hex lattice mode svd to separate function
Former-commit-id: dddd45e135bce176863e70a2256b9906575b9aa8
This commit is contained in:
Marek Nečada
parent
f41caf6203
commit
c1db33fcf6
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@ -301,116 +301,17 @@ klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
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kxmaplist = np.concatenate((np.array([0]),np.cumsum(np.linalg.norm(np.diff(klist, axis=0), axis=-1))))
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'''
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klist = qpms.generate_trianglepoints(kdensity, v3d=True, include_origin=True)*3*math.pi/(3*kdensity*hexside)
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TMatrices_om = TMatrices_interp(freq)
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# In[ ]:
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n2id = np.identity(2*nelem)
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n2id.shape = (2,nelem,2,nelem)
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nan = float('nan')
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filecount = 0
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for one in (1,):
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omega = freq # from args; k_0 * c / math.sqrt(epsilon_b)
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k_0 = omega * math.sqrt(epsilon_b) / c
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tdic = qpms.hexlattice_get_AB(lMax,k_0*hexside,maxlayer)
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#print(filecount, omega/eV*hbar)
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#sys.stdout.flush()
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a_self = tdic['a_self'][:,:nelem,:nelem]
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b_self = tdic['b_self'][:,:nelem,:nelem]
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a_u2d = tdic['a_u2d'][:,:nelem,:nelem]
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b_u2d = tdic['b_u2d'][:,:nelem,:nelem]
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a_d2u = tdic['a_d2u'][:,:nelem,:nelem]
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b_d2u = tdic['b_d2u'][:,:nelem,:nelem]
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unitcell_translations = tdic['self_tr']*hexside*s3
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u2d_translations = tdic['u2d_tr']*hexside*s3
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d2u_translations = tdic['d2u_tr']*hexside*s3
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if gaussianSigma:
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unitcell_envelope = np.exp(-np.sum(tdic['self_tr']**2,axis=-1)/(2*gaussianSigma**2))
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u2d_envelope = np.exp(-np.sum(tdic['u2d_tr']**2,axis=-1)/(2*gaussianSigma**2))
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d2u_envelope = np.exp(-np.sum(tdic['d2u_tr']**2,axis=-1)/(2*gaussianSigma**2))
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TMatrices_om = TMatrices_interp(omega)
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if svdout:
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svUfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svVfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svSfullTElist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
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svUfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svVfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svSfullTMlist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
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minsvTElist = np.full((klist.shape[0], svn),np.nan)
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minsvTMlist = np.full((klist.shape[0], svn),np.nan)
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leftmatrixlist = np.full((klist.shape[0],2,2,nelem,2,2,nelem),np.nan,dtype=complex)
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isNaNlist = np.zeros((klist.shape[0]), dtype=bool)
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# sem nějaká rozumná smyčka
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for ki in range(klist.shape[0]):
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k = klist[ki]
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if (k_0*k_0 - k[0]*k[0] - k[1]*k[1] < 0):
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isNaNlist[ki] = True
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continue
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phases_self = np.exp(1j*np.tensordot(k,unitcell_translations,axes=(0,-1)))
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phases_u2d = np.exp(1j*np.tensordot(k,u2d_translations,axes=(0,-1)))
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phases_d2u = np.exp(1j*np.tensordot(k,d2u_translations,axes=(0,-1)))
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if gaussianSigma:
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phases_self *= unitcell_envelope
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phases_u2d *= u2d_envelope
