculates the photoelectric, elastic, and inelastic absorption of a chemical compound.

Calculates the photoelectric, elastic, and inelastic absorption of a chemical compound.

Args:

• energy (np.array): energy scale in [keV].

• compound (string): chemical sum formula (e.g. ‘SiO2’)

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.mpr_compds(energy, formulas, concentrations, E0, rho_formu)

Calculates the photoelectric, elastic, and inelastic absorption of a mix of compounds.

Returns the photoelectric absorption for a sum of different chemical compounds.

Args:

• energy (np.array): energy scale in [keV].

• formulas (list of strings): list of chemical sum formulas

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.myprho(energy, Z, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

Calculates the photoelectric, elastic, and inelastic absorption of an element Z

Calculates the photelectric , elastic, and inelastic absorption of an element Z. Z can be atomic number or element symbol.

Args:

• energy (np.array): energy scale in [keV].

• Z (string or int): atomic number or string of element symbol.

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.nonzeroavg(y=None)

XRStools.xrs_utilities.odefctn(y, t, abb0, abb1, abb7, abb8, lex, sgbeta, y0, c1)

#% [T,Y] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS,P1,P2,…) passes the additional #% parameters P1,P2,… to the ODE function as ODEFUN(T,Y,P1,P2…), and to #% all functions specified in OPTIONS. Use OPTIONS = [] as a place holder if #% no options are set.

XRStools.xrs_utilities.odefctn_CN(yCN, t, abb0, abb1, abb7, abb8N, lex, sgbeta, y0, c1)

XRStools.xrs_utilities.parseformula(formula)

Parses a chemical sum formula.

Parses the constituing elements and stoichiometries from a given chemical sum formula.

Args:

• formula (string): string of a chemical formula (e.g. ‘SiO2’, ‘Ba8Si46’, etc.)

Returns:

• elements (list): list of strings of constituting elemental symbols.

• stoichiometries (list): list of according stoichiometries in the same order as ‘elements’.

XRStools.xrs_utilities.plotpenetrationdepth(energy, formulas, concentrations, densities)

opens a plot window of the penetration depth of a mixture of chemical formulas with certain concentrations and densities plotted along the given energy vector

XRStools.xrs_utilities.plottransmission(energy, formulas, concentrations, densities, thickness)

opens a plot with the transmission plotted along the given energy vector

XRStools.xrs_utilities.primtoconv(hklprim)

primtoconv converts diamond structure reciprocal lattice expressed in primitive basis to the conventional basis (Palaiseau -> Helsinki conversion) from S. Huotari

XRStools.xrs_utilities.pz2e1(w2, pz, th)

Calculates the incident energy for a specific scattered photon and momentum value.

Returns the incident energy for a given photon energy and scattering angle. This function is translated from Keijo Hamalainen’s Matlab implementation (KH 29.05.96).

Args:

• w2 (float): scattered photon energy in [keV]

• pz (np.array): pz scale in [a.u.]

• th (float): scattering angle two theta in [deg]

Returns:

• w1 (np.array): incident energy in [keV]

XRStools.xrs_utilities.read_dft_wfn(element, n, l, spin=None, directory='/usr/lib/python3/dist-packages/XRStools/resources/data')

read_dft_wfn Parses radial parts of wavefunctions.

Args:

• element (str): Element symbol.

• n (int): Main quantum number.

• l (int): Orbital quantum number.

• spin (str): Which spin channel, default is average over up and down.

• directory (str): Path to directory where the wavefunctions can be found.

Returns:

• r (np.array): radius

• wfn (np.array):

XRStools.xrs_utilities.readbiggsdata(filename, element)

Reads Hartree-Fock Profile of element ‘element’ from values tabulated by Biggs et al. (Atomic Data and Nuclear Data Tables 16, 201-309 (1975)) as provided by the DABAX library (http://ftp.esrf.eu/pub/scisoft/xop2.3/DabaxFiles/ComptonProfiles.dat). input: filename = path to the ComptonProfiles.dat file (the file should be distributed with this package) element = string of element name returns:

• data = the data for the according element as in the file:

  • #UD Columns:

  • #UD col1: pz in atomic units

  • #UD col2: Total compton profile (sum over the atomic electrons

  • #UD col3,…coln: Compton profile for the individual sub-shells

• occupation = occupation number of the according shells

• bindingen = binding energies of the accorting shells

• colnames = strings of column names as used in the file

XRStools.xrs_utilities.readfio(prefix, scannumber, repnumber=0)

if repnumber = 0: reads a spectra-file (name: prefix_scannumber.fio) if repnumber > 1: reads a spectra-file (name: prefix_scannumber_rrepnumber.fio)

XRStools.xrs_utilities.readp01image(filename)

reads a detector file from PetraIII beamline P01

XRStools.xrs_utilities.readp01scan(prefix, scannumber)

reads a whole scan from PetraIII beamline P01 (experimental)

XRStools.xrs_utilities.readp01scan_rep(prefix, scannumber, repetition)

reads a whole scan with repititions from PetraIII beamline P01 (experimental)

XRStools.xrs_utilities.savitzky_golay(y, window_size, order, deriv=0, rate=1)

Smooth (and optionally differentiate) data with a Savitzky-Golay filter. The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techniques.

Parameters:

• y : array_like, shape (N,) the values of the time history of the signal.

• window_size : int the length of the window. Must be an odd integer number.

• order : int the order of the polynomial used in the filtering. Must be less then window_size - 1.

• deriv: int the order of the derivative to compute (default = 0 means only smoothing)

Returns

• ys : ndarray, shape (N) the smoothed signal (or it’s n-th derivative).

Notes:

The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.

Examples

t = np.linspace(-4, 4, 500)
y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)
ysg = savitzky_golay(y, window_size=31, order=4)
import matplotlib.pyplot as plt
plt.plot(t, y, label='Noisy signal')
plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
plt.plot(t, ysg, 'r', label='Filtered signal')
plt.legend()
plt.show()

References ::

1

A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.

2

Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688

XRStools.xrs_utilities.sgolay2d(z, window_size, order, derivative=None)

XRStools.xrs_utilities.sigmainc(Z, energy, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

sigmainc Calculates the Incoherent Scattering Cross Section in cm^2/g using Log-Log Fit.

Args:

• z (int or string): Element number or elements symbol.

• energy (float or array): Energy (can be number or vector)

Returns:

• tau (float or array): Photoelectric cross section in [cm**2/g]

Adapted from original Matlab function of Keijo Hamalainen.

XRStools.xrs_utilities.specread(filename, nscan)

reads scan “nscan” from SPEC-file “filename”

INPUT:

• filename = string with the SPEC-file name

• nscan = number (int) of desired scan

OUTPUT:

• data =

• motors =

• counters = dictionary

XRStools.xrs_utilities.spline2(x, y, x2)

Extrapolates the smaller and larger valuea as a constant

XRStools.xrs_utilities.split_hdf5_address(dataadress)

XRStools.xrs_utilities.stiff_compl_matrix_Si(e1, e2, e3, ansys=False)

stiff_compl_matrix_Si Returns stiffnes and compliance tensor of Si for a given orientation.

Args:

• e1 (np.array): unit vector normal to crystal surface

• e2 (np.array): unit vector crystal surface

• e3 (np.array): unit vector orthogonal to e2

Returns:

• S (np.array): compliance tensor in new coordinate system

• C (np.array): stiffnes tensor in new coordinate system

• E (np.array): Young’s modulus in [GPa]

• G (np.array): shear modulus in [GPa]

• nu (np.array): Poisson ratio

Copied from S.I. of L. Zhang et al. “Anisotropic elasticity of silicon and its application to the modelling of X-ray optics.” J. Synchrotron Rad. 21, no. 3 (2014): 507-517.

XRStools.xrs_utilities.sumx(A)

Short-hand command to sum over 1st dimension of a N-D matrix (N>2) and to squeeze it to N-1-D matrix.

XRStools.xrs_utilities.svd_my(M, maxiter=100, eta=0.1)

XRStools.xrs_utilities.taupgen(e, hkl=[6, 6, 0], crystals='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0)

% TAUPGEN Calculates the reflectivity curves of bent crystals % % function [refl,e,dev]=taupgen_new(e,hkl,crystals,R,dev,alpha); % % e = fixed nominal energy in keV % hkl = reflection order vector, e.g. [1 1 1] % crystals = crystal string, e.g. ‘si’ or ‘ge’ % R = bending radius in meters % dev = deviation parameter for which the % curve will be calculated (vector) (optional) % alpha = asymmetry angle % based on a FORTRAN program of Michael Krisch % Translitterated to Matlab by Simo Huotari 2006, 2007 % Is far away from being good matlab writing - mostly copy&paste from % the fortran routines. Frankly, my dear, I don’t give a damn. % Complaints -> /dev/null

XRStools.xrs_utilities.taupgen_amplitude(e, hkl=[6, 6, 0], crystals='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0)

% TAUPGEN Calculates the reflectivity curves of bent crystals % % function [refl,e,dev]=taupgen_new(e,hkl,crystals,R,dev,alpha); % % e = fixed nominal energy in keV % hkl = reflection order vector, e.g. [1 1 1] % crystals = crystal string, e.g. ‘si’ or ‘ge’ % R = bending radius in meters % dev = deviation parameter for which the % curve will be calculated (vector) (optional) % alpha = asymmetry angle % based on a FORTRAN program of Michael Krisch % Translitterated to Matlab by Simo Huotari 2006, 2007 % Is far away from being good matlab writing - mostly copy&paste from % the fortran routines. Frankly, my dear, I don’t give a damn. % Complaints -> /dev/null

XRStools.xrs_utilities.tauphoto(Z, energy, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

tauphoto Calculates Photoelectric Cross Section in cm^2/g using Log-Log Fit.

Args:

• z (int or string): Element number or elements symbol.

• energy (float or array): Energy (can be number or vector)

Returns:

• tau (float or array): Photoelectric cross section in [cm**2/g]

Adapted from original Matlab function of Keijo Hamalainen.

XRStools.xrs_utilities.unconstrained_mf(A, numComp=3, maxIter=1000, tol=1e-08)

unconstrained_mf Returns main components from an off-diagonal Matrix (energy-loss x angular-departure), using the power method iteratively on the different main components.

XRStools.xrs_utilities.vangle(v1, v2)

vangle Calculates the angle between two cartesian vectors v1 and v2 in degrees.

Args:

• v1 (np.array): first vector.

• v2 (np.array): second vector.

Returns:

• th (float): angle between first and second vector.

Function by S. Huotari, adopted for Python.

XRStools.xrs_utilities.vec2mat(x, F, C, F_up, C_up, n, k, m)

XRStools.xrs_utilities.vrot(v, vaxis, phi)

vrot Rotates a vector around a given axis.

Args:

• v (np.array): vector to be rotated

• vaxis (np.array): rotation axis

• phi (float): angle [deg] respecting the right-hand rule

Returns:

• v2 (np.array): new rotated vector

Function by S. Huotari (2007) adopted to Python.

XRStools.xrs_utilities.vrot2(vector1, vector2, angle)

rotMatrix Rotate vector1 around vector2 by an angle.

XRStools.xrs_utilities.xas_fluo_correct(ene, mu, formula, fluo_ene, edge_ene, angin, angout)

xas_fluo_correct Fluorescence yield over-absorption correction as in Larch/Athena. see: https://www3.aps.anl.gov/haskel/FLUO/Fluo-manual.pdf

Args:

• ene (np.array): energy axis in [keV]

• mu (np.array): measured fluorescence spectrum

• formula (str): chemical sum formulas (e.g. ‘SiO2’)

• fluo_ene (float): energy in keV of main fluorescence line

• edge_ene (float): edge energy in [keV]

• angin (float): incidence angle (relative to sample normal) [deg.]

• angout (float): exit angle (relative to sample normal) [deg.]

