Source code for BigDFT.DoS

"""
This module is used to display the Density of States (DoS).

The Main Class of this module is :py:class:`DoS`. Essentially,
such class interpret the information coming from a set of energies and
represents in this way a curve that smears such energies.
"""


AU_eV = 27.21138386


[docs]class DiracSuperposition(): """Sum of weighted Dirac deltas. Defines a superposition of Dirac deltas which can be used to plot the density of states. Such deltas are given on a per k-point basis and can be also equipped with a array of weights, which may be useful to define Partial Density of States. Args: dos (matrix): array containing the density of states per each k-point. Should be of shape 2, a list of energies per kpoint wgts(float, array, matrix): contains the weights of each of the k-points. Could be a constant, in which case the same weight is applied everywhere, a list (on a k-point basis), or a matrix, where each energy have its own weight. """ def __init__(self, dos, wgts=[1.0]): import numpy as np self.dos = dos if isinstance(wgts, float): self.norm = [wgts] else: self.norm = wgts # set range for this distribution e_min = 1.e100 e_max = -1.e100 ddos = np.ravel(dos) if len(ddos) > 0: e_min = min(e_min, np.min(ddos) - 0.05 * (np.max(ddos) - np.min(ddos))) e_max = max(e_max, np.max(ddos) + 0.05 * (np.max(ddos) - np.min(ddos))) self.xlim = (e_min, e_max)
[docs] def curve(self, xs, sigma, wgts=None): """Output the quantities to be plotted. Returns the x,y arrays that can be passed to plotting programs to represent the DoS. Args: xs (list): xrange of the output. sigma (float): smearing of the energies, as returned by :py:meth:`peaks`. wgts (list): array of further weights to be applied, if needed Returns: collections.NamedTuple: x,y numpy arrays of the curve in the specified range. """ from numpy import ones from collections import namedtuple Curve = namedtuple('DoSCurve', 'x y') dos_g = 0.0 idos = 0 for norm, dos in zip(self.norm, self.dos): if wgts is not None: norms = wgts[idos]*norm idos += 1 else: norms = ones(len(dos))*norm kptcurve = self.peaks(xs, dos, norms, sigma) dos_g += kptcurve return Curve(x=xs, y=dos_g)
[docs] def peak(self, omega, e, sigma): """ Define if a peak is a Gaussian or a Lorenzian (temporarily only the gaussian is defined) """ import numpy as np nfac = np.sqrt(2.0*np.pi) val = np.exp(- (omega - e)**2 / (2.0 * sigma**2))/(nfac*sigma) return val
[docs] def peaks(self, xs, dos, norms, sigma): """ Return the array of the whole set of peaks """ curve = 0.0 for e, nrm in zip(dos, norms): curve += self.peak(xs, e, sigma)*nrm return curve
def _bandarray_to_data(jspin, bandarrays): lbl = 'up' if jspin == 0 else 'dw' kptlists = [[], []] for orbs in bandarrays: for ispin, norbs in enumerate(orbs.info): if norbs == 0 or ispin != jspin: continue # energy values kptlists[0].append(orbs[ispin, :norbs]) # normalization kptlists[1].append(orbs.kwgt*(1.0-2*ispin)) # print 'kpt',kptlists return kptlists, lbl if norbs != 0 else ''
