def GetGdirAngle(coords1, coords2, coords3, r_21=None, r_23=None):
"""Calculate direction of energy gradients between bond angle atoms.
Args:
coords1 (float*): 3 cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 cartesian coordinates [Angstrom] of atom2.
coords3 (float*): 3 cartesian coordinates [Angstrom] of atom3.
r_21 (float): Distance between atom2 and atom1 (default None).
r_23 (float): Distance between atom2 and atom3 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*): vectors in the direction of
max increasing bond angle.
"""
if r_21 is not None:
r_21 = geomcalc.GetRij(coords2, coords1)
if r_23 is not None:
r_23 = geomcalc.GetRij(coords2, coords3)
u_21 = geomcalc.GetUij(coords2, coords1, r_21)
u_23 = geomcalc.GetUij(coords2, coords3, r_23)
cp = geomcalc.GetUcp(u_21, u_23)
gdir1 = geomcalc.GetUcp(u_21, cp) / r_21
gdir3 = geomcalc.GetUcp(cp, u_23) / r_23
gdir2 = -1.0 * (gdir1 + gdir3)
return gdir1, gdir2, gdir3
def GetGDirTorsion(coords1, coords2, coords3, coords4, r_12=None, r_23=None,
r_34=None):
"""Calculate direction of energy gradients between torsion atoms.
Args:
coords1 (float*): 3 cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 cartesian coordinates [Angstrom] of atom2.
coords3 (float*): 3 cartesian coordinates [Angstrom] of atom3.
coords4 (float*): 3 cartesian coordinates [Angstrom] of atom4.
r_12 (float): Distance between atom1 and atom2 (default None).
r_23 (float): Distance between atom2 and atom3 (default None).
r_34 (float): Distance between atom3 and atom4 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*), gdir4 (float*): Vectors in
the direction of max increasing torsion angle.
"""
u_21 = geomcalc.GetUij(coords2, coords1, r_12)
u_34 = geomcalc.GetUij(coords3, coords4, r_34)
u_23 = geomcalc.GetUij(coords2, coords3, r_23)
u_32 = -1.0 * u_23
a_123 = geomcalc.GetAijk(coords1, coords2, coords3, r_12, r_23)
a_432 = geomcalc.GetAijk(coords4, coords3, coords2, r_34, r_23)
s_123 = math.sin(const.DEG2RAD * a_123)
s_432 = math.sin(const.DEG2RAD * a_432)
c_123 = math.cos(const.DEG2RAD * a_123)
c_432 = math.cos(const.DEG2RAD * a_432)
gdir1 = geomcalc.GetUcp(u_21, u_23) / (r_12*s_123)
gdir4 = geomcalc.GetUcp(u_34, u_32) / (r_34*s_432)
gdir2 = (r_12/r_23*c_123 - 1.0)*gdir1 - (r_34/r_23*c_432)*gdir4
gdir3 = (r_34/r_23*c_432 - 1.0)*gdir4 - (r_12/r_23*c_123)*gdir1
return gdir1, gdir2, gdir3, gdir4
def GetGdirOutofplane(coords1,
coords2,
coords3,
coords4,
oop,
r_31=None,
r_32=None,
r_34=None):
"""Calculate direction of energy gradients between outofplane atoms.
Args:
coords1 (float*): 3 cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 cartesian coordinates [Angstrom] of atom2.
coords3 (float*): 3 cartesian coordinates [Angstrom] of atom3.
coords4 (float*): 3 cartesian coordinates [Angstrom] of atom4.
oop (float): Out-of-plane angles bewteen atoms 1, 2, 3, and 4.
r_31 (float): Distance between atom3 and atom1 (default None).
r_32 (float): Distance between atom3 and atom2 (default None).
r_34 (float): Distance between atom3 and atom4 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*), gdir4 (float*): Vectors in
the direction of max increasing outofplane angle.
"""
if r_31 is not None:
r_31 = geomcalc.GetRij(coords3, coords1)
if r_32 is not None:
r_32 = geomcalc.GetRij(coords3, coords2)
if r_34 is not None:
r_34 = geomcalc.GetRij(coords3, coords4)
u_31 = geomcalc.GetUij(coords3, coords1, r_31)
u_32 = geomcalc.GetUij(coords3, coords2, r_32)
u_34 = geomcalc.GetUij(coords3, coords4, r_34)
cp_3234 = geomcalc.GetCp(u_32, u_34)
cp_3431 = geomcalc.GetCp(u_34, u_31)
cp_3132 = geomcalc.GetCp(u_31, u_32)
a_132 = geomcalc.GetAijk(coords1, coords3, coords2)
s_132 = math.sin(const.DEG2RAD * a_132)
c_132 = math.cos(const.DEG2RAD * a_132)
c_oop = math.cos(const.DEG2RAD * oop)
t_oop = math.tan(const.DEG2RAD * oop)
gdir1 = ((1.0 / r_31) * (cp_3234 / (c_oop * s_132) - (t_oop / s_132**2) *
(u_31 - c_132 * u_32)))
gdir2 = ((1.0 / r_32) * (cp_3431 / (c_oop * s_132) - (t_oop / s_132**2) *
(u_32 - c_132 * u_31)))
gdir4 = ((1.0 / r_34) * (cp_3132 / (c_oop * s_132) - (t_oop * u_34)))
gdir3 = -1.0 * (gdir1 + gdir2 + gdir4)
return gdir1, gdir2, gdir3, gdir4
def GetEBoundI(k_box, bound, coords, origin, boundtype):
"""Calculate simulation boundary energy of an atom.
