def psim(state, N=None, DIM=None, fixed=None, visualize=False, order=2, state0=None, grid=None):
qm, qm_1, qm_2, pm, mum_1, mum_2 = tj.state_to_weinstein_darboux(state, N, DIM)
qf = fixed[0]
if order >= 1:
qf_1 = fixed[1]
if order >= 2:
qf_2 = fixed[2]
w = [1, 0.5, 0.2]
# weighting between different order terms
# value
v0 = qm - qf
m0 = w[0] * np.einsum("ia,ia", v0, v0) # 1./N ??
if order >= 1:
v1 = qm_1 - qf_1
m1 = w[1] * np.einsum("iab,iab", v1, v1) # 1./N ??
if order >= 2:
v2 = qm_2 - qf_2
m2 = w[2] * np.einsum("iabg,iabg", v2, v2) # 1./N ??
# gradient
dq0 = w[0] * 2.0 * v0 # 1./N ??
if order >= 1:
dq1 = w[1] * 2.0 * v1 # 1./N ??
if order >= 2:
dq2 = w[2] * 2.0 * v2 # 1./N ??
# print "point sim: m0 " + str(m0) + ", m1 " + str(m1) + ", m2 " + str(m2)
## visualization
if visualize:
plt.figure(1)
plt.clf()
plt.plot(qf[:, 0], qf[:, 1], "bo")
plt.plot(qm[:, 0], qm[:, 1], "rx")
# grid
if state0 != None and grid != None:
(reggrid, Nx, Ny) = grid
(_, _, mgridts) = tj.integrate(state0, pts=reggrid)
mgridT = mgridts[-1:].reshape(-1, DIM)
pg.plotGrid(mgridT, Nx, Ny)
# generate vertices of a circle
N_vert = 20
circle_verts = np.zeros([2, N_vert + 1])
theta = np.linspace(0, 2 * np.pi, N_vert)
circle_verts[0, 0:N_vert] = 0.2 * np.cos(theta)
circle_verts[1, 0:N_vert] = 0.2 * np.sin(theta)
verts = np.zeros([2, N_vert + 1])
units = np.ones(N_vert + 1)
for i in range(0, len(qm)):
plt.arrow(
qm[i, 0], qm[i, 1], 0.2 * pm[i, 0], 0.2 * pm[i, 1], head_width=0.2, head_length=0.2, fc="b", ec="b"
)
if qm_1 != None:
verts = np.dot(qm_1[i, :, :], circle_verts) + np.outer(qm[i, :], units)
plt.plot(verts[0], verts[1], "r-")
border = 0.4
plt.xlim(min(np.vstack((qf, qm))[:, 0]) - border, max(np.vstack((qf, qm))[:, 0]) + border)
plt.ylim(min(np.vstack((qf, qm))[:, 1]) - border, max(np.vstack((qf, qm))[:, 1]) + border)
plt.axis("equal")
plt.draw()
if order == 0:
return (m0, (dq0,))
elif order == 1:
return (m0 + m1, (dq0, dq1))
else:
return (m0 + m1 + m2, (dq0, dq1, dq2))
def imsim( state, N=None, imshape=None, DIM=None, h=None, imms=None, Dimms=None, imf=None, imm=None, simfs=None, sDimfs=None, sgrid=None, visualize=False, state0=None, grid=None, order=None, imgrid=None, hscaling=None, SIGMA=None, imfs=None):
q,q_1,q_2,p,mu_1,mu_2 = tj.state_to_weinstein_darboux( state,N,DIM )
sampleq = partial(sample,d2unzip(q,N), hscaling=hscaling)
simms = sampleq(imms)
#sDimms = [apply_2d_slices(sampleq, Dimms[i]) for i in range(np.shape(Dimms)[0])]
sDimms = [apply_2d_slices(partial(sampleq, imms), derivs[i]) for i in range(len(derivs))]
d = DIM
delta = np.identity(DIM)
one = np.ones([DIM])
one_minus_delta = np.ones([DIM,DIM])-np.eye(DIM)
