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linearized.py
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linearized.py
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from opt_einsum import contract # idk why but its required to avoid bug in contract with numpy arrays
import torch
import numpy as np
from tqdm.auto import tqdm
import scipy.sparse.linalg
from scipy.sparse.linalg import LinearOperator,aslinearoperator
from functorch import jvp,vjp
from math import prod
import torch
from opt_einsum import contract
def _toN(t):
if isinstance(t,list):
return [_toN(tt) for tt in t]
elif isinstance(t,torch.Tensor):
return t.detach().cpu().tolist()
else:
return t
def _toP(t):
if isinstance(t,list):
return [_toP(tt) for tt in t]
elif isinstance(t,torch.Tensor):
return t.detach().cpu().numpy()
else:
return t
def wrap_pytorch(func):
def _wrapper(v_numpy):
assert len(v_numpy.shape)==1 or (len(v_numpy.shape)==2 and v_numpy.shape[1]==1)
v_torch=torch.tensor(v_numpy).reshape(-1)
u_torch=func(v_torch)
u_numpy=u_torch.detach().cpu().numpy()
if len(v_torch.shape)>1:
u_numpy=u_numpy.reshape(-1,1)
else:
u_numpy=u_numpy.reshape(-1)
return u_numpy
return _wrapper
def wrap_pbar(pbar):
def _decorator(func):
def _wrapper(*args1,**args2):
rtvals=func(*args1,**args2)
pbar.update(1)
return rtvals
return _wrapper
return _decorator
from HOTRGZ2 import forward_layer, HOTRG_layer
def get_linearized_cylinder_np(T0):
assert isinstance(T0,np.ndarray)
dimT=prod(T0.shape)
pbar=tqdm()
@wrap_pbar(pbar)
def matvec(v):
# print('np')
# print('v',v[:10])
# print('T0',T0.reshape(-1)[:10])
v1=contract('iIab,jJbc,kKcd,lLda,IJKL->ijkl',T0,T0,T0,T0,v.reshape(T0.shape)).reshape(-1)
# print('v1',v1[:10])
return v1
@wrap_pbar(pbar)
def rmatvec(u):
return contract('iIab,jJbc,kKcd,lLda,ijkl->IJKL',T0,T0,T0,T0,u.conj().reshape(T0.shape)).conj().reshape(-1)
return LinearOperator(shape=(dimT,dimT),matvec=matvec,rmatvec=rmatvec)
def get_linearized_cylinder(T0):
dimT=prod(T0.shape)
pbar=tqdm()
@wrap_pbar(pbar)
@wrap_pytorch
def matvec(v):
# print('torch')
# print('v',v[:10])
# print('T0',T0.reshape(-1)[:10])
v1=contract('iIab,jJbc,kKcd,lLda,IJKL->ijkl',T0,T0,T0,T0,v.reshape(T0.shape)).reshape(-1)
# print('v1',v1[:10])
return v1
@wrap_pbar(pbar)
@wrap_pytorch
def rmatvec(u):
return contract('iIab,jJbc,kKcd,lLda,ijkl->IJKL',T0,T0,T0,T0,u.conj().reshape(T0.shape)).conj().reshape(-1)
return LinearOperator(shape=(dimT,dimT),matvec=matvec,rmatvec=rmatvec)
import jax
from HOTRGZ2_jax import forward_layer as forward_layer_jax,HOTRGLayer as HOTRGLayer_jax, HOTRG_layer as HOTRG_layer_jax
from copy import deepcopy
def get_linearized_HOTRG_jax(T0,layers):
dimT=prod(T0.shape)
T0=_toP(T0)
layers=[HOTRGLayer_jax(**{k:_toP(v) for k,v in layer.__dict__.items()}) for layer in layers]
for layer in layers:
if layer.ww: layer.ww=_toP(layer.ww)
if layer.gg: layer.gg=_toP(layer.gg)
if layer.hh: layer.hh=_toP(layer.hh)
pbar=tqdm()
print(f'dimension: {dimT}x{dimT}')
def forward_layers(v):
v=v.reshape(T0.shape)
for layer in layers:
v=forward_layer_jax(v,v,layer)
pbar.update(1)
return v.reshape(-1)
v0=T0.reshape(-1)
v1, M = jax.linearize(forward_layers, v0)
