def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
class SimplexTest(unittest.TestCase):
def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
def test_in_simplex(self):
self.assertTrue(self.simplex.in_simplex([0.1, 0.1, 0.1]))
self.assertFalse(self.simplex.in_simplex([0.6, 0.6, 0.6]))
for i in range(10):
coord = np.random.random_sample(size=3) / 3
self.assertTrue(self.simplex.in_simplex(coord))
def test_2dtriangle(self):
s = Simplex([[0, 1], [1, 1], [1, 0]])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.5]),
[0.5, 0, 0.5])
np.testing.assert_almost_equal(s.bary_coords([0.5, 1]), [0.5, 0.5, 0])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.75]),
[0.5, 0.25, 0.25])
np.testing.assert_almost_equal(s.bary_coords([0.75, 0.75]),
[0.25, 0.5, 0.25])
s = Simplex([[1, 1], [1, 0]])
self.assertRaises(ValueError, s.bary_coords, [0.5, 0.5])
def test_volume(self):
# Should be value of a right tetrahedron.
self.assertAlmostEqual(self.simplex.volume, 1 / 6)
class SimplexTest(unittest.TestCase):
def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
def test_in_simplex(self):
self.assertTrue(self.simplex.in_simplex([0.1, 0.1, 0.1]))
self.assertFalse(self.simplex.in_simplex([0.6, 0.6, 0.6]))
for i in range(10):
coord = np.random.random_sample(size=3) / 3
self.assertTrue(self.simplex.in_simplex(coord))
def test_2dtriangle(self):
s = Simplex([[0, 1], [1, 1], [1, 0]])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.5]), [0.5, 0, 0.5])
np.testing.assert_almost_equal(s.bary_coords([0.5, 1]), [0.5, 0.5, 0])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.75]), [0.5, 0.25, 0.25])
np.testing.assert_almost_equal(s.bary_coords([0.75, 0.75]), [0.25, 0.5, 0.25])
s = Simplex([[1, 1], [1, 0]])
self.assertRaises(ValueError, s.bary_coords, [0.5, 0.5])
def test_volume(self):
# Should be value of a right tetrahedron.
self.assertAlmostEqual(self.simplex.volume, 1/6)
class SimplexTest(unittest.TestCase):
def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
def test_in_simplex(self):
self.assertTrue(self.simplex.in_simplex([0.1, 0.1, 0.1]))
self.assertFalse(self.simplex.in_simplex([0.6, 0.6, 0.6]))
for i in xrange(10):
coord = np.random.random_sample(size=(3)) / 3
self.assertTrue(self.simplex.in_simplex(coord))
def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
class SimplexTest(unittest.TestCase):
def setUp(self):
coords = []
coords.append([0, 0, 0])
coords.append([0, 1, 0])
coords.append([0, 0, 1])
coords.append([1, 0, 0])
self.simplex = Simplex(coords)
def test_in_simplex(self):
self.assertTrue(self.simplex.in_simplex([0.1, 0.1, 0.1]))
self.assertFalse(self.simplex.in_simplex([0.6, 0.6, 0.6]))
for i in xrange(10):
coord = np.random.random_sample(size=(3)) / 3
self.assertTrue(self.simplex.in_simplex(coord))
def _in_facet(self, facet, comp):
"""
Checks if a composition is in a facet.
Args:
facet: facet to test.
comp: Composition to test.
"""
els = self._pd.elements
dim = len(els)
if dim > 1:
coords = self._pd.qhull_data[facet, :-1]
simplex = Simplex(coords)
comp_point = [comp.get_atomic_fraction(e) for e in els[1:]]
return simplex.in_simplex(comp_point, PDAnalyzer.numerical_tol)
else:
return True
def _in_facet(self, facet, comp):
"""
Checks if a composition is in a facet.
Args:
facet: facet to test.
comp: Composition to test.
"""
els = self._pd.elements
dim = len(els)
if dim > 1:
coords = self._pd.qhull_data[facet, :-1]
simplex = Simplex(coords)
comp_point = [comp.get_atomic_fraction(e) for e in els[1:]]
return simplex.in_simplex(comp_point, PDAnalyzer.numerical_tol)
else:
return True
def _in_facet(self, facet, entry):
"""
Checks if a Pourbaix Entry is in a facet.
Args:
facet: facet to test.
entry: Pourbaix Entry to test.
"""
dim = len(self._keys)
if dim > 1:
coords = [np.array(self._pd.qhull_data[facet[i]][0:dim - 1])
for i in range(len(facet))]
simplex = Simplex(coords)
comp_point = [entry.npH, entry.nPhi]
return simplex.in_simplex(comp_point,
PourbaixAnalyzer.numerical_tol)
else:
return True
def _in_facet(self, facet, entry):
"""
Checks if a Pourbaix Entry is in a facet.
Args:
facet: facet to test.
entry: Pourbaix Entry to test.