# value
v0 = simfs-simms
m0 = (h**d)*np.einsum('i,i',v0,v0)
if order >= 1:
v1 = sDimfs[0]-np.einsum('bi,iba->ai',sDimms[0],q_1)
m1 = (h**(d+2))/12*np.einsum('ai,ai',v1,v1)
if order >= 2:
G = sDimfs[1] \
-np.einsum('dci,idb,ica->abi',sDimms[1],q_1,q_1) \
-np.einsum('ci,icab->abi',sDimms[0],q_2)
m2 = (h**(d+2))/12*np.einsum('i,aai->',v0,G) \
+ (h**(d+4))/(5*2**6)*np.einsum('aai,aai->',G,G) \
+ (h**(d+4))/(9*2**6)*np.einsum('ab,aai,bbi->',one_minus_delta,G,G) \
+ (h**(d+4))/(9*2**6)*np.einsum('ab,abi,abi->',one_minus_delta,G,G)
# debug output
if order >= 0:
logging.info("m0: " + str(m0))
if order >= 1:
logging.info("m1: " + str(m1))
#logging.info("sDimfs[0]: " + str(sDimfs[0]))
#logging.info("moving: " + str(np.einsum('bi,iba->ai',sDimms[0],q_1)))
if order >= 2:
logging.info("m2: " + str(m2))
#logging.info("G: " + str(G))
#logging.info("sDimfs[1]: " + str(sDimfs[1]))
#logging.info("moving: " + str(np.einsum('dci,idb,ica->abi',sDimms[1],q_1,q_1)+np.einsum('ci,icab->abi',sDimms[0],q_2)))
# gradient
# dq0
g00 = -2*(h**d)*np.einsum('i,ai->ia',v0,sDimms[0])
dq0 = g00
if order >= 1:
g01 = -(h**(d+2))/6*np.einsum('bai,ibe,ec,ci->ia',sDimms[1],q_1,delta,v1)
dq0 = dq0+g01
if order >= 2:
g02 = -(h**(d+2))/12*np.einsum('ai,ddi->ia',sDimms[0],G)
G1 = -np.einsum('bcai,ibe,icd->deai',sDimms[2],q_1,q_1) \
-np.einsum('cai,icde->deai',sDimms[1],q_2)
g03 = (h**(d+2))/12*np.einsum('i,ddai->ia',v0,G1)
g04 = (h**(d+4))/(5*2**5)*np.einsum('ddi,ddai->ia',G,G1) \
+(h**(d+4))/(9*2**5)*np.einsum('de,ddi,eeai->ia',one_minus_delta,G,G1) \
+(h**(d+4))/(9*2**5)*np.einsum('de,dei,deai->ia',one_minus_delta,G,G1)
dq0 = dq0+g02+g03+g04
# rescale
dq0 = hscaling*dq0
# dq1
if order >= 1:
g10 = -(h**(d+2))/6*np.einsum('ai,bi->iab',sDimms[0],v1)
dq1 = g10
if order >= 2:
G2 = -np.einsum('aci,ice,db->deabi',sDimms[1],q_1,delta) \
-np.einsum('aci,icd,eb->deabi',sDimms[1],q_1,delta)
g11 = (h**(d+2))/12*np.einsum('i,ddabi->iab',v0,G2)
g12 = (h**(d+4))/(5*2**5)*np.einsum('ddi,ddabi->iab',G,G2) \
+(h**(d+4))/(9*2**5)*np.einsum('de,ddi,eeabi->iab',one_minus_delta,G,G2) \
+(h**(d+4))/(9*2**5)*np.einsum('de,dei,deabi->iab',one_minus_delta,G,G2)
dq1 = dq1+g11+g12
# dq2
if order >= 2:
G3 = -np.einsum('bd,ce,ai->deabci',delta,delta,sDimms[0])
g21 = (h**(d+2))/12*np.einsum('i,bc,bcabci->iabc',v0,delta,G3)
g22 = (h**(d+4))/(5*2**5)*np.einsum('ddi,ddabci->iabc',G,G3) \
+(h**(d+4))/(9*2**5)*np.einsum('de,ddi,eeabci->iabc',one_minus_delta,G,G3) \
+(h**(d+4))/(9*2**5)*np.einsum('de,dei,deabci->iabc',one_minus_delta,G,G3)
dq2 = g21+g22
# visualization
if visualize:
logging.info("iteration visualization output")
x = np.arange(imshape[0])
