def get_kmap(self,
E_kin=30,
dk=0.03,
phi=0,
theta=0,
psi=0,
Ak_type='no',
polarization='p',
alpha=60,
beta=90,
gamma=0,
symmetrization='no'):
"""Returns a kmap slice from the orbital data.
Args:
E_kin (float): Kinetic energy in eV.
dk (float): Desired k-resolution in kmap in Angstroem^-1.
phi (float): Euler orientation angle phi in degree.
theta (float): Euler orientation angle theta in degree.
psi (float): Euler orientation angle psi in degree.
Ak_type (string): Treatment of |A.k|^2: either 'no',
'toroid', 'NanoESCA', 'only-toroid' or 'only-NanoESCA'.
polarization (string): Either 'p', 's', 'unpolarized',
'C+', 'C-' or 'CDAD'.
alpha (float): Angle of incidence plane in degree.
beta (float): Azimuth of incidence plane in degree.
gamma (float/str): Damping factor for final state in
Angstroem^-1. str = 'auto' sets gamms automatically
symmetrization (str): either 'no', '2-fold', '2-fold+mirror',
'3-fold', '3-fold+mirror','4-fold', '4-fold+mirror'
Returns:
(PlotData): PlotData containing the kmap slice.
"""
# Compute new hemispherical cut if E_kin or dk has changed
new_cut = self.check_new_cut(E_kin, dk)
if new_cut: self.set_kinetic_energy(E_kin, dk)
# Rotate molecule (that is, rotate hemisphere) if angles have changed
# ... and symmetrize kmap if necessary
new_orientation = self.check_new_orientation(phi, theta, psi)
new_symmetrization = self.check_new_symmetrization(symmetrization)
if new_symmetrization or new_orientation:
self.set_orientation(phi, theta, psi)
self.set_symmetry(symmetrization)
# Compute polarization factor if parameters have changed
new_Ak = self.check_new_Ak(Ak_type, polarization, alpha, beta, gamma)
if new_cut or new_Ak:
self.set_polarization(Ak_type, polarization, alpha, beta, gamma)
if Ak_type == 'only-toroid' or Ak_type == 'only-NanoESCA':
return PlotData(self.Ak['data'], self.kmap['krange'])
else:
return PlotData(self.Ak['data'] * self.kmap['data'],
self.kmap['krange'])
def test_incorrect_sub(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 3], [-1, 1]]
second_plot_data = PlotData(data, range_)
self.assertRaises(ValueError, self.plot_data.__sub__, second_plot_data)
self.assertRaises(TypeError, self.plot_data.__sub__, 'string')
def change_polarization(self,
Ak_type='no',
polarization='p',
alpha=60,
beta=90,
gamma=0):
self.set_polarization(Ak_type, polarization, alpha, beta, gamma)
return PlotData(self.Ak['data'] * self.kmap['data'],
self.kmap['krange'])
def test_add(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
added_plot_data = self.plot_data + second_plot_data
npt.assert_equal(added_plot_data.data, [[8, 10, 12], [14, 16, 18]])
added_plot_data = self.plot_data + 4
npt.assert_equal(added_plot_data.data, [[5, 6, 7], [8, 9, 10]])
def test_correct_initialization(self):
npt.assert_equal(self.plot_data.data, self.data)
npt.assert_equal(self.plot_data.range, self.range_)
npt.assert_equal(self.plot_data.data.shape, (2, 3))
npt.assert_equal(self.plot_data.x_axis, [1., 1.5, 2.])
npt.assert_equal(self.plot_data.y_axis, [-1., 1.])
npt.assert_equal(self.plot_data.step_size, [0.5, 2.])
