Added coords.py from mrdna

arbdmodel/coords.py

+import numpy as np
+from scipy.optimize import newton
+
+def minimizeRmsd(coordsB, coordsA, weights=None, maxIter=100):
+    ## Going through many iterations wasn't really needed
+    tol = 1
+    count = 0
+
+    R = np.eye(3)
+    comB = np.zeros([3,])
+    cNext = coordsB
+
+    while tol > 1e-6:
+        q,cB,comA = _minimizeRmsd(cNext,coordsA, weights)
+        R = R.dot(quaternion_to_matrix(q))
+        assert( np.all(np.isreal( R )) )
+
+        comB += cB
+        cLast = cNext
+        cNext = (coordsB-comB).dot(R)
+
+        tol = np.sum(((cNext-cLast)**2)[:]) / np.max(np.shape(coordsB))
+        if count > maxIter:
+            Exception("Exceeded maxIter (%d)" % maxIter)
+        count += 1
+
+    print("%d iterations",count)
+    return R, comB, comA
+
+
+def minimizeRmsd(coordsB, coordsA, weights=None):
+    q,comA,comB = _minimizeRmsd(coordsB, coordsA, weights)
+    assert( np.all(np.isreal( q )) )
+    return quaternion_to_matrix(q),comA,comB
+
+
+## http://onlinelibrary.wiley.com/doi/10.1002/jcc.21439/full
+def _minimizeRmsd(coordsB, coordsA, weights=None):
+    A = coordsA
+    B = coordsB
+
+    shapeA,shapeB = [np.shape(X) for X in (A,B)]
+    for s in (shapeA,shapeB):  assert( len(s) == 2 )
+
+    A,B = [X.T if s[1] > s[0] else X for X,s in zip([A,B],(shapeA,shapeB))] # TODO: print warning
+
+    shapeA,shapeB = [np.shape(X) for X in (A,B)]
+    assert( shapeA == shapeB )
+    for X,s in zip((A,B),(shapeA,shapeB)):
+        assert( s[1] == 3 and s[0] >= s[1] )
+    
+    # if weights is None: weights = np.ones(len(A))
+    if weights is None:
+        comA,comB = [np.mean( X, axis=0 ) for X in (A,B)]
+    else:
+        assert( len(weights[:]) == len(B) )
+        W = np.diag(weights)
+        comA,comB = [np.sum( W.dot(X), axis=0 ) / np.sum(W) for X in (A,B)]
+
+    A = np.array( A-comA )
+    B = np.array( B-comB )
+
+    if weights is None:
+        s = A.T.dot(B)
+    else:
+        s = A.T.dot(W.dot(B))
+    
+    sxx,sxy,sxz = s[0,:]
+    syx,syy,syz = s[1,:]
+    szx,szy,szz = s[2,:]
+    
+    K = [[ sxx+syy+szz, syz-szy, szx-sxz, sxy-syx],
+         [syz-szy,  sxx-syy-szz, sxy+syx, sxz+szx],
+         [szx-sxz, sxy+syx, -sxx+syy-szz, syz+szy],
+         [sxy-syx, sxz+szx, syz+szy, -sxx-syy+szz]]
+    K = np.array(K)
+
+    # GA = np.trace( A.T.dot(W.dot(A)) )
+    # GB = np.trace( B.T.dot(W.dot(B)) )
+        
+    ## Finding GA/GB can be done more quickly
+    # I = np.eye(4)
+    # x0 = (GA+GB)*0.5
+    # vals = newtoon(lambda x: np.det(K-x*I), x0 = x0)
+
+    vals, vecs = np.linalg.eig(K)
+    i = np.argmax(vals)
+    q = vecs[:,i]
+
+    # RMSD = np.sqrt( (GA+GB-2*vals[i]) / len(A) )
+    # print("CHECK:", K.dot(q)-vals[i]*q )
+    return q, comB, comA
+
+def quaternion_to_matrix(q):
+    assert(len(q) == 4)
+
+    ## It looks like the wikipedia article I used employed a less common convention for q (see below
+    ## http://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions#Rotation_matrix_.E2.86.94_quaternion
+    # q1,q2,q3,q4 = q
+    # R = [[1-2*(q2*q2 + q3*q3),    2*(q1*q2 - q3*q4),    2*(q1*q3 + q2*q4)],
+    #      [  2*(q1*q2 + q3*q4),  1-2*(q1*q1 + q3*q3),    2*(q2*q3 - q1*q4)],
+    #      [  2*(q1*q3 - q2*q4),    2*(q1*q4 + q2*q3),  1-2*(q2*q2 + q1*q1)]]
+
+    q = q / np.linalg.norm(q)
+    q0,q1,q2,q3 = q