y = np.arange(imshape[1])
plt.figure(1)
plt.clf()
scimms = samplecross((x,y),imms).reshape(imshape)
cmin = np.min([np.min(simms),np.min(simfs),np.min(scimms)])
cmax = np.max([np.max(simms),np.max(simfs),np.max(scimms)])
plt.imshow(scimms.T,vmin=cmin,vmax=cmax)
plt.plot(d2zip(sgrid)[:,0],d2zip(sgrid)[:,1],'bo')
plt.plot(q[:,0],q[:,1],'rx')
plt.gray()
plt.colorbar()
plotJacobians(q,q_1)
#plt.quiver(q[:,0],q[:,1],dq0[:,0],dq0[:,1],color='y')
plt.xlim(0,imshape[0])
plt.ylim(0,imshape[1])
#plt.quiver(q[:,0],q[:,1],g00[:,0],g00[:,1])
plt.figure(2)
plt.clf()
plt.imshow(rse(simfs,N).T,vmin=cmin,vmax=cmax)
plt.colorbar()
plt.figure(3)
plt.clf()
plt.imshow(rse(simms,N).T,vmin=cmin,vmax=cmax)
plt.colorbar()
plt.figure(4)
plt.clf()
plt.imshow(rse(v0,N).T)
plt.colorbar()
plt.figure(5)
plt.clf()
plt.imshow(rse(sDimms[0][0,:],N).T)
plt.colorbar()
# grid plot
if sgrid != None:
qf = d2zip(sgrid)
plt.figure(6)
plt.clf()
plt.plot(qf[:,0],qf[:,1],'bo')
plt.plot(q[:,0],q[:,1],'rx')
# grid
if state0 != None and grid != None:
(reggrid,Nx,Ny) = grid
(_,_,mgridts) = tj.integrate(state0,pts=reggrid)
mgridT = mgridts[-1:].reshape(-1,DIM)
pg.plotGrid(mgridT,Nx,Ny)
## generate vertices of a circle
#N_vert = 20
#circle_verts = np.zeros( [ 2 , N_vert + 1 ] )
#theta = np.linspace(0,2*np.pi, N_vert )
#circle_verts[0,0:N_vert] = SIGMA*np.cos(theta)
#circle_verts[1,0:N_vert] = SIGMA*np.sin(theta)
#verts = np.zeros([2, N_vert + 1])
#units = np.ones( N_vert + 1)
#for i in range(0,len(q)):
# plt.arrow(q[i,0], q[i,1], 0.2*p[i,0], 0.2*p[i,1],\
# head_width=0.2, head_length=0.2,\
# fc='b', ec='b')
# if (q_1 != None):
# verts = np.dot(q_1[i,:,:], circle_verts ) \
# + np.outer(q[i,:],units)
# plt.plot(verts[0],verts[1],'r-')
border = 0.4
plt.xlim(min(np.vstack((qf,q))[:,0])-border,max(np.vstack((qf,q))[:,0])+border)
plt.ylim(min(np.vstack((qf,q))[:,1])-border,max(np.vstack((qf,q))[:,1])+border)
plt.axis('equal')
# warped images
if state0 != None and imgrid != None and imf != None and imm != None:
# fixed image, interpolated
plt.figure(20)
plt.clf()
simf = sample(d2unzip(imgrid),imf,hscaling=hscaling);
plt.imshow(simf.reshape(sqrt(simf.shape[0]),sqrt(simf.shape[0])).T)
plt.colorbar()
# fixed image, interpolated
plt.figure(21)
plt.clf()
simf = sample(d2unzip(imgrid),imfs,hscaling=hscaling);
plt.imshow(simf.reshape(sqrt(simf.shape[0]),sqrt(simf.shape[0])).T)
plt.colorbar()
# moving image, interpolated without transformation
plt.figure(22)
plt.clf()
simf = sample(d2unzip(imgrid),imm,hscaling=hscaling);
plt.imshow(simf.reshape(sqrt(simf.shape[0]),sqrt(simf.shape[0])).T)
plt.colorbar()
# moving image, interpolated without transformation
plt.figure(23)
