def projectOnSphere( xyz, radius=None, center=None ):
"""
Project the coordinates xyz on a sphere with a given radius around
a given center.
:param xyz: cartesian coordinates
:type xyz: array N x 3 of float
:param radius: radius of target sphere, if not provided the maximal
distance to center will be used (default: None)
:type radius: float
:param center: center of the sphere, if not given the average of xyz
will be assigned to the center (default: None)
:type center: array 0 x 3 of float
:return: array of cartesian coordinates (x, y, z)
:rtype: array
"""
if center is None:
center = N0.average( xyz )
if radius is None:
radius = max( N0.sqrt( N0.sum( N0.power( xyz - center, 2 ), 1 ) ) )
rtp = cartesianToPolar( xyz - center )
rtp[ :, 0 ] = radius
return polarToCartesian( rtp ) + center
def projectOnSphere(xyz, radius=None, center=None):
"""
Project the coordinates xyz on a sphere with a given radius around
a given center.
:param xyz: cartesian coordinates
:type xyz: array N x 3 of float
:param radius: radius of target sphere, if not provided the maximal
distance to center will be used (default: None)
:type radius: float
:param center: center of the sphere, if not given the average of xyz
will be assigned to the center (default: None)
:type center: array 0 x 3 of float
:return: array of cartesian coordinates (x, y, z)
:rtype: array
"""
if center is None:
center = N0.average(xyz)
if radius is None:
radius = max(N0.sqrt(N0.sum(N0.power(xyz - center, 2), 1)))
rtp = cartesianToPolar(xyz - center)
rtp[:, 0] = radius
return polarToCartesian(rtp) + center
def pairwiseRmsd( self, aMask=None, noFit=0 ):
"""
Calculate rmsd between each 2 coordinate frames.
:param aMask: atom mask
:type aMask: [1|0]
:return: frames x frames array of float
:rtype: array
"""
frames = self.frames
if aMask is not None:
frames = N0.compress( aMask, frames, 1 )
result = N0.zeros( (len( frames ), len( frames )), N0.Float32 )
for i in range(0, len( frames ) ):
for j in range( i+1, len( frames ) ):
if noFit:
d = N0.sqrt(N0.sum(N0.power(frames[i]-frames[j], 2), 1))
result[i,j] = result[j,i] = N0.sqrt( N0.average(d**2) )
else:
rt, rmsdLst = rmsFit.match( frames[i], frames[j], 1 )
result[i,j] = result[j,i] = rmsdLst[0][1]
return result
def error(self, msm, d2):
"""
@param msm: membership matrix
@type msm: array('f')
@param d2: distance from data to the centers
@type d2: array('f')
@return: weighted error
@rtype: float
"""
p = N0.power(msm, self.w)
product = N0.dot(p, N0.transpose(d2))
return N0.trace(product)
def error(self, msm, d2):
"""
@param msm: membership matrix
@type msm: array('f')
@param d2: distance from data to the centers
@type d2: array('f')
@return: weighted error
@rtype: float
"""
p = N0.power(msm, self.w)
product = N0.dot(p, N0.transpose(d2))
return N0.trace(product)
def variance(x, avg = None):
"""
Variance, S{sigma}^2
:param x: data
:type x: array('f') or float
:param avg: use this average, otherwise calculated from x
:type avg: float OR None
:return: float
:rtype: float
"""
if avg is None:
avg = N0.average(x)
if len(x) == 1:
return 0.0
return N0.sum(N0.power(N0.array(x) - avg, 2)) / (len(x) - 1.)
def variance(x, avg=None):
"""
Variance, S{sigma}^2
:param x: data
:type x: array('f') or float
:param avg: use this average, otherwise calculated from x
:type avg: float OR None
:return: float
:rtype: float
"""
if avg is None:
avg = N0.average(x)
if len(x) == 1:
return 0.0
return N0.sum(N0.power(N0.array(x) - avg, 2)) / (len(x) - 1.)
def getFluct_global( self, mask=None ):
"""
Get RMS of each atom from it's average position in trajectory.
The frames should be superimposed (fit() ) to a reference.
:param mask: N x 1 list/Numpy array of 0|1, (N=atoms),
atoms to be considered.
:type mask: [1|0]
:return: Numpy array ( N_unmasked x 1 ) of float.
