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ConfPrune.pyx
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ConfPrune.pyx
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# -*- coding: utf-8 -*-
"""
Created on Fri Jan 30 12:33:18 2015
@author: ke291
Cython file for conformer alignment and RMSD pruning. Called by Gaussian.py
and NWChem.py
"""
from math import sqrt
from libc.stdlib cimport malloc, free
"""
Main function of this file. Takes an array of [x, y, z] for each molecule,
as well as a list of atom symbols in the same order as their coordinates
Translates both molecules to origin, gets the rotation matrix from quatfit
and rotates the second molecule to align with the first
"""
def RMSDPrune(Isomers, settings):
for iso in Isomers:
if len(iso.Conformers) < settings.PerStructConfLimit:
continue
else:
conformers, cutoff = StrictRMSDPrune(iso.Conformers, iso.Atoms, settings.InitialRMSDcutoff,
settings.PerStructConfLimit)
iso.Conformers = conformers
iso.RMSDCutoff = cutoff
return Isomers
def AdaptRMSDPrune(conformers, atoms, cutoff, ConfLimit):
ToDel = []
cdef long int c1, c2
cdef long int l = len(conformers)
cdef double res
cdef double *RMSDMatrix = <double *>malloc(l * l * sizeof(double))
for c1 in range(0, l):
for c2 in range(c1, l):
if c1==c2:
RMSDMatrix[c2 + c1*l]=0.0
else:
res = AlignedRMS(conformers[c1], conformers[c2], atoms)
RMSDMatrix[c2 + c1*l] = res
RMSDMatrix[c1 + c2*l] = res
#Check for similar conformations
for c1 in range(0, l):
for c2 in range(0, l):
if c1!=c2 and (not c1 in ToDel) and (not c2 in ToDel):
if RMSDMatrix[c2 + c1*l]<cutoff:
ToDel.append(c2)
AdjCutoff = cutoff
while (l-len(ToDel))>ConfLimit:
AdjCutoff +=0.2
ToDel = []
for c1 in range(0, l):
for c2 in range(0, l):
if c1!=c2 and (not c1 in ToDel) and (not c2 in ToDel):
if RMSDMatrix[c2 + c1*l]<AdjCutoff:
ToDel.append(c2)
#return PrunedConformers
free(RMSDMatrix)
return AdjCutoff
def StrictRMSDPrune(conformers, atoms, cutoff, ConfLimit):
ToDel = []
cdef long int c1, c2
cdef long int l = len(conformers)
cdef double res
cdef double *RMSDMatrix = <double *>malloc(l * l * sizeof(double))
for c1 in range(0, l):
for c2 in range(c1, l):
if c1==c2:
RMSDMatrix[c2 + c1*l]=0.0
else:
res = AlignedRMS(conformers[c1], conformers[c2], atoms)
RMSDMatrix[c2 + c1*l] = res
RMSDMatrix[c1 + c2*l] = res
#Check for similar conformations
for c1 in range(0, l):
for c2 in range(0, l):
if c1!=c2 and (not c1 in ToDel) and (not c2 in ToDel):
if RMSDMatrix[c2 + c1*l]<cutoff:
ToDel.append(c2)
AdjCutoff = cutoff
while (l-len(ToDel))>ConfLimit:
AdjCutoff +=0.2
ToDel = []
for c1 in range(0, l):
for c2 in range(0, l):
if c1!=c2 and (not c1 in ToDel) and (not c2 in ToDel):
if RMSDMatrix[c2 + c1*l]<AdjCutoff:
ToDel.append(c2)
#Compose set of non-redundant conformations
PrunedConformers = []
for c in range(0, l):
if not c in ToDel:
PrunedConformers.append(conformers[c])
#return PrunedConformers
free(RMSDMatrix)
return PrunedConformers, AdjCutoff
def AlignMolecules(mol1, mol2, atoms):
w= []
#prepare weights
for a in atoms:
atomnum = GetAtomNum(a)
#w.append(GetAtomWeight(atomnum))
w.append(1)
#move both molecules to origin
mol1 = Move2Origin(mol1, w)
