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https://github.com/baker-laboratory/RoseTTAFold-All-Atom.git
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716 lines
43 KiB
Python
716 lines
43 KiB
Python
import sys
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import numpy as np
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import torch
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SYMA = 1.0
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def generateC(angs, eps=1e-6):
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L = angs.shape[0]
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Rs = torch.eye(3, device=angs.device).repeat(L,1,1)
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Rs[:,1,1] = torch.cos(angs)
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Rs[:,1,2] = -torch.sin(angs)
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Rs[:,2,1] = torch.sin(angs)
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Rs[:,2,2] = torch.cos(angs)
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return Rs
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def generateD(angs, eps=1e-6):
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L = angs.shape[0]
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Rs = torch.eye(3, device=angs.device).repeat(2*L,1,1)
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Rs[:L,1,1] = torch.cos(angs)
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Rs[:L,1,2] = -torch.sin(angs)
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Rs[:L,2,1] = torch.sin(angs)
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Rs[:L,2,2] = torch.cos(angs)
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Rx = torch.tensor([[-1.,0,0],[0,-1,0],[0,0,1]],device=angs.device)
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Rs[L:] = torch.einsum('ij,bjk->bik',Rx,Rs[:L])
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return Rs
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def find_symm_subs(xyz,Rs,metasymm):
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com = xyz[:,:,1].mean(dim=-2)
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rcoms = torch.einsum('sij,bj->si', Rs, com)
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subsymms, nneighs = metasymm
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subs = []
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for i in range(len(subsymms)):
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drcoms = torch.linalg.norm(rcoms[0,:] - rcoms[subsymms[i],:], dim=-1)
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_,subs_i = torch.topk(drcoms,nneighs[i],largest=False)
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subs_i,_ = torch.sort( subsymms[i][subs_i] )
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subs.append(subs_i)
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subs=torch.cat(subs)
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xyz_new = torch.einsum('sij,braj->bsrai', Rs[subs], xyz).reshape(
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xyz.shape[0],-1,xyz.shape[2],3)
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return xyz_new, subs
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def update_symm_subs(xyz,subs,Rs,metasymm):
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xyz_new = torch.einsum('sij,braj->bsrai', Rs[subs], xyz).reshape(
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xyz.shape[0],-1,xyz.shape[2],3)
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return xyz_new
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def get_symm_map(subs,O):
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symmmask = torch.zeros(O,dtype=torch.long)
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symmmask[subs] = torch.arange(1,subs.shape[0]+1)
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return symmmask
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def rotation_from_matrix(R, eps=1e-4):
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w, W = torch.linalg.eig(R.T)
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i = torch.where(abs(torch.real(w) - 1.0) < eps)[0]
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if (len(i)==0):
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i = torch.tensor([0])
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print ('rotation_from_matrix w',torch.real(w))
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print ('rotation_from_matrix R.T',R.T)
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axis = torch.real(W[:, i[-1]]).squeeze()
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cosa = (torch.trace(R) - 1.0) / 2.0
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if abs(axis[2]) > eps:
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sina = (R[1, 0] + (cosa-1.0)*axis[0]*axis[1]) / axis[2]
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elif abs(axis[1]) > eps:
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sina = (R[0, 2] + (cosa-1.0)*axis[0]*axis[2]) / axis[1]
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else:
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sina = (R[2, 1] + (cosa-1.0)*axis[1]*axis[2]) / axis[0]
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angle = torch.atan2(sina, cosa)
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return angle, axis
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def kabsch(pred, true):
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def rmsd(V, W, eps=1e-6):
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L = V.shape[0]
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return torch.sqrt(torch.sum((V-W)*(V-W)) / L + eps)
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def centroid(X):
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return X.mean(dim=-2, keepdim=True)
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cP = centroid(pred)
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cT = centroid(true)
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pred = pred - cP
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true = true - cT
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C = torch.matmul(pred.permute(1,0), true)
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V, S, W = torch.svd(C)
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d = torch.ones([3,3], device=pred.device)
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d[:,-1] = torch.sign(torch.det(V)*torch.det(W))
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U = torch.matmul(d*V, W.permute(1,0)) # (IB, 3, 3)
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rpred = torch.matmul(pred, U) # (IB, L*3, 3)
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rms = rmsd(rpred, true)
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return rms, U, cP, cT
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# do lines X0->X and Y0->Y intersect?
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def intersect(X0,X,Y0,Y,eps=0.1):
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mtx = torch.cat(
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(torch.stack((X0,X0+X,Y0,Y0+Y)), torch.ones((4,1))) , axis=1
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)
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det = torch.linalg.det( mtx )
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return (torch.abs(det) <= eps)
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def get_angle(X,Y):
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angle = torch.acos( torch.clamp( torch.sum(X*Y), -1., 1. ) )
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if (angle > np.pi/2):
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angle = np.pi - angle
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return angle
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# given the coordinates of a subunit +
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def get_symmetry(xyz, mask, rms_cut=2.5, nfold_cut=0.1, angle_cut=0.05, trans_cut=2.0):
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nops = xyz.shape[0]
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L = xyz.shape[1]//2
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# PASS 1: find all symm axes
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symmaxes = []
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for i in range(nops):
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# if there are multiple biomt records, this may occur.
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# rather than try to rescue, we will take the 1st (typically author-assigned)
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offset0 = torch.linalg.norm(xyz[i,:L,1]-xyz[0,:L,1], dim=-1)
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if (torch.mean(offset0)>1e-4):
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continue
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# get alignment
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mask_i = mask[i,:L,1]*mask[i,L:,1]
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xyz_i = xyz[i,:L,1][mask_i,:]
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xyz_j = xyz[i,L:,1][mask_i,:]
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rms_ij, Uij, cI, cJ = kabsch(xyz_i, xyz_j)
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if (rms_ij > rms_cut):
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#print (i,'rms',rms_ij)
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continue
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# get axis and point symmetry about axis
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angle, axis = rotation_from_matrix(Uij)
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nfold = 2*np.pi/torch.abs(angle)
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# a) ensure integer # of subunits per rotation
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if (torch.abs( nfold - torch.round(nfold) ) > nfold_cut ):
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#print ('nfold fail',nfold)
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continue
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nfold = torch.round(nfold).long()
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# b) ensure rotation only (no translation)
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delCOM = torch.mean(xyz_i, dim=-2) - torch.mean(xyz_j, dim=-2)
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trans_dot_symaxis = nfold * torch.abs(torch.dot(delCOM, axis))
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if (trans_dot_symaxis > trans_cut ):
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#print ('trans fail',trans_dot_symaxis)
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continue
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# 3) get a point on the symm axis from CoMs and angle
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cIJ = torch.sign(angle) * (cJ-cI).squeeze(0)
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dIJ = torch.linalg.norm(cIJ)
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p_mid = (cI+cJ).squeeze(0) / 2
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u = cIJ / dIJ # unit vector in plane of circle
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v = torch.cross(axis, u) # unit vector from sym axis to p_mid
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r = dIJ / (2*torch.sin(angle/2))
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d = torch.sqrt( r*r - dIJ*dIJ/4 ) # distance from mid-chord to center
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point = p_mid - (d)*v
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# check if redundant
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toadd = True
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for j,(nf_j,ax_j,pt_j,err_j) in enumerate(symmaxes):
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if (not intersect(pt_j,ax_j,point,axis)):
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continue
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angle_j = get_angle(ax_j,axis)
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if (angle_j < angle_cut):
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if (nf_j < nfold): # stored is a subsymmetry of complex, overwrite
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symmaxes[j] = (nfold, axis, point, i)
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toadd = False
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if (toadd):
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symmaxes.append( (nfold, axis, point, i) )
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# PASS 2: combine
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symmgroup = 'C1'
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subsymm = []
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if len(symmaxes)==1:
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symmgroup = 'C%d'%(symmaxes[0][0])
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subsymm = [symmaxes[0][3]]
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elif len(symmaxes)>1:
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symmaxes = sorted(symmaxes, key=lambda x: x[0], reverse=True)
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angle = get_angle(symmaxes[0][1],symmaxes[1][1])
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subsymm = [symmaxes[0][3],symmaxes[1][3]]
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# 2-fold and n-fold intersect at 90 degress => Dn
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if (symmaxes[1][0] == 2 and torch.abs(angle-np.pi/2) < angle_cut):
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symmgroup = 'D%d'%(symmaxes[0][0])
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else:
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# polyhedral rules:
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# 3-Fold + 2-fold intersecting at acos(-1/sqrt(3)) -> T
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angle_tgt = np.arccos(-1/np.sqrt(3))
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if (symmaxes[0][0] == 3 and symmaxes[1][0] == 2 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'T'
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# 3-Fold + 2-fold intersecting at asin(1/sqrt(3)) -> O
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angle_tgt = np.arcsin(1/np.sqrt(3))
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if (symmaxes[0][0] == 3 and symmaxes[1][0] == 2 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'O'
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# 4-Fold + 3-fold intersecting at acos(1/sqrt(3)) -> O
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angle_tgt = np.arccos(1/np.sqrt(3))
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if (symmaxes[0][0] == 4 and symmaxes[1][0] == 3 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'O'
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# 3-Fold + 2-fold intersecting at 0.5*acos(sqrt(5)/3) -> I
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angle_tgt = 0.5*np.arccos(np.sqrt(5)/3)
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if (symmaxes[0][0] == 3 and symmaxes[1][0] == 2 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'I'
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# 5-Fold + 2-fold intersecting at 0.5*acos(1/sqrt(5)) -> I
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angle_tgt = 0.5*np.arccos(1/np.sqrt(5))
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if (symmaxes[0][0] == 5 and symmaxes[1][0] == 2 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'I'
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# 5-Fold + 3-fold intersecting at 0.5*acos((4*sqrt(5)-5)/15) -> I
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angle_tgt = 0.5*np.arccos((4*np.sqrt(5)-5)/15)
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if (symmaxes[0][0] == 5 and symmaxes[1][0] == 3 and torch.abs(angle - angle_tgt) < angle_cut):
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symmgroup = 'I'
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else:
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pass
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#fd: we could use a single symmetry here instead.