Returns:

• ene (np.array): energy axis in [keV]

• mu_corr (np.array): corrected fluorescence spectrum

XRStools.XRStool Package

XRStools.xrs_calctools Module

XRStools.xrs_calctools.alterGROatomNames(filename, oldName, newName)

XRStools.xrs_calctools.axsfTrajParser(filename)

axsfTrajParser

XRStools.xrs_calctools.boxParser(filename)

parseXYZfile Reads an xyz-style file.

XRStools.xrs_calctools.broaden_diagram(e, s, params=[1.0, 1.0, 537.5, 540.0], npoints=1000)

function [e2,s2] = broaden_diagram2(e,s,params,npoints)

% BROADEN_DIAGRAM2 Broaden a StoBe line diagram % % [ENE2,SQW2] = BROADEN_DIAGRAM2(ENE,SQW,PARAMS,NPOINTS) % % gives the broadened spectrum SQW2(ENE2) of the line-spectrum % SWQ(ENE). Each line is substituted with a Gaussian peak, % the FWHM of which is determined by PARAMS. ENE2 is a linear % scale of length NPOINTS (default 1000). % % PARAMS = [f_min f_max emin max] % % For ENE <= e_min, FWHM = f_min. % For ENE >= e_max, FWHM = f_min. % FWHM increases linearly from [f_min f_max] between [e_min e_max]. % % T Pylkkanen @ 2008-04-18 [17:37]

XRStools.xrs_calctools.broaden_linear(spec, params=[0.8, 8, 537.5, 550], npoints=1000)

broadens a spectrum with a Gaussian of width params[0] below params[2] and width params[1] above params[3], width increases linear in between. returns two-column numpy array of length npoints with energy and the broadened spectrum

XRStools.xrs_calctools.calculateCOMlist(atomList)

calculateCOMlist Calculates center of mass for a list of atoms.

XRStools.xrs_calctools.calculateRIJhist(atoms, boxLength, DELR=0.01, MAXBIN=1000)

XRStools.xrs_calctools.calculateRIJhist2_arb(atoms1, atoms2, lattice, lattice_inv, DELR=0.01, MAXBIN=1000)

XRStools.xrs_calctools.calculateRIJhist_arb(atoms1, atoms2, lattice, lattice_inv, DELR=0.01, MAXBIN=1000)

XRStools.xrs_calctools.changeOHBondLength(h2oMol, fraction, boxLength=None, oName='O', hName='H')

XRStools.xrs_calctools.convg(x, y, fwhm)

Convolution with Gaussian

XRStools.xrs_calctools.countHbonds(mol1, mol2, Roocut=3.6, Rohcut=2.4, Aoooh=30.0)

XRStools.xrs_calctools.countHbonds_orig(mol1, mol2, Roocut=3.6, Rohcut=2.4, Aoooh=30.0)

XRStools.xrs_calctools.countHbonds_pbc(mol1, mol2, boxLength, Roocut=3.6, Rohcut=2.4, Aoooh=30.0)

XRStools.xrs_calctools.count_HBonds_pbc_arb(mol1, mol2, lattice, lattice_inv, Roocut=3.6, Rohcut=2.4, Aoooh=30.0)

XRStools.xrs_calctools.count_OO_neighbors(list_of_o_atoms, Roocut, boxLength=None)

XRStools.xrs_calctools.count_OO_neighbors_pbc(list_of_o_atoms, Roocut, boxLength, numbershells=1)

XRStools.xrs_calctools.cut_spec(spec, emin=None, emax=None)

deletes lines of matrix with first column smaller than emin and larger than emax

class XRStools.xrs_calctools.erkale(prefix, postfix, fromnumber, tonumber, step, stepformat=2)

Bases: object

class to analyze ERKALE XRS results.

broaden_lin(params=[0.8, 8, 537.5, 550], npoints=1000)

cut_broadspecs(emin=None, emax=None)

cut_rawspecs(emin=None, emax=None)

norm_area(emin=None, emax=None)

norm_max()

plot_spec()

sum_specs()

XRStools.xrs_calctools.findAllWaters(point, waterMols, o_name, cutoff)

XRStools.xrs_calctools.findHexaneMolecules(box, c_atoms, CC_cut=1.7, CH_cut=1.2)

XRStools.xrs_calctools.findMethanolMolecules(box, CO_cut=1.6, CH_cut=1.2, OH_cut=1.2)

XRStools.xrs_calctools.findMolecule(xyzAtoms, molAtomList)

XRStools.xrs_calctools.find_H2O_molecules(o_atoms, h_atoms, boxLength=None)

XRStools.xrs_calctools.find_H2O_molecules_PBC_arb(o_atoms, h_atoms, lattice, lattice_inv, OH_cutoff=1.5)

XRStools.xrs_calctools.gauss(x, x0, fwhm)

XRStools.xrs_calctools.gauss1(x, x0, fwhm)

returns a gaussian with peak value normalized to unity a[0] = peak position a[1] = Full Width at Half Maximum

XRStools.xrs_calctools.gauss_areanorm(x, x0, fwhm)

area-normalized gaussian

XRStools.xrs_calctools.getDistVector(atom1, atom2)

XRStools.xrs_calctools.getDistVectorPBC_arb(atom1, atom2, lattice, lattice_inv)

getDistVectorPBC_arb

Calculates the distance vector between two atoms from an arbitrary simulation box using the minimum image convention.

Args:

atom1 (obj): Instance of the xzyAtom class. atom2 (obj): Instance of the xzyAtom class. lattice (np.array): Array with lattice vectors as columns. lattice_inv (np.array): Inverse of lattice.

Returns:

The distance vector between the two atoms (np.array).

XRStools.xrs_calctools.getDistVectorPbc(atom1, atom2, boxLength)

XRStools.xrs_calctools.getDistance(atom1, atom2)

XRStools.xrs_calctools.getDistancePBC_arb(atom1, atom2, lattice, lattice_inv)

getDistancePBC_arb

Calculates the distance of two atoms from an arbitrary simulation box using the minimum image convention.

Args:

atom1 (obj): Instance of the xzyAtom class. atom2 (obj): Instance of the xzyAtom class. lattice (np.array): Array with lattice vectors as columns. lattice_inv (np.array): Inverse of lattice.

Returns:

The distance between the two atoms.

XRStools.xrs_calctools.getDistancePbc(atom1, atom2, boxLength)

XRStools.xrs_calctools.getDistsFromMolecule(point, listOfMolecules, o_name=None)

XRStools.xrs_calctools.getPeriodicTestBox(xyzAtoms, boxLength, numbershells=1)

XRStools.xrs_calctools.getPeriodicTestBox_arb(xyzAtoms, lattice, lattice_inv, lx=[- 1, 1], ly=[- 1, 1], lz=[- 1, 1])

XRStools.xrs_calctools.getPeriodicTestBox_molecules(Molecules, boxLength, numbershells=1)

XRStools.xrs_calctools.getTetraParameter(o_atoms, boxLength=None)

according to NATURE, VOL 409, 18 JANUARY 2001

XRStools.xrs_calctools.getTranslVec(atom1, atom2, boxLength)

getTranslVec Returns the translation vector that brings atom2 closer to atom1 in case atom2 is further than boxLength away.

XRStools.xrs_calctools.getTranslVec_geocen(mol1COM, mol2COM, boxLength)

getTranslVec_geocen

XRStools.xrs_calctools.groBoxParser(filename, nanoMeter=True)

groBoxParser Parses an gromacs GRO-style file for the xyzBox class.

XRStools.xrs_calctools.groTrajecParser(filename, nanoMeter=True)

groTrajecParser Parses an gromacs GRO-style file for the xyzBox class.

XRStools.xrs_calctools.keithBoxParser(cell_fname, coord_fname)

keithBoxParser

Reads structure files from Keith’s SiO2 simulations.

XRStools.xrs_calctools.load_erkale_spec(filename)

returns an erkale spectrum

XRStools.xrs_calctools.load_erkale_specs(prefix, postfix, fromnumber, tonumber, step, stepformat=2)

returns a list of erkale spectra

XRStools.xrs_calctools.load_stobe_specs(prefix, postfix, fromnumber, tonumber, step, stepformat=2)

load a bunch of StoBe calculations, which filenames are made up of the prefix, postfix, and the counter in the between the prefix and postfix runs from ‘fromnumber’ to ‘tonumber’ in steps of ‘step’ (number of digits is ‘stepformat’)

XRStools.xrs_calctools.parseOCEANinputFile(fname)

parseOCEANinputFile

Parses an OCEAN input file and returns lattice vectors, atom names, and relative atom positions.

Args:

• fname (str): Absolute filename of OCEAN input file.

• atoms (list): List of elemental symbols in the same order as they appear in the input file.

Returns:

• lattice (np.array): Array of lattice vectors.

• rel_coords (np.array): Array of relative atomic coordinates.

• oceaatoms (list): List of atomic names.

XRStools.xrs_calctools.parsePwscfFile(fname)

parsePwscfFile

Parses a PWSCF file and returns a xyzBox object.

Args:

fname (str): Absolute filename of OCEAN input file.

Returns:

xyzBox object

XRStools.xrs_calctools.parseVaspFile(fname)

parseVaspFile

Parses a VASPS file and returns a xyzBox object.

Args:

fname (str): Absolute filename of VASP file.

Returns:

xyzBox object

XRStools.xrs_calctools.parseXYZfile(filename)

parseXYZfile Reads an xyz-style file.

XRStools.xrs_calctools.readxas(filename)

function output = readxas(filename)%[e,p,s,px,py,pz] = readxas(filename)

% READSTF Load StoBe fort.11 (XAS output) data % % [E,P,S,PX,PY,PZ] = READXAS(FILENAME) % % E energy transfer [eV] % P dipole transition intensity % S r^2 transition intensity % PX dipole transition intensity along x % PY dipole transition intensity along y % PZ dipole transition intensity along z % % as line diagrams. % % T Pylkkanen @ 2011-10-17

XRStools.xrs_calctools.repair_h2o_molecules_pbc(h2o_mols, boxLength)

XRStools.xrs_calctools.sorter(elem)

XRStools.xrs_calctools.spline2(x, y, x2)

Extrapolates the smaller and larger valuea as a constant

class XRStools.xrs_calctools.stobe(prefix, postfix, fromnumber, tonumber, step, stepformat=2)

Bases: object

class to analyze StoBe results

broaden_lin(params=[0.8, 8, 537.5, 550], npoints=1000)

cut_rawspecs(emin=None, emax=None)

norm_area(emin, emax)

sum_specs()

XRStools.xrs_calctools.translateOcean2FDMNES_p1(ocean_in, fdmnes_out, header_file)

XRStools.xrs_calctools.vaspBoxParser(filename)

groTrajecParser Parses an gromacs GRO-style file for the xyzBox class.

XRStools.xrs_calctools.vaspTrajecParser(filename, min_boxes=0, max_boxes=1000)

groTrajecParser Parses an gromacs GRO-style file for the xyzBox class.

XRStools.xrs_calctools.writeFDMNESinput_file(xyzAtoms, fname, Filout, Range, Radius, Edge, NRIXS, Absorber, Green=False, SCF=False)

writeFDMNESinput_file Writes an input file to be used for FDMNES.

XRStools.xrs_calctools.writeFEFFinput_arb(fname, headerfile, xyzBox, exatom, edge)

writeFEFFinput_arb

XRStools.xrs_calctools.writeMD1Input(fname, box, headerfile, exatomNo=0)

writeWFN1input Writes an input for cp.x by Quantum espresso for electronic wave function minimization.

XRStools.xrs_calctools.writeOCEAN_XESInput(fname, box, headerfile, exatomNo=0)

writeOCEAN_XESInput Writes an input for ONEAN XES calculation for 17 molecule water boxes.

XRStools.xrs_calctools.writeOCEANinput(fname, headerfile, xyzBox, exatom, edge, subshell)

writeOCEANinput

XRStools.xrs_calctools.writeOCEANinput_arb(fname, headerfile, xyzBox, exatom, edge, subshell)

writeOCEANinput

XRStools.xrs_calctools.writeOCEANinput_full(fname, xyzBox, exatom, edge, subshell)

Writes a complete OCEAN input file.