mol2 = Move2Origin(mol2, w)
#QuatrFit to get the rotation matrix
u = qtrfit(mol1, mol2, w)
#RotateMolecule
mol1 = RotMol(mol1, u)
return mol1, mol2, w
#Converts to pure geometry data, aligns molecules and
#returns the RMSD of the aligned molecules
def AlignedRMS(mol1, mol2, atoms):
#Convert to pure geometry data from [atomsym,text x,text y,text z]
mol1b = []
mol2b = []
for a in mol1:
mol1b.append([float(x) for x in a])
for a in mol2:
mol2b.append([float(x) for x in a])
(amol1, amol2, w) = AlignMolecules(mol1b, mol2b, atoms)
return RMSMol(amol1, amol2, w)
#calculates the RMS between the two molecules
def RMSMol(mol1, mol2, w):
e = [0.0, 0.0, 0.0]
for i in range(0, len(mol1)):
e[0] += w[i] * (mol1[i][0] - mol2[i][0])**2
e[1] += w[i] * (mol1[i][1] - mol2[i][1])**2
e[2] += w[i] * (mol1[i][2] - mol2[i][2])**2
return sqrt(sum(e)/sum(w))
def NMR_RMS(s1, s2):
e = 0
for i in range(0, len(s1)):
e += (s1[i] - s2[i])**2
return sqrt(e/len(s1))
#Rotates molecule, given an array of atoms and a rotation matrix
#molecule is an array of form a[atom][coordinate]
def RotMol(mol, u):
t = [0.0, 0.0, 0.0]
for i in range(0, len(mol)):
t[0] = u[0][0] * mol[i][0] + u[0][1] * mol[i][1] + u[0][2] * mol[i][2]
t[1] = u[1][0] * mol[i][0] + u[1][1] * mol[i][1] + u[1][2] * mol[i][2]
t[2] = u[2][0] * mol[i][0] + u[2][1] * mol[i][1] + u[2][2] * mol[i][2]
mol[i][0] = t[0]
mol[i][1] = t[1]
mol[i][2] = t[2]
return mol
#Translates the molecule so that it's centroid is at the origin
#weights can be atomic weights or numbers?
def Move2Origin(mol, weights):
xsum = 0.0
ysum = 0.0
zsum = 0.0
wsum = 0.0
for i in range(0, len(mol)):
xsum += mol[i][0] * sqrt(weights[i])
ysum += mol[i][1] * sqrt(weights[i])
zsum += mol[i][2] * sqrt(weights[i])
wsum += sqrt(weights[i])
xsum /= wsum
ysum /= wsum
zsum /= wsum
for i in range(0, len(mol)):
mol[i][0] -= xsum
mol[i][1] -= ysum
mol[i][2] -= zsum
return mol
def GetAtomNum(symbol):
Lookup = ['H', 'He', 'Li', 'Be', 'B', 'C','N','O','F','Ne','Na','Mg','Al',\
'Si','P','S','Cl','Ar','K','Ca','Sc','Ti','V','Cr','Mn','Fe','Co',\
'Ni','Cu','Zn','Ga','Ge','As','Se','Br','Kr','Rb','Sr','Y','Zr',\
'Nb','Mo','Tc','Ru','Rh','Pd','Ag','Cd','In','Sn','Sb','Te','I',\
'Xe','Cs','Ba','La','Ce','Pr','Nd','Pm','Sm','Eu','Gd','Tb','Dy',\
'Ho','Er','Tm','Yb','Lu','Hf','Ta','W','Re','Os','Ir','Pt','Au',\
'Hg','Tl','Pb','Bi','Po','At','Rn']
if symbol in Lookup:
return Lookup.index(symbol) + 1
else:
return 0
def GetAtomWeight(AtomNum):
Lookup = [1, 4, 7, 9, 11, 12, 14, 16, 19, 20, 23, 24, 27, 28, 31, 32, 35,\
40, 39, 40, 45, 48, 51, 52, 55, 56, 59, 59, 64, 65, 70, 73, 75,\
79, 80, 84, 85, 88, 89, 91, 93, 96, 98, 101, 103, 106, 108, 112,\
115, 119, 122, 128, 127, 131, 133, 137]
return Lookup[AtomNum-1]
"""
* This routine is a python translation of the QTRFIT Fortran routine
* of David Heisterberg
*
* David J. Heisterberg
* The Ohio Supercomputer Center, 1224 Kinnear Rd,
* Columbus, OH 43212-1163
* (614)292-6036; [email protected]
*
* Python translation by K Ermanis 2015
*
* QTRFIT
* Find the quaternion, q,[and left rotation matrix, u]
* that minimizes
* |qTBq - A| ^ 2 [|uB - A| ^ 2]
* This is equivalent to maximizing Re (qTBTqA).