self.data = [[1, 2, np.nan], [4, np.inf, 6]]
plot_data = PlotData(self.data, self.range_)
npt.assert_equal(plot_data.data, [[1, 2, np.nan], [4, np.nan, 6]])
def test_mul(self):
data = [[2, 2, 2], [3, 3, 3]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
mul_plot_data = self.plot_data * second_plot_data
npt.assert_equal(mul_plot_data.data, [[2, 4, 6], [12, 15, 18]])
mul_plot_data = second_plot_data * self.plot_data
npt.assert_equal(mul_plot_data.data, [[2, 4, 6], [12, 15, 18]])
mul_plot_data = self.plot_data * 4
npt.assert_equal(mul_plot_data.data, [[4, 8, 12], [16, 20, 24]])
def test_sub(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
subed_plot_data = self.plot_data - second_plot_data
npt.assert_equal(subed_plot_data.data, [[-6, -6, -6], [-6, -6, -6]])
subed_plot_data = self.plot_data - np.array(data)
npt.assert_equal(subed_plot_data.data, [[-6, -6, -6], [-6, -6, -6]])
subed_plot_data = self.plot_data - 4
npt.assert_equal(subed_plot_data.data, [[-3, -2, -1], [0, 1, 2]])
def slice_from_index(self, index, axis=0):
if axis == 0:
data = self.data[index, :, :]
range_ = [self.axes[2].range, self.axes[1].range]
elif axis == 1:
data = self.data[:, index, :]
range_ = [self.axes[2].range, self.axes[0].range]
elif axis == 2:
data = self.data[:, :, index]
range_ = [self.axes[1].range, self.axes[0].range]
else:
raise ValueError('axis has to be between 1 and 3')
return PlotData(data, range_)
# kMap.py Imports
from kmap.library.plotdata import PlotData
from kmap.model.crosshair_model import CrosshairAnnulusModel
# This script demonstrates the working and functionality for crosshairs
# in kmap on a simple 9x11 grid.
# New Crosshair
x, y, radius, width = 0, 0, 1.5, 1.5
crosshair = CrosshairAnnulusModel(x=x, y=y, radius=radius, width=width)
# Use 7x7 as data from which we cut to better demonstrate working
# The data goes from 0-49 and the pixel center acts is the whole number
global data
data = PlotData(np.reshape(np.array(range(99)), (9, 11)), [[-5, 5], [-4, 4]])
global extent
extent = data.range.flatten() + [-0.5, 0.5, -0.5, 0.5]
export = {}
def plot(axis, x, y, r, w, region, inverted, title=''):
# Helper Function plotting crosshair and data
# Set Crosshair
crosshair.x = x
crosshair.y = y
crosshair.radius = r
crosshair.width = w
def setUp(self):
self.data = [[1, 2, 3], [4, 5, 6]]
self.range_ = [[1, 2], [-1, 1]]
self.plot_data = PlotData(self.data, self.range_)
class TestPlotData(unittest.TestCase):
def setUp(self):
self.data = [[1, 2, 3], [4, 5, 6]]
self.range_ = [[1, 2], [-1, 1]]
self.plot_data = PlotData(self.data, self.range_)
def test_correct_initialization(self):
npt.assert_equal(self.plot_data.data, self.data)
npt.assert_equal(self.plot_data.range, self.range_)
npt.assert_equal(self.plot_data.data.shape, (2, 3))
npt.assert_equal(self.plot_data.x_axis, [1., 1.5, 2.])
npt.assert_equal(self.plot_data.y_axis, [-1., 1.])
npt.assert_equal(self.plot_data.step_size, [0.5, 2.])
self.data = [[1, 2, np.nan], [4, np.inf, 6]]
plot_data = PlotData(self.data, self.range_)
npt.assert_equal(plot_data.data, [[1, 2, np.nan], [4, np.nan, 6]])
def test_incorrect_data_shape(self):
self.data = [1, 2, 3, 4, 5, 6]
self.assertRaises(TypeError, PlotData, self.data, self.range_)
def test_too_small_data(self):
self.data = [[1], [2]]
self.assertRaises(TypeError, PlotData, self.data, self.range_)
def test_incorrect_range_shape(self):
self.range_ = [[1, 2]]
self.assertRaises(TypeError, PlotData, self.data, self.range_)
def test_incorrect_range_values(self):
self.range_ = [[1, 2], [np.nan, 1]]
self.assertRaises(ValueError, PlotData, self.data, self.range_)
self.range_ = [[1, 2], [np.inf, 1]]
self.assertRaises(ValueError, PlotData, self.data, self.range_)
def test_basic_interpolation(self):
new_x_axis = [1.5, 2]
new_y_axis = [-0.5, 0, 0.5]
new_data = self.plot_data.interpolate(new_x_axis, new_y_axis)
npt.assert_equal(new_data.data,
[[2.75, 3.75], [3.5, 4.5], [4.25, 5.25]])
npt.assert_equal(self.plot_data.data, self.data)
new_x_axis = [-2, 1]
new_y_axis = [0, -0.5, -10]
new_data = self.plot_data.interpolate(new_x_axis, new_y_axis)
npt.assert_equal(new_data.data,
[[np.nan, 2.5], [np.nan, 1.75], [np.nan, np.nan]])
new_x_axis = [1, 1.25, 1.5, 2]
new_y_axis = [-1, -0.25, 0.5, 1]
new_data = self.plot_data.interpolate(new_x_axis, new_y_axis)
npt.assert_equal(new_data.data,
[[1., 1.5, 2., 3.], [2.125, 2.625, 3.125, 4.125],
[3.25, 3.75, 4.25, 5.25], [4., 4.5, 5., 6.]])
