def _get_mps(hgen_l, hgen_r, phi, direction, labels):
'''Combining hgen_l and hgen_r to get the matrix product state.'''
NL, NR = hgen_l.N, hgen_r.N
phi = tensor.Tensor(phi, labels=['al', 'sl+1', 'al+2', 'sl+2']) #l=NL-1
if direction == '->':
A = hgen_l.evolutor.A(NL - 1, dense=True) #get A[sNL](NL-1,NL)
A = tensor.Tensor(A, labels=['sl+1', 'al', 'al+1\''])
phi = tensor.contract([A, phi])
phi = phi.chorder([0, 2, 1]) #now we get phi(al+1,sl+2,al+2)
#decouple phi into S*B, B is column-wise othorgonal
U, S, V = svd(phi.reshape([phi.shape[0], -1]), full_matrices=False)
U = tensor.Tensor(U, labels=['al+1\'', 'al+1'])
A = (A * U) #get A(al,sl+1,al+1)
B = transpose(
V.reshape([S.shape[0], phi.shape[1], phi.shape[2]]),
axes=(1, 2, 0)
) #al+1,sl+2,al+2 -> sl+2,al+2,al+1, stored in column wise othorgonal format
else:
B = hgen_r.evolutor.A(NR - 1, dense=True) #get B[sNR](NL+1,NL+2)
B = tensor.Tensor(B, labels=['sl+2', 'al+2',
'al+1\'']).conj() #!the conjugate?
phi = tensor.contract([phi, B])
#decouple phi into A*S, A is row-wise othorgonal
U, S, V = svd(phi.reshape([phi.shape[0] * phi.shape[1], -1]),
full_matrices=False)
V = tensor.Tensor(V, labels=['al+1', 'al+1\''])
B = (V * B).chorder([1, 2, 0]).conj(
) #al+1,sl+2,al+2 -> sl+2,al+2,al+1, for B is in transposed order by default.
A = transpose(
U.reshape([phi.shape[0], phi.shape[1], S.shape[0]]),
axes=(1, 0, 2)
) #al,sl+1,al+1 -> sl+1,al,al+1, stored in column wise othorgonal format
AL = hgen_l.evolutor.get_AL(dense=True)[:-1] + [A]
BL = [B] + hgen_r.evolutor.get_AL(dense=True)[::-1][1:]
AL = [transpose(ai, axes=(1, 0, 2)) for ai in AL]
BL = [transpose(bi, axes=(1, 0, 2)).conj() for bi in BL] #transpose
mps = MPS(AL=AL,
BL=BL,
S=S,
labels=labels,
forder=range(NL) + range(NL, NL + NR)[::-1])
return mps