Args:

• fname (str): Filename for the input file to be written.

• xyzBox (xyzBox): Instance of the xyzBox class to be converted into an OCEAN input file.

• exatom (str): Atomic symbol for the excited atom.

• edge (int): Integer defining which shell to excite (e.g. 0 for K-shell, 1 for L, etc.).

• subshell (int): Integer defining which sub-shell to excite ( e.g. 0 for s, 1 for p, etc.).

XRStools.xrs_calctools.writeOCEANinput_new(fname, headerfile, xyzBox, exatom, edge, subshell)

writeOCEANinput

XRStools.xrs_calctools.writePWinuptFile(fname, box, param_dict)

writePWinuptFile

XRStools.xrs_calctools.writeRelXYZfile(filename, n_atoms, boxLength, title, xyzAtoms, inclAtomNames=True)

XRStools.xrs_calctools.writeWFN1waterInput(fname, box, headerfile, exatomNo=0)

writeWFN1input Writes an input for cp.x by Quantum espresso for electronic wave function minimization.

XRStools.xrs_calctools.writeXYZfile(filename, numberOfAtoms, title, list_of_xyzAtoms)

XRStools.xrs_calctools.writeXYZtrajectory(filename, boxes)

class XRStools.xrs_calctools.xyzAtom(name, coordinates, number)

Bases: object

xyzAtom

Class to hold information about and manipulate a single atom in xyz-style format.

Args. :

• name (str): Atomic symbol.

• coordinates (np.array): Array of xyz-coordinates.

• number (int): Integer, e.g. number of atom in a cluster.

getAnglePBCarb(atom2, atom3, lattice, lattice_inv, degrees=True)

get_angle Return angle between the three given atoms (as seen from atom2).

getCoordinates()

getDist(atom)

getDistPBCarb(atom, lattice, lattice_inv)

getNorm()

load_spectrum(file_name)

load_spectrum_all_pol(prefix, num_pols, printing=False)

normalize_spectrum(normrange)

translateSelf(vector)

translateSelf_arb(lattice, lattice_inv, vector)

class XRStools.xrs_calctools.xyzBox(xyzAtoms, boxLength=None, title=None)

Bases: object

xyzBox

Class to hold information about and manipulate a xyz-periodic cubic box.

Args.:

• xyzAtoms (list): List of instances of the xyzAtoms class that make up the molecule.

• boxLength (float): Box length.

changeOHBondlength(fraction, oName='O', hName='H')

changeOHBondlength Changes all OH covalent bond lengths inside the box by a fraction.

count_contact_pairs(name_1, name_2, cutoff, counter_name='contact_pair')

count_hbonds(Roocut=3.6, Rohcut=2.4, Aoooh=30.0, counter_name='num_H_bonds', counter_name2='H_bond_angles')

count_hbonds Counts the number of hydrogen bonds around all oxygen atoms and sets that number as attribute to the accorting xyzAtom.

count_neighbors(name1, name2, cutoff_low=0.0, cutoff_high=2.0, counter_name='num_OO_shell')

count_neighbors

Counts number of neighbors (of name2) around atom of name1.

Args:

• name1 (str): Name of first type of atom.

• name2 (str): Name of second type of atom.

• cutoff_low (float): Lower cutoff (Angstrom).

• cutoff_high (float): Upper cutoff (Angstrom).

• counter_name (str): Attribute namer under which the result should be saved.

deleteTip4pCOM()

deleteTip4pCOM Deletes the ficticious atoms used in the TIP4P water model.

findMethAndHexMolecules(CO_cut=1.6, CH_cut=1.2, OH_cut=1.2, CC_cut=1.7)

CH3OH

findMethanolMolecules(CO_cut=1.6, CH_cut=1.2, OH_cut=1.2)

CH3OH

find_hydroniums(OH_cutoff=1.5)

find_hydroniums Returns a list of hydronium molecules.

find_hydroxides(OH_cutoff=1.5)

find_hydroxides Returns a list of hydroxide molecules.

find_tmao_molecules_arb(CH_cut=1.2, CN_cut=1.6, NO_cut=1.5, CC_cut=2.5)

find_tmao_molecules Returns a list of TMAO molecules.

find_urea_molecules_arb(NH_cut=1.2, CN_cut=1.6, CO_cut=1.5)

find_urea_molecules Returns a list of Urea molecules.

getCoordinates()

getCoordinates Return coordinates of all atoms in the cluster.

getDistVectorPBC_arb(atom1, atom2)

getDistVectorPBC_arb

Calculates the distance vector between two atoms from an arbitrary simulation box using the minimum image convention.

Args:

atom1 (obj): Instance of the xzyAtom class. atom2 (obj): Instance of the xzyAtom class.

Returns:

The distance vector between the two atoms (np.array).

getDistancePBC_arb(atom1, atom2)

getDistancePBC_arb Calculates the distance of two atoms from an arbitrary simulation box using the minimum image convention.

Args:

atom1 (obj): Instance of the xzyAtom class. atom2 (obj): Instance of the xzyAtom class.

Returns:

The distance between the two atoms.

getTetraParameter()

getTetraParameter Returns a list of tetrahedrality paprameters, according to NATURE, VOL 409, 18 JANUARY (2001).

UNTESTED!!!

get_OO_neighbors(Roocut=3.6)

get_OO_neighbors Returns list of numbers of nearest oxygen neighbors within readius ‘Roocut’.

get_OO_neighbors_pbc(Roocut=3.6)

get_OO_neighbors_pbc Returns a list of numbers of nearest oxygen atoms, uses periodic boundary conditions.

get_angle(atom1, atom2, atom3, degrees=True)

get_angle Return angle between the three given atoms (as seen from atom2).

get_angle_arb(atom1, atom2, atom3, degrees=True)

get_angle Return angle between the three given atoms (as seen from atom2).

get_atoms_by_name(name)

get_atoms_by_name Return a list of all xyzAtoms of a given name ‘name’.

get_atoms_from_molecules()

get_atoms_from_molecules Parses all atoms inside self.xyzMolecules into self.xyzAtoms (useful for turning an xyzMolecule into an xyzBox).

get_h2o_molecules(o_name='O', h_name='H')

get_h2o_molecules Finds all water molecules inside the box and collects them inside the self.xyzMolecules attribute.

get_h2o_molecules_arb(o_name='O', h_name='H')

get_hbonds(Roocut=3.6, Rohcut=2.4, Aoooh=30.0)

get_hbonds Counts the hydrogen bonds inside the box, returns the number of H-bond donors and H-bond acceptors.

multiplyBoxPBC(numShells)

multiplyBoxPBC Applies the periodic boundary conditions and multiplies the box in shells around the original.

multiplyBoxPBC_arb(lx=[- 1, 1], ly=[- 1, 1], lz=[- 1, 1])

multiplyBoxPBC_arb Applies the periodic boundary conditions and multiplies the box in shells around the original. Works with arbitrary lattices.

normalize_arb_spectrum(normrange, attribute)

normalize_spectrum(normrange)

scatterPlot()

scatterPlot Opens a plot window with a scatter-plot of all coordinates of the box.

setBoxLength(boxLength, angstrom=True)

setBoxLength Set the box length.

translateAtomsMinimumImage(lattice, lattice_inv)

translateAtomsMinimumImage

Brings back all atoms into the original box using periodic boundary conditions and minimal image convention.

writeBox(filename)

writeBox Creates an xyz-style text file with all coordinates of the box.

writeClusters(cenatom_name, number, cutoff, prefix, postfix='.xyz')

writeXYZclusters Write water clusters into files.

writeClusters_arb(cenatom_name, number, cutoff, prefix, postfix='.xyz', test_box_multiplyer=1)

writeXYZclusters Write water clusters into files.

writeFDMNESinput(fname, Filout, Range, Radius, Edge, NRIXS, Absorber)

writeFDMNESinput Creates an input file to be used for q-dependent calculations with FDMNES.

writeH2Oclusters(cutoff, prefix, postfix='.xyz', o_name='O', h_name='H')

writeXYZclusters Write water clusters into files.

writeMoleculeCluster(molAtomList, fname, cutoff=None, numH2Omols=None, o_name='O', h_name='H', mol_center=None)

writeMoleculeCluster Careful, this works only for a single molecule in water.

writeOCEANinput(fname, headerfile, exatom, edge, subshell)

writeOCEANinput Creates an OCEAN input file based on the headerfile.

writeRelBox(filename, inclAtomNames=True)

writeRelBox Writes all relative atom coordinates into a text file (useful as OCEAN input).

class XRStools.xrs_calctools.xyzMolecule(xyzAtoms, title=None)

Bases: object

xyzMolecule

Class to hold information about and manipulate an xyz-style molecule.

Args.:

• xyzAtoms (list): List of instances of the xyzAtoms class that make up the molecule.

appendAtom(Atom)

appendAtom Add an xzyAtom to the molecule.

getCoordinates()

getCoordinates Return coordinates of all atoms in the cluster.

getCoordinates_name(name)

getCoordinates_name Return coordintes of all atoms with ‘name’.

getGeometricCenter()

getGeometricCenter Return the geometric center of the xyz-molecule.

getGeometricCenter_arb(lattice, lattice_inv)

get_atoms_by_name(name)

get_atoms_by_name Return a list of all xyzAtoms of a given name ‘name’.

popAtom(xyzAtom)

popAtom Delete an xyzAtom from the molecule.

scatterPlot()

scatterPlot Opens a plot window with a scatter-plot of all coordinates of the molecule.

translateAtomsMinimumImage(lattice, lattice_inv, center=array([0., 0., 0.]))

translateAtomsMinimumImage

Brings back all atoms into the original box using periodic boundary conditions and minimal image convention.

translateSelf(vector)

translateSelf Translate all atoms of the molecule by a vector ‘vector’.

writeXYZfile(fname)

writeXYZfile Creates an xyz-style text file with all coordinates of the molecule.

XRStools.xrs_calctools.xyzTrajecParser(filename, boxLength, firstBox=0, lastBox=- 1)

Parses a Trajectory of xyz-files.

Args:

filename (str): Filename of the xyz Trajectory file.

Returns:

A list of xzyBoxes.

class XRStools.xrs_calctools.xyzTrajectory(xyzBoxes)

Bases: object

getRDF(atom1='O', atom2='O', MAXBIN=1000, DELR=0.01, RHO=1.0)

getRDF2_arb(atom1='O', atom2='O', MAXBIN=1000, DELR=0.01, RHO=1.0)

getRDF_arb(atom1='O', atom2='O', MAXBIN=1000, DELR=0.01, RHO=1.0)

loadAXSFtraj(filename)

writeRandBox(filename)

writeXYZtraj(filename)

XRStools.xrs_extraction Module

class XRStools.xrs_extraction.HF_dataset(data, formulas, stoich_weights, edges)

Bases: object

dataset A class to hold all information from HF Compton profiles necessary to subtract background from the experiment.

get_C_edges_av(element, edge, columns)

get_C_total(columns)

get_J_total_av(columns)

class XRStools.xrs_extraction.edge_extraction(exp_data, formulas, stoich_weights, edges, prenormrange=[5, inf])

Bases: object

edge_extraction Class to destill core edge spectra from x-ray Raman scattering experiments.

analyzerAverage(roi_numbers, errorweighing=True)

analyzerAverage Averages signals from several crystals before background subtraction.