def test_update_interpolation(self):
new_x_axis = [1.5, 2]
new_y_axis = [-0.5, 0, 0.5]
new_data = self.plot_data.interpolate(new_x_axis,
new_y_axis,
update=True)
npt.assert_equal(new_data.data,
[[2.75, 3.75], [3.5, 4.5], [4.25, 5.25]])
npt.assert_equal(self.plot_data.data,
[[2.75, 3.75], [3.5, 4.5], [4.25, 5.25]])
def test_increase_range(self):
new_x_axis = [0, 1, 2, 3]
new_y_axis = [-1, 0, 1, 2]
new_data = self.plot_data.interpolate(new_x_axis,
new_y_axis,
update=True)
npt.assert_equal(
new_data.data,
[[np.nan, 1., 3., np.nan], [np.nan, 2.5, 4.5, np.nan],
[np.nan, 4., 6., np.nan], [np.nan, np.nan, np.nan, np.nan]])
npt.assert_equal(self.plot_data.x_axis, [0, 1, 2, 3])
npt.assert_equal(self.plot_data.y_axis, [-1, 0, 1, 2])
def test_add(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
added_plot_data = self.plot_data + second_plot_data
npt.assert_equal(added_plot_data.data, [[8, 10, 12], [14, 16, 18]])
added_plot_data = self.plot_data + 4
npt.assert_equal(added_plot_data.data, [[5, 6, 7], [8, 9, 10]])
def test_incorrect_add(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 3], [-1, 1]]
second_plot_data = PlotData(data, range_)
self.assertRaises(ValueError, self.plot_data.__add__, second_plot_data)
self.assertRaises(TypeError, self.plot_data.__add__, 'string')
def test_sub(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
subed_plot_data = self.plot_data - second_plot_data
npt.assert_equal(subed_plot_data.data, [[-6, -6, -6], [-6, -6, -6]])
subed_plot_data = self.plot_data - np.array(data)
npt.assert_equal(subed_plot_data.data, [[-6, -6, -6], [-6, -6, -6]])
subed_plot_data = self.plot_data - 4
npt.assert_equal(subed_plot_data.data, [[-3, -2, -1], [0, 1, 2]])
def test_incorrect_sub(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 3], [-1, 1]]
second_plot_data = PlotData(data, range_)
self.assertRaises(ValueError, self.plot_data.__sub__, second_plot_data)
self.assertRaises(TypeError, self.plot_data.__sub__, 'string')
def test_mul(self):
data = [[2, 2, 2], [3, 3, 3]]
range_ = [[1, 2], [-1, 1]]
second_plot_data = PlotData(data, range_)
mul_plot_data = self.plot_data * second_plot_data
npt.assert_equal(mul_plot_data.data, [[2, 4, 6], [12, 15, 18]])
mul_plot_data = second_plot_data * self.plot_data
npt.assert_equal(mul_plot_data.data, [[2, 4, 6], [12, 15, 18]])
mul_plot_data = self.plot_data * 4
npt.assert_equal(mul_plot_data.data, [[4, 8, 12], [16, 20, 24]])
def test_incorrect_mul(self):
data = [[7, 8, 9], [10, 11, 12]]
range_ = [[1, 3], [-1, 1]]
second_plot_data = PlotData(data, range_)
self.assertRaises(ValueError, self.plot_data.__mul__, second_plot_data)
self.assertRaises(TypeError, self.plot_data.__mul__, 'string')
self.assertRaises(ValueError, self.plot_data.__rmul__,
second_plot_data)
self.assertRaises(TypeError, self.plot_data.__rmul__, 'string')
def test_pow(self):
pow_plot_data = self.plot_data**2
npt.assert_equal(pow_plot_data.data, [[1, 4, 9], [16, 25, 36]])
def set_symmetry(self, symmetrization):
"""Symmterizes the kmap.