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phases_d2u *= d2u_envelope
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leftmatrix = np.zeros((2,2,nelem, 2,2,nelem), dtype=complex)
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# 0: u,E<--u,E
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# 1: d,M<--d,M
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leftmatrix[0,0,:,0,0,:] = np.tensordot(a_self,phases_self, axes=(0,-1)) # u2u, E2E
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leftmatrix[1,0,:,1,0,:] = leftmatrix[0,0,:,0,0,:] # d2d, E2E
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leftmatrix[0,1,:,0,1,:] = leftmatrix[0,0,:,0,0,:] # u2u, M2M
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leftmatrix[1,1,:,1,1,:] = leftmatrix[0,0,:,0,0,:] # d2d, M2M
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leftmatrix[0,0,:,0,1,:] = np.tensordot(b_self,phases_self, axes=(0,-1)) # u2u, M2E
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leftmatrix[0,1,:,0,0,:] = leftmatrix[0,0,:,0,1,:] # u2u, E2M
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leftmatrix[1,1,:,1,0,:] = leftmatrix[0,0,:,0,1,:] # d2d, E2M
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leftmatrix[1,0,:,1,1,:] = leftmatrix[0,0,:,0,1,:] # d2d, M2E
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leftmatrix[0,0,:,1,0,:] = np.tensordot(a_d2u, phases_d2u,axes=(0,-1)) #d2u,E2E
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leftmatrix[0,1,:,1,1,:] = leftmatrix[0,0,:,1,0,:] #d2u, M2M
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leftmatrix[1,0,:,0,0,:] = np.tensordot(a_u2d, phases_u2d,axes=(0,-1)) #u2d,E2E
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leftmatrix[1,1,:,0,1,:] = leftmatrix[1,0,:,0,0,:] #u2d, M2M
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leftmatrix[0,0,:,1,1,:] = np.tensordot(b_d2u, phases_d2u,axes=(0,-1)) #d2u,M2E
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leftmatrix[0,1,:,1,0,:] = leftmatrix[0,0,:,1,1,:] #d2u, E2M
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leftmatrix[1,0,:,0,1,:] = np.tensordot(b_u2d, phases_u2d,axes=(0,-1)) #u2d,M2E
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leftmatrix[1,1,:,0,0,:] = leftmatrix[1,0,:,0,1,:] #u2d, E2M
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#leftmatrix is now the translation matrix T
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for j in range(2):
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leftmatrix[j] = -np.tensordot(TMatrices_om[j], leftmatrix[j], axes=([-2,-1],[0,1]))
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# at this point, jth row of leftmatrix is that of -MT
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leftmatrix[j,:,:,j,:,:] += n2id
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#now we are done, 1-MT
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leftmatrixlist[ki] = leftmatrix
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svdres = hexlattice_zsym_getSVD(TMatrices_om=TMatrices_om, epsilon_b=epsilon_b, hexside=hexside, maxlayer=maxlayer,
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omega=freq, klist=klist, gaussianSigma=gaussianSigma, onlyNmin=(0 if svdout else svn))
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if svdout:
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((svUfullTElist, svSfullTElist, svVfullTElist), (svUfullTMlist, svSfullTMlist, svVfullTMlist)) = svdres
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(minsvElist, minsvTMlist) = (svSfullTElist[...,-svn:], svSfullTMlist[...,-svn:])
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else:
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minsvTElist, minsvTMlist = svdres
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nnlist = np.logical_not(isNaNlist)
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leftmatrixlist_s = np.reshape(leftmatrixlist,(klist.shape[0], 2*2*nelem,2*2*nelem))[nnlist]
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leftmatrixlist_TE = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TEč,TEč)]
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leftmatrixlist_TM = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TMč,TMč)]
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#svarr = np.linalg.svd(leftmatrixlist_TE, compute_uv=False)
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#argsortlist = np.argsort(svarr, axis=-1)[...,:svn]
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#minsvTElist[nnlist] = svarr[...,argsortlist]
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#minsvTElist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TE, compute_uv=False), axis=-1)
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if svdout:
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svUfullTElist[nnlist], svSfullTElist[nnlist], svVfullTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=True)
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svUfullTMlist[nnlist], svSfullTMlist[nnlist], svVfullTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=True)