return LinearOperator(shape=(dimT,dimT),matvec=M)
def get_linearized_HOTRG_full_jax(T0,options):
dimT=prod(T0.shape)
T0=_toP(T0)
pbar=tqdm()
print(f'dimension: {dimT}x{dimT}')
@wrap_pbar(pbar)
def forward_layers(v):
v=v.reshape(T0.shape)
for i in range(len(T0.shape)//2):
v,_=HOTRG_layer_jax(v,v,max_dim=T0.shape[0],options=options,Tref=v)
pbar.update(1)
return v.reshape(-1)
v0=T0.reshape(-1)
v1, M = jax.linearize(forward_layers, v0)
return LinearOperator(shape=(dimT,dimT),matvec=M)
from functorch import jvp,vjp
def get_linearized_HOTRG_autodiff(T0,layers):
dimT=prod(T0.shape)
pbar=tqdm()
print(f'dimension: {dimT}x{dimT}')
def forward_layers(v):
v=v.reshape(T0.shape)
for layer in layers:
v=forward_layer(v,v,layer)
return v.reshape(-1)
v0=T0.reshape(-1)
@wrap_pbar(pbar)
@wrap_pytorch
def matvec(v):
# https://pytorch.org/functorch/nightly/generated/functorch.jvp.html
_,u=jvp(forward_layers,primals=(v0,),tangents=(v,))
return u
# https://pytorch.org/functorch/stable/generated/functorch.vjp.html
_,vjpfunc=vjp(forward_layers,v0)
@wrap_pbar(pbar)
@wrap_pytorch
def rmatvec(u):
v=vjpfunc(u)[0]
return v
return LinearOperator(shape=(dimT,dimT),matvec=matvec,rmatvec=rmatvec)
def get_linearized_HOTRG_full_autodiff(T0,options):
dimT=prod(T0.shape)
pbar=tqdm()
print(f'dimension: {dimT}x{dimT}')
def forward_layers(v):
v=v.reshape(T0.shape)
for i in range(len(T0.shape)//2):
v,_=HOTRG_layer(v,v,max_dim=T0.shape[0],options=options,Tref=v)
return v.reshape(-1)
v0=T0.reshape(-1)
@wrap_pbar(pbar)
@wrap_pytorch
def matvec(v):
# https://pytorch.org/functorch/nightly/generated/functorch.jvp.html
_,u=jvp(forward_layers,primals=(v0,),tangents=(v,))
return u
# https://pytorch.org/functorch/stable/generated/functorch.vjp.html
_,vjpfunc=vjp(forward_layers,v0)
@wrap_pbar(pbar)
@wrap_pytorch
def rmatvec(u):
v=vjpfunc(u)[0]
return v
return LinearOperator(shape=(dimT,dimT),matvec=matvec,rmatvec=rmatvec)
def verify_linear_operator(M,tol=1e-9,nTests=20):
print('checking linearity of M with tol=',tol)
for i in range(nTests):
v=np.random.randn(M.shape[1])
Mv=M._matvec(v)
M2v=M._matvec(2*v)
assert np.linalg.norm(2*Mv-M2v)<max(tol,tol*np.linalg.norm(M2v))
print('checking linearity of M^H with tol=',tol)
for i in range(nTests):
u=np.random.randn(M.shape[0])
MHu=M._rmatvec(u)
MH2u=M._rmatvec(2*u)
assert np.linalg.norm(2*MHu-MH2u)<max(tol,tol*np.linalg.norm(MH2u))
print('checking if M^H is the hermitian conjugate of M with tol=',tol)
for i in range(nTests):
u=np.random.randn(M.shape[0])
v=np.random.randn(M.shape[1])
uMv=u.conj()@M._matvec(v)
vHMHuH=v.conj()@M._rmatvec(u)
assert (np.abs(uMv-vHMHuH.conj())<max(tol,tol*np.abs(uMv)))
print('checking symmetric of M^H M with tol=',tol)
for i in range(nTests):
u=np.random.randn(M.shape[0])
v=np.random.randn(M.shape[0])
uHMHMv=u.conj()@M._rmatvec(M._matvec(v))
vHMHMu=v.conj()@M._rmatvec(M._matvec(u))
assert (np.abs(uHMHMv-vHMHMu)<max(tol,tol*np.abs(vHMHMu)))
print('checking symmetric of M M^H with tol=',tol)
for i in range(nTests):
u=np.random.randn(M.shape[1])
v=np.random.randn(M.shape[1])
uHMMHv=u.conj()@M._matvec(M._rmatvec(v))
vHMMHu=v.conj()@M._matvec(M._rmatvec(u))