Args:
symmetrization (str): either 'no', '2-fold', '2-fold+mirror',
'3-fold', '3-fold+mirror','4-fold', '4-fold+mirror'
"""
data = PlotData(self.kmap['data'], self.kmap['krange'])
if symmetrization == '2-fold':
data.symmetrise(symmetry='2-fold', update=True)
elif symmetrization == '2-fold+mirror':
data.symmetrise(symmetry='2-fold', mirror=True, update=True)
elif symmetrization == '3-fold':
data.symmetrise(symmetry='3-fold', update=True)
elif symmetrization == '3-fold+mirror':
data.symmetrise(symmetry='3-fold', mirror=True, update=True)
elif symmetrization == '4-fold':
data.symmetrise(symmetry='4-fold', update=True)
elif symmetrization == '4-fold+mirror':
data.symmetrise(symmetry='4-fold', mirror=True, update=True)
self.kmap['data'] = data.data
self.kmap['symmetrization'] = symmetrization
def matrix_inversion(self):
"""Calling this method will trigger a direct fit via matrix inversion.
Ax = y --> A^-1y = x
Returns:
(list): A list of MinimizerResults. One for each slice
fitted.
"""
# Calculate all the orbital maps once for speed
orbital_kmaps_vector = np.array([
self._cut_region(self.get_orbital_kmap(orbital.ID,
self.parameters)).data
for orbital in self.orbitals
])
# Filter later for non variable parameters
vary_vector = [
self.parameters['w_' + str(orbital.ID)].vary
for orbital in self.orbitals
]
vary_vector.append(self.parameters['c'].vary)
# Initial values important if orbital or background is not varied
initials = [
self.parameters['w_' + str(orbital.ID)].value
for orbital in self.orbitals
]
initials.append(self.parameters['c'].value)
weights = []
for index in self.slice_policy[1]:
sliced_plot_data = self.get_sliced_kmap(index)
sliced_kmap = self._cut_region(sliced_plot_data).data
background = self._get_background(self.parameters)
# Transform background to a equally sized map
if not isinstance(background, np.ndarray):
background *= np.ones(orbital_kmaps_vector[0].shape)
background[np.isnan(sliced_kmap)] = 0
background = self._cut_region(
PlotData(background, sliced_plot_data.range)).data
aux = np.append(orbital_kmaps_vector, [background], axis=0)
# All zero background would lead to singular matrix
if np.all(background == 0):
vary_vector[-1] = False
# Subtract orbitals not to be varied from the sliced data once
for i, (kmap, initial) in enumerate(zip(aux, initials)):
if not vary_vector[i]:
sliced_kmap -= initial * kmap
N = len(aux)
A = np.zeros((N, N))
y = np.zeros(N)
for i in range(N):
y[i] = np.nansum(sliced_kmap * aux[i])
for j in range(N):
A[i, j] = np.nansum(aux[i] * aux[j])
result = np.array(initials)
try:
result[vary_vector] = np.linalg.solve(
A[np.ix_(vary_vector, vary_vector)], y[vary_vector])
except np.linalg.LinAlgError as err:
if 'Singular matrix' in str(err):
result = np.zeros(y.shape)
print(
'WARNING: Slice {index} produced a singular matrix.\nPlease make sure the background is non zero and there aren\'t identical orbitals loaded.'
)
else:
raise
if N == len(orbital_kmaps_vector):
# == No background
result = np.append(result, 0)
weights.append([index, result])
return self._construct_minimizer_result(weights)
