def generalized_leapfrog_softabs_op(q,p,epsilon,Ham,delta=0.1): # input output point object # can take anything but should output tensor stat = gleapfrog_stat() dV,H_,dH = Ham.V.getdH_tensor(q) lam, Q = eigen(H_) # dphidq outputs and inputs takes flattened gradient in flattened form p.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq(lam,dH,Q,dV) p.load_flatten() rho = p.flattened_tensor.clone() pprime = p.flattened_tensor.clone() deltap = delta + 0.5 count = 0 while (deltap > delta) and (count < 5): # dtaudq returns gradient in flattened form pprime = rho - epsilon * 0.5 * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) deltap = torch.max(torch.abs(p.flattened_tensor-pprime)) p.flattened_tensor.copy_(pprime) p.load_flatten() count = count + 1 sigma = q.point_clone() qprime = q.flattened_tensor.clone() deltaq = delta + 0.5 _,H_ = Ham.V.getH_tensor(sigma) olam,oQ = eigen(H_) count = 0 while (deltaq > delta) and (count < 5): _,H_ = Ham.V.getH_tensor(q) lam,Q = eigen(H_) qprime = sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p.flattened_tensor,olam,oQ) + \ 0.5 * epsilon* Ham.T.dtaudp(p.flattened_tensor,lam,Q) deltaq = torch.max(torch.abs(q.flattened_tensor-qprime)) q.flattened_tensor.copy_(qprime) q.load_flatten() count = count + 1 if deltaq>delta: stat.second_divergent = True stat.divergent =True #print("second fi div") return(q,p,stat) else: stat.second_divergent = False q.flattened_tensor.copy_(qprime) q.load_flatten() dV,H_,dH = Ham.V.getdH_tensor(q) lam,Q = eigen(H_) p.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) p.load_flatten() p.flattened_tensor -=0.5 * epsilon * Ham.T.dphidq(lam,dH,Q,dV) p.load_flatten() return(q,p,stat)
def evaluate_scalar(self,q_point=None,p_point=None): if not q_point is None: self.linkedV.load_point(q_point) if not p_point is None: self.load_point(p_point) _, H_ = self.linkedV.getH_tensor() #debug_dict.update({"abstract":_.clone()}) lam, Q = eigen(H_) temp = softabs_map(lam, self.metric.msoftabsalpha) inv_exp_H = torch.mm(torch.mm(Q, torch.diag(1/temp)), torch.t(Q)) #print("abstract p {}".format(self.flattened_tensor)) #print("inv_exp_H {}".format(inv_exp_H)) o = 0.5 * torch.dot(self.flattened_tensor, torch.mv(inv_exp_H, self.flattened_tensor)) temp2 = 0.5 * torch.log((temp)).sum() #print("alpha {}".format(self.metric.msoftabsalpha)) #print("lam {}".format(lam)) #print("H_ {}".format(H_)) #print("H_2 {}".format(torch.mm(torch.mm(Q, torch.diag(temp)), torch.t(Q)))) #print("msoftabslambda {}".format(temp)) #print("abstract tau {}".format(o)) #print("abstract logdetmetric {}".format(temp2)) output = o + temp2 return (output)
def T_givenq(p): _,H_ = getH(q,V) out = eigen(H_.data) lam = out[0] Q = out[1] temp = softabs_map(lam,alpha) inv_exp_H = torch.mm(torch.mm(Q,torch.diag(1/temp)),torch.t(Q)) o = 0.5 * torch.dot(p.data,torch.mv(inv_exp_H,p.data)) temp2 = 0.5 * torch.log((temp)).sum() return(o + temp2)
def T_givenq(p): _, H_ = getH(q, V) #debug_dict.update({"explicit":_.data.clone()}) out = eigen(H_.data) lam = out[0] Q = out[1] temp = softabs_map(lam, alpha) #print("explicit p {}".format(q.data)) inv_exp_H = torch.mm(torch.mm(Q, torch.diag(1 / temp)), torch.t(Q)) o = 0.5 * torch.dot(p.data, torch.mv(inv_exp_H, p.data)) temp2 = 0.5 * torch.log((temp)).sum() print("explicit tau {}".format(o)) print("explicit logdetmetric {}".format(temp2)) return (o + temp2)