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# But these cases mostly are bad BIOUNIT annotations...
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#print ('nomatch',angle, [(x,y) for x,_,_,y in symmaxes])
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return symmgroup, subsymm
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def symm_subunit_matrix(symmid):
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if (symmid[0]=='C'):
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nsub = int(symmid[1:])
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symmatrix = (
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torch.arange(nsub)[:,None]-torch.arange(nsub)[None,:]
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)%nsub
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angles = torch.linspace(0,2*np.pi,nsub+1)[:nsub]
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Rs = generateC(angles)
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metasymm = (
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[torch.arange(nsub)],
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[min(3,nsub)]
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)
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if (nsub==1):
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D = 0.0
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else:
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est_radius = 2.0*SYMA
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theta = 2.0*np.pi/nsub
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D = est_radius/np.sin(theta/2)
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offset = torch.tensor([ 0.0,0.0,float(D) ])
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elif (symmid[0]=='D'):
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nsub = int(symmid[1:])
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cblk=(torch.arange(nsub)[:,None]-torch.arange(nsub)[None,:])%nsub
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symmatrix=torch.zeros((2*nsub,2*nsub),dtype=torch.long)
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symmatrix[:nsub,:nsub] = cblk
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symmatrix[:nsub,nsub:] = cblk+nsub
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symmatrix[nsub:,:nsub] = cblk+nsub
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symmatrix[nsub:,nsub:] = cblk
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angles = torch.linspace(0,2*np.pi,nsub+1)[:nsub]
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Rs = generateD(angles)
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metasymm = (
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[torch.arange(nsub), nsub+torch.arange(nsub)],
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[min(3,nsub),2]
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)
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#metasymm = (
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# [torch.arange(2*nsub)],
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# [min(2*nsub,5)]
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#)
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est_radius = 2.0*SYMA
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theta1 = 2.0*np.pi/nsub
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theta2 = np.pi
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D1 = est_radius/np.sin(theta1/2)
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D2 = est_radius/np.sin(theta2/2)
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offset = torch.tensor([ float(D2),0.0,float(D1) ])
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#offset = torch.tensor([ 0.0,0.0,0.0 ])
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elif (symmid=='T'):
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symmatrix=torch.tensor(
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[[ 0, 1, 2, 3, 8, 11, 9, 10, 4, 6, 7, 5],
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[ 1, 0, 3, 2, 9, 10, 8, 11, 5, 7, 6, 4],
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[ 2, 3, 0, 1, 10, 9, 11, 8, 6, 4, 5, 7],
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[ 3, 2, 1, 0, 11, 8, 10, 9, 7, 5, 4, 6],
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[ 4, 6, 7, 5, 0, 1, 2, 3, 8, 11, 9, 10],
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[ 5, 7, 6, 4, 1, 0, 3, 2, 9, 10, 8, 11],
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[ 6, 4, 5, 7, 2, 3, 0, 1, 10, 9, 11, 8],
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[ 7, 5, 4, 6, 3, 2, 1, 0, 11, 8, 10, 9],
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[ 8, 11, 9, 10, 4, 6, 7, 5, 0, 1, 2, 3],
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[ 9, 10, 8, 11, 5, 7, 6, 4, 1, 0, 3, 2],
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[10, 9, 11, 8, 6, 4, 5, 7, 2, 3, 0, 1],
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[11, 8, 10, 9, 7, 5, 4, 6, 3, 2, 1, 0]])
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Rs = torch.zeros(12,3,3)
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Rs[ 0]=torch.tensor([[1.000000,0.000000,0.000000],[0.000000,1.000000,0.000000],[0.000000,0.000000,1.000000]])