[docs]class DoS(): """Density of states class. Extract a quantity which is associated to the DoS, that can be plotted Args: bandarrays (list): a list of :py:class:`~BigDFT.BZ.BandArray` class instances. energies (array-like): a list of energies to be plotted. Useful for plotting a single DoS from an array. evals (dict): dictionary of eigenvalues from a logfile yaml serialization. May be useful if a :py:class:`~BigDFT.Logfiles.Logfile` class is not available. logfiles_dict(dict): dictionary of :py:class:`~BigDFT.Logfiles.Logfile` class instances as values to be employed to create the set of DoS. The keys of the dictionary are the labels of the corresponding curves. reference_fermi_level (float): useful in the case of a logfiles_dict. the value of the reference fermi level is compared with the fermi level of all the logfiles in order to align all the curves. It is assumed that the fermi levels are properly defined in all the logfiles. units (str): The units of the provided energies, and fermi_level. Should be `AU` of `eV`. label (str): label of the curve. sigma (float): smearing of the energies. Always provided in eV. fermi_level(float): set the value of the fermi energy. norm (float, list): weights of the :py:class:`DiracSuperposition` instantation for each of the k-points. sdos : spatial density of states instantiation **kwargs: keyword arguments of the :py:meth:`set_range` method. """ def __init__(self, bandarrays=None, energies=None, evals=None, logfiles_dict=None, units='eV', reference_fermi_level=None, label='1', sigma=0.2, fermi_level=None, norm=1.0, sdos=None, **kwargs): import numpy as np self.ens = [] self.labels = [] self.ef = None if bandarrays is not None: self.append_from_bandarray(bandarrays, label) if evals is not None: self.append_from_dict(evals, label) if energies is not None: self.append(np.array([energies]), label=label, units=units, norm=(np.array([norm]) if isinstance(norm, float) else norm)) if logfiles_dict is not None: shifts = {} for lb, log in logfiles_dict.items(): self.append_from_bandarray(log.evals, label=lb) if reference_fermi_level is not None: sh = reference_fermi_level - log.fermi_level shifts[lb] = sh*self._conversion_factor(units='AU') if len(shifts) > 0: self.fermi_level(reference_fermi_level, units='AU') self.shift_curves(shifts) self.sigma = sigma self.fermi_level(fermi_level, units=units) self.set_range(**kwargs) if sdos is not None: self._embed_sdos(sdos) def _embed_sdos(self, sdos): self.sdos = [] for i, xdos in enumerate(sdos): self.sdos.append({'coord': xdos['coord']}) jdos = 0 for subspin in xdos['dos']: if len(subspin[0]) == 0: continue d = {'doslist': subspin} try: self.ens[jdos]['sdos'].append(d) except KeyError: self.ens[jdos]['sdos'] = [d] jdos += 1
[docs] def append_from_bandarray(self, bandarrays, label): """Add a new band array to the previous DoS. This method can be called to include in the DoS the energies which come from another run. Args: bandarrays (BigDFT.BZ.BandArray): a instance of the eigenvalues which come from a logfile. Can be retrieved by the `BigDFT.Logfiles.Logfile.evals` attribute of the class. label (str): id of the run. """ import numpy as np for jspin in range(2): kptlists, lbl = _bandarray_to_data(jspin, bandarrays) self.append(np.array(kptlists[0]), label=label+lbl, units='AU', norm=np.array(kptlists[1]))
[docs] def append_from_dict(self, evals, label): """Get the energies from the different flavours given by the dict.""" import numpy as np evs = [[], []] ef = None for ev in evals: occ = self._get_ev(ev, ['e_occ', 'e_occupied']) if occ: ef = max(occ) vrt = self._get_ev(ev, ['e_vrt', 'e_virt']) eigen = False if occ: eigen = occ if vrt: eigen = vrt if not eigen: eigen = self._get_ev(ev) if not occ and not vrt and eigen: ef = max(eigen) if not eigen: continue for i, e in enumerate(eigen): if e: evs[i].append(e) for i, energs in enumerate(evs): if len(energs) == 0: continue self.append(np.array(energs), label=label, units='AU', norm=1.0-2.0*i) if ef: self.fermi_level(ef, units='AU')