:rtype: array
"""
frames = self.frames
if mask is not None:
frames = N0.compress( mask, frames, 1 )
## mean position of each atom in all frames
avg = N0.average( frames )
return N0.average(N0.sqrt(N0.sum(N0.power(frames - avg, 2), 2) ))
def rowDistances( x, y ):
"""
Calculate the distances between the items of two arrays (of same shape)
after least-squares superpositioning.
:param x: first set of coordinates
:type x: array('f')
:param y: second set of coordinates
:type y: array('f')
:return: array( len(x), 'f' ), distance between x[i] and y[i] for all i
:rtype: array
"""
## find transformation for best match
r, t = findTransformation(x, y)
## transform coordinates
z = N0.dot(y, N0.transpose(r)) + t
## calculate row distances
return N0.sqrt(N0.sum(N0.power(x - z, 2), 1))
def rowDistances(x, y):
"""
Calculate the distances between the items of two arrays (of same shape)
after least-squares superpositioning.
:param x: first set of coordinates
:type x: array('f')
:param y: second set of coordinates
:type y: array('f')
:return: array( len(x), 'f' ), distance between x[i] and y[i] for all i
:rtype: array
"""
## find transformation for best match
r, t = findTransformation(x, y)
## transform coordinates
z = N0.dot(y, N0.transpose(r)) + t
## calculate row distances
return N0.sqrt(N0.sum(N0.power(x - z, 2), 1))
def pca( self, atomMask=None, frameMask=None, fit=1 ):
"""
Calculate principal components of trajectory frames.
:param atomMask: 1 x N_atoms, [111001110..] atoms to consider
(default: all)
:type atomMask: [1|0]
:param frameMask: 1 x N_frames, [001111..] frames to consider
(default all )
:type frameMask: [1|0]
:return: (N_frames x N_frames), (1 x N_frames),
projection of each frame in PC space, eigenvalue of each PC
:rtype: array, array, array
"""
if frameMask is None: frameMask = N0.ones( len( self.frames ), N0.Int32 )
if atomMask is None: atomMask = N0.ones(self.getRef().lenAtoms(),
N0.Int32)
if fit:
self.fit( atomMask )
refxyz = N0.average( self.frames, 0 )
data = N0.compress( frameMask, self.frames, 0 )
data = data - refxyz
data = N0.compress( atomMask, data, 1 )
## reduce to 2D array
data = N0.array( map( N0.ravel, data ) )
V, L, U = LA.svd( data )
return U, V * L, N0.power(L, 2)
def calc_cluster_center(self, msm):
p = N0.power(msm, self.w)
ccenter = N0.transpose(N0.dot(p, self.data))
return N0.transpose(ccenter / N0.sum(p, 1))
def calc_membership_matrix(self, d2):
## remove 0s (if a cluster center is exactly on one item)
d2 = N0.clip(d2, N0.power(1e200, 1 - self.w), 1e300)
q = N0.power(d2, 1. / (1. - self.w))
return q / N0.sum(q)
def clusterPartitionCoefficient(self):
return N0.sum(N0.power(self.msm, self.w), 1) / self.npoints
def nonFuzzyIndex(self):
p = N0.power(self.msm, self.w)
return (self.n_cluster * N0.sum(N0.sum(p)) -
self.npoints) / (self.npoints * (self.n_cluster - 1))
def match(x, y, n_iterations=1, z=2, eps_rmsd=0.5, eps_stdv=0.05):
"""
Matches two arrays onto each other, while iteratively removing outliers.
Superimposed array y would be C{ N0.dot(y, N0.transpose(r)) + t }.