plt.clf()
simf = sample(d2unzip(imgrid),imms,hscaling=hscaling);
plt.imshow(simf.reshape(sqrt(simf.shape[0]),sqrt(simf.shape[0])).T)
plt.colorbar()
# moving image, interpolated
plt.figure(24)
plt.clf()
(_,_,mimgridts) = tj.integrate(state0,pts=imgrid)
mimgridT = mimgridts[-1:].reshape(-1,DIM)
simm = sample(d2unzip(mimgridT),imm,hscaling=hscaling);
plt.imshow(simm.reshape(sqrt(simm.shape[0]),sqrt(simm.shape[0])).T)
plt.colorbar()
# moving image, interpolated
plt.figure(25)
plt.clf()
simm = sample(d2unzip(mimgridT),imms,hscaling=hscaling);
plt.imshow(simm.reshape(sqrt(simm.shape[0]),sqrt(simm.shape[0])).T)
plt.colorbar()
plt.draw()
#plt.show(block=False)
# save figures
for i in plt.get_fignums():
plt.figure(i)
try:
os.mkdir('output/%s' % os.getpid() )
except:
None
plt.savefig('output/%s/figure%d.eps' % (os.getpid(),i) )
if order == 0:
return (m0, (dq0, ))
elif order == 1:
return (m0+m1, (dq0,dq1))
else:
return (m0+m1+m2, (dq0,dq1,dq2))
def F(sim, nonmoving, x, weights=None, adjint=True, order=2, scalegrad=None, simGradCheck=False, energyGradCheck=False, visualize=False):
"""
Function that scipy's optimize function will call for returning the value
and gradient for a given x. The forward and adjoint integration is called
from this function using the values supplied by the similarity measure.
"""
N = sim['N']
DIM = sim['DIM']
i = 0
q = np.reshape( nonmoving[i:(i+N*DIM)] , [N,DIM] )
tj.gaussian.N = N
tj.gaussian.DIM = DIM
tj.gaussian.SIGMA = tj.SIGMA
K,DK,D2K,D3K,D4K,D5K,D6K = tj.derivatives_of_kernel(q,q)
# input
state0 = np.append(nonmoving, x)
if order < 1:
state0 = np.append(state0, np.zeros(N*DIM**2)) # append mu_1
if order < 2:
state0 = np.append(state0, np.zeros(N*DIM*tj.triuDim())) # append mu_2
# shift from triangular to symmetric
state0 = tj.triangular_to_state(state0)
triunonmoving = nonmoving
triux = x
nonmoving = state0[0:state0.size/2]
x = state0[state0.size/2:]
# rescale
if scalegrad:
#logging.debug("rescaling, SIGMA " + str(tj.SIGMA))
q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 )
if order >= 1:
mu0_1 = tj.SIGMA*mu0_1
if order == 2:
mu0_2 = tj.SIGMA*mu0_2
state0 = tj.weinstein_darboux_to_state(q0,q0_1,q0_2,p0,mu0_1,mu0_2)
q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 )
# flow
(t_span, y_span) = tj.integrate(state0)
stateT = y_span[-1]
# debug
qT,qT_1,qT_2,pT,muT_1,muT_2 = tj.state_to_weinstein_darboux( stateT )
#logging.info("q0: " + str(q0))
#logging.info("p0_2: " + str(p0))
#logging.info("qT: " + str(qT))
logging.info("||p0||: " + str(np.linalg.norm(p0)))
logging.info("||mu0_1||: " + str(np.linalg.norm(mu0_1)))
logging.info("||mu0_2||: " + str(np.linalg.norm(mu0_2)))