def _get_ev(self, ev, keys=None): "Get the correct list of the energies for this eigenvalue" res = False if keys is None: ener = ev.get('e') spin = ev.get('s') if ener and spin == 1: res = [ener] elif ener and spin == -1: res = [None, ener] else: for k in keys: if k in ev: res = ev[k] if not isinstance(res, list): res = [res] break return res
[docs] def append(self, energies, label=None, units='eV', norm=1.0): """Include other DoS inside the instance. Args: energies (list): energies of the superpsition. label (str): id of the DoS. units (str): units of the energies. Can be AU or eV. norm (float, list): weights of the density of states. """ if not isinstance(norm, float) and len(norm) == 0: return dos = self._conversion_factor(units)*energies self.ens.append({'dos': DiracSuperposition(dos, wgts=norm)}) lbl = label if label is not None else str(len(self.labels)+1) self.labels.append(lbl) self.set_range()
def _conversion_factor(self, units): if units == 'AU': fac = AU_eV elif units == 'eV': fac = 1.0 else: raise ValueError('Unrecognized units ('+units+')') return fac
[docs] def fermi_level(self, fermi_level, units='eV'): """ Set the fermi level of the DoS. Args: fermi_level (float): the value of the chemical potential. units (str): the units of this value. can be `AU` or `eV`. """ if fermi_level is not None: self.ef = fermi_level*self._conversion_factor(units)
[docs] def set_range(self, npts=None, e_min=None, e_max=None, deltae=None): """Adjust the range of the curves to be plotted/represented. This function can be called if it is necessary to adjust the range of the curves. Args: npts (int): minimum number of points of the curves. deltae (float): minimum resolution of the x range. Always in eV. e_min (float): Minimum value of the energy. Always in eV. e_max (float): Maximum value of the energy. Always in eV. """ import numpy as np npts = npts if npts is not None else getattr(self, 'npts', 2500) em = 1.e100 eM = -1.e100 demin = 1.e100 for dos in self.ens: mn, mx = dos['dos'].xlim em = min(em, mn) eM = max(eM, mx) demin = min(demin, (eM-em)/npts) # reassign windowing self.emin = max( em, getattr(self, 'emin', -1.e100) if e_min is None else e_min) self.emax = min( eM, getattr(self, 'emax', 1.e100) if e_max is None else e_max) self.deltae = min(demin, getattr(self, 'deltae', 1.e100)) self.npts = npts self.range = np.arange(self.emin, self.emax, self.deltae)
[docs] def get_curves(self, range=None, sigma=None): """Get the curves of the DoS instance, ready for plotting. This function provides a dictionary of data for each of the curves which can be plots by the :py:meth:`plot` method. They can be retrieved also to be plotted with other plotting tools. Args: range (array): the xrange to be employed for the curves. If not provided, use the :py:attr:`range` attribute of the instance. sigma (float): the smearing of the dos. If not provided, use the :py:attr:`sigma` attribute of the instance. Returns: collections.OrderedDict: a dicitonary of a `label: (x,y)` items, where x,y are the data to be plotted. (x,y) is a `py:class:~collections.namedtuple` class instance, as returned from `DiracSuperposition`. """ from collections import OrderedDict if range is None: xr = self.range else: xr = range sg = sigma if sigma is not None else self.sigma return OrderedDict((lb, c['dos'].curve(xr, sg)) for lb, c in zip(self.labels, self.ens))