def generate_momentum(self, q): #if lam == None or Q == None: # H_ = self.linkedV.getH_tensor() # lam, Q = eigen(H_) _, H_ = self.linkedV.getH_tensor(q) lam, Q = eigen(H_) temp = torch.mm( Q, torch.diag(torch.sqrt(softabs_map(lam, self.metric.msoftabsalpha)))) out = point(None, self) out.flattened_tensor.copy_(torch.mv(temp, torch.randn(len(lam)))) out.load_flatten() return (out)
def generate_momentum(q): # if lam == None or Q == None: # H_ = self.linkedV.getH_tensor() # lam, Q = eigen(H_) _, H_ = getH(q, V) lam, Q = eigen(H_.data) # print(lam) # print(Q) #exit() # print(lam.shape) # print(type(lam)) # print(type(lam[0])) # exit() #print(lam) #exit() temp = torch.mm(Q, torch.diag(torch.sqrt(softabs_map(lam, alpha)))) out = temp.mv(torch.randn(len(lam))) # print(temp) # exit() return (out)
def generate_momentum(self,q): #if lam == None or Q == None: # H_ = self.linkedV.getH_tensor() # lam, Q = eigen(H_) _, H_ = self.linkedV.getH_tensor(q) lam, Q = eigen(H_) #print(lam) #print(Q) #print(lam.shape) #print(type(lam)) #print(type(lam[0])) #exit() temp = torch.mm(Q, torch.diag(torch.sqrt(softabs_map(lam, self.metric.msoftabsalpha)))) #print(temp) #exit() out = point(list_tensor=self.list_tensor,pointtype="p",need_flatten=self.need_flatten) out.flattened_tensor.copy_(torch.mv(temp, torch.randn(len(lam)))) out.load_flatten() return(out)
def evaluate_scalar(self): _, H_ = self.linkedV.getH_tensor() lam, Q = eigen(H_) temp = softabs_map(lam, self.metric.msoftabsalpha) inv_exp_H = torch.mm(torch.mm(Q, torch.diag(1 / temp)), torch.t(Q)) #print("inv_exp_H {}".format(inv_exp_H)) o = 0.5 * torch.dot(self.flattened_tensor, torch.mv(inv_exp_H, self.flattened_tensor)) temp2 = 0.5 * torch.log((temp)).sum() #print("alpha {}".format(self.metric.msoftabsalpha)) #print("lam {}".format(lam)) #print("H_ {}".format(H_)) #print("H_2 {}".format(torch.mm(torch.mm(Q, torch.diag(temp)), torch.t(Q)))) #print("msoftabslambda {}".format(temp)) print("tau {}".format(o)) print("logdetmetric {}".format(temp2)) output = o + temp2 return (output)
inv_exp_H = torch.mm(torch.mm(Q,torch.diag(1/temp)),torch.t(Q)) o = 0.5 * torch.dot(p.data,torch.mv(inv_exp_H,p.data)) temp2 = 0.5 * torch.log((temp)).sum() return(o + temp2) return(T_givenq) def H(q,p,alpha): # returns float return(V(q).data[0] + T(q,alpha)(p)) store = torch.zeros((chain_l,dim)) g,H_ = getH(q,V) lam,Q = eigen(H_.data) begin = time.time() for i in range(chain_l): print("round {}".format(i)) out = rmhmc_step(q,H,0.1,10,alp,0.1,V) store[i,]=out[0].data q.data = out[0].data totalt = time.time() - begin store = store[burn_in:,] store = store.numpy() empCov = np.cov(store,rowvar=False) emmean = np.mean(store,axis=0) print("length of chain is {}".format(chain_l)) print("burn in is {}".format(burn_in))