"""
dim = len(self._keys)
if dim > 1:
coords = [np.array(self._pd.qhull_data[facet[i]][0:dim - 1])
for i in xrange(len(facet))]
simplex = Simplex(coords)
comp_point = [entry.npH, entry.nPhi]
return simplex.in_simplex(comp_point,
PourbaixAnalyzer.numerical_tol)
else:
return True
def test_2dtriangle(self):
s = Simplex([[0, 1], [1, 1], [1, 0]])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.5]),
[0.5, 0, 0.5])
np.testing.assert_almost_equal(s.bary_coords([0.5, 1]), [0.5, 0.5, 0])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.75]),
[0.5, 0.25, 0.25])
np.testing.assert_almost_equal(s.bary_coords([0.75, 0.75]),
[0.25, 0.5, 0.25])
s = Simplex([[1, 1], [1, 0]])
self.assertRaises(ValueError, s.bary_coords, [0.5, 0.5])
def get_chempot_range_map(self, elements, referenced=True, joggle=True,
force_use_pyhull=False):
"""
Returns a chemical potential range map for each stable entry.
Args:
elements: Sequence of elements to be considered as independent
variables. E.g., if you want to show the stability ranges
of all Li-Co-O phases wrt to uLi and uO, you will supply
[Element("Li"), Element("O")]
referenced: If True, gives the results with a reference being the
energy of the elemental phase. If False, gives absolute values.
joggle (boolean): Whether to joggle the input to avoid precision
errors.
force_use_pyhull (boolean): Whether the pyhull algorithm is always
used, even when scipy is present.
Returns:
Returns a dict of the form {entry: [simplices]}. The list of
simplices are the sides of the N-1 dim polytope bounding the
allowable chemical potential range of each entry.
"""
all_chempots = []
pd = self._pd
facets = pd.facets
for facet in facets:
chempots = self.get_facet_chempots(facet)
all_chempots.append([chempots[el] for el in pd.elements])
inds = [pd.elements.index(el) for el in elements]
el_energies = {el: 0.0 for el in elements}
if referenced:
el_energies = {el: pd.el_refs[el].energy_per_atom
for el in elements}
chempot_ranges = collections.defaultdict(list)
vertices = [list(range(len(self._pd.elements)))]
if len(all_chempots) > len(self._pd.elements):
vertices = get_facets(all_chempots, joggle=joggle,
force_use_pyhull=force_use_pyhull)
for ufacet in vertices:
for combi in itertools.combinations(ufacet, 2):
data1 = facets[combi[0]]
data2 = facets[combi[1]]
common_ent_ind = set(data1).intersection(set(data2))
if len(common_ent_ind) == len(elements):
common_entries = [pd.qhull_entries[i]
for i in common_ent_ind]
data = np.array([[all_chempots[i][j]
- el_energies[pd.elements[j]]
for j in inds] for i in combi])
sim = Simplex(data)
for entry in common_entries:
chempot_ranges[entry].append(sim)
return chempot_ranges
def _in_facet(self, facet, comp):
"""
Checks if a composition is in a facet.
Args:
facet:
facet to test.
comp:
Composition to test.
"""
dim = len(self._pd.elements)
if dim > 1:
coords = [np.array(self._pd.qhull_data[facet[i]][0:dim - 1])
for i in xrange(len(facet))]
simplex = Simplex(coords)
comp_point = [comp.get_atomic_fraction(self._pd.elements[i])
for i in xrange(1, len(self._pd.elements))]
return simplex.in_simplex(comp_point, PDAnalyzer.numerical_tol)
else:
return True
def test_2dtriangle(self):
s = Simplex([[0, 1], [1, 1], [1, 0]])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.5]), [0.5, 0, 0.5])
np.testing.assert_almost_equal(s.bary_coords([0.5, 1]), [0.5, 0.5, 0])
np.testing.assert_almost_equal(s.bary_coords([0.5, 0.75]), [0.5, 0.25, 0.25])
np.testing.assert_almost_equal(s.bary_coords([0.75, 0.75]), [0.25, 0.5, 0.25])
s = Simplex([[1, 1], [1, 0]])
self.assertRaises(ValueError, s.bary_coords, [0.5, 0.5])
def _in_facet(self, facet, comp):
"""
Checks if a composition is in a facet.
Args:
facet:
facet to test.
comp:
Composition to test.
"""
els = self._pd.elements
dim = len(els)
if dim > 1:
coords = [
np.array(self._pd.qhull_data[facet[i]][0:dim - 1])
for i in xrange(len(facet))
]
simplex = Simplex(coords)
comp_point = [
comp.get_atomic_fraction(els[i]) for i in xrange(1, len(els))
]
return simplex.in_simplex(comp_point, PDAnalyzer.numerical_tol)
else:
return True
def get_chempot_range_map(self, elements):
"""
Returns a chemical potential range map for each stable entry.