:param n_iterations: number of calculations::
1 .. no iteration
0 .. until convergence
:type n_iterations: 1|0
:param z: number of standard deviations for outlier definition (default: 2)
:type z: float
:param eps_rmsd: tolerance in rmsd (default: 0.5)
:type eps_rmsd: float
:param eps_stdv: tolerance in standard deviations (default: 0.05)
:type eps_stdv: float
:return: (r,t), [ [percent_considered, rmsd_for_it, outliers] ]
:rtype: (array, array), [float, float, int]
"""
iter_trace = []
rmsd_old = 0
stdv_old = 0
n = 0
converged = 0
mask = N0.ones(len(y), N0.Int32 )
while not converged:
## find transformation for best match
r, t = findTransformation(N0.compress(mask, x, 0),
N0.compress(mask, y, 0))
## transform coordinates
xt = N0.dot(y, N0.transpose(r)) + t
## calculate row distances
d = N0.sqrt(N0.sum(N0.power(x - xt, 2), 1)) * mask
## calculate rmsd and stdv
rmsd = N0.sqrt(N0.average(N0.compress(mask, d)**2))
stdv = MU.SD(N0.compress(mask, d))
## check conditions for convergence
d_rmsd = abs(rmsd - rmsd_old)
d_stdv = abs(1 - stdv_old / stdv)
if d_rmsd < eps_rmsd and d_stdv < eps_stdv:
converged = 1
else:
rmsd_old = rmsd
stdv_old = stdv
## store result
perc = round(float(N0.sum(mask)) / float(len(mask)), 2)
## throw out non-matching rows
mask = N0.logical_and(mask, N0.less(d, rmsd + z * stdv))
outliers = N0.nonzero( N0.logical_not( mask ) )
iter_trace.append([perc, round(rmsd, 3), outliers])
n += 1
if n_iterations and n >= n_iterations:
break
return (r, t), iter_trace
def nonFuzzyIndex(self):
p = N0.power(self.msm, self.w)
return (self.n_cluster*N0.sum(N0.sum(p))-
self.npoints)/(self.npoints*(self.n_cluster-1))
def clusterPartitionCoefficient(self):
return N0.sum(N0.power(self.msm, self.w), 1)/self.npoints
def fit( self, mask=None, ref=None, n_it=1,
prof='rms', verbose=1, fit=1, **profInfos ):
"""
Superimpose all coordinate frames on reference coordinates. Put rms
values in a profile. If n_it > 1, the fraction of atoms considered
for the fit is put into a profile called |prof|_considered
(i.e. by default 'rms_considered').
:param mask: atom mask, atoms to consider default: [all]
:type mask: [1|0]
:param ref: use as reference, default: None, average Structure
:type ref: PDBModel
:param n_it: number of fit iterations, kicking out outliers on the way
1 -> classic single fit, 0 -> until convergence
(default: 1)
:type n_it: int
:param prof: save rms per frame in profile of this name, ['rms']
:type prof: str
:param verbose: print progress info to STDERR (default: 1)
:type verbose: 1|0
:param fit: transform frames after match, otherwise just calc rms
(default: 1)
:type fit: 1|0
:param profInfos: additional key=value pairs for rms profile info []
:type profInfos: key=value
"""
if ref is None:
refxyz = N0.average( self.frames, 0 )
else:
refxyz = ref.getXyz()
if mask is None:
mask = N0.ones( len( refxyz ), N0.Int32 )
refxyz = N0.compress( mask, refxyz, 0 )
if verbose: T.errWrite( "rmsd fitting..." )
rms = [] ## rms value of each frame
non_outliers = [] ## fraction of atoms considered for rms and fit
iterations = [] ## number of iterations performed on each frame
for i in range(0, len( self.frames) ):
xyz = self.frames[i]
if n_it != 1:
(r, t), rmsdList = rmsFit.match( refxyz,
N0.compress( mask, xyz, 0), n_it)
iterations.append( len( rmsdList ) )
non_outliers.append( rmsdList[-1][0] )
xyz_transformed = N0.dot( xyz, N0.transpose(r)) + t
rms += [ rmsdList[-1][1] ]
else:
r, t = rmsFit.findTransformation( refxyz,
N0.compress( mask, xyz, 0))
xyz_transformed = N0.dot( xyz, N0.transpose(r)) + t
d = N0.sqrt(N0.sum(N0.power( N0.compress(mask, xyz_transformed,0)\
- refxyz, 2), 1))
rms += [ N0.sqrt( N0.average(d**2) ) ]
if fit:
self.frames[i] = xyz_transformed.astype(N0.Float32)
if verbose and i%100 == 0:
T.errWrite( '#' )
self.setProfile( prof, rms, n_iterations=n_it, **profInfos )
if non_outliers:
self.setProfile( prof+'_considered', non_outliers,
n_iterations=n_it,
comment='fraction of atoms considered for iterative fit' )
if verbose: T.errWrite( 'done\n' )
def getFluct_local( self, mask=None, border_res=1,
left_atoms=['C'], right_atoms=['N'], verbose=1 ):
"""
Get mean displacement of each atom from it's average position after
fitting of each residue to the reference backbone coordinates of itself
and selected atoms of neighboring residues to the right and left.