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minsvTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=False)[...,-svn:]
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#svarr = np.linalg.svd(leftmatrixlist_TM, compute_uv=False)
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#argsortlist = np.argsort(svarr, axis=-1)[...,:svn]
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#minsvTMlist[nnlist] = svarr[...,argsortlist]
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#minsvTMlist[nnlist] = np.amin(np.linalg.svd(leftmatrixlist_TM, compute_uv=False), axis=-1)
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minsvTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=False)[...,-svn:]
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'''
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omlist = np.broadcast_to(omegalist[:,nx], minsvTElistarr[...,0].shape)
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kxmlarr = np.broadcast_to(kxmaplist[nx,:], minsvTElistarr[...,0].shape)
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klist = np.concatenate((k0Mlist,kMK1list,kK10list,k0K2list,kK2Mlist), axis=0)
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'''
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''' The new pretty diffracted order drawing '''
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maxlayer_reciprocal=4
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@ -436,3 +436,99 @@ def hexlattice_get_AB(lMax, k_hexside, maxlayer, circular=True, return_points =
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return d
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def hexlattice_zsym_getSVD(TMatrices_om, epsilon_b, hexside, maxlayer, omega, klist, gaussianSigma=False, onlyNmin=0):
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n2id = np.identity(2*nelem)
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n2id.shape = (2,nelem,2,nelem)
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nan = float('nan')
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k_0 = omega * math.sqrt(epsilon_b) / c
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tdic = qpms.hexlattice_get_AB(lMax,k_0*hexside,maxlayer)
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a_self = tdic['a_self'][:,:nelem,:nelem]
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b_self = tdic['b_self'][:,:nelem,:nelem]
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a_u2d = tdic['a_u2d'][:,:nelem,:nelem]
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b_u2d = tdic['b_u2d'][:,:nelem,:nelem]
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a_d2u = tdic['a_d2u'][:,:nelem,:nelem]
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b_d2u = tdic['b_d2u'][:,:nelem,:nelem]
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unitcell_translations = tdic['self_tr']*hexside*s3
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u2d_translations = tdic['u2d_tr']*hexside*s3
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d2u_translations = tdic['d2u_tr']*hexside*s3
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if gaussianSigma:
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unitcell_envelope = np.exp(-np.sum(tdic['self_tr']**2,axis=-1)/(2*gaussianSigma**2))
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u2d_envelope = np.exp(-np.sum(tdic['u2d_tr']**2,axis=-1)/(2*gaussianSigma**2))
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d2u_envelope = np.exp(-np.sum(tdic['d2u_tr']**2,axis=-1)/(2*gaussianSigma**2))
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#TMatrices_om = TMatrices_interp(omega)
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if(not onlyNmin):
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svUfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svVfullTElist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svSfullTElist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
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svUfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svVfullTMlist = np.full((klist.shape[0], 2*nelem, 2*nelem), np.nan, dtype=complex)
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svSfullTMlist = np.full((klist.shape[0], 2*nelem), np.nan, dtype=complex)
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else:
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minsvTElist = np.full((klist.shape[0], onlyNmin),np.nan)
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minsvTMlist = np.full((klist.shape[0], onlyNmin),np.nan)
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leftmatrixlist = np.full((klist.shape[0],2,2,nelem,2,2,nelem),np.nan,dtype=complex)
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isNaNlist = np.zeros((klist.shape[0]), dtype=bool)
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# sem nějaká rozumná smyčka
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for ki in range(klist.shape[0]):
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k = klist[ki]
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if (k_0*k_0 - k[0]*k[0] - k[1]*k[1] < 0):