* This is equivalent to finding the largest
* eigenvalue and corresponding
* eigenvector of the matrix
* [V2 VUx VUy VUz ]
* [VUx Ux2 UxUy UzUx]
* [VUy UxUy Uy2 UyUz]
* [VUz UzUx UyUz Uz2 ]
* where
* V2 = Bx Ax + By Ay + Bz Az
* Ux2 = Bx Ax - By Ay - Bz Az
* Uy2 = By Ay - Bz Az - Bx Ax
* Uz2 = Bz Az - Bx Ax - By Ay
* VUx = Bz Ay - By Az
* VUy = Bx Az - Bz Ax
* VUz = By Ax - Bx Ay
* UxUy = Bx Ay + By Ax
* UyUz = By Az + Bz Ay
* UzUx = Bz Ax + Bx Az
* The left rotation matrix, u, is obtained from q by
* u = qT1q
* INPUT
* n - number of points
* b - molecule to be rotated
* a - reference molecule
* w - weight vector
* OUTPUT
* z - eigenvalue
* q - the best-fit quaternion
* u - the best-fit left rotation matrix
* nr - number of jacobi sweeps required
KE:
structure of molecule data:
a[atomnr][coordinate]
"""
cdef double v[4][4]
cdef double d[4]
def qtrfit(mol, refmol, w):
cdef int n = len(mol)
cdef double xxyx = 0.0, xxyy = 0.0, xxyz = 0.0, xyyx = 0.0, xyyy = 0.0
cdef double xyyz = 0.0, xzyx = 0.0, xzyy = 0.0, xzyz = 0.0
cdef double c[4][4]
cdef double q[4]
cdef int i, j
#generate the upper triangle of the quadratic form matrix:
for i in range(0,n):
xxyx += mol[i][0] * refmol[i][0] * w[i]
xxyy += mol[i][0] * refmol[i][1] * w[i]
xxyz += mol[i][0] * refmol[i][2] * w[i]
xyyx += mol[i][1] * refmol[i][0] * w[i]
xyyy += mol[i][1] * refmol[i][1] * w[i]
xyyz += mol[i][1] * refmol[i][2] * w[i]
xzyx += mol[i][2] * refmol[i][0] * w[i]
xzyy += mol[i][2] * refmol[i][1] * w[i]
xzyz += mol[i][2] * refmol[i][2] * w[i]
c[0][0] = xxyx + xyyy + xzyz
c[0][1] = xzyy - xyyz
c[1][1] = xxyx - xyyy - xzyz
c[0][2] = xxyz - xzyx
c[1][2] = xxyy + xyyx
c[2][2] = xyyy - xzyz - xxyx
c[0][3] = xyyx - xxyy
c[1][3] = xzyx + xxyz
c[2][3] = xyyz + xzyy
c[3][3] = xzyz - xxyx - xyyy
#Diagonalize c
cdef double **ret
ret = qtrjac(c, 4, 4)
#extract the desired quaternion
cdef double z = d[3]
q[0] = v[0][3]
q[1] = v[1][3]
q[2] = v[2][3]
q[3] = v[3][3]
#generate the rotation matrix
u = q2mat(q)
return u
cdef double** qtrjac(double a[4][4], int n, int np):
"""v = [[0.0, 0.0, 0.0, 0.0],[0.0, 0.0, 0.0, 0.0],\
[0.0, 0.0, 0.0, 0.0],[0.0, 0.0, 0.0, 0.0]]
d = [0.0, 0.0, 0.0, 0.0]
onorm = 0.0