def generalized_leapfrog(q, p, epsilon, Ham, delta=1e-8, debug_dict=None): # input output point object # can take anything but should output tensor #print("first q abstract {}".format(q.flattened_tensor)) #print("first p abstract {}".format(p.flattened_tensor)) q_dummy = q.point_clone() p_dummy = p.point_clone() stat = gleapfrog_stat() dV, H_, dH = Ham.V.getdH_tensor(q_dummy) #print("dH abstract {}".format(dH)) lam, Q = eigen(H_) #print("second q abstract {}".format(q.flattened_tensor)) #print("second p abstract {}".format(p.flattened_tensor)) # dphidq outputs and inputs takes flattened gradient in flattened form p_dummy.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq( lam=lam, dH=dH, Q=Q, dV=dV) #print("third q abstract {}".format(q.flattened_tensor)) #print("third p abstract {}".format(p.flattened_tensor)) #p.load_flatten() rho = p_dummy.flattened_tensor.clone() pprime = p_dummy.flattened_tensor.clone() deltap = delta + 0.5 count = 0 while (deltap > delta) and (count < 10): # dtaudq returns gradient in flattened form pprime.copy_(rho - epsilon * 0.5 * Ham.T.dtaudq( p_flattened_tensor=p_dummy.flattened_tensor, dH=dH, Q=Q, lam=lam)) deltap = torch.max(torch.abs(p_dummy.flattened_tensor - pprime)) p_dummy.flattened_tensor.copy_(pprime) p_dummy.load_flatten() count = count + 1 if deltap > delta: if deltap > 50: stat.divergent = True #stat.divergent = True stat.first_divergent = True #print("pprime {}".format(pprime)) #print("deltap {}".format(deltap)) #print("first fi div") #print(count) #return (q, p, stat) return (q_dummy, p_dummy, stat) else: stat.first_divergent = False #print(first_fi_divergent) #print(p.flattened_tensor) sigma = q_dummy.point_clone() qprime = q_dummy.flattened_tensor.clone() deltaq = delta + 0.5 _, H_ = Ham.V.getH_tensor(sigma) olam, oQ = eigen(H_) count = 0 while (deltaq > delta) and (count < 10): _, H_ = Ham.V.getH_tensor(q_dummy) lam, Q = eigen(H_) qprime.copy_(sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p_dummy.flattened_tensor,olam,oQ) + \ 0.5 * epsilon* Ham.T.dtaudp(p_dummy.flattened_tensor,lam,Q)) deltaq = torch.max(torch.abs(q_dummy.flattened_tensor - qprime)) q_dummy.flattened_tensor.copy_(qprime) q_dummy.load_flatten() count = count + 1 if deltaq > delta: stat.second_divergent = True if deltaq > 50: stat.divergent = True #print("deltaq {}".format(deltaq)) #print("second fi div") #assert stat.divergent #return(q,p,stat) return (q_dummy, p_dummy, stat) else: stat.second_divergent = False #print("H is {}".format(Ham.evaluate(q,p))) dV, H_, dH = Ham.V.getdH_tensor(q_dummy) #print(q.flattened_tensor) lam, Q = eigen(H_) #print(0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam)) p_dummy.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq( p_dummy.flattened_tensor, dH, Q, lam) #print("H is {}".format(Ham.evaluate(q, p))) #p.load_flatten() p_dummy.flattened_tensor -= 0.5 * epsilon * Ham.T.dphidq(lam, dH, Q, dV) #p.load_flatten() #print("yes") #debug_dict.update({"abstract": p.flattened_tensor.clone()}) #return(q,p,stat) return (q_dummy, p_dummy, stat) # def generalized_leapfrog_softabsdiag(q,p,epsilon,Ham,delta=0.1): # # input output point object # # can take anything but should output tensor # stat = gleapfrog_stat() # dV,mdiagH,mgraddiagH = Ham.V.get_graddiagH(q) # #print(dV.shape) # #exit() # mlambda,_ = Ham.T.fcomputeMetric(mdiagH) # # dphidq outputs and inputs takes flattened gradient in flattened form # p.