#if order >= 1:
#logging.info("q0_1: " + str(q0_1))
#logging.info("qT_1: " + str(qT_1))
#logging.info("mu0_1: " + str(mu0_1))
#if order >= 2:
#logging.info("q0_2: " + str(q0_2))
#logging.info("qT_2: " + str(qT_2))
#logging.info("mu0_2: " + str(mu0_2))
#logging.info("qT-q0: " + str(qT-q0))
#logging.info("qT_1-q0_1: " + str(qT_1-q0_1))
#logging.info("qT_2-q0_2: " + str(qT_2-q0_2))
simT = sim['f'](stateT, state0=state0, visualize=visualize)
# debug
#logging.info('match term (before flow/after flow/diff): ' + str(sim['f'](state0)[0]) + '/' + str(simT[0]) + '/' + str(sim['f'](state0)[0]-simT[0]))
logging.info('match term after flow: ' + str(simT[0]))
Ediff = tj.Hamiltonian(q0,p0,mu0_1,mu0_2) # path energy from Hamiltonian
logging.info('Hamiltonian: ' + str(Ediff))
if not adjint:
return weights[1]*simT[0]+weights[0]*Ediff
dq = simT[1][0]
if order >= 1:
dq_1 = simT[1][1]
else:
dq_1 = np.zeros(q0_1.shape)
if order >= 2:
dq_2 = simT[1][2]
else:
dq_2 = np.zeros(q0_2.shape)
logging.info("||dq||: " + str(np.linalg.norm(dq)))
logging.info("||dq_1||: " + str(np.linalg.norm(dq_1)))
logging.info("||dq_2||: " + str(np.linalg.norm(dq_2)))
ds1 = tj.weinstein_darboux_to_state(dq,dq_1,dq_2,np.zeros(dq.shape),np.zeros(dq_1.shape),np.zeros(dq_2.shape),N,DIM)
if simGradCheck:
logging.info("computing finite difference approximation of sim gradient")
fsim = lambda x: sim['f'](np.hstack( (x,stateT[x.size:],) ), state0=state0)[0]
findiffgrad = approx_fprime(stateT[0:N*DIM+N*DIM**2+N*DIM**3],fsim,1e-5)
compgrad = ds1[0:N*DIM+N*DIM**2+N*DIM**3]
graderr = np.max(abs(findiffgrad-compgrad))
logging.debug("sim gradient numerical check error: %e",graderr)
logging.debug("finite diff gradient: " + str(findiffgrad))
logging.debug("computed gradient: " + str(compgrad))
logging.debug("difference: " + str(findiffgrad-compgrad))
if energyGradCheck:
logging.info("computing finite difference approximation of energy gradient")
fsim = lambda x: tj.Hamiltonian(q0,np.reshape(x[0:N*DIM],[N,DIM]),np.reshape(x[N*DIM:N*DIM+N*DIM**2],[N,DIM,DIM]),np.reshape(x[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3],[N,DIM,DIM,DIM]))
findiffgrad = approx_fprime(np.hstack((p0.flatten(),mu0_1.flatten(),mu0_2.flatten(),)),fsim,1e-7)
compgrad = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2)
graderr = np.max(abs(findiffgrad-compgrad))
logging.debug("energy gradient numerical check error: %e",graderr)
logging.debug("finite diff gradient: " + str(findiffgrad))
logging.debug("computed gradient: " + str(compgrad))
logging.debug("difference: " + str(findiffgrad-compgrad))
(t_span, y_span) = tj.adj_integrate(stateT,ds1)