Args:
elements:
Sequence of elements to be considered as independent variables.
E.g., if you want to show the stability ranges of all Li-Co-O
phases wrt to uLi and uO, you will supply
[Element("Li"), Element("O")]
Returns:
Returns a dict of the form {entry: [simplices]}. The list of
simplices are the sides of the N-1 dim polytope bounding the
allowable chemical potential range of each entry.
"""
all_chempots = []
pd = self._pd
facets = pd.facets
for facet in facets:
chempots = self.get_facet_chempots(facet)
all_chempots.append([chempots[el] for el in pd.elements])
inds = [pd.elements.index(el) for el in elements]
el_energies = {el: pd.el_refs[el].energy_per_atom for el in elements}
chempot_ranges = collections.defaultdict(list)
for ufacet in ConvexHull(all_chempots).vertices:
for combi in itertools.combinations(ufacet, 2):
data1 = facets[combi[0]]
data2 = facets[combi[1]]
common_ent_ind = set(data1).intersection(set(data2))
if len(common_ent_ind) == len(elements):
common_entries = [
pd.qhull_entries[i] for i in common_ent_ind
]
data = np.array([[
all_chempots[i][j] - el_energies[pd.elements[j]]
for j in inds
] for i in combi])
sim = Simplex(data)
for entry in common_entries:
chempot_ranges[entry].append(sim)
return chempot_ranges
def simplices(self):
"""
Returns the simplices of the convex hull.
"""
return [Simplex([self.points[i] for i in v]) for v in self.vertices]
def simplices(self):
"""
Returns the simplices of the triangulation.
"""
return [Simplex([self.points[i] for i in v]) for v in self.vertices]
def __init__(self, entries, elements=None):
"""
Standard constructor for phase diagram.
Args:
entries ([PDEntry]): A list of PDEntry-like objects having an
energy, energy_per_atom and composition.
elements ([Element]): Optional list of elements in the phase
diagram. If set to None, the elements are determined from
the the entries themselves.
"""
if elements is None:
elements = set()
for entry in entries:
elements.update(entry.composition.elements)
elements = list(elements)
dim = len(elements)
el_refs = {}
for el in elements:
el_entries = list(
filter(
lambda e: e.composition.is_element and e.composition.
elements[0] == el, entries))
if len(el_entries) == 0:
raise PhaseDiagramError(
"There are no entries associated with terminal {}.".format(
el))
el_refs[el] = min(el_entries, key=lambda e: e.energy_per_atom)
data = []
for entry in entries:
comp = entry.composition
row = [comp.get_atomic_fraction(el) for el in elements]
row.append(entry.energy_per_atom)
data.append(row)
data = np.array(data)
self.all_entries_hulldata = data[:, 1:]
#use only entries with negative formation energy
vec = [el_refs[el].energy_per_atom for el in elements] + [-1]
form_e = -np.dot(data, vec)
#make sure that if there are multiple entries at the same composition
#within 1e-4 eV/atom of each other, only use the lower energy one.
#This fixes the precision errors in the convex hull.
#This is significantly faster than grouping by composition and then
#taking the lowest energy of each group
ind = []
prev_c = [] # compositions within 1e-4 of current entry
prev_e = [] # energies of those compositions
for i in np.argsort([e.energy_per_atom for e in entries]):
if form_e[i] > -self.formation_energy_tol:
continue
epa = entries[i].energy_per_atom
#trim the front of the lists
while prev_e and epa > 1e-4 + prev_e[0]:
prev_c.pop(0)
prev_e.pop(0)
frac_comp = entries[i].composition.fractional_composition
if frac_comp not in prev_c:
ind.append(i)
prev_e.append(epa)
prev_c.append(frac_comp)
#add the elemental references
ind.extend([entries.index(el) for el in el_refs.values()])
qhull_entries = [entries[i] for i in ind]
qhull_data = data[ind][:, 1:]
#add an extra point to enforce full dimensionality
#this point will be present in all upper hull facets
extra_point = np.zeros(dim) + 1 / dim
extra_point[-1] = np.max(qhull_data) + 1
qhull_data = np.concatenate([qhull_data, [extra_point]], axis=0)
if dim == 1:
self.facets = [qhull_data.argmin(axis=0)]
else:
facets = get_facets(qhull_data)
finalfacets = []
for facet in facets:
#skip facets that include the extra point
if max(facet) == len(qhull_data) - 1:
continue
m = qhull_data[facet]
m[:, -1] = 1
if abs(np.linalg.det(m)) > 1e-14:
finalfacets.append(facet)
self.facets = finalfacets
self.simplices = [Simplex(qhull_data[f, :-1]) for f in self.facets]
self.all_entries = entries
self.qhull_data = qhull_data
self.dim = dim
self.el_refs = el_refs
self.elements = elements
self.qhull_entries = qhull_entries