:param mask: N_atoms x 1 array of 0||1, atoms for which fluctuation
should be calculated
:type mask: array
:param border_res: number of neighboring residues to use for fitting
:type border_res: int
:param left_atoms: atoms (names) to use from these neighbore residues
:type left_atoms: [str]
:param right_atoms: atoms (names) to use from these neighbore residues
:type right_atoms: [str]
:return: Numpy array ( N_unmasked x 1 ) of float
:rtype: array
"""
if mask is None:
mask = N0.ones( len( self.frames[0] ), N0.Int32 )
if verbose: T.errWrite( "rmsd fitting per residue..." )
residues = N0.nonzero( self.ref.atom2resMask( mask ) )
## backbone atoms used for fit
fit_atoms_right = N0.nonzero( self.ref.mask( right_atoms ) )
fit_atoms_left = N0.nonzero( self.ref.mask( left_atoms ) )
## chain index of each residue
rchainMap = N0.take( self.ref.chainMap(), self.ref.resIndex() )
result = []
for res in residues:
i_res, i_border = self.__resWindow(res, border_res, rchainMap,
fit_atoms_left, fit_atoms_right)
try:
if not len( i_res ): raise PDBError('empty residue')
t_res = self.takeAtoms( i_res + i_border )
i_center = range( len( i_res ) )
mask_BB = t_res.ref.maskBB() * t_res.ref.maskHeavy()
## fit with border atoms ..
t_res.fit( ref=t_res.ref, mask=mask_BB, verbose=0 )
## .. but calculate only with center residue atoms
frames = N0.take( t_res.frames, i_center, 1 )
avg = N0.average( frames )
rmsd = N0.average(N0.sqrt(N0.sum(N0.power(frames - avg, 2), 2) ))
result.extend( rmsd )
if verbose: T.errWrite('#')
except ZeroDivisionError:
result.extend( N0.zeros( len(i_res), N0.Float32 ) )
T.errWrite('?' + str( res ))
if verbose: T.errWriteln( "done" )
return result
def calc_membership_matrix(self, d2):
## remove 0s (if a cluster center is exactly on one item)
d2 = N0.clip( d2, N0.power(1e200, 1-self.w), 1e300 )
q = N0.power(d2, 1. / (1. - self.w))
return q / N0.sum(q)
def match(x, y, n_iterations=1, z=2, eps_rmsd=0.5, eps_stdv=0.05):
"""
Matches two arrays onto each other, while iteratively removing outliers.
Superimposed array y would be C{ N0.dot(y, N0.transpose(r)) + t }.
:param n_iterations: number of calculations::
1 .. no iteration
0 .. until convergence
:type n_iterations: 1|0
:param z: number of standard deviations for outlier definition (default: 2)
:type z: float
:param eps_rmsd: tolerance in rmsd (default: 0.5)
:type eps_rmsd: float
:param eps_stdv: tolerance in standard deviations (default: 0.05)
:type eps_stdv: float
:return: (r,t), [ [percent_considered, rmsd_for_it, outliers] ]
:rtype: (array, array), [float, float, int]
"""
iter_trace = []
rmsd_old = 0
stdv_old = 0
n = 0
converged = 0
mask = N0.ones(len(y), N0.Int32)
while not converged:
## find transformation for best match
r, t = findTransformation(N0.compress(mask, x, 0),
N0.compress(mask, y, 0))
## transform coordinates
xt = N0.dot(y, N0.transpose(r)) + t
## calculate row distances
d = N0.sqrt(N0.sum(N0.power(x - xt, 2), 1)) * mask
## calculate rmsd and stdv
rmsd = N0.sqrt(N0.average(N0.compress(mask, d)**2))
stdv = MU.SD(N0.compress(mask, d))
## check conditions for convergence
d_rmsd = abs(rmsd - rmsd_old)
d_stdv = abs(1 - stdv_old / stdv)
if d_rmsd < eps_rmsd and d_stdv < eps_stdv:
converged = 1
else:
rmsd_old = rmsd
stdv_old = stdv
## store result
perc = round(float(N0.sum(mask)) / float(len(mask)), 2)
## throw out non-matching rows
mask = N0.logical_and(mask, N0.less(d, rmsd + z * stdv))
outliers = N0.nonzero(N0.logical_not(mask))
iter_trace.append([perc, round(rmsd, 3), outliers])
n += 1
if n_iterations and n >= n_iterations:
break
return (r, t), iter_trace
def calc_cluster_center(self, msm):
p = N0.power(msm, self.w)
ccenter = N0.transpose(N0.dot(p, self.data))
return N0.transpose(ccenter / N0.sum(p, 1))