adjstate0 = y_span[-1]
assert(nonmoving.size+x.size<=adjstate0.size/2)
gradE = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2)
assert(adjstate0.size/2-nonmoving.size == gradE.size) # gradE doesn't include point variations currently
gradE = gradE[0:x.size]
grad0 = weights[1]*adjstate0[adjstate0.size/2+nonmoving.size:adjstate0.size/2+nonmoving.size+x.size] + weights[0]*gradE # transported gradient + grad of energy
adjstate0[adjstate0.size/2+nonmoving.size:adjstate0.size/2+nonmoving.size+grad0.size] = grad0
grad0 = tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size])[triunonmoving.size:triunonmoving.size+triux.size]
grad0 = np.ndarray.flatten(grad0)
# rescale
if scalegrad:
if order >= 1:
grad0[N*DIM:N*DIM+N*DIM**2] = tj.SIGMA*grad0[N*DIM:N*DIM+N*DIM**2]
if order == 2:
grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] = tj.SIGMA*grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3]
# visualization
dq0,dq0_1,dq0_2,dp0,dmu0_1,dmu0_2 = tj.state_to_weinstein_darboux( adjstate0[adjstate0.size/2:adjstate0.size],N,DIM )
#logging.info("dp0: " + str(dp0))
logging.info("||dp0|| final: " + str(np.linalg.norm(dp0)))
#logging.info("dmu0_1: " + str(dmu0_1))
logging.info("||dmu0_1|| final: " + str(np.linalg.norm(dmu0_1)))
#logging.info("dmu0_2: " + str(dmu0_2))
logging.info("||dmu0_2|| final: " + str(np.linalg.norm(dmu0_2)))
#logging.info("adjstate0: " + str(adjstate0))
#logging.info("grad0: " + str(grad0))
#plt.figure(0)
#plt.quiver(q0[:,0],q0[:,1],dp0[:,0],dp0[:,1])
## pause
#raw_input("F: Press ENTER to continue")
return (weights[1]*simT[0]+weights[0]*Ediff, grad0)
for i in range(0,len(q)):
plt.arrow(q[i,0], q[i,1], 0.2*p[i,0], 0.2*p[i,1],\
head_width=0.2, head_length=0.2,\
fc='b', ec='b')
if (q1 != None):
verts = np.dot(q1[i,:,:], circle_verts ) \
+ np.outer(q[i,:],units)
print np.shape( verts )
print np.shape( q1 )
plt.plot(verts[0],verts[1],'b-')
plt.axis([- W, W,- W, W ])
return f
y_data = np.load('output/state_data.npy')
time_data = np.load('output/time_data.npy')
#print 'shape of y_data is ' + str( y_data.shape )
N_timestep = y_data.shape[0]
print 'generating png files'
for k in range(0,N_timestep):
q,q_1,q_2,p,mu_1,mu_2 = tj.state_to_weinstein_darboux( y_data[k] )
f = display_velocity_field(q,p,mu_1,mu_2,q_1)
time_s = str(time_data[k])
plt.suptitle('t = '+ time_s[0:4] , fontsize=16 , x = 0.75 , y = 0.25 )
fname = './movie_frames/frame_'+str(k)+'.png'
f.savefig( fname )
plt.close(f)
print 'done'
def Fdisp(sim, nonmoving, x, adjint=True, weights=None, order=2, scalegrad=None):
"""
As F above but using linear displacement instead of integrating the flows. For testing.