Args:

• roi_numberslist, str

  list of ROI numbers to average over of keyword for analyzer chamber (e.g. ‘VD’,’VU’,’VB’,’HR’,’HL’,’HB’)

• errorweighingboolean (True by default)

  keyword if error weighing should be used for the averaging or not

removeCorePearsonAv(element, edge, range1, range2, weights=[2, 1], HFcore_shift=0.0, guess=None, scaling=None, return_background=False, show_plots=True)

removeCorePearsonAv

guess (list): [position, FWHM, shape, intensity, ax, b, scale ]

removeCorePearsonAv_new(element, edge, range1, range2, HFcore_shift=0.0, guess=None, scaling=None, return_background=False, reg_lam=10)

removeCorePearsonAv_new

removePearsonAv(element, edge, range1, range2=None, weights=[2, 1], guess=None, scale=1.0, HFcore_shift=0.0)

removePearsonAv

removePolyCoreAv(element, edge, range1, range2, weights=[1, 1], guess=[1.0, 0.0, 0.0], ewindow=100.0)

removePolyCoreAv Subtract a polynomial from averaged data guided by the HF core Compton profile.

Args

• element : str String (e.g. ‘Si’) for the element you want to work on.

• edge: str String (e.g. ‘K’ or ‘L23’) for the edge to extract.

• range1 : list List with start and end value for fit-region 1.

• range2 : list List with start and end value for fit-region 2.

• weigths : list of ints List with weights for the respective fit-regions 1 and 2. Default is [1,1].

• guess : list List of starting values for the fit. Default is [1.0,0.0,0.0] (i.e. a quadratic function. Change the number of guess values to get other degrees of polynomials (i.e. [1.0, 0.0] for a constant, [1.0,0.0,0.0,0.0] for a cubic, etc.). The first guess value passed is for scaling of the experimental data to the HF core Compton profile.

• ewindow: float Width of energy window used in the plot. Default is 100.0.

save_average_Sqw(filename, emin=None, emax=None, normrange=None)

save_average_Sqw Save the S(q,w) into a ascii file (energy loss, S(q,w), Poisson errors).

Args:

• filename : str Filename for the ascii file.

• emin : float Use this to save only part of the spectrum.

• emax : float Use this to save only part of the spectrum.

• normrange : list of floats E_start and E_end for possible area-normalization before saving.

class XRStools.xrs_extraction.functorObjectV(y, eloss, hfcore, lam)

Bases: object

funct(a, eloss)

XRStools.xrs_extraction.map_chamber_names(name)

map_chamber_names Maps names of chambers to range of ROI numbers.

class XRStools.xrs_extraction.valence_CP

Bases: object

valence_CP Class to organize information about extracted experimental valence Compton profiles.

get_asymmetry()

get_pzscale()

XRStools.xrs_imaging Module

XRStools.xrs_read Module

XRStools.xrs_scans Module

XRStools.xrs_ComptonProfiles Module

class XRStools.xrs_ComptonProfiles.AtomProfile(element, filename, stoichiometry=1.0)

Bases: object

AtomProfile

Class to construct and handle Hartree-Fock atomic Compton Profile of a single atoms.

Attributes:

• filename : string Path and filename to the HF profile table.

• element : string Element symbol as in the periodic table.

• elementNr : int Number of the element as in the periodic table.

• shells : list of strings Names of the shells.

• edges : list List of edge onsets (eV).

• C_total : np.array Total core Compton profile.

• J_total : np.array Total Compton profile.

• V_total : np.array Total valence Compton profile.

• CperShell : dict. of np.arrays Core Compton profile per electron shell.

• JperShell : dict. of np.arrays Total Compton profile per electron shell.

• VperShell : dict. of np.arrays Valence Compton profile per electron shell.

• stoichiometry : float, optional Stoichiometric weight (default is 1.0).

• atomic_weight : float Atomic weight.

• atomic_density : float Density (g/cm**3).

• twotheta : float Scattering angle 2Th (degrees).

• alpha : float Incident angle (degrees).

• beta : float Exit angle (degrees).

• thickness : float Sample thickness (cm).

absorptionCorrectProfiles(alpha, thickness, geometry='transmission')

absorptionCorrectProfiles

Apply absorption correction to the Compton profiles on energy loss scale.

Args:

• alpha :float Angle of incidence (degrees).

• beta : float Exit angle for the scattered x-rays (degrees). If ‘beta’ is negative, transmission geometry is assumed, if ‘beta’ is positive, reflection geometry.

• thickness : float Sample thickness.

get_elossProfiles(E0, twotheta, correctasym=None, valence_cutoff=20.0)

get_elossProfiles Convert the HF Compton profile on to energy loss scale.

Args: E0 : float

Analyzer energy, enery of the scattered r-rays.

twothetafloat or list of floats

Scattering angle 2Th.

correctasymfloat, optional

Scaling factor to be multiplied to the asymmetry.

valence_cutofffloat, optional

Energy cut off as to what is considered the boundary between core and valence.

get_stoichiometry()

class XRStools.xrs_ComptonProfiles.ComptonProfiles(element)

Bases: object

Class for multiple HF Compton profiles.

This class should hold one or more instances of the ComptonProfile class and have methods to return profiles from single atoms, single shells, all atoms. It should be able to apply corrections etc. on those…

Attributes:

• element (string): Element symbol as in the periodic table.

• elementNr (int) : Number of the element as in the periodic table.

• shells (list) :

• edges (list) :

• C (np.array) :

• J (np.array) :

• V (np.array) :

• CperShell (dict. of np.arrays):

• JperShell (dict. of np.arrays):

• VperShell (dict. of np.arrays):

class XRStools.xrs_ComptonProfiles.FormulaProfile(formula, filename, weight=1)

Bases: object

FormulaProfile

Class to construct and handle Hartree-Fock atomic Compton Profile of a single chemical compound.

Attributes

• filename : string Path and filename to Biggs database.

• formula : string Chemical sum formula for the compound of interest (e.g. ‘SiO2’ or ‘H2O’).

• elements : list of strings List of atomic symbols that make up the chemical sum formula.

• stoichiometries : list of integers List of the stoichimetric weights for each of the elements in the list elements.

• element_Nrs : list of integers List of atomic numbers for each element in the elements list.

• AtomProfiles : list of AtomProfiles List of instances of the AtomProfiles class for each element in the list.

• eloss : np.ndarray Energy loss scale for the Compton profiles.

• C_total : np.ndarray Core HF Compton profile (one column per 2Th).

• J_total : np.ndarray Total HF Compton profile (one column per 2Th).

• V_total :np.ndarray Valence HF Compton profile (one column per 2Th).

• E0 : float Analyzer energy (keV).

• twotheta : float, list, or np.ndarray Value or list/np.ndarray of the scattering angle.

get_correctecProfiles(densities, alpha, beta, samthick)

get_elossProfiles(E0, twotheta, correctasym=None, valence_cutoff=20.0)

get_stoichWeight()

class XRStools.xrs_ComptonProfiles.HFProfile(formulas, stoich_weights, filename)

Bases: object

HFProfile

Class to construct and handle Hartree-Fock atomic Compton Profile of sample composed of several chemical compounds.

Attributes

get_elossProfiles(E0, twotheta, correctasym=None, valence_cutoff=20.0)

XRStools.xrs_ComptonProfiles.HRcorrect(pzprofile, occupation, q)

Returns the first order correction to filled 1s, 2s, and 2p Compton profiles.

Implementation after Holm and Ribberfors (citation …).

Args:

• pzprofile (np.array): Compton profile (e.g. tabulated from Biggs) to be corrected (2D matrix).

• occupation (list): electron configuration.

• q (float or np.array): momentum transfer in [a.u.].

Returns:

• asymmetry (np.array): asymmetries to be added to the raw profiles (normalized to the number of electrons on pz scale)

XRStools.xrs_ComptonProfiles.PzProfile(element, filename)

Returnes tabulated HF Compton profiles.

Reads in tabulated HF Compton profiles from the Biggs paper, interpolates them, and normalizes them to the # of electrons in the shell.

Args:

• element (string): element symbol (e.g. ‘Si’, ‘Al’, etc.)

• filename (string): absolute path and filename to tabulated profiles

Returns:

• CP_profile (np.array): Matrix of the Compton profile * 1. column: pz-scale * 2. … n. columns: Compton profile of nth shell

• binding_energy (list): binding energies of shells

• occupation_num (list): number of electrons in the according shells

class XRStools.xrs_ComptonProfiles.SqwPredict

Bases: object

Class to build a S(q,w) prediction based on HF Compton Profiles.

Attributes:

• sampleStr (list of strings): one string per compound (e.g. [‘C’,’SiO2’])

• concentrations (list of floats): relative compositional weight for each compound

XRStools.xrs_ComptonProfiles.elossProfile(element, filename, E0, tth, correctasym=None, valence_cutoff=20.0)

Returns HF Compton profiles on energy loss scale.

Uses the PzProfile function to read read in Biggs HF profiles and converts them onto energy loss scale. The profiles are cut at the respective electron binding energies and are normalized to the f-sum rule (i.e. S(q,w) is in units of [1/eV]).

Args:

• element (string): element symbol.

• filename (string): absolute path and filename to tabulated Compton profiles.

• E0 (float): analyzer energy in [keV].

• tth (float): scattering angle two theta in [deg].

• correctasym (np.array): vector of scaling factors to be applied.

• valence_cutoff (float): energy value below which edges are considered as valence

Returns:

• enScale (np.array): energy loss scale in [eV]

• J_total (np.array): total S(q,w) in [1/eV]

• C_total (np.array): core contribution to S(q,w) in [1/eV]

• V_total (np.array): valence contribution to S(q,w) in [1/eV], the valence is defined by valence_cutoff

• q (np.array): momentum transfer in [a.u]

• J_shell (dict of np.arrays): dictionary of contributions for each shell, the key are defines as in Biggs table.

• C_shell (dict of np.arrays): same as J_shell for core contribution

• V_shell (dict of np.arrays): same as J_shell for valence contribution

XRStools.xrs_ComptonProfiles.getAtomicDensity(Z)

Returns the atomic density.

XRStools.xrs_ComptonProfiles.getAtomicWeight(Z)

Returns the atomic weight.

XRStools.xrs_ComptonProfiles.list_duplicates(seq)

XRStools.xrs_ComptonProfiles.mapShellNames(shell_str, atomicNumber)

mapShellNames

Translates to and from spectroscopic edge notation and the convention of the Biggs database.

Args:

• shell_str : string Spectroscopic symbol to be converted to Biggs database convention.

• atomicNumber : int Z for the atom in question.

XRStools.xrs_ComptonProfiles.parseChemFormula(ChemFormula)

XRStools.xrs_ComptonProfiles.trapz_weights(x)

XRStools.xrs_fileIO Module

XRStools.xrs_fileIO.EdfRead(fname)

XRStools.xrs_fileIO.FabioEdfRead(fname)

Returns the EDF-data using FabIO.

XRStools.xrs_fileIO.PrepareEdfMatrix(scan_length, num_pix_x, num_pix_y)

Returns np.zeros of the shape of the detector.

XRStools.xrs_fileIO.PrepareEdfMatrix_TwoImages(scan_length, num_pix_x, num_pix_y)

Returns np.zeros for old data (horizontal and vertical Maxipix images in different files).

XRStools.xrs_fileIO.PyMcaEdfRead(fname)

Returns the EDF-data using PyMCA.

XRStools.xrs_fileIO.PyMcaSpecRead(filename, nscan)

Returns data, counter-names, and EDF-files using PyMCA.

XRStools.xrs_fileIO.PyMcaSpecRead_my(filename, nscan)

Returns data, counter-names, and EDF-files using PyMCA.

XRStools.xrs_fileIO.ReadEdfImages(ccdcounter, num_pix_x, num_pix_y, path, EdfPrefix, EdfName, EdfPostfix)

Reads a series of EDF-images and returs them in a 3D Numpy array (horizontal and vertical Maxipix images in different files).

XRStools.xrs_fileIO.ReadEdfImages_PyMca(ccdcounter, path, EdfPrefix, EdfName, EdfPostfix)

Reads a series of EDF-images and returs them in a 3D Numpy array (horizontal and vertical Maxipix images in different files).

