Author: bugman
Date: Sun Oct 29 03:57:04 2006
New Revision: 2683
URL: http://svn.gna.org/viewcvs/relax?rev=2683&view=rev
Log:
Creation of a uniform distribution of unit vectors on a sphere using uniform
spherical angles.
The function 'self.uniform_vect_dist_spherical_angles()' has been added to
the file
'generic_fns/pdb.py'. This function has the explicit purpose of generating a
uniform distribution
of unit vectors on a sphere. It does this by using a linear distribution of
values of the azimuthal
angle theta in combination with an arc-cos distribution of values of the
polar angle. Each is
incremented one by one and unit vectors from the spherical angles are
calculated. This creates both
radial arrays corresponding to the longitude and horizontal latitudinal
arrays of vectors.
For the tensor PDB file, this currently generates a number of non-bonded H
atoms distributed 1
Angstrom form the origin of the PDB frame. This will soon be transformed
into the diffusion frame,
the unit vectors scaled to the appropriate diffusion rate, and the atoms
joined.
Modified:
branches/tensor_pdb/generic_fns/pdb.py
Modified: branches/tensor_pdb/generic_fns/pdb.py
URL:
http://svn.gna.org/viewcvs/relax/branches/tensor_pdb/generic_fns/pdb.py?rev=2683&r1=2682&r2=2683&view=diff
==============================================================================
--- branches/tensor_pdb/generic_fns/pdb.py (original)
+++ branches/tensor_pdb/generic_fns/pdb.py Sun Oct 29 03:57:04 2006
@@ -20,8 +20,8 @@
#
#
###############################################################################
-from math import sqrt
-from Numeric import Float64, dot, zeros
+from math import sqrt, cos, pi, sin
+from Numeric import Float64, arccos, dot, zeros
from os import F_OK, access
from re import compile
import Scientific.IO.PDB
@@ -233,13 +233,12 @@
# The atom and atomic connections data structures.
self.atomic_data = {}
- # Chain ID, residue number, residue name, chemical name, occupancy,
and default element.
+ # Chain ID, residue number, residue name, chemical name, and
occupancy.
chain_id = 'A'
res_num = 1
res_name = 'TNS'
chemical_name = 'Tensor'
occupancy = 1.0
- element = 'H'
# Center of mass.
@@ -279,6 +278,14 @@
print " Dpar vector (scaled): " + `Dpar_vect`
print " Relative to center of mass: " + `pos`
print
+
+
+ # Uniform vector distribution.
+ ##############################
+
+ vectors = self.uniform_vect_dist_spherical_angles()
+ for i in xrange(len(vectors)):
+ self.atom_add(atom_id='H'+`i`, element='H', pos=vectors[i])
# Create the PDB file.
@@ -622,6 +629,73 @@
# Replace the temporary vector list with the normalised average
vector.
data.xh_vect = ave_vector / sqrt(dot(ave_vector, ave_vector))
+
+
+ def uniform_vect_dist_spherical_angles(self, inc=20):
+ """Uniform distribution of vectors on a sphere using uniform
spherical angles.
+
+ This function returns an array of unit vectors uniformly distributed
within 3D space. To
+ create the distribution, uniform spherical angles are used. The two
spherical angles are
+ defined as
+
+ theta = 2.pi.u,
+ phi = cos^-1(2v - 1),
+
+ where
+
+ u in [0, 1),
+ v in [0, 1].
+
+ Because theta is defined between [0, pi] and phi is defined between
[0, 2pi], for a uniform
+ distribution u is only incremented half of 'inc'. The unit vectors
are gerenated using the
+ equation
+
+ | cos(theta) * sin(phi) |
+ vector = | sin(theta) * sin(phi) |.
+ | cos(phi) |
+ """
+
+ # The inc argument must be an even number.
+ if inc%2:
+ raise RelaxError, "The increment value of " + `inc` + " must be
an even number."
+
+ # Generate the increment values of u.
+ u = zeros(inc, Float64)
+ val = 1.0 / float(inc)
+ for i in xrange(inc):
+ u[i] = float(i) * val
+
+ # Generate the increment values of v.
+ v = zeros(inc/2+1, Float64)
+ val = 1.0 / float(inc/2)
+ for i in xrange(inc/2+1):
+ v[i] = float(i) * val
+
+ # Generate the distribution of spherical angles theta.
+ theta = 2.0 * pi * u
+
+ # Generate the distribution of spherical angles phi.
+ phi = arccos(2.0 * v - 1.0)
+
+
+ # Generate the distribution of vectors.
+ vectors = []
+ for j in xrange(len(v)):
+ for i in xrange(len(u)):
+ # X coordinate.
+ x = cos(theta[i]) * sin(phi[j])
+
+ # Y coordinate.
+ y = sin(theta[i])* sin(phi[j])
+
+ # Z coordinate.
+ z = cos(phi[j])
+
+ # Append the vector.
+ vectors.append([x, y, z])
+
+ # Return the array of vectors.
+ return vectors
def write_pdb_file(self, file, chain_id, res_num, res_name,
chemical_name, occupancy):
r2683 - /branches/tensor_pdb/generic_fns/pdb.py