Args:
k_box (float): Spring constant [kcal/(mol*A^2)] of boundary.
bound (float): Distance from origin [Angstrom] of boundary.
coords (float*): Array of cartesian coordinates [Angstrom] of atom.
origin (float*): Array of cartesian coordiantes [Angstrom] of origin of
simulation.
boundtype (str): 'cube' or 'sphere', type of boundary condition.
Returns:
e_bound_i (float): Boundary energy [kcal/mol] of atom.
"""
e_bound_i = 0.0
if (boundtype == 'cube'):
for j in range(const.NUMDIM):
scale = 1.0 if (abs(coords[j] - origin[j]) >= bound) else 0.0
e_bound_i += (scale * k_box *
(abs(coords[j] - origin[j]) - bound)**2)
elif (boundtype == 'sphere'):
r_io = geomcalc.GetRij(origin, coords)
u_io = geomcalc.GetUij(origin, coords)
scale = 1.0 if (r_io >= bound) else 0.0
e_bound_i += scale * k_box * (r_io - bound)**2
return e_bound_i
def GetGBoundI(k_box, bound, coord, origin, boundtype):
"""Calculate energy gradient magnitude of boundary energy.
Args:
k_box (float): Spring constant [kcal/(mol*A^2)] of boundary.
bound (float): Distance from origin [Angstrom] of boundary.
coords (float*): Array of cartesian coordinates [Angstrom] of atom.
origin (float*): Array of cartesian coordiantes [Angstrom] of origin of
simulation.
boundtype (str): 'cube' or 'sphere', type of boundary condition.
Returns:
g_bound_i (float): Magnitude of energy gradient [kcal/(mol*A)].
"""
g_bound_i = numpy.zeros(const.NUMDIM)
if boundtype == 'cube':
for j in range(const.NUMDIM):
sign = 1.0 if (coord[j] - origin[j]) <= 0.0 else -1.0
scale = 1.0 if abs(coord[j] - origin[j]) >= bound else 0.0
g_bound_i[j] = (-2.0 * sign * scale * k_box *
(abs(coord[j]) - bound))
elif boundtype == 'sphere':
r_io = geomcalc.GetRij(origin, coord)
u_io = geomcalc.GetUij(origin, coord)
scale = 1.0 if r_io >= bound else 0.0
g_bound_i = 2.0 * scale * k_box * (r_io - bound) * u_io
return g_bound_i
def GetGdirInter(coords1, coords2, r_12=None):
"""Calculate direction of energy gradient between atom pair.
Args:
coords1 (float*): 3 Cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 Cartesian coordiantes [Angstrom] of atom2.
r_ij (float): Distance between atom1 and atom2 (default None).
Returns:
gdir1 (float*), gdir2 (float*): unit vectors in the direction of max
increasing inter-atomic distance.
"""
gdir1 = geomcalc.GetUij(coords2, coords1, r_12)
gdir2 = -1.0 * gdir1
return gdir1, gdir2
def testAntiReflexive(self):
"""Asserts opposite value for inverted order of inputs."""
params = ARBITRARY_XYZ2, ARBITRARY_XYZ1
self.assertListAlmostEqual(geomcalc.GetUij(*params), UNIT_VECTOR_21)
def testArbitrary(self):
"""Asserts correct unit vector between arbitrary points in 3d space."""
params = ARBITRARY_XYZ1, ARBITRARY_XYZ2
self.assertListAlmostEqual(geomcalc.GetUij(*params), UNIT_VECTOR_12)
def testOnAxisZ(self):
"""Asserts correct on-axis unit vector between points on the z-axis."""
params = POSITIVE_ARBITRARY_Z, NEGATIVE_ARBITRARY_Z
self.assertListAlmostEqual(geomcalc.GetUij(*params), NEGATIVE_UNIT_Z)
def testUnitLength(self):
"""Asserts correct direction for points separated by unit distance."""
params = POSITIVE_UNIT_X, ORIGIN
self.assertListAlmostEqual(geomcalc.GetUij(*params), NEGATIVE_UNIT_X)
def testSamePoint(self):
"""Asserts zero vector between identical points."""
params = ARBITRARY_XYZ1, ARBITRARY_XYZ1
self.assertListAlmostEqual(geomcalc.GetUij(*params), ORIGIN)