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Rs[ 1]=torch.tensor([[-1.000000,0.000000,0.000000],[0.000000,-1.000000,0.000000],[0.000000,0.000000,1.000000]])
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Rs[ 2]=torch.tensor([[-1.000000,0.000000,0.000000],[0.000000,1.000000,0.000000],[0.000000,0.000000,-1.000000]])
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Rs[ 3]=torch.tensor([[1.000000,0.000000,0.000000],[0.000000,-1.000000,0.000000],[0.000000,0.000000,-1.000000]])
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Rs[ 4]=torch.tensor([[0.000000,0.000000,1.000000],[1.000000,0.000000,0.000000],[0.000000,1.000000,0.000000]])
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Rs[ 5]=torch.tensor([[0.000000,0.000000,1.000000],[-1.000000,0.000000,0.000000],[0.000000,-1.000000,0.000000]])
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Rs[ 6]=torch.tensor([[0.000000,0.000000,-1.000000],[-1.000000,0.000000,0.000000],[0.000000,1.000000,0.000000]])
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Rs[ 7]=torch.tensor([[0.000000,0.000000,-1.000000],[1.000000,0.000000,0.000000],[0.000000,-1.000000,0.000000]])
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Rs[ 8]=torch.tensor([[0.000000,1.000000,0.000000],[0.000000,0.000000,1.000000],[1.000000,0.000000,0.000000]])
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Rs[ 9]=torch.tensor([[0.000000,-1.000000,0.000000],[0.000000,0.000000,1.000000],[-1.000000,0.000000,0.000000]])
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Rs[10]=torch.tensor([[0.000000,1.000000,0.000000],[0.000000,0.000000,-1.000000],[-1.000000,0.000000,0.000000]])
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Rs[11]=torch.tensor([[0.000000,-1.000000,0.000000],[0.000000,0.000000,-1.000000],[1.000000,0.000000,0.000000]])
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nneigh = 5
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metasymm = (
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[torch.arange(12)],
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[6]
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)
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est_radius = 4.0*SYMA
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offset = torch.tensor([ 1.0,0.0,0.0 ])
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offset = est_radius * offset / torch.linalg.norm(offset)
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metasymm = (
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[torch.arange(12)],
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[6]
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)
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elif (symmid=='O'):
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symmatrix=torch.tensor(
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[[ 0, 1, 2, 3, 8, 11, 9, 10, 4, 6, 7, 5, 12, 13, 15, 14, 19, 17,
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18, 16, 22, 21, 20, 23],
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[ 1, 0, 3, 2, 9, 10, 8, 11, 5, 7, 6, 4, 13, 12, 14, 15, 18, 16,
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19, 17, 23, 20, 21, 22],
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[ 2, 3, 0, 1, 10, 9, 11, 8, 6, 4, 5, 7, 14, 15, 13, 12, 17, 19,
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16, 18, 20, 23, 22, 21],
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[ 3, 2, 1, 0, 11, 8, 10, 9, 7, 5, 4, 6, 15, 14, 12, 13, 16, 18,
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17, 19, 21, 22, 23, 20],
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[ 4, 6, 7, 5, 0, 1, 2, 3, 8, 11, 9, 10, 16, 18, 17, 19, 21, 22,
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23, 20, 15, 14, 12, 13],
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[ 5, 7, 6, 4, 1, 0, 3, 2, 9, 10, 8, 11, 17, 19, 16, 18, 20, 23,
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22, 21, 14, 15, 13, 12],
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[ 6, 4, 5, 7, 2, 3, 0, 1, 10, 9, 11, 8, 18, 16, 19, 17, 23, 20,
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21, 22, 13, 12, 14, 15],
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[ 7, 5, 4, 6, 3, 2, 1, 0, 11, 8, 10, 9, 19, 17, 18, 16, 22, 21,
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20, 23, 12, 13, 15, 14],
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[ 8, 11, 9, 10, 4, 6, 7, 5, 0, 1, 2, 3, 20, 23, 22, 21, 14, 15,
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13, 12, 17, 19, 16, 18],
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[ 9, 10, 8, 11, 5, 7, 6, 4, 1, 0, 3, 2, 21, 22, 23, 20, 15, 14,
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12, 13, 16, 18, 17, 19],
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[10, 9, 11, 8, 6, 4, 5, 7, 2, 3, 0, 1, 22, 21, 20, 23, 12, 13,
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15, 14, 19, 17, 18, 16],
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[11, 8, 10, 9, 7, 5, 4, 6, 3, 2, 1, 0, 23, 20, 21, 22, 13, 12,
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14, 15, 18, 16, 19, 17],
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[12, 13, 15, 14, 19, 17, 18, 16, 22, 21, 20, 23, 0, 1, 2, 3, 8, 11,
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9, 10, 4, 6, 7, 5],
