def linePlaneIntersectionNumeric(p1, p2, p3, p4, p5):
if not useNumeric:
return linePlaneIntersection(p1, p2, p3, p4, p5)
if useNumpy:
top = [[1., 1., 1., 1.], [p1[0], p2[0], p3[0], p4[0]],
[p1[1], p2[1], p3[1], p4[1]], [p1[2], p2[2], p3[2], p4[2]]]
topDet = numpy.linalg.det(top)
bottom = [[1., 1., 1., 0.], [p1[0], p2[0], p3[0], p5[0] - p4[0]],
[p1[1], p2[1], p3[1], p5[1] - p4[1]],
[p1[2], p2[2], p3[2], p5[2] - p4[2]]]
botDet = numpy.linalg.det(bottom)
else: # actually use numeric
top = Matrix.Matrix([[1., 1., 1., 1.], [p1[0], p2[0], p3[0], p4[0]],
[p1[1], p2[1], p3[1], p4[1]],
[p1[2], p2[2], p3[2], p4[2]]])
topDet = LinearAlgebra.determinant(top)
bottom = Matrix.Matrix([[1., 1., 1., 0.],
[p1[0], p2[0], p3[0], p5[0] - p4[0]],
[p1[1], p2[1], p3[1], p5[1] - p4[1]],
[p1[2], p2[2], p3[2], p5[2] - p4[2]]])
botDet = LinearAlgebra.determinant(bottom)
if topDet == 0.0 or botDet == 0.0:
return False
t = -topDet / botDet
x = p4[0] + (p5[0] - p4[0]) * t
y = p4[1] + (p5[1] - p4[1]) * t
z = p4[2] + (p5[2] - p4[2]) * t
return [x, y, z]
def linePlaneIntersectionNumeric(p1, p2, p3, p4, p5):
if not useNumeric:
return linePlaneIntersection(p1, p2, p3, p4, p5)
if useNumpy:
top = [
[1., 1., 1., 1.],
[p1[0], p2[0], p3[0], p4[0]], [p1[1], p2[1], p3[1], p4[1]],
[p1[2], p2[2], p3[2], p4[2]]]
topDet = numpy.linalg.det(top)
bottom = [
[1., 1., 1., 0.], [p1[0], p2[0], p3[0], p5[0]-p4[0]],
[p1[1], p2[1], p3[1], p5[1]-p4[1]], [p1[2], p2[2], p3[2], p5[2]-p4[2]]]
botDet = numpy.linalg.det(bottom)
else: # actually use numeric
top = Matrix.Matrix(
[[1., 1., 1., 1.], [p1[0], p2[0], p3[0], p4[0]], [p1[1], p2[1],
p3[1], p4[1]], [p1[2], p2[2], p3[2], p4[2]]])
topDet = LinearAlgebra.determinant(top)
bottom = Matrix.Matrix(
[[1., 1., 1., 0.], [p1[0], p2[0], p3[0], p5[0]-p4[0]], [p1[1],
p2[1], p3[1], p5[1]-p4[1]], [p1[2], p2[2], p3[2], p5[2]-p4[2]]])
botDet = LinearAlgebra.determinant(bottom)
if topDet == 0.0 or botDet == 0.0:
return False
t = -topDet/botDet
x = p4[0] + (p5[0]-p4[0]) * t
y = p4[1] + (p5[1]-p4[1]) * t
z = p4[2] + (p5[2]-p4[2]) * t
return [x, y, z]
def _gaussian(self, mean, cvm, x):
m = len(mean)
assert cvm.shape == (m, m), \
'bad sized covariance matrix, %s' % str(cvm.shape)
try:
det = LinearAlgebra.determinant(cvm)
inv = LinearAlgebra.inverse(cvm)
a = det**-0.5 * (2 * Numeric.pi)**(-m / 2.0)
dx = x - mean
b = -0.5 * Numeric.matrixmultiply( \
Numeric.matrixmultiply(dx, inv), dx)
return a * Numeric.exp(b)
except OverflowError:
# happens when the exponent is negative infinity - i.e. b = 0
# i.e. the inverse of cvm is huge (cvm is almost zero)
return 0
def EnergyFromBoxShape(self, strain):
if self.atoms == None:
return
if self.debug:
unstrainedEnergy = self.atoms.GetPotentialEnergy()
unstrainedSCVs = ApplyStrain(self.atoms, strain)
if self.debug >= 2:
print "volume:",LA.determinant(self.atoms.GetUnitCell())
energy = self.atoms.GetPotentialEnergy()
# restore original state
self.atoms.GetUnitCell().SetBasis(unstrainedSCVs)
if self.debug:
if abs(unstrainedEnergy - self.atoms.GetPotentialEnergy()) > 1.e-10:
print unstrainedEnergy,self.atoms.GetPotentialEnergy()
raise StandardError
return energy
def EnergyFromBoxShape(self, strain):
if self.atoms == None:
return
if self.debug:
unstrainedEnergy = self.atoms.GetPotentialEnergy()
unstrainedSCVs = ApplyStrain(self.atoms, strain)
if self.debug >= 2:
print "volume:", LA.determinant(self.atoms.GetUnitCell())
energy = self.atoms.GetPotentialEnergy()
# restore original state
self.atoms.GetUnitCell().SetBasis(unstrainedSCVs)
if self.debug:
if abs(unstrainedEnergy -
self.atoms.GetPotentialEnergy()) > 1.e-10:
print unstrainedEnergy, self.atoms.GetPotentialEnergy()
raise StandardError
return energy
