def __init__(self, width, folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
def __init__(self, width,
folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
def __init__(self, width, folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == 'ComplexGauss':
self.func = ComplexGauss(width)
elif folding == 'ComplexLorentz':
self.func = ComplexLorentz(width)
elif folding == 'RealLorentzPole':
self.func = LorentzPole(width, imag=False)
elif folding == 'ImaginaryLorentzPole':
self.func = LorentzPole(width, imag=True)
elif folding == 'Voigt':
self.func = Voigt(width)
elif folding is None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
class Folder:
"""Fold a function with normalised Gaussians or Lorentzians"""
def __init__(self, width,
folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
def fold(self, x, y, dx=None, min=None, max=None):
X = np.array(x)
assert len(X.shape) == 1
Y = np.array(y)
assert X.shape[0] == Y.shape[0]
if self.func is None:
xl = X
yl = Y
else:
if min is None:
min = np.min(X) - 4 * self.width
if max is None:
max = np.max(X) + 4 * self.width
if dx is None:
dx = self.width / 4.
xl = np.arange(min, max + 0.5 * dx, dx)
# weight matrix
weightm = np.empty((xl.shape[0], X.shape[0]))
for i, x in enumerate(X):
weightm[:, i] = self.func.get(xl - x)
yl = np.dot(weightm, Y)
return xl, yl
class Folder:
"""Fold a function with normalised Gaussians or Lorentzians"""
def __init__(self, width, folding='Gauss'):
self.width = width
if folding == 'Gauss':
self.func = Gauss(width)
elif folding == 'Lorentz':
self.func = Lorentz(width)
elif folding == None:
self.func = None
else:
raise RuntimeError('unknown folding "' + folding + '"')
def fold(self, x, y, dx=None, min=None, max=None):
X = np.array(x)
assert len(X.shape) == 1
Y = np.array(y)
assert X.shape[0] == Y.shape[0]
if self.func is None:
xl = X
yl = Y
else:
if min is None:
min = np.min(X) - 4 * self.width
if max is None:
max = np.max(X) + 4 * self.width
if dx is None:
dx = self.width / 4.
xl = np.arange(min, max + 0.5 * dx, dx)
# weight matrix
weightm = np.empty((xl.shape[0], X.shape[0]))
for i, x in enumerate(X):
weightm[:, i] = self.func.get(xl - x)
yl = np.dot(weightm, Y)
return xl, yl
from math import exp, pi, sqrt
import numpy as np
from gpaw.gauss import Gauss, Lorentz
from gpaw.test import equal
from gpaw.utilities.folder import Folder
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
# folder function
for name in ['Gauss', 'Lorentz']:
folder = Folder(width, name)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
if name == 'Lorentz':
from math import exp, pi, sqrt
import numpy as np
from gpaw.gauss import Gauss, Lorentz
from gpaw.test import equal
from gpaw.utilities.folder import Folder, Voigt
# Gauss and Lorentz functions
width = 0.5
x = 1.5
equal(Gauss(width).get(x),
exp(- x**2 / 2 / width**2) / sqrt(2 * pi) / width,
1.e-15)
equal(Lorentz(width).get(x),
width / (x**2 + width**2) / pi,
1.e-15)
# folder function
for name in ['Gauss', 'Lorentz', 'Voigt']:
folder = Folder(width, name)
x = [0, 2]
y = [[2, 0, 1], [1, 1, 1]]
xl, yl = folder.fold(x, y, dx=.7)
# check first value
exec('func = {0}(width)'.format(name))