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[13, 12, 14, 15, 18, 16, 19, 17, 23, 20, 21, 22, 1, 0, 3, 2, 9, 10,
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8, 11, 5, 7, 6, 4],
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[14, 15, 13, 12, 17, 19, 16, 18, 20, 23, 22, 21, 2, 3, 0, 1, 10, 9,
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11, 8, 6, 4, 5, 7],
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[15, 14, 12, 13, 16, 18, 17, 19, 21, 22, 23, 20, 3, 2, 1, 0, 11, 8,
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10, 9, 7, 5, 4, 6],
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[16, 18, 17, 19, 21, 22, 23, 20, 15, 14, 12, 13, 4, 6, 7, 5, 0, 1,
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2, 3, 8, 11, 9, 10],
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[17, 19, 16, 18, 20, 23, 22, 21, 14, 15, 13, 12, 5, 7, 6, 4, 1, 0,
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3, 2, 9, 10, 8, 11],
|
|
[18, 16, 19, 17, 23, 20, 21, 22, 13, 12, 14, 15, 6, 4, 5, 7, 2, 3,
|
|
0, 1, 10, 9, 11, 8],
|
|
[19, 17, 18, 16, 22, 21, 20, 23, 12, 13, 15, 14, 7, 5, 4, 6, 3, 2,
|
|
1, 0, 11, 8, 10, 9],
|
|
[20, 23, 22, 21, 14, 15, 13, 12, 17, 19, 16, 18, 8, 11, 9, 10, 4, 6,
|
|
7, 5, 0, 1, 2, 3],
|
|
[21, 22, 23, 20, 15, 14, 12, 13, 16, 18, 17, 19, 9, 10, 8, 11, 5, 7,
|
|
6, 4, 1, 0, 3, 2],
|
|
[22, 21, 20, 23, 12, 13, 15, 14, 19, 17, 18, 16, 10, 9, 11, 8, 6, 4,
|
|
5, 7, 2, 3, 0, 1],
|
|
[23, 20, 21, 22, 13, 12, 14, 15, 18, 16, 19, 17, 11, 8, 10, 9, 7, 5,
|
|
4, 6, 3, 2, 1, 0]])
|
|
Rs = torch.zeros(24,3,3)
|
|
Rs[0]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[1]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[2]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[3]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[4]=torch.tensor([[ 0.000000, 0.000000,1.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[5]=torch.tensor([[ 0.000000, 0.000000,1.000000],[-1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[6]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[-1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[7]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[8]=torch.tensor([[ 0.000000, 1.000000,0.000000],[ 0.000000, 0.000000,1.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[9]=torch.tensor([[ 0.000000,-1.000000,0.000000],[ 0.000000, 0.000000,1.000000],[-1.000000, 0.000000,0.000000]])
|
|
Rs[10]=torch.tensor([[ 0.000000, 1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[-1.000000, 0.000000,0.000000]])
|
|
Rs[11]=torch.tensor([[ 0.000000,-1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[12]=torch.tensor([[ 0.000000, 1.000000,0.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[13]=torch.tensor([[ 0.000000,-1.000000,0.000000],[-1.000000, 0.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[14]=torch.tensor([[ 0.000000, 1.000000,0.000000],[-1.000000, 0.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[15]=torch.tensor([[ 0.000000,-1.000000,0.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[16]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000, 0.000000,1.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[17]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000, 0.000000,1.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[18]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[19]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[20]=torch.tensor([[ 0.000000, 0.000000,1.000000],[ 0.000000, 1.000000,0.000000],[-1.000000, 0.000000,0.000000]])
|
|
Rs[21]=torch.tensor([[ 0.000000, 0.000000,1.000000],[ 0.000000,-1.000000,0.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[22]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[ 0.000000, 1.000000,0.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[23]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[ 0.000000,-1.000000,0.000000],[-1.000000, 0.000000,0.000000]])
|
|
|
|
est_radius = 6.0*SYMA
|
|
offset = torch.tensor([ 1.0,0.0,0.0 ])
|
|
offset = est_radius * offset / torch.linalg.norm(offset)
|
|
metasymm = (
|
|
[torch.arange(24)],
|
|
[6]
|
|
)
|
|
elif (symmid=='I'):
|
|
symmatrix=torch.tensor(
|
|
[[ 0, 4, 3, 2, 1, 5, 33, 49, 41, 22, 10, 27, 51, 59, 38, 15, 16, 17,
|
|
18, 19, 40, 21, 9, 32, 48, 55, 39, 11, 28, 52, 45, 42, 23, 6, 34, 50,
|
|
58, 37, 14, 26, 20, 8, 31, 47, 44, 30, 46, 43, 24, 7, 35, 12, 29, 53,
|
|
56, 25, 54, 57, 36, 13],
|
|
[ 1, 0, 4, 3, 2, 6, 34, 45, 42, 23, 11, 28, 52, 55, 39, 16, 17, 18,
|
|
19, 15, 41, 22, 5, 33, 49, 56, 35, 12, 29, 53, 46, 43, 24, 7, 30, 51,
|
|
59, 38, 10, 27, 21, 9, 32, 48, 40, 31, 47, 44, 20, 8, 36, 13, 25, 54,
|
|
57, 26, 50, 58, 37, 14],
|
|
[ 2, 1, 0, 4, 3, 7, 30, 46, 43, 24, 12, 29, 53, 56, 35, 17, 18, 19,
|
|
15, 16, 42, 23, 6, 34, 45, 57, 36, 13, 25, 54, 47, 44, 20, 8, 31, 52,
|
|
55, 39, 11, 28, 22, 5, 33, 49, 41, 32, 48, 40, 21, 9, 37, 14, 26, 50,
|
|
58, 27, 51, 59, 38, 10],
|
|
[ 3, 2, 1, 0, 4, 8, 31, 47, 44, 20, 13, 25, 54, 57, 36, 18, 19, 15,
|
|
16, 17, 43, 24, 7, 30, 46, 58, 37, 14, 26, 50, 48, 40, 21, 9, 32, 53,
|
|
56, 35, 12, 29, 23, 6, 34, 45, 42, 33, 49, 41, 22, 5, 38, 10, 27, 51,
|
|
59, 28, 52, 55, 39, 11],
|
|
[ 4, 3, 2, 1, 0, 9, 32, 48, 40, 21, 14, 26, 50, 58, 37, 19, 15, 16,
|
|
17, 18, 44, 20, 8, 31, 47, 59, 38, 10, 27, 51, 49, 41, 22, 5, 33, 54,