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq(dV=dV,mdiagH=mdiagH,mgraddiagH=mgraddiagH,mlambda=mlambda) # p.load_flatten() # rho = p.flattened_tensor.clone() # pprime = p.flattened_tensor.clone() # deltap = delta + 0.5 # count = 0 # while (deltap > delta) and (count < 5): # # dtaudq returns gradient in flattened form # pprime = rho - epsilon * 0.5 * Ham.T.dtaudq(p.flattened_tensor,mdiagH,mlambda,mgraddiagH) # deltap = torch.max(torch.abs(p.flattened_tensor-pprime)) # p.flattened_tensor.copy_(pprime) # p.load_flatten() # count = count + 1 # if deltap>delta: # stat.divergent = True # stat.first_divergent = True # #print("pprime {}".format(pprime)) # #print("deltap {}".format(deltap)) # #print("first fi div") # #print(count) # return (q, p, stat) # else: # stat.first_divergent = False # p.flattened_tensor.copy_(pprime) # p.load_flatten() # # sigma = q.point_clone() # qprime = q.flattened_tensor.clone() # deltaq = delta + 0.5 # # _,mdiagH = Ham.V.getdiagH_tensor(sigma) # omlambda,_ = Ham.T.fcomputeMetric(mdiagH) # count = 0 # while (deltaq > delta) and (count < 5): # _,mdiagH = Ham.V.getdiagH_tensor(q) # mlambda,_ = Ham.T.fcomputeMetric(mdiagH) # qprime = sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p.flattened_tensor,omlambda) + \ # 0.5 * epsilon* Ham.T.dtaudp(p.flattened_tensor,mlambda) # deltaq = torch.max(torch.abs(q.flattened_tensor-qprime)) # q.flattened_tensor.copy_(qprime) # q.load_flatten() # count = count + 1 # if deltaq>delta: # stat.second_divergent = True # stat.divergent =True # #print("second fi div") # return(q,p,stat) # else: # stat.second_divergent = False # q.flattened_tensor.copy_(qprime) # q.load_flatten() # #print("H is {}".format(Ham.evaluate(q,p))) # # dV, mdiagH, mgraddiagH = Ham.V.get_graddiagH(q) # mlambda, _ = Ham.T.fcomputeMetric(mdiagH) # # p.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,mdiagH,mlambda,mgraddiagH) # p.load_flatten() # p.flattened_tensor -=0.5 * epsilon * Ham.T.dphidq(dV,mdiagH,mgraddiagH,mlambda) # p.load_flatten() # # return(q,p,stat) # # def generalized_leapfrog_softabs_op(q,p,epsilon,Ham,delta=0.1): # # input output point object # # can take anything but should output tensor # stat = gleapfrog_stat() # dV,H_,dH = Ham.V.getdH_tensor(q) # lam, Q = eigen(H_) # # dphidq outputs and inputs takes flattened gradient in flattened form # p.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq(lam,dH,Q,dV) # p.load_flatten() # rho = p.flattened_tensor.clone() # pprime = p.flattened_tensor.clone() # deltap = delta + 0.5 # count = 0 # while (deltap > delta) and (count < 5): # # dtaudq returns gradient in flattened form # pprime = rho - epsilon * 0.5 * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) # deltap = torch.max(torch.abs(p.flattened_tensor-pprime)) # p.flattened_tensor.copy_(pprime) # p.load_flatten() # count = count + 1 # # sigma = q.point_clone() # qprime = q.flattened_tensor.clone() # deltaq = delta + 0.5 # # _,H_ = Ham.V.getH_tensor(sigma) # olam,oQ = eigen(H_) # count = 0 # while (deltaq > delta) and (count < 5): # _,H_ = Ham.V.getH_tensor(q) # lam,Q = eigen(H_) # qprime = sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p.flattened_tensor,olam,oQ) + \ # 0.5 * epsilon* Ham.T.dtaudp(p.flattened_tensor,lam,Q) # deltaq = torch.max(torch.abs(q.flattened_tensor-qprime)) # q.flattened_tensor.copy_(qprime) # q.load_flatten() # count = count + 1 # # if deltaq>delta: # stat.second_divergent = True # stat.divergent =True # #print("second fi div") # return(q,p,stat) # else: # stat.second_divergent = False # q.flattened_tensor.copy_(qprime) # q.load_flatten() # dV,H_,dH = Ham.V.getdH_tensor(q) # lam,Q = eigen(H_) # # p.