XRStools.xrs_fileIO.ReadEdfImages_TwoImages(ccdcounter, num_pix_x, num_pix_y, path, EdfPrefix_h, EdfPrefix_v, EdfNmae, EdfPostfix)

Reads a series of EDF-images and returs them in a 3D Numpy array (horizontal and vertical Maxipix images in different files).

XRStools.xrs_fileIO.ReadEdfImages_my(ccdcounter, path, EdfPrefix, EdfName, EdfPostfix)

Reads a series of EDF-images and returs them in a 3D Numpy array (horizontal and vertical Maxipix images in different files).

XRStools.xrs_fileIO.ReadEdf_justFirstImage(ccdcounter, path, EdfPrefix, EdfName, EdfPostfix)

XRStools.xrs_fileIO.ReadScanFromFile(fname)

Returns a scan stored in a Numpy archive.

XRStools.xrs_fileIO.SilxSpecRead(filename, nscan)

Returns data, motors, counter-names, and labels using Silx.

XRStools.xrs_fileIO.SpecRead(filename, nscan)

Parses a SPEC file and returns a specified scan.

Args:

• filename (string): SPEC file name (inlc. path)

• nscan (int): Number of the desired scan.

Returns:

• data (np.array): array of the data from the specified scan.

• motors (list): list of all motor positions from the header of the specified scan.

• counters (dict): all counters in a dictionary with the counter names as keys.

XRStools.xrs_fileIO.WriteScanToFile(fname, data, motors, counters, edfmats)

Writes a scan into a Numpy archive.

XRStools.xrs_fileIO.dump_on_file_list(filename)

XRStools.xrs_fileIO.myEdfRead(filename)

Returns EDF-data, if PyMCA is not installed (this is slow).

XRStools.xrs_fileIO.readbiggsdata(filename, element)

Reads Hartree-Fock Profile of element ‘element’ from values tabulated by Biggs et al. (Atomic Data and Nuclear Data Tables 16, 201-309 (1975)) as provided by the DABAX library (http://ftp.esrf.eu/pub/scisoft/xop2.3/DabaxFiles/ComptonProfiles.dat). input: filename = path to the ComptonProfiles.dat file (the file should be distributed with this package) element = string of element name returns: data = the data for the according element as in the file:

#UD Columns: #UD col1: pz in atomic units #UD col2: Total compton profile (sum over the atomic electrons #UD col3,…coln: Compton profile for the individual sub-shells

occupation = occupation number of the according shells bindingen = binding energies of the accorting shells colnames = strings of column names as used in the file

XRStools.xrs_prediction Module

class XRStools.xrs_prediction.absolute_cross_section(beam_obj, sample_obj, analyzer_obj, detector_obj, thomson_obj, compton_profile_obj)

Bases: object

Class to calculate an expected cross section in absolute counts using objects of the ‘beam’, ‘sample’, ‘analyzer’, ‘detector’, ‘thomson’, and ‘compton_profile’ classes.

calc_abs_cross_section()

calc_num_scatterers()

Calculates number of scatterers/atoms using beam size, sample thickness, sample densites, sample molar masses (so far does not differentiate between target atoms and random sample atoms)

plot_abs_cross_section()

save_hdf5(fname, group_name='sample1')

save_hdf5 Save the results in an HDF5 file. Note:

HDF5 files are strange for overwriting files.

Args:

fname (str): Path and filename for the HDF5 file.

save_txt(file_name, header='')

class XRStools.xrs_prediction.analyzer(material='Si', hkl=[6, 6, 0], mask_d=60.0, bend_r=1.0, energy_resolution=0.5, diced=False, thickness=500.0, database_dir='/build/xrstools-IINVV3/xrstools-0.15.0+git20210910+c147919d/XRStools')

Bases: object

Class to describe things related to the analyzer crystal used. Default values are for a Si(660) crystal.

get_bend_r()

get_diced()

get_efficiency(energy=None)

Calculates the efficiency of the analyzer crystal based on the calculated reflectivity curve. The efficiency is calculated by averaging over the energy resolution set upon class initialization. energy = energy (in [keV]) for wich the efficiency is to be calculated

get_energy_resolution()

get_energy_resolution_keV()

get_hkl()

get_mask_d()

get_material()

get_reflectivity(energy, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0)

Calculates the reflectivity curve for a given analyzer crystal. Checks in the directory self.database_dir, if desired reflectivity curve has been calculated before. IN: energy = energy at which the reflectivity is to be calculated in [keV] dev = deviation parameter for which the curve is to be calculated alpha = deviation angle from exact Bragg angle [deg]

get_solid_angle()

get_thickness()

plot_reflectivity(mode='energy')

Generates and opens a plot of the calculated reflectivity curve. mode = keyword for which x-axis is to be used, can be ‘energy’ or ‘angle’

set_bend_r(bend_r)

set_diced(diced)

set_hkl(hkl)

set_mask_d(mask_d)

set_material(material)

set_thickness(thickness)

class XRStools.xrs_prediction.beam(i0_intensity, beam_height, beam_width, divergence=None)

Bases: object

Class to describe incident beam related things.

get_beam_cross_section_area()

Calculates the beam cross section area.

get_beam_height()

get_beam_height_cm()

get_beam_width()

get_beam_width_cm()

get_divergence()

get_i0_intensity()

XRStools.xrs_prediction.cla()

class XRStools.xrs_prediction.compton_profiles(sample_obj, eloss_range=array([0.000e+00, 1.000e-01, 2.000e-01, ..., 9.997e+02, 9.998e+02, 9.999e+02]), E0=9.7)

Bases: object

Class to hold construct HF Compton profiles for an object of the sample class.

calc_HF_profiles()

calc_pure_HF_profiles()

get_E0()

get_HF_profiles()

get_energy_in_keV()

get_tth()

plot_HF_profile()

class XRStools.xrs_prediction.detector(energy=9.68, thickness=500, material='Si', pixel_size=[256, 768])

Bases: object

Class to describe detector related things. All default values are meant for the ESRF MAXIPIX detector.

get_efficiency(energy=None)

calculates the detector efficiency at the given energy (simply given by the absorption of the detector active material).

get_energy()

get_material()

get_size()

get_thickness()

set_energy(energy)

set_material(material)

set_size(size)

set_thickness(thickness)

XRStools.xrs_prediction.get_all_input(filename='prediction.inp')

Adds default values if input is missing in the input-file and a default value exists for the missing one.

XRStools.xrs_prediction.input_file_parser(filename)

Parses an input file, which has a structure like the example input file (‘prediction.inp’) provided in the examples/ folder. (Python lists and numpy arrays have to be profived without white spaces in their definitions, e.g. ‘hkl = [6,6,0]’ instead of ‘hkl = [6, 6, 0]’)

XRStools.xrs_prediction.main()

class XRStools.xrs_prediction.matrix_element(R1, R2)

Bases: object

compute(k)

compute Calculates the matrix elements for a given k or range of k.

write_H5(filename)

write_H5 Creates an HDF5 file to store the matrix elements.

Args:

• fname (str) : Full path and filename for the HDF5 file to be created.

write_ascii(filename)

write_ascii Creates an ascii-file and writes matrix elements.

Args:

• fname (str) : Full path and filename for the ascii file to be created.

class XRStools.xrs_prediction.radial_wave_function

Bases: object

load_from_PP(Z, n, l, path='/home/christoph/programs/atomic_wavefunctions/', spin_polarized=False)

load_from_sympy(Z, n, l)

XRStools.xrs_prediction.run(filename='prediction.inp')

Function to create a spectrum prediction from input parameters provided in the input file filename. Generates a figure with the result.

class XRStools.xrs_prediction.sample(chem_formulas, concentrations, densities, angle_tth, sample_thickness, angle_in=None, angle_out=None, shape='sphere', molar_masses=None)

Bases: object

Class to describe a sample.

get_absorption_correction(energy1, energy2, thickness=None)

Calculates the absorption correction factor for the sample to be multiplied with experimental data to correct for absorption effects. energy1 = numpy array of energies in [keV] for which the factor is to be calculated energy2 = numpy array of energies in [keV] for which the factor is to be calculated

get_alpha()

get_average_densities()

get_beta()

get_concentrations()

get_densities()

get_energy1()

get_energy2()

get_formulas()

get_molar_masses()

get_murho(energy1, energy2=None)

Calculates the total photoelectric absorption coefficient of the sample for the two energies given. Returns only one array, if only one energy axis is defined. energy1 = numpy array of energies in [keV] energy2 = numpy array of energies in [keV] (defalt is None, i.e. only one mu is returned)

get_shape()

get_thickness()

get_tth()

plot_inv_absorption(energy1, energy2, range_of_thickness=array([0., 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3, 0.31, 0.32, 0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4, 0.41, 0.42, 0.43, 0.44, 0.45, 0.46, 0.47, 0.48, 0.49]))

Generates a figure which plots 1/Abscorr for the sample as a function of different thicknesses. This is usefull for finding optimum sample thicknesses for an experiment. energy1 = energy in [keV] at the desired edge energy2 = energy in [keV] at the elastic range_of_thickness = numpy array of sample thicknesses in [cm]

!!! right now all samples are treates as if spherical !!!

class XRStools.xrs_prediction.thomson(omega_1, omega_2, tth, scattering_plane='vertical', polarization=0.99)

Bases: object

Class to take care of the Thomson scattering cross section.

get_thomson_factor()

Calculates the Thomson scattering factor.

XRStools.xrs_rois Module

XRStools.xrs_utilities Module

XRStools.xrs_utilities.Chi(chi, degrees=True)

rotation around (1,0,0), pos sense

XRStools.xrs_utilities.HRcorrect(pzprofile, occupation, q)

Returns the first order correction to filled 1s, 2s, and 2p Compton profiles.

Implementation after Holm and Ribberfors (citation …).

Args:

• pzprofile (np.array): Compton profile (e.g. tabulated from Biggs) to be corrected (2D matrix).

• occupation (list): electron configuration.

• q (float or np.array): momentum transfer in [a.u.].

Returns:

asymmetry (np.array): asymmetries to be added to the raw profiles (normalized to the number of electrons on pz scale)

XRStools.xrs_utilities.NNMFcost(x, A, F, C, F_up, C_up, n, k, m)

NNMFcost Returns cost and gradient for NNMF with constraints.

XRStools.xrs_utilities.NNMFcost_der(x, A, F, C, F_up, C_up, n, k, m)

XRStools.xrs_utilities.NNMFcost_old(x, A, W, H, W_up, H_up)

NNMFcost Returns cost and gradient for NNMF with constraints.

XRStools.xrs_utilities.Omega(omega, degrees=True)

rotation around (0,0,1), pos sense

XRStools.xrs_utilities.Phi(phi, degrees=True)

rotation around (0,1,0), neg sense

XRStools.xrs_utilities.Rx(chi, degrees=True)

Rx Rotation matrix for vector rotations around the [1,0,0]-direction.

Args:

• chi (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.Ry(phi, degrees=True)

Ry Rotation matrix for vector rotations around the [0,1,0]-direction.

Args:

• phi (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.Rz(omega, degrees=True)

Rz Rotation matrix for vector rotations around the [0,0,1]-direction.

Args:

• omega (float) : Angle of rotation.

• degrees(bool) : Angle given in radians or degrees.

Returns:

• 3x3 rotation matrix.

XRStools.xrs_utilities.TTsolver1D(el_energy, hkl=[6, 6, 0], crystal='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0, chitable_prefix='/home/christoph/sources/XRStools/data/chitables/chitable_')

TTsolver Solves the Takagi-Taupin equation for a bent crystal.

This function is based on a Matlab implementation by S. Huotari of M. Krisch’s Fortran programs.

Args:

• el_energy (float): Fixed nominal (working) energy in keV.

• hkl (array): Reflection order vector, e.g. [6, 6, 0]

• crystal (str): Crystal used (can be silicon ‘Si’ or ‘Ge’)

• R (float): Crystal bending radius in m.

• dev (np.array): Deviation parameter (in arc. seconds) for which the reflectivity curve should be calculated.

• alpha (float): Crystal assymetry angle.