"""
# input
N = sim['N'] # debug
DIM = sim['DIM'] # debug
tj.gaussian.N = N
tj.gaussian.DIM = DIM
tj.gaussian.SIGMA = tj.SIGMA
#x = np.append(x, np.zeros(N*DIM**3)) # debug
state0 = np.append(nonmoving, x)
if order < 1:
state0 = np.append(state0, np.zeros(N*DIM**2)) # append mu_1
if order < 2:
state0 = np.append(state0, np.zeros(N*DIM**3)) # append mu_2
# shift from triangular to symmetric
#assert(np.allclose(state0,tj.state_to_triangular(tj.triangular_to_state(state0))))
state0 = tj.triangular_to_state(state0)
triunonmoving = nonmoving
triux = x
nonmoving = state0[0:state0.size/2]
x = state0[state0.size/2:]
# rescale
if scalegrad:
#logging.debug("rescaling, SIGMA " + str(tj.SIGMA))
q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 )
if order >= 1:
mu0_1 = tj.SIGMA*mu0_1
if order == 2:
mu0_2 = tj.SIGMA*mu0_2
state0 = tj.weinstein_darboux_to_state(q0,q0_1,q0_2,p0,mu0_1,mu0_2)
q0,q0_1,q0_2,p0,mu0_1,mu0_2 = tj.state_to_weinstein_darboux( state0 )
# displacement
qT = q0+p0
qT_1 = q0_1+mu0_1
qT_2 = q0_2+mu0_2
stateT = tj.weinstein_darboux_to_state(qT,qT_1,qT_2,p0,mu0_1,mu0_2)
# debug
#qT,qT_1,qT_2,pT,muT_1,muT_2 = tj.state_to_weinstein_darboux( stateT )
#logging.info("q0_1: " + str(q0_1))
#logging.info("q0_2: " + str(q0_2))
#logging.info("p0: " + str(p0))
#logging.info("mu0_1: " + str(mu0_1))
#logging.info("mu0_2: " + str(mu0_2))
#logging.info("qT: " + str(qT))
#logging.info("qT_1: " + str(qT_1))
#logging.info("qT_2: " + str(qT_2))
#logging.info("qT-q0: " + str(qT-q0))
#logging.info("qT_1-q0_1: " + str(qT_1-q0_1))
#logging.info("qT_2-q0_2: " + str(qT_2-q0_2))
logging.info("||p0||: " + str(np.linalg.norm(p0)))
logging.info("||mu0_1||: " + str(np.linalg.norm(mu0_1)))
logging.info("||mu0_2||: " + str(np.linalg.norm(mu0_2)))
simT = sim['f'](stateT)
# debug
logging.info('match term (after flow): ' + str(simT[0]))
Ediff = tj.Hamiltonian(q0,p0,mu0_1,mu0_2) # path energy from Hamiltonian
logging.info('Hamiltonian: ' + str(Ediff))
if not adjint:
return weights[1]*simT[0]+weights[0]*Ediff
dq = simT[1][0]
if order >= 1:
dq_1 = simT[1][1]
else:
dq_1 = np.zeros([N,DIM,DIM])
if order >= 2:
dq_2 = simT[1][2]
else:
dq_2 = np.zeros([N,DIM,DIM,DIM])
ds1 = tj.weinstein_darboux_to_state(np.zeros(dq.shape),np.zeros(dq_1.shape),np.zeros(dq_2.shape),dq,dq_1,dq_2,sim['N'],sim['DIM'])
adjstate0 = np.append(np.zeros(ds1.size), ds1)
assert(nonmoving.size+x.size==adjstate0.size/2)
gradE = tj.grad_Hamiltonian(q0,p0,mu0_1,mu0_2)
assert(adjstate0.size/2-nonmoving.size == gradE.size) # gradE doesn't include point variations currently
grad0 = np.array(weights[1]*adjstate0[adjstate0.size/2+nonmoving.size:] + weights[0]*gradE) # transported gradient + grad of energy
# get from symmetric to triangular form
#assert(np.allclose(adjstate0[adjstate0.size/2:adjstate0.size],tj.triangular_to_state(tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size]))))
grad0 = tj.state_to_triangular(adjstate0[adjstate0.size/2:adjstate0.size])[triunonmoving.size:triunonmoving.size+triux.size]
grad0 = np.ndarray.flatten(grad0)
# rescale
if scalegrad:
if order >= 1:
grad0[N*DIM:N*DIM+N*DIM**2] = tj.SIGMA*grad0[N*DIM:N*DIM+N*DIM**2]
if order == 2:
grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3] = tj.SIGMA*grad0[N*DIM+N*DIM**2:N*DIM+N*DIM**2+N*DIM**3]
# debug
#grad0 = grad0[0:N*DIM+N*DIM**2]
logging.info("||dq||: " + str(np.linalg.norm(dq)))
logging.info("||dq_1||: " + str(np.linalg.norm(dq_1)))
logging.info("||dq_2||: " + str(np.linalg.norm(dq_2)))
#logging.info("grad0: " + str(grad0))
## pause
#raw_input("Fdisp: Press ENTER to continue")
return (weights[1]*simT[0]+weights[0]*Ediff, grad0)