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) # p.load_flatten() # p.flattened_tensor -=0.5 * epsilon * Ham.T.dphidq(lam,dH,Q,dV) # p.load_flatten() # # return(q,p,stat) # # def generalized_leapfrog_softabs_op_diag(q,p,epsilon,Ham,delta=0.1): # # input output point object # # can take anything but should output tensor # stat = gleapfrog_stat() # dV,H_,dH = Ham.V.getdH_tensor(q) # lam, Q = eigen(H_) # # dphidq outputs and inputs takes flattened gradient in flattened form # p.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq(lam,dH,Q,dV) # p.load_flatten() # rho = p.flattened_tensor.clone() # pprime = p.flattened_tensor.clone() # deltap = delta + 0.5 # count = 0 # while (deltap > delta) and (count < 10): # # dtaudq returns gradient in flattened form # pprime = rho - epsilon * 0.5 * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) # deltap = torch.max(torch.abs(p.flattened_tensor-pprime)) # p.flattened_tensor.copy_(pprime) # p.load_flatten() # count = count + 1 # if deltap>delta: # stat.divergent = True # stat.first_divergent = True # #print("pprime {}".format(pprime)) # #print("deltap {}".format(deltap)) # #print("first fi div") # #print(count) # return (q, p, stat) # else: # stat.first_divergent = False # p.flattened_tensor.copy_(pprime) # p.load_flatten() # # sigma = q.point_clone() # qprime = q.flattened_tensor.clone() # deltaq = delta + 0.5 # # _,H_ = Ham.V.getH_tensor(sigma) # olam,oQ = eigen(H_) # count = 0 # while (deltaq > delta) and (count < 10): # _,H_ = Ham.V.getH_tensor(q) # lam,Q = eigen(H_) # qprime = sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p.flattened_tensor,olam,oQ) + \ # 0.5 * epsilon* Ham.T.dtaudp(p.flattened_tensor,lam,Q) # deltaq = torch.max(torch.abs(q.flattened_tensor-qprime)) # q.flattened_tensor.copy_(qprime) # q.load_flatten() # count = count + 1 # # if deltaq>delta: # stat.second_divergent = True # stat.divergent =True # #print("second fi div") # return(q,p,stat) # else: # stat.second_divergent = False # q.flattened_tensor.copy_(qprime) # q.load_flatten() # dV,H_,dH = Ham.V.getdH_tensor(q) # lam,Q = eigen(H_) # # p.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) # p.load_flatten() # p.flattened_tensor -=0.5 * epsilon * Ham.T.dphidq(lam,dH,Q,dV) # p.load_flatten() # # return(q,p) # def rmhmc_step(init_q,epsilon,L,Ham,evolve_t=None,careful=True): # # # Ham.diagnostics = time_diagnositcs() # q = init_q.point_clone() # # init_p = Ham.T.generate_momentum(q) # p = init_p.point_clone() # current_H = Ham.evaluate(q,p) # num_transitions = L # divergent = False # # for i in range(L): # out = Ham.integrator(q,p,epsilon,Ham) # q = out[0] # p = out[1] # if careful: # temp_H = Ham.evaluate(q, p) # if (abs(temp_H - current_H) > 1000): # return_q = init_q # return_p = None # return_H = current_H # accept_rate = 0 # accepted = False # divergent = True # num_transitions = i # break # if not divergent: # proposed_H = Ham.evaluate(q,p) # u = numpy.random.rand(1) # # if (abs(current_H - proposed_H) > 1000): # divergent = True # else: # divergent = False # accept_rate = math.exp(min(0,current_H - proposed_H)) # if u < accept_rate: # next_q = q # proposed_p = p # next_H = proposed_H # accepted = True # else: # next_q = init_q # proposed_p = None # accepted = False # next_H = current_H # return(next_q,proposed_p,init_p,next_H,accepted,accept_rate,divergent,num_transitions)