|
|
57, 36, 13, 25, 24, 7, 30, 46, 43, 34, 45, 42, 23, 6, 39, 11, 28, 52,
|
|
55, 29, 53, 56, 35, 12],
|
|
[ 5, 33, 49, 41, 22, 0, 4, 3, 2, 1, 15, 16, 17, 18, 19, 10, 27, 51,
|
|
59, 38, 45, 42, 23, 6, 34, 50, 58, 37, 14, 26, 40, 21, 9, 32, 48, 55,
|
|
39, 11, 28, 52, 25, 54, 57, 36, 13, 35, 12, 29, 53, 56, 30, 46, 43, 24,
|
|
7, 20, 8, 31, 47, 44],
|
|
[ 6, 34, 45, 42, 23, 1, 0, 4, 3, 2, 16, 17, 18, 19, 15, 11, 28, 52,
|
|
55, 39, 46, 43, 24, 7, 30, 51, 59, 38, 10, 27, 41, 22, 5, 33, 49, 56,
|
|
35, 12, 29, 53, 26, 50, 58, 37, 14, 36, 13, 25, 54, 57, 31, 47, 44, 20,
|
|
8, 21, 9, 32, 48, 40],
|
|
[ 7, 30, 46, 43, 24, 2, 1, 0, 4, 3, 17, 18, 19, 15, 16, 12, 29, 53,
|
|
56, 35, 47, 44, 20, 8, 31, 52, 55, 39, 11, 28, 42, 23, 6, 34, 45, 57,
|
|
36, 13, 25, 54, 27, 51, 59, 38, 10, 37, 14, 26, 50, 58, 32, 48, 40, 21,
|
|
9, 22, 5, 33, 49, 41],
|
|
[ 8, 31, 47, 44, 20, 3, 2, 1, 0, 4, 18, 19, 15, 16, 17, 13, 25, 54,
|
|
57, 36, 48, 40, 21, 9, 32, 53, 56, 35, 12, 29, 43, 24, 7, 30, 46, 58,
|
|
37, 14, 26, 50, 28, 52, 55, 39, 11, 38, 10, 27, 51, 59, 33, 49, 41, 22,
|
|
5, 23, 6, 34, 45, 42],
|
|
[ 9, 32, 48, 40, 21, 4, 3, 2, 1, 0, 19, 15, 16, 17, 18, 14, 26, 50,
|
|
58, 37, 49, 41, 22, 5, 33, 54, 57, 36, 13, 25, 44, 20, 8, 31, 47, 59,
|
|
38, 10, 27, 51, 29, 53, 56, 35, 12, 39, 11, 28, 52, 55, 34, 45, 42, 23,
|
|
6, 24, 7, 30, 46, 43],
|
|
[10, 27, 51, 59, 38, 15, 16, 17, 18, 19, 0, 4, 3, 2, 1, 5, 33, 49,
|
|
41, 22, 50, 58, 37, 14, 26, 45, 42, 23, 6, 34, 55, 39, 11, 28, 52, 40,
|
|
21, 9, 32, 48, 30, 46, 43, 24, 7, 20, 8, 31, 47, 44, 25, 54, 57, 36,
|
|
13, 35, 12, 29, 53, 56],
|
|
[11, 28, 52, 55, 39, 16, 17, 18, 19, 15, 1, 0, 4, 3, 2, 6, 34, 45,
|
|
42, 23, 51, 59, 38, 10, 27, 46, 43, 24, 7, 30, 56, 35, 12, 29, 53, 41,
|
|
22, 5, 33, 49, 31, 47, 44, 20, 8, 21, 9, 32, 48, 40, 26, 50, 58, 37,
|
|
14, 36, 13, 25, 54, 57],
|
|
[12, 29, 53, 56, 35, 17, 18, 19, 15, 16, 2, 1, 0, 4, 3, 7, 30, 46,
|
|
43, 24, 52, 55, 39, 11, 28, 47, 44, 20, 8, 31, 57, 36, 13, 25, 54, 42,
|
|
23, 6, 34, 45, 32, 48, 40, 21, 9, 22, 5, 33, 49, 41, 27, 51, 59, 38,
|
|
10, 37, 14, 26, 50, 58],
|
|
[13, 25, 54, 57, 36, 18, 19, 15, 16, 17, 3, 2, 1, 0, 4, 8, 31, 47,
|
|
44, 20, 53, 56, 35, 12, 29, 48, 40, 21, 9, 32, 58, 37, 14, 26, 50, 43,
|
|
24, 7, 30, 46, 33, 49, 41, 22, 5, 23, 6, 34, 45, 42, 28, 52, 55, 39,
|
|
11, 38, 10, 27, 51, 59],
|
|
[14, 26, 50, 58, 37, 19, 15, 16, 17, 18, 4, 3, 2, 1, 0, 9, 32, 48,
|
|
40, 21, 54, 57, 36, 13, 25, 49, 41, 22, 5, 33, 59, 38, 10, 27, 51, 44,
|
|
20, 8, 31, 47, 34, 45, 42, 23, 6, 24, 7, 30, 46, 43, 29, 53, 56, 35,
|
|
12, 39, 11, 28, 52, 55],
|
|
[15, 16, 17, 18, 19, 10, 27, 51, 59, 38, 5, 33, 49, 41, 22, 0, 4, 3,
|
|
2, 1, 55, 39, 11, 28, 52, 40, 21, 9, 32, 48, 50, 58, 37, 14, 26, 45,
|
|
42, 23, 6, 34, 35, 12, 29, 53, 56, 25, 54, 57, 36, 13, 20, 8, 31, 47,
|
|
44, 30, 46, 43, 24, 7],
|
|
[16, 17, 18, 19, 15, 11, 28, 52, 55, 39, 6, 34, 45, 42, 23, 1, 0, 4,
|
|
3, 2, 56, 35, 12, 29, 53, 41, 22, 5, 33, 49, 51, 59, 38, 10, 27, 46,
|
|
43, 24, 7, 30, 36, 13, 25, 54, 57, 26, 50, 58, 37, 14, 21, 9, 32, 48,
|
|
40, 31, 47, 44, 20, 8],
|
|
[17, 18, 19, 15, 16, 12, 29, 53, 56, 35, 7, 30, 46, 43, 24, 2, 1, 0,
|
|
4, 3, 57, 36, 13, 25, 54, 42, 23, 6, 34, 45, 52, 55, 39, 11, 28, 47,
|
|
44, 20, 8, 31, 37, 14, 26, 50, 58, 27, 51, 59, 38, 10, 22, 5, 33, 49,
|
|
41, 32, 48, 40, 21, 9],
|
|
[18, 19, 15, 16, 17, 13, 25, 54, 57, 36, 8, 31, 47, 44, 20, 3, 2, 1,
|
|
0, 4, 58, 37, 14, 26, 50, 43, 24, 7, 30, 46, 53, 56, 35, 12, 29, 48,
|
|
40, 21, 9, 32, 38, 10, 27, 51, 59, 28, 52, 55, 39, 11, 23, 6, 34, 45,
|
|
42, 33, 49, 41, 22, 5],
|
|
[19, 15, 16, 17, 18, 14, 26, 50, 58, 37, 9, 32, 48, 40, 21, 4, 3, 2,
|
|
1, 0, 59, 38, 10, 27, 51, 44, 20, 8, 31, 47, 54, 57, 36, 13, 25, 49,
|
|
41, 22, 5, 33, 39, 11, 28, 52, 55, 29, 53, 56, 35, 12, 24, 7, 30, 46,
|
|
43, 34, 45, 42, 23, 6],
|
|
[20, 8, 31, 47, 44, 30, 46, 43, 24, 7, 35, 12, 29, 53, 56, 25, 54, 57,
|
|
36, 13, 0, 4, 3, 2, 1, 5, 33, 49, 41, 22, 10, 27, 51, 59, 38, 15,
|
|
16, 17, 18, 19, 40, 21, 9, 32, 48, 55, 39, 11, 28, 52, 45, 42, 23, 6,
|
|
34, 50, 58, 37, 14, 26],
|
|
[21, 9, 32, 48, 40, 31, 47, 44, 20, 8, 36, 13, 25, 54, 57, 26, 50, 58,
|
|
37, 14, 1, 0, 4, 3, 2, 6, 34, 45, 42, 23, 11, 28, 52, 55, 39, 16,
|
|
17, 18, 19, 15, 41, 22, 5, 33, 49, 56, 35, 12, 29, 53, 46, 43, 24, 7,
|
|
30, 51, 59, 38, 10, 27],
|
|
[22, 5, 33, 49, 41, 32, 48, 40, 21, 9, 37, 14, 26, 50, 58, 27, 51, 59,
|
|
38, 10, 2, 1, 0, 4, 3, 7, 30, 46, 43, 24, 12, 29, 53, 56, 35, 17,
|
|
18, 19, 15, 16, 42, 23, 6, 34, 45, 57, 36, 13, 25, 54, 47, 44, 20, 8,
|
|
31, 52, 55, 39, 11, 28],
|
|
[23, 6, 34, 45, 42, 33, 49, 41, 22, 5, 38, 10, 27, 51, 59, 28, 52, 55,
|
|
39, 11, 3, 2, 1, 0, 4, 8, 31, 47, 44, 20, 13, 25, 54, 57, 36, 18,
|
|
19, 15, 16, 17, 43, 24, 7, 30, 46, 58, 37, 14, 26, 50, 48, 40, 21, 9,
|
|
32, 53, 56, 35, 12, 29],
|
|
[24, 7, 30, 46, 43, 34, 45, 42, 23, 6, 39, 11, 28, 52, 55, 29, 53, 56,
|
|
35, 12, 4, 3, 2, 1, 0, 9, 32, 48, 40, 21, 14, 26, 50, 58, 37, 19,
|
|
15, 16, 17, 18, 44, 20, 8, 31, 47, 59, 38, 10, 27, 51, 49, 41, 22, 5,
|
|
33, 54, 57, 36, 13, 25],
|
|
[25, 54, 57, 36, 13, 35, 12, 29, 53, 56, 30, 46, 43, 24, 7, 20, 8, 31,
|
|
47, 44, 5, 33, 49, 41, 22, 0, 4, 3, 2, 1, 15, 16, 17, 18, 19, 10,
|
|
27, 51, 59, 38, 45, 42, 23, 6, 34, 50, 58, 37, 14, 26, 40, 21, 9, 32,