Returns:

• refl (np.array): Reflectivity curve.

• e (np.array): Deviation from Bragg angle in meV.

• dev (np.array): Deviation from Bragg angle in microrad.

XRStools.xrs_utilities.absCorrection(mu1, mu2, alpha, beta, samthick, geometry='transmission')

absCorrection

Calculates absorption correction for given mu1 and mu2. Multiply the measured spectrum with this correction factor. This is a translation of Keijo Hamalainen’s Matlab function (KH 30.05.96).

Args

• mu1 : np.array Absorption coefficient for the incident energy in [1/cm].

• mu2 : np.array Absorption coefficient for the scattered energy in [1/cm].

• alpha : float Incident angle relative to plane normal in [deg].

• beta : float Exit angle relative to plane normal [deg].

• samthick : float Sample thickness in [cm].

• geometry : string, optional Key word for different sample geometries (‘transmission’, ‘reflection’, ‘sphere’). If geometry is set to ‘sphere’, no angular dependence is assumed.

Returns

• ac : np.array Absorption correction factor. Multiply this with your measured spectrum.

XRStools.xrs_utilities.abscorr2(mu1, mu2, alpha, beta, samthick)

Calculates absorption correction for given mu1 and mu2. Multiply the measured spectrum with this correction factor.

This is a translation of Keijo Hamalainen’s Matlab function (KH 30.05.96).

Args:

• mu1 (np.array): absorption coefficient for the incident energy in [1/cm].

• mu2 (np.array): absorption coefficient for the scattered energy in [1/cm].

• alpha (float): incident angle relative to plane normal in [deg].

• beta (float): exit angle relative to plane normal [deg] (for transmission geometry use beta < 0).

• samthick (float): sample thickness in [cm].

Returns:

• ac (np.array): absorption correction factor. Multiply this with your measured spectrum.

XRStools.xrs_utilities.addch(xold, yold, n, n0=0, errors=None)

# ADDCH Adds contents of given adjacent channels together # # [x2,y2] = addch(x,y,n,n0) # x = original x-scale (row or column vector) # y = original y-values (row or column vector) # n = number of channels to be summed up # n0 = offset for adding, default is 0 # x2 = new x-scale # y2 = new y-values # # KH 17.09.1990 # Modified 29.05.1995 to include offset

XRStools.xrs_utilities.bidiag_reduction(A)

function [U,B,V]=bidiag_reduction(A) % [U B V]=bidiag_reduction(A) % Algorithm 6.5-1 in Golub & Van Loan, Matrix Computations % Johns Hopkins University Press % Finds an upper bidiagonal matrix B so that A=U*B*V’ % with U,V orthogonal. A is an m x n matrix

XRStools.xrs_utilities.bootstrapCNNMF(A, F_ini, C_ini, F_up, C_up, Niter)

bootstrapCNNMF Constrained non-negative matrix factorization with bootstrapping for error estimates.

XRStools.xrs_utilities.bootstrapCNNMF_old(A, k, Aerr, F_ini, C_ini, F_up, C_up, Niter=100)

bootstrapCNNMF Constrained non-negative matrix factorization with bootstrapping for error estimates.

XRStools.xrs_utilities.bragg(hkl, e, xtal='Si')

% BRAGG Calculates Bragg angle for given reflection in RAD % output=bangle(hkl,e,xtal) % hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; % e=energy in keV % xtal=’Si’, ‘Ge’, etc. (check dspace.m) or d0 (Si default) % % KH 28.09.93 %

class XRStools.xrs_utilities.bragg_refl(crystal, hkl, alpha=0.0)

Bases: object

Dynamical theory of diffraction.

get_chi(energy, crystal=None, hkl=None)

get_nff(nff_path=None)

get_polarization_factor(tth, case='sigma')

Calculate polarization factor.

get_reflectivity(energy, delta_theta, case='sigma')

get_reflectivity_bent(energy, delta_theta, R)

XRStools.xrs_utilities.braggd(hkl, e, xtal='Si')

# BRAGGD Calculates Bragg angle for given reflection in deg # Call BRAGG.M # output=bangle(hkl,e,xtal) # hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; # e=energy in keV # xtal=’Si’, ‘Ge’, etc. (check dspace.m) or d0 (Si default) # # KH 28.09.93

XRStools.xrs_utilities.cNNMF_chris(A, W_fixed, W_free, maxIter=100, verbose=True)

XRStools.xrs_utilities.cixsUBfind(x, G, Q_sample, wi, wo, lambdai, lambdao)

cixsUBfind

XRStools.xrs_utilities.cixsUBgetAngles_primo(Q)

XRStools.xrs_utilities.cixsUBgetAngles_secondo(Q)

XRStools.xrs_utilities.cixsUBgetAngles_terzo(Q)

XRStools.xrs_utilities.cixsUBgetQ_primo(tthv, tthh, psi)

returns the Q0 given the detector position (tthv, tth) and th crystal orientation. This orientation is calculated considering :

the Bragg condition and the rotation around the G vector :

this rotation is defined by psi which is a rotation around G

XRStools.xrs_utilities.cixsUBgetQ_secondo(tthv, tthh, psi)

XRStools.xrs_utilities.cixsUBgetQ_terzo(tthv, tthh, psi)

XRStools.xrs_utilities.cixs_primo(tthv, tthh, psi, anal_braggd=86.5)

cixs_primo

XRStools.xrs_utilities.cixs_secondo(tthv, tthh, psi, anal_braggd=86.5)

cixs_secondo

XRStools.xrs_utilities.cixs_terzo(tthv, tthh, psi, anal_braggd=86.5)

cixs_terzo

XRStools.xrs_utilities.compute_matrix_elements(R1, R2, k, r)

XRStools.xrs_utilities.con2mat(x, W, H, W_up, H_up)

XRStools.xrs_utilities.constrained_mf(A, W_ini, W_up, coeff_ini, coeff_up, maxIter=1000, tol=1e-08, maxIter_power=1000)

cfactorizeOffDiaMatrix constrained version of factorizeOffDiaMatrix Returns main components from an off-diagonal Matrix (energy-loss x angular-departure).

XRStools.xrs_utilities.constrained_svd(M, U_ini, S_ini, VT_ini, U_up, max_iter=10000, verbose=False)

constrained_nnmf Approximate singular value decomposition with constraints.

function [U, S, V] = constrained_svd(M,U_ini,S_ini,V_ini,U_up,max_iter=10000,verbose=False)

XRStools.xrs_utilities.convertSplitEDF2EDF(foldername)

converts the old style EDF files (one image for horizontal and one image for vertical chambers) to the new style EDF (one single image).

Arg:

foldername (str): Path to folder with all the EDF-files to be

converted.

XRStools.xrs_utilities.convg(x, y, fwhm)

Convolution with Gaussian x = x-vector y = y-vector fwhm = fulll width at half maximum of the gaussian with which y is convoluted

XRStools.xrs_utilities.convtoprim(hklconv)

convtoprim converts diamond structure reciprocal lattice expressed in conventional lattice vectors to primitive one (Helsinki -> Palaiseau conversion) from S. Huotari

XRStools.xrs_utilities.cshift(w1, th)

cshift Calculates Compton peak position.

Args:

• w1 (float, array): Incident energy in [keV].

• th (float): Scattering angle in [deg].

Returns:

• w2 (foat, array): Energy of Compton peak in [keV].

Funktion adapted from Keijo Hamalainen.

XRStools.xrs_utilities.delE_JohannAberration(E, A, R, Theta)

Calculates the Johann aberration of a spherical analyzer crystal.

Args:

E (float): Working energy in [eV]. A (float): Analyzer aperture [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Johann abberation in [eV].

XRStools.xrs_utilities.delE_dicedAnalyzerIntrinsic(E, Dw, Theta)

Calculates the intrinsic energy resolution of a diced crystal analyzer.

Args:

E (float): Working energy in [eV]. Dw (float): Darwin width of the used reflection [microRad]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Intrinsic energy resolution of a perfect analyzer crystal.

XRStools.xrs_utilities.delE_offRowland(E, z, A, R, Theta)

Calculates the off-Rowland contribution of a spherical analyzer crystal.

Args:

E (float): Working energy in [eV]. z (float): Off-Rowland distance [mm]. A (float): Analyzer aperture [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Off-Rowland contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.delE_pixelSize(E, p, R, Theta)

Calculates the pixel size contribution to the resolution function of a diced analyzer crystal.

Args:

E (float): Working energy in [eV]. p (float): Pixel size in [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Pixel size contribution in [eV] to the energy resolution for a diced analyzer crystal.

XRStools.xrs_utilities.delE_sourceSize(E, s, R, Theta)

Calculates the source size contribution to the resolution function.

Args:

E (float): Working energy in [eV]. s (float): Source size in [mm]. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Source size contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.delE_stressedCrystal(E, t, v, R, Theta)

Calculates the stress induced contribution to the resulution function of a spherically bent crystal analyzer.

Args:

E (float): Working energy in [eV]. t (float): Absorption length in the analyzer material [mm]. v (float): Poisson ratio of the analyzer material. R (float): Radius of the Rowland circle [mm]. Theta (float): Analyzer Bragg angle [degree].

Returns:

Stress-induced contribution in [eV] to the energy resolution.

XRStools.xrs_utilities.diode(current, energy, thickness=0.03)

diode Calculates the number of photons incident for a Si PIPS diode.

Args:

• current (float): Diode current in [pA].

• energy (float): Photon energy in [keV].

• thickness (float): Thickness of Si active layer in [cm].

Returns:

• flux (float): Number of photons per second.

Function adapted from Matlab function by S. Huotari.

XRStools.xrs_utilities.dspace(hkl=[6, 6, 0], xtal='Si')

% DSPACE Gives d-spacing for given xtal % d=dspace(hkl,xtal) % hkl can be a matrix i.e. hkl=[1,0,0 ; 1,1,1]; % xtal=’Si’,’Ge’,’LiF’,’InSb’,’C’,’Dia’,’Li’ (case insensitive) % if xtal is number this is user as a d0 % % KH 28.09.93 % SH 2005 %

class XRStools.xrs_utilities.dtxrd(hkl, energy, crystal='Si', asym_angle=0.0, angular_range=[- 0.0005, 0.0005], angular_step=1e-08)

Bases: object

class to hold all things dynamic theory of diffraction.

get_anomalous_absorption(energy=None)

get_eta(angular_range, angular_step=1e-08)

get_extinction_length(energy=None)

get_reflection_width()

get_reflectivity(angular_range=None, angular_step=None)

set_asymmetry(alpha)

negative alpha -> more grazing incidence

set_energy(energy)

set_hkl(hkl)

XRStools.xrs_utilities.dtxrd_anomalous_absorption(energy, hkl, alpha=0.0, crystal='Si', angular_range=array([- 0.0005]))

XRStools.xrs_utilities.dtxrd_extinction_length(energy, hkl, alpha=0.0, crystal='Si')

XRStools.xrs_utilities.dtxrd_reflectivity(energy, hkl, alpha=0.0, crystal='Si', angular_range=array([- 0.0005]))

XRStools.xrs_utilities.e2pz(w1, w2, th)

Calculates the momentum scale and the relativistic Compton cross section correction according to P. Holm, PRA 37, 3706 (1988).

This function is translated from Keijo Hamalainen’s Matlab implementation (KH 29.05.96).

Args:

• w1 (float or np.array): incident energy in [keV]

• w2 (float or np.array): scattered energy in [keV]

• th (float): scattering angle two theta in [deg]

returns:

• pz (float or np.array): momentum scale in [a.u.]

• cf (float or np.array): cross section correction factor such that: J(pz) = cf * d^2(sigma)/d(w2)*d(Omega) [barn/atom/keV/srad]

XRStools.xrs_utilities.edfread(filename)

reads edf-file with filename “filename” OUTPUT: data = 256x256 numpy array

XRStools.xrs_utilities.edfread_test(filename)

reads edf-file with filename “filename” OUTPUT: data = 256x256 numpy array

here is how i opened the HH data: data = np.fromfile(f,np.int32) image = np.reshape(data,(dim,dim))

XRStools.xrs_utilities.element(z)

Converts atomic number into string of the element symbol and vice versa.