assert (np.abs(uHMMHv-vHMMHu)<max(tol,tol*np.abs(uHMMHv)))
print('verification success')
return True
def check_hermicity(M,tol=1e-9,nTests=20):
assert M.shape[0]==M.shape[1]
print('checking hermicity with tol=',tol)
for i in range(nTests):
u=np.random.randn(M.shape[0])
v=np.random.randn(M.shape[1])
uMv=u@M._matvec(v)
uMHv=u@M._rmatvec(v)
error=np.abs(uMv-uMHv)
print('error is ',error,' / ',np.abs(uMv))
if (np.abs(uMv-uMHv)>=max(tol,tol*np.abs(uMv))):
print('hermicity is False')
return False
print('hermicity is True')
return True
def mysvd(M,k=10,tol=0,maxiter=500):
M=aslinearoperator(M)
dim=M.shape[1]
k=min(k,min(M.shape))
eigvecs,eigvals=[],[]
tols=tol if isinstance(tol,list) else [tol]*k
maxiters=maxiter if isinstance(maxiter,list) else [maxiter]*k
pbar1=tqdm(range(k),leave=False)
for j in pbar1:
v=np.random.randn(dim);v=v/np.linalg.norm(v)
with tqdm(range(maxiters[j]),leave=False) as pbar:
for i in pbar:
vn=M.rmatvec(M.matvec(v))
for u in eigvecs:
vn=vn-u*(u.conj()@vn)
if np.linalg.norm(vn)==0:
raise ValueError
eig=np.linalg.norm(vn)/np.linalg.norm(v)
vn=vn/np.linalg.norm(vn)
err=np.linalg.norm(vn-v)
v=vn
pbar1.set_postfix(eig=eig,err=err)
if err<=tols[j]:
pbar.close()
break
if err>tols[j]:
print('Not Converged! err=',err)
print('eig=',eig)
eigvecs.append(v)
eigvals.append(eig)
u=np.array([v/np.linalg.norm(v) for v in [M*v for v in eigvecs]]).T
s=np.array(np.abs(eigvals))**.5
vh=np.array(eigvecs).conj()
return u,s,vh
def myeigh(M,k=10,tol=0,maxiter=500,impose_hermitian=True):
M=aslinearoperator(M)
dim=M.shape[1]
k=min(k,min(M.shape))
eigvecs,eigvals=[],[]
tols=tol if isinstance(tol,list) else [tol]*k
maxiters=maxiter if isinstance(maxiter,list) else [maxiter]*k
pbar1=tqdm(range(k),leave=False)
for j in pbar1:
v=np.random.randn(dim);v=v/np.linalg.norm(v)
with tqdm(range(maxiters[j]),leave=False) as pbar:
for i in pbar:
if impose_hermitian:
vn=(M.rmatvec(v)+M.matvec(v))/2
else:
vn=M.matvec(v)
for u in eigvecs:
vn=vn-u*(u.conj()@vn)
if np.linalg.norm(vn)==0:
raise ValueError
eig=np.linalg.norm(vn)/np.linalg.norm(v)
vn=vn/np.linalg.norm(vn)
err=np.linalg.norm(vn-v)
v=vn
pbar1.set_postfix(eig=eig,err=err)
if err<=tols[j]:
pbar.close()
break
if err>tols[j]:
print('Not Converged! err=',err)
print('eig=',eig)
eigvecs.append(v)
eigvals.append(eig)
eigvecs=np.array(eigvecs)
eigvals=np.array(eigvals)
return eigvals,eigvecs.T
def myeig_old(M,k=10,tol=1e-7,maxiter=200):
dim=M.shape[0]
eigvecs,eigvals=[],[]
tols=tol if isinstance(tol,list) else [tol]*k
maxiters=maxiter if isinstance(maxiter,list) else [maxiter]*k
pbar1=tqdm(range(k),leave=False)
for j in pbar1:
v=np.random.randn(dim);v=v/np.linalg.norm(v)
pbar=tqdm(range(maxiters[j]),leave=False)
for i in pbar:
vn=M*v
for u in eigvecs:
vn=vn-u*(u@vn)
eig=np.linalg.norm(vn)/np.linalg.norm(v)
#print(eig)
if np.linalg.norm(vn)==0:
break
vn=vn/np.linalg.norm(vn)
err=np.linalg.norm(vn-v)
pbar.set_postfix(err=err)
pbar1.set_postfix(eig=eig)
if err<=tols[j]:
break
v=vn
eigvecs.append(v)
eigvals.append(eig)
return eigvals,np.array(eigvecs).T
#M=np.random.randn(5,4)
#u,s,vh=mysvd(scipy.sparse.linalg.aslinearoperator(M))
#print(np.linalg.norm([email protected](s)@vh-M))