dnorm = 0.0
b = 0.0
dma = 0.0
q = 0.0
t= 0.0
c = 0.0
s = 0.0
atemp = 0.0
vtemp = 0.0
dtemp = 0.0
nrot = 128"""
cdef double onorm, dnorm, b, dma, q, t, c, s, atemp, vtemp, dtemp
cdef int nrot = 128
cdef int j, i, l, k
for j in range(0,n):
for i in range(0,n):
v[i][j]=0.0
v[j][j] = 1.0
d[j] = a[j][j]
for l in range(0, nrot):
dnorm = 0.0
onorm = 0.0
for j in range(0, n):
dnorm += abs(d[j])
for i in range(j-1):
onorm += abs(a[i][j])
if (onorm + dnorm) <= dnorm:
break
for j in range(1, n):
for i in range(0,j-1):
b = a[i][j]
if (abs(b)>0.0):
dma = d[j] - d[i]
if (abs(dma)+abs(b) < abs(dma)):
t = b/dma
else:
q = 0.5 * dma / b
t = fsign(1.0 / (abs(q) + sqrt(1.0 + q*q)), q)
c = 1.0 / sqrt(t*t + 1.0)
s = t * c
a[i][j] = 0.0
for k in range(0, i-1):
atemp = c * a[k][i] - s * a[k][j]
a[k][j] = s * a[k][i] + c * a[k][j]
a[k][i] = atemp
for k in range(i+1, j):
atemp = c * a[i][k] - s * a[k][j]
a[k][j] = s * a[i][k] + c * a[k][j]
a[i][k] = atemp
for k in range(j, n):
atemp = c * a[i][k] - s * a[j][k]
a[j][k] = s * a[i][k] + c * a[j][k]
a[i][k] = atemp
for k in range(0, n):
vtemp = c * v[k][i] - s * v[k][j]
v[k][j] = s * v[k][i] + c * v[k][j]
v[k][i] = vtemp
dtemp = c * c * d[i] + s * s * d[j] - 2.0 + c * s * b
d[j] = s * s * d[i] + c * c * d[j] + 2.0 * c * s * b
d[i] = dtemp
nrot = l
for j in range(0, n-1):
k = j
dtemp = d[k]
for i in range(j, n):
if d[i]<dtemp:
k = i
dtemp = d[k]
if k>j:
d[k] = d[j]
d[j] = dtemp
for i in range(0, n):
dtemp = v[i][k]
v[i][k] = v[i][j]
v[i][j] = dtemp
cdef double ret[5][4]
for i in range(0,4):
for j in range(0,4):
ret[i][j]=v[i][j]
for i in range(0,4):
ret[4][i] = d[i]
cdef q2mat(double q[4]):
u = [[0.0, 0.0, 0.0],[0.0, 0.0, 0.0],[0.0, 0.0, 0.0]]
u[0][0] = q[0]*q[0] + q[1]*q[1] - q[2]*q[2] - q[3]*q[3]
u[1][0] = 2.0 *(q[1] * q[2] - q[0] * q[3])
u[2][0] = 2.0 *(q[1] * q[3] + q[0] * q[2])
u[0][1] = 2.0 *(q[2] * q[1] + q[0] * q[3])
u[1][1] = q[0]*q[0] - q[1]*q[1] + q[2]*q[2] - q[3]*q[3]
u[2][1] = 2.0 *(q[2] * q[3] - q[0] * q[1])
u[0][2] = 2.0 *(q[3] * q[1] - q[0] * q[2])
u[1][2] = 2.0 *(q[3] * q[2] + q[0] * q[1])
u[2][2] = q[0]*q[0] - q[1]*q[1] - q[2]*q[2] + q[3]*q[3]
return u
def fsign(a, b):
if (b>=0):
return a
else:
return -a