Returns atomic number of given element, if z is a string of the element symbol or string of element symbol of given atomic number z.

Args:

• z (string or int): string of the element symbol or atomic number.

Returns:

• Z (string or int): string of the element symbol or atomic number.

XRStools.xrs_utilities.energy(d, ba)

% ENERGY Calculates energy corrresponing to Bragg angle for given d-spacing % function e=energy(dspace,bragg_angle) % % dspace for reflection % bragg_angle in DEG % % KH 28.09.93

XRStools.xrs_utilities.energy_monoangle(angle, d=1.6374176589984608)

% ENERGY Calculates energy corrresponing to Bragg angle for given d-spacing % function e=energy(dspace,bragg_angle) % % dspace for reflection (defaulf for Si(311) reflection) % bragg_angle in DEG % % KH 28.09.93 %

XRStools.xrs_utilities.fermi(rs)

fermi Calculates the plasmon energy (in eV), Fermi energy (in eV), Fermi momentum (in a.u.), and critical plasmon cut-off vector (in a.u.).

Args:

• rs (float): electron separation parameter

Returns:

• wp (float): plasmon energy (in eV)

• ef (float): Fermi energy (in eV)

• kf (float): Fermi momentum (in a.u.)

• kc (float): critical plasmon cut-off vector (in a.u.)

Based on Matlab function from A. Soininen.

XRStools.xrs_utilities.find_center_of_mass(x, y)

Returns the center of mass (first moment) for the given curve y(x)

XRStools.xrs_utilities.find_diag_angles(q, x0, U, B, Lab, beam_in, lambdai, lambdao, tol=1e-08, method='BFGS')

find_diag_angles Finds the FOURC spectrometer and sample angles for a desired q.

Args:

• q (array): Desired momentum transfer in Lab coordinates.

• x0 (list): Guesses for the angles (tthv, tthh, chi, phi, omega).

• U (array): 3x3 U-matrix Lab-to-sample transformation.

• B (array): 3x3 B-matrix reciprocal lattice to absolute units transformation.

• lambdai (float): Incident x-ray wavelength in Angstrom.

• lambdao (float): Scattered x-ray wavelength in Angstrom.

• tol (float): Toleranz for minimization (see scipy.optimize.minimize)

• method (str): Method for minimization (see scipy.optimize.minimize)

Returns:

• ans (array): tthv, tthh, phi, chi, omega

XRStools.xrs_utilities.fwhm(x, y)

finds full width at half maximum of the curve y vs. x returns f = FWHM x0 = position of the maximum

XRStools.xrs_utilities.gauss(x, x0, fwhm)

XRStools.xrs_utilities.get_UB_Q(tthv, tthh, phi, chi, omega, **kwargs)

get_UB_Q Returns the momentum transfer and scattering vectors for given FOURC spectrometer and sample angles. U-, B-matrices and incident/scattered wavelength are passed as keyword-arguments.

Args:

• tthv (float): Spectrometer vertical 2Theta angle.

• tthh (float): Spectrometer horizontal 2Theta angle.

• chi (float): Sample rotation around x-direction.

• phi (float): Sample rotation around y-direction.

• omega (float): Sample rotation around z-direction.

• kwargs (dict): Dictionary with key-word arguments:

  • kwargs[‘U’] (array): 3x3 U-matrix Lab-to-sample transformation.

  • kwargs[‘B’] (array): 3x3 B-matrix reciprocal lattice to absolute units transformation.

  • kwargs[‘lambdai’] (float): Incident x-ray wavelength in Angstrom.

  • kwargs[‘lambdao’] (float): Scattered x-ray wavelength in Angstrom.

Returns:

• Q_sample (array): Momentum transfer in sample coordinates.

• Ki_sample (array): Incident beam direction in sample coordinates.

• Ko_sample (array): Scattered beam direction in sample coordinates.

XRStools.xrs_utilities.get_gnuplot_rgb(start=None, end=None, length=None)

get_gnuplot_rgb Prints out a progression of RGB hex-keys to use in Gnuplot.

Args:

• start (array): RGB code to start from (must be numbers out of [0,1]).

• end (array): RGB code to end at (must be numbers out of [0,1]).

• length (int): How many colors to print out.

XRStools.xrs_utilities.get_num_of_MD_steps(time_ps, time_step)

Calculates the number of steps in an MD simulation for a desired time (in ps) and given step size (in a.u.)

Args:

time_ps (float): Desired time span (ps). time_step (float): Chosen time step (a.u.).

Returns:

The number of steps required to span the desired time span.

XRStools.xrs_utilities.getpenetrationdepth(energy, formulas, concentrations, densities)

returns the penetration depth of a mixture of chemical formulas with certain concentrations and densities

XRStools.xrs_utilities.gettransmission(energy, formulas, concentrations, densities, thickness)

returns the transmission through a sample composed of chemical formulas with certain densities mixed to certain concentrations, and a thickness

XRStools.xrs_utilities.hex2rgb(hex_val)

XRStools.xrs_utilities.hlike_Rwfn(n, l, r, Z)

hlike_Rwfn Returns an array with the radial part of a hydrogen-like wave function.

Args:

• n (integer): main quantum number n

• l (integer): orbitalquantum number l

• r (array): vector of radii on which the function should be evaluated

• Z (float): effective nuclear charge

XRStools.xrs_utilities.householder(b, k)

function H = householder(b, k) % H = householder(b, k) % Atkinson, Section 9.3, p. 611 % b is a column vector, k an index < length(b) % Constructs a matrix H that annihilates entries % in the product H*b below index k

% $Id: householder.m,v 1.1 2008-01-16 15:33:30 mike Exp $ % M. M. Sussman

XRStools.xrs_utilities.interpolate_M(xc, xi, yi, i0)

Linear interpolation scheme after Martin Sundermann that conserves the absolute number of counts.

ONLY WORKS FOR EQUALLY/EVENLY SPACED XC, XI!

Args:

xc (np.array): The x-coordinates of the interpolated values. xi (np.array): The x-coordinates of the data points, must be increasing. yi (np.array): The y-coordinates of the data points, same length as xp. i0 (np.array): Normalization values for the data points, same length as xp.

Returns:

ic (np.array): The interpolated and normalized data points.

from scipy.interpolate import Rbf x = arange(20) d = zeros(len(x)) d[10] = 1 xc = arange(0.5,19.5) rbfi = Rbf(x, d) di = rbfi(xc)

XRStools.xrs_utilities.is_allowed_refl_fcc(H)

is_allowed_refl_fcc Check if given reflection is allowed for a FCC lattice.

Args:

• H (array, list, tuple): H=[h,k,l]

Returns:

• boolean

XRStools.xrs_utilities.lindhard_pol(q, w, rs=3.93, use_corr=False, lifetime=0.28)

lindhard_pol Calculates the Lindhard polarizability function (RPA) for certain q (a.u.), w (a.u.) and rs (a.u.).

Args:

• q (float): momentum transfer (in a.u.)

• w (float): energy (in a.u.)

• rs (float): electron parameter

• use_corr (boolean): if True, uses Bernardo’s calculation for n(k) instead of the Fermi function.

• lifetime (float): life time (default is 0.28 eV for Na).

Based on Matlab function by S. Huotari.

XRStools.xrs_utilities.makeprofile(element, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35.0, correctasym=None)

takes the profiles from ‘makepzprofile()’, converts them onto eloss scale and normalizes them to S(q,w) [1/eV] input: element = element symbol (e.g. ‘Si’, ‘Al’, etc.) filename = path and filename to tabulated profiles E0 = scattering energy [keV] tth = scattering angle [deg] returns: enscale = energy loss scale J = total CP C = only core contribution to CP V = only valence contribution to CP q = momentum transfer [a.u.]

XRStools.xrs_utilities.makeprofile_comp(formula, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35, correctasym=None)

returns the compton profile of a chemical compound with formula ‘formula’ input: formula = string of a chemical formula (e.g. ‘SiO2’, ‘Ba8Si46’, etc.) filename = path and filename to tabulated profiles E0 = scattering energy [keV] tth = scattering angle [deg] returns: eloss = energy loss scale J = total CP C = only core contribution to CP V = only valence contribution to CP q = momentum transfer [a.u.]

XRStools.xrs_utilities.makeprofile_compds(formulas, concentrations=None, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat', E0=9.69, tth=35.0, correctasym=None)

returns sum of compton profiles from a lost of chemical compounds weighted by the given concentration

XRStools.xrs_utilities.makepzprofile(element, filename='/usr/lib/python3/dist-packages/XRStools/resources/data/ComptonProfiles.dat')

constructs compton profiles of element ‘element’ on pz-scale (-100:100 a.u.) from the Biggs tables provided in ‘filename’

input:

• element = element symbol (e.g. ‘Si’, ‘Al’, etc.)

• filename = path and filename to tabulated profiles

returns:

• pzprofile = numpy array of the CP: * 1. column: pz-scale * 2. … n. columns: compton profile of nth shell * binden = binding energies of shells * occupation = number of electrons in the according shells

XRStools.xrs_utilities.mat2con(W, H, W_up, H_up)

XRStools.xrs_utilities.mat2vec(F, C, F_up, C_up, n, k, m)

class XRStools.xrs_utilities.maxipix_det(name, spot_arrangement)

Bases: object

Class to store some useful values from the detectors used. To be used for arranging the ROIs.

get_det_name()

get_pixel_range()

XRStools.xrs_utilities.momtrans_au(e1, e2, tth)

Calculates the momentum transfer in atomic units input: e1 = incident energy [keV] e2 = scattered energy [keV] tth = scattering angle [deg] returns: q = momentum transfer [a.u.] (corresponding to sin(th)/lambda)

XRStools.xrs_utilities.momtrans_inva(e1, e2, tth)

Calculates the momentum transfer in inverse angstrom input: e1 = incident energy [keV] e2 = scattered energy [keV] tth = scattering angle [deg] returns: q = momentum transfer [a.u.] (corresponding to sin(th)/lambda)

XRStools.xrs_utilities.mpr(energy, compound)

Calculates the photoelectric, elastic, and inelastic absorption of a chemical compound.

Calculates the photoelectric, elastic, and inelastic absorption of a chemical compound.

Args:

• energy (np.array): energy scale in [keV].

• compound (string): chemical sum formula (e.g. ‘SiO2’)

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.mpr_compds(energy, formulas, concentrations, E0, rho_formu)

Calculates the photoelectric, elastic, and inelastic absorption of a mix of compounds.

Returns the photoelectric absorption for a sum of different chemical compounds.

Args:

• energy (np.array): energy scale in [keV].

• formulas (list of strings): list of chemical sum formulas

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.myprho(energy, Z, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

Calculates the photoelectric, elastic, and inelastic absorption of an element Z

Calculates the photelectric , elastic, and inelastic absorption of an element Z. Z can be atomic number or element symbol.

Args:

• energy (np.array): energy scale in [keV].

• Z (string or int): atomic number or string of element symbol.

Returns:

• murho (np.array): absorption coefficient normalized by the density.

• rho (float): density in UNITS?

• m (float): atomic mass in UNITS?

XRStools.xrs_utilities.nonzeroavg(y=None)

XRStools.xrs_utilities.odefctn(y, t, abb0, abb1, abb7, abb8, lex, sgbeta, y0, c1)

#% [T,Y] = ODE23(ODEFUN,TSPAN,Y0,OPTIONS,P1,P2,…) passes the additional #% parameters P1,P2,… to the ODE function as ODEFUN(T,Y,P1,P2…), and to #% all functions specified in OPTIONS. Use OPTIONS = [] as a place holder if #% no options are set.