|
|
48, 55, 39, 11, 28, 52],
|
|
[26, 50, 58, 37, 14, 36, 13, 25, 54, 57, 31, 47, 44, 20, 8, 21, 9, 32,
|
|
48, 40, 6, 34, 45, 42, 23, 1, 0, 4, 3, 2, 16, 17, 18, 19, 15, 11,
|
|
28, 52, 55, 39, 46, 43, 24, 7, 30, 51, 59, 38, 10, 27, 41, 22, 5, 33,
|
|
49, 56, 35, 12, 29, 53],
|
|
[27, 51, 59, 38, 10, 37, 14, 26, 50, 58, 32, 48, 40, 21, 9, 22, 5, 33,
|
|
49, 41, 7, 30, 46, 43, 24, 2, 1, 0, 4, 3, 17, 18, 19, 15, 16, 12,
|
|
29, 53, 56, 35, 47, 44, 20, 8, 31, 52, 55, 39, 11, 28, 42, 23, 6, 34,
|
|
45, 57, 36, 13, 25, 54],
|
|
[28, 52, 55, 39, 11, 38, 10, 27, 51, 59, 33, 49, 41, 22, 5, 23, 6, 34,
|
|
45, 42, 8, 31, 47, 44, 20, 3, 2, 1, 0, 4, 18, 19, 15, 16, 17, 13,
|
|
25, 54, 57, 36, 48, 40, 21, 9, 32, 53, 56, 35, 12, 29, 43, 24, 7, 30,
|
|
46, 58, 37, 14, 26, 50],
|
|
[29, 53, 56, 35, 12, 39, 11, 28, 52, 55, 34, 45, 42, 23, 6, 24, 7, 30,
|
|
46, 43, 9, 32, 48, 40, 21, 4, 3, 2, 1, 0, 19, 15, 16, 17, 18, 14,
|
|
26, 50, 58, 37, 49, 41, 22, 5, 33, 54, 57, 36, 13, 25, 44, 20, 8, 31,
|
|
47, 59, 38, 10, 27, 51],
|
|
[30, 46, 43, 24, 7, 20, 8, 31, 47, 44, 25, 54, 57, 36, 13, 35, 12, 29,
|
|
53, 56, 10, 27, 51, 59, 38, 15, 16, 17, 18, 19, 0, 4, 3, 2, 1, 5,
|
|
33, 49, 41, 22, 50, 58, 37, 14, 26, 45, 42, 23, 6, 34, 55, 39, 11, 28,
|
|
52, 40, 21, 9, 32, 48],
|
|
[31, 47, 44, 20, 8, 21, 9, 32, 48, 40, 26, 50, 58, 37, 14, 36, 13, 25,
|
|
54, 57, 11, 28, 52, 55, 39, 16, 17, 18, 19, 15, 1, 0, 4, 3, 2, 6,
|
|
34, 45, 42, 23, 51, 59, 38, 10, 27, 46, 43, 24, 7, 30, 56, 35, 12, 29,
|
|
53, 41, 22, 5, 33, 49],
|
|
[32, 48, 40, 21, 9, 22, 5, 33, 49, 41, 27, 51, 59, 38, 10, 37, 14, 26,
|
|
50, 58, 12, 29, 53, 56, 35, 17, 18, 19, 15, 16, 2, 1, 0, 4, 3, 7,
|
|
30, 46, 43, 24, 52, 55, 39, 11, 28, 47, 44, 20, 8, 31, 57, 36, 13, 25,
|
|
54, 42, 23, 6, 34, 45],
|
|
[33, 49, 41, 22, 5, 23, 6, 34, 45, 42, 28, 52, 55, 39, 11, 38, 10, 27,
|
|
51, 59, 13, 25, 54, 57, 36, 18, 19, 15, 16, 17, 3, 2, 1, 0, 4, 8,
|
|
31, 47, 44, 20, 53, 56, 35, 12, 29, 48, 40, 21, 9, 32, 58, 37, 14, 26,
|
|
50, 43, 24, 7, 30, 46],
|
|
[34, 45, 42, 23, 6, 24, 7, 30, 46, 43, 29, 53, 56, 35, 12, 39, 11, 28,
|
|
52, 55, 14, 26, 50, 58, 37, 19, 15, 16, 17, 18, 4, 3, 2, 1, 0, 9,
|
|
32, 48, 40, 21, 54, 57, 36, 13, 25, 49, 41, 22, 5, 33, 59, 38, 10, 27,
|
|
51, 44, 20, 8, 31, 47],
|
|
[35, 12, 29, 53, 56, 25, 54, 57, 36, 13, 20, 8, 31, 47, 44, 30, 46, 43,
|
|
24, 7, 15, 16, 17, 18, 19, 10, 27, 51, 59, 38, 5, 33, 49, 41, 22, 0,
|
|
4, 3, 2, 1, 55, 39, 11, 28, 52, 40, 21, 9, 32, 48, 50, 58, 37, 14,
|
|
26, 45, 42, 23, 6, 34],
|
|
[36, 13, 25, 54, 57, 26, 50, 58, 37, 14, 21, 9, 32, 48, 40, 31, 47, 44,
|
|
20, 8, 16, 17, 18, 19, 15, 11, 28, 52, 55, 39, 6, 34, 45, 42, 23, 1,
|
|
0, 4, 3, 2, 56, 35, 12, 29, 53, 41, 22, 5, 33, 49, 51, 59, 38, 10,
|
|
27, 46, 43, 24, 7, 30],
|
|
[37, 14, 26, 50, 58, 27, 51, 59, 38, 10, 22, 5, 33, 49, 41, 32, 48, 40,
|
|
21, 9, 17, 18, 19, 15, 16, 12, 29, 53, 56, 35, 7, 30, 46, 43, 24, 2,
|
|
1, 0, 4, 3, 57, 36, 13, 25, 54, 42, 23, 6, 34, 45, 52, 55, 39, 11,
|
|
28, 47, 44, 20, 8, 31],
|
|
[38, 10, 27, 51, 59, 28, 52, 55, 39, 11, 23, 6, 34, 45, 42, 33, 49, 41,
|
|
22, 5, 18, 19, 15, 16, 17, 13, 25, 54, 57, 36, 8, 31, 47, 44, 20, 3,
|
|
2, 1, 0, 4, 58, 37, 14, 26, 50, 43, 24, 7, 30, 46, 53, 56, 35, 12,
|
|
29, 48, 40, 21, 9, 32],
|
|
[39, 11, 28, 52, 55, 29, 53, 56, 35, 12, 24, 7, 30, 46, 43, 34, 45, 42,
|
|
23, 6, 19, 15, 16, 17, 18, 14, 26, 50, 58, 37, 9, 32, 48, 40, 21, 4,
|
|
3, 2, 1, 0, 59, 38, 10, 27, 51, 44, 20, 8, 31, 47, 54, 57, 36, 13,
|
|
25, 49, 41, 22, 5, 33],
|
|
[40, 21, 9, 32, 48, 55, 39, 11, 28, 52, 45, 42, 23, 6, 34, 50, 58, 37,
|
|
14, 26, 20, 8, 31, 47, 44, 30, 46, 43, 24, 7, 35, 12, 29, 53, 56, 25,
|
|
54, 57, 36, 13, 0, 4, 3, 2, 1, 5, 33, 49, 41, 22, 10, 27, 51, 59,
|
|
38, 15, 16, 17, 18, 19],
|
|
[41, 22, 5, 33, 49, 56, 35, 12, 29, 53, 46, 43, 24, 7, 30, 51, 59, 38,
|
|
10, 27, 21, 9, 32, 48, 40, 31, 47, 44, 20, 8, 36, 13, 25, 54, 57, 26,
|
|
50, 58, 37, 14, 1, 0, 4, 3, 2, 6, 34, 45, 42, 23, 11, 28, 52, 55,
|
|
39, 16, 17, 18, 19, 15],
|
|
[42, 23, 6, 34, 45, 57, 36, 13, 25, 54, 47, 44, 20, 8, 31, 52, 55, 39,
|
|
11, 28, 22, 5, 33, 49, 41, 32, 48, 40, 21, 9, 37, 14, 26, 50, 58, 27,
|
|
51, 59, 38, 10, 2, 1, 0, 4, 3, 7, 30, 46, 43, 24, 12, 29, 53, 56,
|
|
35, 17, 18, 19, 15, 16],
|
|
[43, 24, 7, 30, 46, 58, 37, 14, 26, 50, 48, 40, 21, 9, 32, 53, 56, 35,
|
|
12, 29, 23, 6, 34, 45, 42, 33, 49, 41, 22, 5, 38, 10, 27, 51, 59, 28,
|
|
52, 55, 39, 11, 3, 2, 1, 0, 4, 8, 31, 47, 44, 20, 13, 25, 54, 57,
|
|
36, 18, 19, 15, 16, 17],
|
|
[44, 20, 8, 31, 47, 59, 38, 10, 27, 51, 49, 41, 22, 5, 33, 54, 57, 36,
|
|
13, 25, 24, 7, 30, 46, 43, 34, 45, 42, 23, 6, 39, 11, 28, 52, 55, 29,
|
|
53, 56, 35, 12, 4, 3, 2, 1, 0, 9, 32, 48, 40, 21, 14, 26, 50, 58,
|
|
37, 19, 15, 16, 17, 18],
|
|
[45, 42, 23, 6, 34, 50, 58, 37, 14, 26, 40, 21, 9, 32, 48, 55, 39, 11,
|
|
28, 52, 25, 54, 57, 36, 13, 35, 12, 29, 53, 56, 30, 46, 43, 24, 7, 20,
|
|
8, 31, 47, 44, 5, 33, 49, 41, 22, 0, 4, 3, 2, 1, 15, 16, 17, 18,
|
|
19, 10, 27, 51, 59, 38],
|
|
[46, 43, 24, 7, 30, 51, 59, 38, 10, 27, 41, 22, 5, 33, 49, 56, 35, 12,
|
|
29, 53, 26, 50, 58, 37, 14, 36, 13, 25, 54, 57, 31, 47, 44, 20, 8, 21,
|
|
9, 32, 48, 40, 6, 34, 45, 42, 23, 1, 0, 4, 3, 2, 16, 17, 18, 19,
|
|
15, 11, 28, 52, 55, 39],
|
|
[47, 44, 20, 8, 31, 52, 55, 39, 11, 28, 42, 23, 6, 34, 45, 57, 36, 13,