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isNaNlist[ki] = True
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continue
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phases_self = np.exp(1j*np.tensordot(k,unitcell_translations,axes=(0,-1)))
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phases_u2d = np.exp(1j*np.tensordot(k,u2d_translations,axes=(0,-1)))
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phases_d2u = np.exp(1j*np.tensordot(k,d2u_translations,axes=(0,-1)))
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if gaussianSigma:
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phases_self *= unitcell_envelope
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phases_u2d *= u2d_envelope
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phases_d2u *= d2u_envelope
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leftmatrix = np.zeros((2,2,nelem, 2,2,nelem), dtype=complex)
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# 0:[u,E<--u,E ]
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# 1:[d,M<--d,M ]
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leftmatrix[0,0,:,0,0,:] = np.tensordot(a_self,phases_self, axes=(0,-1)) # u2u, E2E
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leftmatrix[1,0,:,1,0,:] = leftmatrix[0,0,:,0,0,:] # d2d, E2E
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leftmatrix[0,1,:,0,1,:] = leftmatrix[0,0,:,0,0,:] # u2u, M2M
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leftmatrix[1,1,:,1,1,:] = leftmatrix[0,0,:,0,0,:] # d2d, M2M
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leftmatrix[0,0,:,0,1,:] = np.tensordot(b_self,phases_self, axes=(0,-1)) # u2u, M2E
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leftmatrix[0,1,:,0,0,:] = leftmatrix[0,0,:,0,1,:] # u2u, E2M
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leftmatrix[1,1,:,1,0,:] = leftmatrix[0,0,:,0,1,:] # d2d, E2M
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leftmatrix[1,0,:,1,1,:] = leftmatrix[0,0,:,0,1,:] # d2d, M2E
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leftmatrix[0,0,:,1,0,:] = np.tensordot(a_d2u, phases_d2u,axes=(0,-1)) #d2u,E2E
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leftmatrix[0,1,:,1,1,:] = leftmatrix[0,0,:,1,0,:] #d2u, M2M
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leftmatrix[1,0,:,0,0,:] = np.tensordot(a_u2d, phases_u2d,axes=(0,-1)) #u2d,E2E
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leftmatrix[1,1,:,0,1,:] = leftmatrix[1,0,:,0,0,:] #u2d, M2M
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leftmatrix[0,0,:,1,1,:] = np.tensordot(b_d2u, phases_d2u,axes=(0,-1)) #d2u,M2E
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leftmatrix[0,1,:,1,0,:] = leftmatrix[0,0,:,1,1,:] #d2u, E2M
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leftmatrix[1,0,:,0,1,:] = np.tensordot(b_u2d, phases_u2d,axes=(0,-1)) #u2d,M2E
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leftmatrix[1,1,:,0,0,:] = leftmatrix[1,0,:,0,1,:] #u2d, E2M
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#leftmatrix is now the translation matrix T
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for j in range(2):
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leftmatrix[j] = -np.tensordot(TMatrices_om[j], leftmatrix[j], axes=([-2,-1],[0,1]))
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# at this point, jth row of leftmatrix is that of -MT
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leftmatrix[j,:,:,j,:,:] += n2id
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#now we are done, 1-MT
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leftmatrixlist[ki] = leftmatrix
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nnlist = np.logical_not(isNaNlist)
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leftmatrixlist_s = np.reshape(leftmatrixlist,(klist.shape[0], 2*2*nelem,2*2*nelem))[nnlist]
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leftmatrixlist_TE = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TEč,TEč)]
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leftmatrixlist_TM = leftmatrixlist_s[np.ix_(np.arange(leftmatrixlist_s.shape[0]),TMč,TMč)]
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if(not onlyNmin):
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svUfullTElist[nnlist], svSfullTElist[nnlist], svVfullTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=True)
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svUfullTMlist[nnlist], svSfullTMlist[nnlist], svVfullTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=True)
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return ((svUfullTElist, svSfullTElist, svVfullTElist), (svUfullTMlist, svSfullTMlist, svVfullTMlist))
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else:
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minsvTElist[nnlist] = np.linalg.svd(leftmatrixlist_TE, compute_uv=False)[...,-onlyNmin:]
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minsvTMlist[nnlist] = np.linalg.svd(leftmatrixlist_TM, compute_uv=False)[...,-onlyNmin:]
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