def p_sharp(q, p): _, H = getH(q, V) lam, Q = eigen(H.data) p_s = dtaudp(p.data, alp, lam, Q) return (p_s)
from explicit.genleapfrog_ult_util import eigen import torch, numpy inp = torch.eye(5) input = numpy.array([[0.0, 1], [-1, 0]]) #print(input) #a = torch.from_numpy(input) #print(a) #lam,Q = a.eig(eigenvectors=True) #print(lam) #exit() #lam[:,1]==0 #exit() #print(inp) lam, Q = eigen(inp) exit() print(lam) print(Q) print(Q.mm((lam)).mm(Q.t()))
def generalized_leapfrog(q,p,epsilon,Ham,delta=0.1,debug_dict=None): # input output point object # can take anything but should output tensor #print("first q abstract {}".format(q.flattened_tensor)) #print("first p abstract {}".format(p.flattened_tensor)) stat = gleapfrog_stat() dV,H_,dH = Ham.V.getdH_tensor(q) #print("dH abstract {}".format(dH)) lam, Q = eigen(H_) #print("second q abstract {}".format(q.flattened_tensor)) #print("second p abstract {}".format(p.flattened_tensor)) # dphidq outputs and inputs takes flattened gradient in flattened form p.flattened_tensor -= epsilon * 0.5 * Ham.T.dphidq(lam,dH,Q,dV) #print("third q abstract {}".format(q.flattened_tensor)) #print("third p abstract {}".format(p.flattened_tensor)) p.load_flatten() rho = p.flattened_tensor.clone() pprime = p.flattened_tensor.clone() deltap = delta + 0.5 count = 0 while (deltap > delta) and (count < 10): # dtaudq returns gradient in flattened form pprime.copy_(rho - epsilon * 0.5 * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam)) deltap = torch.max(torch.abs(p.flattened_tensor-pprime)) p.flattened_tensor.copy_(pprime) p.load_flatten() count = count + 1 if deltap>delta: stat.divergent = True stat.first_divergent = True #print("pprime {}".format(pprime)) #print("deltap {}".format(deltap)) #print("first fi div") #print(count) return (q, p, stat) else: stat.first_divergent = False #print(first_fi_divergent) #print(p.flattened_tensor) sigma = q.point_clone() qprime = q.flattened_tensor.clone() deltaq = delta + 0.5 _,H_ = Ham.V.getH_tensor(sigma) olam,oQ = eigen(H_) count = 0 while (deltaq > delta) and (count < 10): _,H_ = Ham.V.getH_tensor(q) lam,Q = eigen(H_) qprime = sigma.flattened_tensor + 0.5 * epsilon * Ham.T.dtaudp(p.flattened_tensor,olam,oQ) + \ 0.5 * epsilon* Ham.T.dtaudp(p.flattened_tensor,lam,Q) deltaq = torch.max(torch.abs(q.flattened_tensor-qprime)) q.flattened_tensor.copy_(qprime) q.load_flatten() count = count + 1 if deltaq>delta: stat.second_divergent = True stat.divergent =True #print("second fi div") return(q,p,stat) else: stat.second_divergent = False #print("H is {}".format(Ham.evaluate(q,p))) dV,H_,dH = Ham.V.getdH_tensor(q) lam,Q = eigen(H_) #print(0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam)) p.flattened_tensor -= 0.5 * epsilon * Ham.T.dtaudq(p.flattened_tensor,dH,Q,lam) #print("H is {}".format(Ham.evaluate(q, p))) p.load_flatten() p.flattened_tensor -= 0.5 * epsilon * Ham.T.dphidq(lam,dH,Q,dV) p.load_flatten() #print("yes") debug_dict.update({"abstract": p.flattened_tensor.clone()}) return(q,p,stat)
def generate(q): lam, Q = eigen(getH(q, V).data) temp = torch.mm(Q, torch.diag(torch.sqrt(softabs_map(lam, alpha)))) out = torch.mv(temp, torch.randn(len(lam))) return (out)
def p_sharp(q, p): lam, Q = eigen(getH(q, V).data) p_s = dtaudp(p.data, alp, lam, Q) return (p_s)