+    R = [[1-2*(q2*q2 + q3*q3),    2*(q1*q2 - q3*q0),    2*(q1*q3 + q2*q0)],
+         [  2*(q1*q2 + q3*q0),  1-2*(q1*q1 + q3*q3),    2*(q2*q3 - q1*q0)],
+         [  2*(q1*q3 - q2*q0),    2*(q1*q0 + q2*q3),  1-2*(q2*q2 + q1*q1)]]
+
+    return np.array(R)
+
+def quaternion_from_matrix( R ):
+    e1 = R[0]
+    e2 = R[1]
+    e3 = R[2]
+    
+    # d1 = 0.5 * np.sqrt( 1+R[0,0]+R[1,1]+R[2,2] )
+    # d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
+    # d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
+    # d2 = 0.5 * np.sqrt( 1+R[0,0]-R[1,1]-R[2,2] )
+
+    d1 = 1+R[0,0]+R[1,1]+R[2,2]
+    d2 = 1+R[0,0]-R[1,1]-R[2,2]
+    d3 = 1-R[0,0]+R[1,1]-R[2,2]
+    d4 = 1-R[0,0]-R[1,1]+R[2,2]
+    
+    maxD = max((d1,d2,d3,d4))
+    d = 0.5 / np.sqrt(maxD)
+
+    if d1 == maxD:
+        return np.array(( 1.0/(4*d),
+                          d * (R[2,1]-R[1,2]),
+                          d * (R[0,2]-R[2,0]),
+                          d * (R[1,0]-R[0,1]) ))
+    elif d2 == maxD:
+        return np.array(( d * (R[2,1]-R[1,2]),
+                          1.0/(4*d),
+                          d * (R[0,1]+R[1,0]),
+                          d * (R[0,2]+R[2,0]) ))
+    elif d3 == maxD:
+        return np.array(( d * (R[0,2]-R[2,0]),
+                          d * (R[0,1]+R[1,0]),
+                          1.0/(4*d),
+                          d * (R[1,2]+R[2,1]) ))
+    elif d4 == maxD:
+        return np.array(( d * (R[1,0]-R[0,1]),
+                          d * (R[0,2]+R[2,0]),
+                          d * (R[1,2]+R[2,1]),
+                          1.0/(4*d) ))
+
+def rotationAboutAxis(axis,angle, normalizeAxis=True):
+    if normalizeAxis: axis = axis / np.linalg.norm(axis)
+    angle = angle * 0.5 * np.pi/180
+    cos = np.cos( angle )
+    sin = np.sin( angle )
+    q = [cos] + [sin*x for x in axis]
+    return quaternion_to_matrix(q)
+
+def readArbdCoords(fname):
+    coords = []
+    with open(fname) as fh:
+        for line in fh:
+            coords.append([float(x) for x in line.split()[1:]])
+    return np.array(coords)
+
+def readAvgArbdCoords(psf,pdb,dcd,rmsdThreshold=3.5):
+    import MDAnalysis as mda
+
+    usel = mda.Universe(psf, dcd)
+    sel = usel.select_atoms("name D*")
+
+    # r0 = ref.xyz[0,ids,:]
+    ts = usel.trajectory[-1]
+    r0 = sel.positions
+    pos = []
+    for t in range(ts.frame-1,-1,-1):
+        usel.trajectory[t]
+        R,comA,comB = minimizeRmsd(sel.positions,r0)
+        r = np.array( [(r-comA).dot(R)+comB for r in sel.positions] )
+        rmsd = np.mean( (r-r0)**2 )
+        r = np.array( [(r-comA).dot(R)+comB for r in usel.atoms.positions] )
+        pos.append( r )
+        if rmsd > rmsdThreshold**2:
+            break
+    t0=t+1
+    print( "Averaging coordinates in %s after frame %d" % (dcd, t0) )
+
+    pos = np.mean(pos, axis=0)
+    return pos
+
+def unit_quat_conversions():
+    for axis in [[0,0,1],[1,1,1],[1,0,0],[-1,-2,0]]:
+        for angle in np.linspace(-180,180,10):
+            R = rotationAboutAxis(axis, angle)
+            R2 = quaternion_to_matrix( quaternion_from_matrix( R ) )
+            if not np.all( np.abs(R-R2) < 0.01 ):
+                import pdb
+                pdb.set_trace()
+                quaternion_to_matrix( quaternion_from_matrix( R ) )
+
+
+if __name__ == "__main__":
+    unit_quat_conversions()
+