XRStools.xrs_utilities.odefctn_CN(yCN, t, abb0, abb1, abb7, abb8N, lex, sgbeta, y0, c1)

XRStools.xrs_utilities.parseformula(formula)

Parses a chemical sum formula.

Parses the constituing elements and stoichiometries from a given chemical sum formula.

Args:

• formula (string): string of a chemical formula (e.g. ‘SiO2’, ‘Ba8Si46’, etc.)

Returns:

• elements (list): list of strings of constituting elemental symbols.

• stoichiometries (list): list of according stoichiometries in the same order as ‘elements’.

XRStools.xrs_utilities.plotpenetrationdepth(energy, formulas, concentrations, densities)

opens a plot window of the penetration depth of a mixture of chemical formulas with certain concentrations and densities plotted along the given energy vector

XRStools.xrs_utilities.plottransmission(energy, formulas, concentrations, densities, thickness)

opens a plot with the transmission plotted along the given energy vector

XRStools.xrs_utilities.primtoconv(hklprim)

primtoconv converts diamond structure reciprocal lattice expressed in primitive basis to the conventional basis (Palaiseau -> Helsinki conversion) from S. Huotari

XRStools.xrs_utilities.pz2e1(w2, pz, th)

Calculates the incident energy for a specific scattered photon and momentum value.

Returns the incident energy for a given photon energy and scattering angle. This function is translated from Keijo Hamalainen’s Matlab implementation (KH 29.05.96).

Args:

• w2 (float): scattered photon energy in [keV]

• pz (np.array): pz scale in [a.u.]

• th (float): scattering angle two theta in [deg]

Returns:

• w1 (np.array): incident energy in [keV]

XRStools.xrs_utilities.read_dft_wfn(element, n, l, spin=None, directory='/usr/lib/python3/dist-packages/XRStools/resources/data')

read_dft_wfn Parses radial parts of wavefunctions.

Args:

• element (str): Element symbol.

• n (int): Main quantum number.

• l (int): Orbital quantum number.

• spin (str): Which spin channel, default is average over up and down.

• directory (str): Path to directory where the wavefunctions can be found.

Returns:

• r (np.array): radius

• wfn (np.array):

XRStools.xrs_utilities.readbiggsdata(filename, element)

Reads Hartree-Fock Profile of element ‘element’ from values tabulated by Biggs et al. (Atomic Data and Nuclear Data Tables 16, 201-309 (1975)) as provided by the DABAX library (http://ftp.esrf.eu/pub/scisoft/xop2.3/DabaxFiles/ComptonProfiles.dat). input: filename = path to the ComptonProfiles.dat file (the file should be distributed with this package) element = string of element name returns:

• data = the data for the according element as in the file:

  • #UD Columns:

  • #UD col1: pz in atomic units

  • #UD col2: Total compton profile (sum over the atomic electrons

  • #UD col3,…coln: Compton profile for the individual sub-shells

• occupation = occupation number of the according shells

• bindingen = binding energies of the accorting shells

• colnames = strings of column names as used in the file

XRStools.xrs_utilities.readfio(prefix, scannumber, repnumber=0)

if repnumber = 0: reads a spectra-file (name: prefix_scannumber.fio) if repnumber > 1: reads a spectra-file (name: prefix_scannumber_rrepnumber.fio)

XRStools.xrs_utilities.readp01image(filename)

reads a detector file from PetraIII beamline P01

XRStools.xrs_utilities.readp01scan(prefix, scannumber)

reads a whole scan from PetraIII beamline P01 (experimental)

XRStools.xrs_utilities.readp01scan_rep(prefix, scannumber, repetition)

reads a whole scan with repititions from PetraIII beamline P01 (experimental)

XRStools.xrs_utilities.savitzky_golay(y, window_size, order, deriv=0, rate=1)

Smooth (and optionally differentiate) data with a Savitzky-Golay filter. The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techniques.

Parameters:

• y : array_like, shape (N,) the values of the time history of the signal.

• window_size : int the length of the window. Must be an odd integer number.

• order : int the order of the polynomial used in the filtering. Must be less then window_size - 1.

• deriv: int the order of the derivative to compute (default = 0 means only smoothing)

Returns

• ys : ndarray, shape (N) the smoothed signal (or it’s n-th derivative).

Notes:

The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.

Examples

t = np.linspace(-4, 4, 500)
y = np.exp( -t**2 ) + np.random.normal(0, 0.05, t.shape)
ysg = savitzky_golay(y, window_size=31, order=4)
import matplotlib.pyplot as plt
plt.plot(t, y, label='Noisy signal')
plt.plot(t, np.exp(-t**2), 'k', lw=1.5, label='Original signal')
plt.plot(t, ysg, 'r', label='Filtered signal')
plt.legend()
plt.show()

References ::

1

A. Savitzky, M. J. E. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.

2

Numerical Recipes 3rd Edition: The Art of Scientific Computing W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688

XRStools.xrs_utilities.sgolay2d(z, window_size, order, derivative=None)

XRStools.xrs_utilities.sigmainc(Z, energy, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

sigmainc Calculates the Incoherent Scattering Cross Section in cm^2/g using Log-Log Fit.

Args:

• z (int or string): Element number or elements symbol.

• energy (float or array): Energy (can be number or vector)

Returns:

• tau (float or array): Photoelectric cross section in [cm**2/g]

Adapted from original Matlab function of Keijo Hamalainen.

XRStools.xrs_utilities.specread(filename, nscan)

reads scan “nscan” from SPEC-file “filename”

INPUT:

• filename = string with the SPEC-file name

• nscan = number (int) of desired scan

OUTPUT:

• data =

• motors =

• counters = dictionary

XRStools.xrs_utilities.spline2(x, y, x2)

Extrapolates the smaller and larger valuea as a constant

XRStools.xrs_utilities.split_hdf5_address(dataadress)

XRStools.xrs_utilities.stiff_compl_matrix_Si(e1, e2, e3, ansys=False)

stiff_compl_matrix_Si Returns stiffnes and compliance tensor of Si for a given orientation.

Args:

• e1 (np.array): unit vector normal to crystal surface

• e2 (np.array): unit vector crystal surface

• e3 (np.array): unit vector orthogonal to e2

Returns:

• S (np.array): compliance tensor in new coordinate system

• C (np.array): stiffnes tensor in new coordinate system

• E (np.array): Young’s modulus in [GPa]

• G (np.array): shear modulus in [GPa]

• nu (np.array): Poisson ratio

Copied from S.I. of L. Zhang et al. “Anisotropic elasticity of silicon and its application to the modelling of X-ray optics.” J. Synchrotron Rad. 21, no. 3 (2014): 507-517.

XRStools.xrs_utilities.sumx(A)

Short-hand command to sum over 1st dimension of a N-D matrix (N>2) and to squeeze it to N-1-D matrix.

XRStools.xrs_utilities.svd_my(M, maxiter=100, eta=0.1)

XRStools.xrs_utilities.taupgen(e, hkl=[6, 6, 0], crystals='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0)

% TAUPGEN Calculates the reflectivity curves of bent crystals % % function [refl,e,dev]=taupgen_new(e,hkl,crystals,R,dev,alpha); % % e = fixed nominal energy in keV % hkl = reflection order vector, e.g. [1 1 1] % crystals = crystal string, e.g. ‘si’ or ‘ge’ % R = bending radius in meters % dev = deviation parameter for which the % curve will be calculated (vector) (optional) % alpha = asymmetry angle % based on a FORTRAN program of Michael Krisch % Translitterated to Matlab by Simo Huotari 2006, 2007 % Is far away from being good matlab writing - mostly copy&paste from % the fortran routines. Frankly, my dear, I don’t give a damn. % Complaints -> /dev/null

XRStools.xrs_utilities.taupgen_amplitude(e, hkl=[6, 6, 0], crystals='Si', R=1.0, dev=array([- 50., - 49., - 48., - 47., - 46., - 45., - 44., - 43., - 42., - 41., - 40., - 39., - 38., - 37., - 36., - 35., - 34., - 33., - 32., - 31., - 30., - 29., - 28., - 27., - 26., - 25., - 24., - 23., - 22., - 21., - 20., - 19., - 18., - 17., - 16., - 15., - 14., - 13., - 12., - 11., - 10., - 9., - 8., - 7., - 6., - 5., - 4., - 3., - 2., - 1., 0., 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22., 23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33., 34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44., 45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55., 56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66., 67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77., 78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88., 89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99., 100., 101., 102., 103., 104., 105., 106., 107., 108., 109., 110., 111., 112., 113., 114., 115., 116., 117., 118., 119., 120., 121., 122., 123., 124., 125., 126., 127., 128., 129., 130., 131., 132., 133., 134., 135., 136., 137., 138., 139., 140., 141., 142., 143., 144., 145., 146., 147., 148., 149.]), alpha=0.0)

% TAUPGEN Calculates the reflectivity curves of bent crystals % % function [refl,e,dev]=taupgen_new(e,hkl,crystals,R,dev,alpha); % % e = fixed nominal energy in keV % hkl = reflection order vector, e.g. [1 1 1] % crystals = crystal string, e.g. ‘si’ or ‘ge’ % R = bending radius in meters % dev = deviation parameter for which the % curve will be calculated (vector) (optional) % alpha = asymmetry angle % based on a FORTRAN program of Michael Krisch % Translitterated to Matlab by Simo Huotari 2006, 2007 % Is far away from being good matlab writing - mostly copy&paste from % the fortran routines. Frankly, my dear, I don’t give a damn. % Complaints -> /dev/null

XRStools.xrs_utilities.tauphoto(Z, energy, logtablefile='/usr/lib/python3/dist-packages/XRStools/resources/data/logtable.dat')

tauphoto Calculates Photoelectric Cross Section in cm^2/g using Log-Log Fit.

Args:

• z (int or string): Element number or elements symbol.

• energy (float or array): Energy (can be number or vector)

Returns:

• tau (float or array): Photoelectric cross section in [cm**2/g]

Adapted from original Matlab function of Keijo Hamalainen.

XRStools.xrs_utilities.unconstrained_mf(A, numComp=3, maxIter=1000, tol=1e-08)

unconstrained_mf Returns main components from an off-diagonal Matrix (energy-loss x angular-departure), using the power method iteratively on the different main components.

XRStools.xrs_utilities.vangle(v1, v2)

vangle Calculates the angle between two cartesian vectors v1 and v2 in degrees.

Args:

• v1 (np.array): first vector.

• v2 (np.array): second vector.

Returns:

• th (float): angle between first and second vector.

Function by S. Huotari, adopted for Python.

XRStools.xrs_utilities.vec2mat(x, F, C, F_up, C_up, n, k, m)

XRStools.xrs_utilities.vrot(v, vaxis, phi)

vrot Rotates a vector around a given axis.

Args:

• v (np.array): vector to be rotated

• vaxis (np.array): rotation axis

• phi (float): angle [deg] respecting the right-hand rule

Returns:

• v2 (np.array): new rotated vector

Function by S. Huotari (2007) adopted to Python.

XRStools.xrs_utilities.vrot2(vector1, vector2, angle)

rotMatrix Rotate vector1 around vector2 by an angle.

XRStools.xrs_utilities.xas_fluo_correct(ene, mu, formula, fluo_ene, edge_ene, angin, angout)

xas_fluo_correct Fluorescence yield over-absorption correction as in Larch/Athena. see: https://www3.aps.anl.gov/haskel/FLUO/Fluo-manual.pdf

Args:

• ene (np.array): energy axis in [keV]

• mu (np.array): measured fluorescence spectrum

• formula (str): chemical sum formulas (e.g. ‘SiO2’)

• fluo_ene (float): energy in keV of main fluorescence line

• edge_ene (float): edge energy in [keV]

• angin (float): incidence angle (relative to sample normal) [deg.]

• angout (float): exit angle (relative to sample normal) [deg.]

Returns:

• ene (np.array): energy axis in [keV]

• mu_corr (np.array): corrected fluorescence spectrum

XRStools.roifinder_and_gui Module