[docs] def shift_curves(self, shift): """Shift the curves. Apply a constant or a per-curve shift on the data. Args: shift (float, list, dict): the shift to be implemented. If it is a constant, it is performed on all the curves. If it is a list, the shif is performed on all the DoS, in appending order. Should have the same length of the labels. If is is a dict, it assumes the shift per label. Only the indicated DoS will be shifted. The units of the shift are always in eV. """ if isinstance(shift, dict): shiftlist = [shift.get(lb, 0.0) for lb in self.labels] elif isinstance(shift, float): shiftlist = [shift for lb in self.labels] else: shiftlist = shift for sh, d in zip(shiftlist, self.ens): d['dos'].dos += sh
[docs] def dump(self, **kwargs): """Represent the dta to be plotted as a table. This is a commodity function that can be used to redirect the output of the DoS into a file. Args: **kwargs: the arguments of the :py:meth:`get_curves` method. Returns: (str): serialized DoS, gnuplot-friendly, can be written in a file. """ curves = self.get_curves(**kwargs) allcv = [] for lb, (x, y) in curves.items(): xrg = x # those are all equal allcv.append(y) buf = '' for i, e in enumerate(xrg): buf += str(e) + ' ' + ' '.join(map(str, [d[i] for d in allcv])) buf += '\n' return buf
[docs] def plot(self, sigma=None, ax=None, smearing_slider=False): """Commodity Function to plot the DoS. Plot the curves which are available. Args: sigma(float): smearing of the curves ax (matplotlib.pyplot.axis): matplotlib axis instance. Created if not given. smearing_slider (bool): If True, a slider is drawn to control the semaring manually. Useful when outside the jupyter inline visualization. Returns: matplotlib.pyplot.axis: The axis instance used for the plot. This is also present in the `ax1` attribute of the class. """ import matplotlib.pyplot as plt from matplotlib.widgets import Slider if sigma is None: sigma = self.sigma if ax is None: self.fig, self.ax1 = plt.subplots(figsize=(6.4, 4.8)) else: self.fig = ax.get_figure() self.ax1 = ax curves = self.get_curves(sigma=sigma) self.plotl = [self.ax1.plot(x, y, label=lb) for lb, (x, y) in curves.items()] self.ax1.set_xlabel('Energy [eV]', fontsize=18) self.ax1.set_ylabel('DoS', fontsize=18) if self.ef is not None: plt.axvline(self.ef, color='k', linestyle='--') if smearing_slider: axcolor = 'lightgoldenrodyellow' try: axsigma = plt.axes([0.2, 0.93, 0.65, 0.03], facecolor=axcolor) except AttributeError: axsigma = plt.axes([0.2, 0.93, 0.65, 0.03], axisbg=axcolor) self.ssig = Slider(axsigma, 'Smearing', 0.0, 0.4, valinit=sigma) self.ssig.on_changed(self.update) if hasattr(self, 'sdos') and self.sdos: self._set_sdos_selector() self._set_sdos() return self.ax1
def _set_sdos_selector(self): import matplotlib.pyplot as plt from matplotlib.widgets import RadioButtons self.sdos_selector = RadioButtons( plt.axes([0.93, 0.05, 0.04, 0.11], axisbg='lightgoldenrodyellow'), ('x', 'y', 'z'), active=1) self.isdos = 1 self.sdos_selector.on_clicked(self._update_sdos) def _set_sdos(self): import numpy xs = self.sdos[self.isdos]['coord'] self._set_sdos_sliders(numpy.min(xs), numpy.max(xs)) self._update_sdos(0.0) # fake value as it is unused def _sdos_curve(self, sdos, vmin, vmax): import numpy xs = self.sdos[self.isdos]['coord'] imin = numpy.argmin(numpy.abs(xs-vmin)) imax = numpy.argmin(numpy.abs(xs-vmax)) doslist = sdos[self.isdos]['doslist'] # norms=self.sdos[self.isdos]['norms'][ispin] tocurve = [0.0 for i in doslist[imin]] for d in doslist[imin:imax+1]: tocurve = [t+dd for t, dd in zip(tocurve, d)] # tocurve=numpy.sum([ d[ispin] for d in doslist[imin:imax+1]],axis=0) return tocurve # float(len(xs))/float(imax+1-imin)*tocurve,norms def _update_sdos(self, val): isdos = self.isdos if val == 'x': isdos = 0 elif val == 'y': isdos = 1 elif val == 'z': isdos = 2 if isdos != self.isdos: self.isdos = isdos self._set_sdos() vmin, vmax = (s.val for s in self.ssdos) if vmax < vmin: self.ssdos[1].set_val(vmin) vmax = vmin if vmin > vmax: self.ssdos[0].set_val(vmax) vmin = vmax # now plot the sdos curve associated to the given value sig = self.ssig.val curves = [] for dos in self.ens: if 'sdos' not in dos: continue renorms = self._sdos_curve(dos['sdos'], vmin, vmax) curve = dos['dos'].curve(self.range, sigma=sig, wgts=renorms) curves.append(curve) if hasattr(self, '_sdos_plots'): for pl, curve in zip(self._sdos_plots, curves): pl[0].set_ydata(curve[1]) else: self._sdos_plots = [] for c in curves: self._sdos_plots.append( self.ax1.plot(*c, label='sdos')) self.ax1.relim() self.ax1.autoscale_view() self.fig.canvas.draw_idle() def _set_sdos_sliders(self, cmin, cmax): import matplotlib.pyplot as plt from futile.Figures import VertSlider if hasattr(self, 'ssdos'): self.ssdos[0].ax.clear() self.ssdos[0].__init__( self.ssdos[0].ax, 'SDos', cmin, cmax, valinit=cmin) self.ssdos[1].ax.clear() self.ssdos[1].__init__(self.ssdos[1].ax, '', cmin, cmax, valinit=cmax) else: axcolor = 'red' axmin = plt.axes([0.93, 0.2, 0.02, 0.65], axisbg=axcolor) axmax = plt.axes([0.95, 0.2, 0.02, 0.65], axisbg=axcolor) self.ssdos = [ VertSlider(axmin, 'SDos', cmin, cmax, valinit=cmin), VertSlider(axmax, '', cmin, cmax, valinit=cmax)] self.ssdos[0].valtext.set_ha('right') self.ssdos[1].valtext.set_ha('left') self.ssdos[0].on_changed(self._update_sdos) self.ssdos[1].on_changed(self._update_sdos)
[docs] def update(self, val): sig = self.ssig.val curves = self.get_curves(sigma=sig) for line, (x, y) in zip(self.plotl, curves.values()): line[0].set_ydata(y) # for i, dos in enumerate(self.ens): # self.plotl[i][0].set_ydata( # dos['dos'].curve(self.range, sigma=sig)[1]) # self.plotl[i][0].set_ydata(self.curve(dos,norm=self.norms[i],sigma=sig)) self.ax1.relim() self.ax1.autoscale_view() self.fig.canvas.draw_idle()
if __name__ == "__main__": import numpy as np energies = np.array([-0.815924953235059, -0.803163374736654, -0.780540200987971, -0.7508806541364, -0.723626807289917, -0.714924448617026, -0.710448085701742, -0.68799028016451, -0.67247569974853, -0.659038909236607, -0.625396293324399, -0.608009041659988, -0.565337910777367, -0.561250536074343, -0.551767438323268, -0.541295070404525, -0.532326667587434, -0.515961980147107, -0.474601108285518, -0.473408476151224, -0.46509070541069, -0.445709086452906, -0.433874403837837, -0.416121660651406, -0.407871082254237, -0.406123490618786, -0.403004188319382, -0.38974739285104, -0.380837488456638, -0.375163102271681, -0.375007771592681, -0.367898783582561, -0.367518948507212, -0.359401585874402, -0.358189406008502, -0.354517727598174, -0.334286389724978, -0.332921810616845, -0.315466259109401, -0.308028853904577, -0.29864142362141, -0.294024743731349, -0.292104129933301, -0.285165738729842, -0.28419932605141, -0.267399999874122, -0.259487769142101, -0.239899780812716, -0.224858003804207, -0.20448050758473, -0.164155133452971, -0.117617164459898, -0.0717938081884113, -0.0526986239898579, -0.0346031190163735, -0.0167949342608791, -0.0135168064347152, -0.0102971895842409, 0.00759271179427191, 0.00974950976249545, 0.010176021051287, 0.0217652761059223, 0.0239924727094222, 0.0413057846713024, 0.0422334333464529, 0.0459150454793617, 0.0517637894860314]) dos = DoS(energies, fermi_level=-0.1) dos.append(0.2+energies) dos.dump(sigma=0.01) dos.plot()