|
|
25, 54, 27, 51, 59, 38, 10, 37, 14, 26, 50, 58, 32, 48, 40, 21, 9, 22,
|
|
5, 33, 49, 41, 7, 30, 46, 43, 24, 2, 1, 0, 4, 3, 17, 18, 19, 15,
|
|
16, 12, 29, 53, 56, 35],
|
|
[48, 40, 21, 9, 32, 53, 56, 35, 12, 29, 43, 24, 7, 30, 46, 58, 37, 14,
|
|
26, 50, 28, 52, 55, 39, 11, 38, 10, 27, 51, 59, 33, 49, 41, 22, 5, 23,
|
|
6, 34, 45, 42, 8, 31, 47, 44, 20, 3, 2, 1, 0, 4, 18, 19, 15, 16,
|
|
17, 13, 25, 54, 57, 36],
|
|
[49, 41, 22, 5, 33, 54, 57, 36, 13, 25, 44, 20, 8, 31, 47, 59, 38, 10,
|
|
27, 51, 29, 53, 56, 35, 12, 39, 11, 28, 52, 55, 34, 45, 42, 23, 6, 24,
|
|
7, 30, 46, 43, 9, 32, 48, 40, 21, 4, 3, 2, 1, 0, 19, 15, 16, 17,
|
|
18, 14, 26, 50, 58, 37],
|
|
[50, 58, 37, 14, 26, 45, 42, 23, 6, 34, 55, 39, 11, 28, 52, 40, 21, 9,
|
|
32, 48, 30, 46, 43, 24, 7, 20, 8, 31, 47, 44, 25, 54, 57, 36, 13, 35,
|
|
12, 29, 53, 56, 10, 27, 51, 59, 38, 15, 16, 17, 18, 19, 0, 4, 3, 2,
|
|
1, 5, 33, 49, 41, 22],
|
|
[51, 59, 38, 10, 27, 46, 43, 24, 7, 30, 56, 35, 12, 29, 53, 41, 22, 5,
|
|
33, 49, 31, 47, 44, 20, 8, 21, 9, 32, 48, 40, 26, 50, 58, 37, 14, 36,
|
|
13, 25, 54, 57, 11, 28, 52, 55, 39, 16, 17, 18, 19, 15, 1, 0, 4, 3,
|
|
2, 6, 34, 45, 42, 23],
|
|
[52, 55, 39, 11, 28, 47, 44, 20, 8, 31, 57, 36, 13, 25, 54, 42, 23, 6,
|
|
34, 45, 32, 48, 40, 21, 9, 22, 5, 33, 49, 41, 27, 51, 59, 38, 10, 37,
|
|
14, 26, 50, 58, 12, 29, 53, 56, 35, 17, 18, 19, 15, 16, 2, 1, 0, 4,
|
|
3, 7, 30, 46, 43, 24],
|
|
[53, 56, 35, 12, 29, 48, 40, 21, 9, 32, 58, 37, 14, 26, 50, 43, 24, 7,
|
|
30, 46, 33, 49, 41, 22, 5, 23, 6, 34, 45, 42, 28, 52, 55, 39, 11, 38,
|
|
10, 27, 51, 59, 13, 25, 54, 57, 36, 18, 19, 15, 16, 17, 3, 2, 1, 0,
|
|
4, 8, 31, 47, 44, 20],
|
|
[54, 57, 36, 13, 25, 49, 41, 22, 5, 33, 59, 38, 10, 27, 51, 44, 20, 8,
|
|
31, 47, 34, 45, 42, 23, 6, 24, 7, 30, 46, 43, 29, 53, 56, 35, 12, 39,
|
|
11, 28, 52, 55, 14, 26, 50, 58, 37, 19, 15, 16, 17, 18, 4, 3, 2, 1,
|
|
0, 9, 32, 48, 40, 21],
|
|
[55, 39, 11, 28, 52, 40, 21, 9, 32, 48, 50, 58, 37, 14, 26, 45, 42, 23,
|
|
6, 34, 35, 12, 29, 53, 56, 25, 54, 57, 36, 13, 20, 8, 31, 47, 44, 30,
|
|
46, 43, 24, 7, 15, 16, 17, 18, 19, 10, 27, 51, 59, 38, 5, 33, 49, 41,
|
|
22, 0, 4, 3, 2, 1],
|
|
[56, 35, 12, 29, 53, 41, 22, 5, 33, 49, 51, 59, 38, 10, 27, 46, 43, 24,
|
|
7, 30, 36, 13, 25, 54, 57, 26, 50, 58, 37, 14, 21, 9, 32, 48, 40, 31,
|
|
47, 44, 20, 8, 16, 17, 18, 19, 15, 11, 28, 52, 55, 39, 6, 34, 45, 42,
|
|
23, 1, 0, 4, 3, 2],
|
|
[57, 36, 13, 25, 54, 42, 23, 6, 34, 45, 52, 55, 39, 11, 28, 47, 44, 20,
|
|
8, 31, 37, 14, 26, 50, 58, 27, 51, 59, 38, 10, 22, 5, 33, 49, 41, 32,
|
|
48, 40, 21, 9, 17, 18, 19, 15, 16, 12, 29, 53, 56, 35, 7, 30, 46, 43,
|
|
24, 2, 1, 0, 4, 3],
|
|
[58, 37, 14, 26, 50, 43, 24, 7, 30, 46, 53, 56, 35, 12, 29, 48, 40, 21,
|
|
9, 32, 38, 10, 27, 51, 59, 28, 52, 55, 39, 11, 23, 6, 34, 45, 42, 33,
|
|
49, 41, 22, 5, 18, 19, 15, 16, 17, 13, 25, 54, 57, 36, 8, 31, 47, 44,
|
|
20, 3, 2, 1, 0, 4],
|
|
[59, 38, 10, 27, 51, 44, 20, 8, 31, 47, 54, 57, 36, 13, 25, 49, 41, 22,
|
|
5, 33, 39, 11, 28, 52, 55, 29, 53, 56, 35, 12, 24, 7, 30, 46, 43, 34,
|
|
45, 42, 23, 6, 19, 15, 16, 17, 18, 14, 26, 50, 58, 37, 9, 32, 48, 40,
|
|
21, 4, 3, 2, 1, 0]])
|
|
Rs = torch.zeros(60,3,3)
|
|
Rs[0]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[1]=torch.tensor([[ 0.500000,-0.809017,0.309017],[ 0.809017 ,0.309017,-0.500000],[ 0.309017, 0.500000,0.809017]])
|
|
Rs[2]=torch.tensor([[-0.309017,-0.500000,0.809017],[ 0.500000,-0.809017,-0.309017],[ 0.809017, 0.309017,0.500000]])
|
|
Rs[3]=torch.tensor([[-0.309017, 0.500000,0.809017],[-0.500000,-0.809017,0.309017],[ 0.809017,-0.309017,0.500000]])
|
|
Rs[4]=torch.tensor([[ 0.500000, 0.809017,0.309017],[-0.809017, 0.309017,0.500000],[ 0.309017,-0.500000,0.809017]])
|
|
Rs[5]=torch.tensor([[-0.809017, 0.309017,0.500000],[ 0.309017,-0.500000,0.809017],[ 0.500000, 0.809017,0.309017]])
|
|
Rs[6]=torch.tensor([[ 0.000000, 1.000000,0.000000],[ 0.000000, 0.000000,1.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[7]=torch.tensor([[ 0.809017 ,0.309017,-0.500000],[ 0.309017, 0.500000,0.809017],[ 0.500000,-0.809017,0.309017]])
|
|
Rs[8]=torch.tensor([[ 0.500000,-0.809017,-0.309017],[ 0.809017, 0.309017,0.500000],[-0.309017,-0.500000,0.809017]])
|
|
Rs[9]=torch.tensor([[-0.500000,-0.809017,0.309017],[ 0.809017,-0.309017,0.500000],[-0.309017, 0.500000,0.809017]])
|
|
Rs[10]=torch.tensor([[-0.500000,-0.809017,0.309017],[-0.809017 ,0.309017,-0.500000],[ 0.309017,-0.500000,-0.809017]])
|
|
Rs[11]=torch.tensor([[-0.809017, 0.309017,0.500000],[-0.309017 ,0.500000,-0.809017],[-0.500000,-0.809017,-0.309017]])
|
|
Rs[12]=torch.tensor([[ 0.000000, 1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[-1.000000, 0.000000,0.000000]])
|
|
Rs[13]=torch.tensor([[ 0.809017 ,0.309017,-0.500000],[-0.309017,-0.500000,-0.809017],[-0.500000 ,0.809017,-0.309017]])
|
|
Rs[14]=torch.tensor([[ 0.500000,-0.809017,-0.309017],[-0.809017,-0.309017,-0.500000],[ 0.309017 ,0.500000,-0.809017]])
|
|
Rs[15]=torch.tensor([[ 0.309017 ,0.500000,-0.809017],[ 0.500000,-0.809017,-0.309017],[-0.809017,-0.309017,-0.500000]])
|
|
Rs[16]=torch.tensor([[ 0.309017,-0.500000,-0.809017],[-0.500000,-0.809017,0.309017],[-0.809017 ,0.309017,-0.500000]])
|
|
Rs[17]=torch.tensor([[-0.500000,-0.809017,-0.309017],[-0.809017, 0.309017,0.500000],[-0.309017 ,0.500000,-0.809017]])
|
|
Rs[18]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[19]=torch.tensor([[-0.500000 ,0.809017,-0.309017],[ 0.809017 ,0.309017,-0.500000],[-0.309017,-0.500000,-0.809017]])
|
|
Rs[20]=torch.tensor([[-0.500000,-0.809017,-0.309017],[ 0.809017,-0.309017,-0.500000],[ 0.309017,-0.500000,0.809017]])
|
|
Rs[21]=torch.tensor([[-1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000],[ 0.000000, 0.000000,1.000000]])
|
|
Rs[22]=torch.tensor([[-0.500000 ,0.809017,-0.309017],[-0.809017,-0.309017,0.500000],[ 0.309017, 0.500000,0.809017]])
|
|
Rs[23]=torch.tensor([[ 0.309017 ,0.500000,-0.809017],[-0.500000, 0.809017,0.309017],[ 0.809017, 0.309017,0.500000]])
|
|
Rs[24]=torch.tensor([[ 0.309017,-0.500000,-0.809017],[ 0.500000 ,0.809017,-0.309017],[ 0.809017,-0.309017,0.500000]])
|
|
Rs[25]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[-1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[26]=torch.tensor([[-0.309017,-0.500000,-0.809017],[-0.500000 ,0.809017,-0.309017],[ 0.809017 ,0.309017,-0.500000]])
|
|
Rs[27]=torch.tensor([[-0.809017,-0.309017,-0.500000],[ 0.309017 ,0.500000,-0.809017],[ 0.500000,-0.809017,-0.309017]])
|
|
Rs[28]=torch.tensor([[-0.809017 ,0.309017,-0.500000],[ 0.309017,-0.500000,-0.809017],[-0.500000,-0.809017,0.309017]])
|
|
Rs[29]=torch.tensor([[-0.309017 ,0.500000,-0.809017],[-0.500000,-0.809017,-0.309017],[-0.809017, 0.309017,0.500000]])
|
|
Rs[30]=torch.tensor([[ 0.809017, 0.309017,0.500000],[-0.309017,-0.500000,0.809017],[ 0.500000,-0.809017,-0.309017]])
|
|
Rs[31]=torch.tensor([[ 0.809017,-0.309017,0.500000],[-0.309017, 0.500000,0.809017],[-0.500000,-0.809017,0.309017]])
|
|
Rs[32]=torch.tensor([[ 0.309017,-0.500000,0.809017],[ 0.500000, 0.809017,0.309017],[-0.809017, 0.309017,0.500000]])
|
|
Rs[33]=torch.tensor([[ 0.000000, 0.000000,1.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000, 1.000000,0.000000]])
|
|
Rs[34]=torch.tensor([[ 0.309017, 0.500000,0.809017],[ 0.500000,-0.809017,0.309017],[ 0.809017 ,0.309017,-0.500000]])
|
|
Rs[35]=torch.tensor([[-0.309017, 0.500000,0.809017],[ 0.500000 ,0.809017,-0.309017],[-0.809017 ,0.309017,-0.500000]])
|
|
Rs[36]=torch.tensor([[ 0.500000, 0.809017,0.309017],[ 0.809017,-0.309017,-0.500000],[-0.309017 ,0.500000,-0.809017]])
|
|
Rs[37]=torch.tensor([[ 1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000]])
|
|
Rs[38]=torch.tensor([[ 0.500000,-0.809017,0.309017],[-0.809017,-0.309017,0.500000],[-0.309017,-0.500000,-0.809017]])
|
|
Rs[39]=torch.tensor([[-0.309017,-0.500000,0.809017],[-0.500000, 0.809017,0.309017],[-0.809017,-0.309017,-0.500000]])
|
|
Rs[40]=torch.tensor([[-0.500000, 0.809017,0.309017],[-0.809017,-0.309017,-0.500000],[-0.309017,-0.500000,0.809017]])
|
|
Rs[41]=torch.tensor([[ 0.500000 ,0.809017,-0.309017],[-0.809017 ,0.309017,-0.500000],[-0.309017, 0.500000,0.809017]])
|
|
Rs[42]=torch.tensor([[ 0.809017,-0.309017,-0.500000],[-0.309017 ,0.500000,-0.809017],[ 0.500000, 0.809017,0.309017]])
|
|
Rs[43]=torch.tensor([[ 0.000000,-1.000000,0.000000],[ 0.000000 ,0.000000,-1.000000],[ 1.000000, 0.000000,0.000000]])
|
|
Rs[44]=torch.tensor([[-0.809017,-0.309017,0.500000],[-0.309017,-0.500000,-0.809017],[ 0.500000,-0.809017,0.309017]])
|
|
Rs[45]=torch.tensor([[ 0.809017,-0.309017,0.500000],[ 0.309017,-0.500000,-0.809017],[ 0.500000 ,0.809017,-0.309017]])
|
|
Rs[46]=torch.tensor([[ 0.309017,-0.500000,0.809017],[-0.500000,-0.809017,-0.309017],[ 0.809017,-0.309017,-0.500000]])
|
|
Rs[47]=torch.tensor([[ 0.000000, 0.000000,1.000000],[-1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[48]=torch.tensor([[ 0.309017, 0.500000,0.809017],[-0.500000 ,0.809017,-0.309017],[-0.809017,-0.309017,0.500000]])
|
|
Rs[49]=torch.tensor([[ 0.809017, 0.309017,0.500000],[ 0.309017 ,0.500000,-0.809017],[-0.500000, 0.809017,0.309017]])
|
|
Rs[50]=torch.tensor([[-0.309017 ,0.500000,-0.809017],[ 0.500000, 0.809017,0.309017],[ 0.809017,-0.309017,-0.500000]])
|
|
Rs[51]=torch.tensor([[ 0.000000 ,0.000000,-1.000000],[ 1.000000, 0.000000,0.000000],[ 0.000000,-1.000000,0.000000]])
|
|
Rs[52]=torch.tensor([[-0.309017,-0.500000,-0.809017],[ 0.500000,-0.809017,0.309017],[-0.809017,-0.309017,0.500000]])
|
|
Rs[53]=torch.tensor([[-0.809017,-0.309017,-0.500000],[-0.309017,-0.500000,0.809017],[-0.500000, 0.809017,0.309017]])
|
|
Rs[54]=torch.tensor([[-0.809017 ,0.309017,-0.500000],[-0.309017, 0.500000,0.809017],[ 0.500000 ,0.809017,-0.309017]])
|
|
Rs[55]=torch.tensor([[ 0.000000,-1.000000,0.000000],[ 0.000000, 0.000000,1.000000],[-1.000000, 0.000000,0.000000]])
|
|
Rs[56]=torch.tensor([[-0.809017,-0.309017,0.500000],[ 0.309017, 0.500000,0.809017],[-0.500000 ,0.809017,-0.309017]])
|
|
Rs[57]=torch.tensor([[-0.500000, 0.809017,0.309017],[ 0.809017, 0.309017,0.500000],[ 0.309017 ,0.500000,-0.809017]])
|
|
Rs[58]=torch.tensor([[ 0.500000 ,0.809017,-0.309017],[ 0.809017,-0.309017,0.500000],[ 0.309017,-0.500000,-0.809017]])
|
|
Rs[59]=torch.tensor([[ 0.809017,-0.309017,-0.500000],[ 0.309017,-0.500000,0.809017],[-0.500000,-0.809017,-0.309017]])
|
|
|
|
est_radius = 10.0*SYMA
|
|
offset = torch.tensor([ 1.0,0.0,0.0 ])
|
|
offset = est_radius * offset / torch.linalg.norm(offset)
|
|
metasymm = (
|
|
[torch.arange(60)],
|
|
[6]
|
|
)
|
|
else:
|
|
print ("Unknown symmetry",symmid)
|
|
assert False
|
|
|
|
return symmatrix,Rs,metasymm,offset |