#coding=utf8
########################################################################
### ###
### Created by Martin Genet, 2016 ###
### ###
### École Polytechnique, Palaiseau, France ###
### ###
########################################################################
import dolfin
import glob
import numpy
import os
import myFEniCSPythonLibrary as myFEniCS
from print_tools import *
########################################################################
dolfin.parameters['form_compiler']['cpp_optimize_flags'] = '-O3'
dolfin.parameters["form_compiler"]["cpp_optimize"] = True
dolfin.parameters["form_compiler"]["optimize"] = False # can't use that for "complex" mechanical models…
########################################################################
def fedic(
working_folder,
working_basename,
images_folder,
images_basename,
mesh_folder,
mesh_basename,
images_k_ref=0,
images_zfill=2,
images_quadrature=None,
mesh_degree=1,
penalty=0.9,
tangent_type="Idef", # Idef, Idef-wHess, Iold, Iref
residual_type="Iref", # Iref, Iold, Iref-then-Iold
relax_type="const", # const, aitken, manual
relax_init=1.0,
relax_n_iter=10,
tol_res=None,
tol_dU=None,
tol_im=None,
n_iter_max=100,
continue_after_fail=0,
print_iterations=0):
tab = 0
print_str(tab,"Loading mesh…")
mesh_filename = mesh_folder+"/"+mesh_basename+".xml"
assert os.path.exists(mesh_filename), "No mesh in "+mesh_filename+". Aborting."
mesh = dolfin.Mesh(mesh_filename)
dX = dolfin.dx(mesh)
mesh_volume = dolfin.assemble(dolfin.Constant(1)*dX)
print_str(tab,"Checking number of frames…")
n_frames = len(glob.glob(images_folder+"/"+images_basename+"_"+"[0-9]"*images_zfill+".vti"))
#n_frames = 2
assert (n_frames > 1), "n_frames = "+str(n_frames)+" <= 1. Aborting."
print_var(tab+1,"n_frames",n_frames)
assert (abs(images_k_ref) < n_frames), "abs(images_k_ref) = "+str(images_k_ref)+" >= n_frames. Aborting."
images_k_ref = images_k_ref%n_frames
print_var(tab+1,"images_k_ref",images_k_ref)
print_str(tab,"Computing quadrature degree for images…")
ref_image_filename = images_folder+"/"+images_basename+"_"+str(images_k_ref).zfill(images_zfill)+".vti"
if (images_quadrature is None):
images_quadrature = myFEniCS.compute_quadrature_degree(
image_filename=ref_image_filename,
mesh=mesh,
verbose=0)
print_var(tab+1,"images_quadrature",images_quadrature)
dolfin.parameters["form_compiler"]["quadrature_degree"] = images_quadrature
print_str(tab,"Loading reference image…")
images_dimension = myVTK.computeImageDimensionality(
image_filename=ref_image_filename,
verbose=0)
assert (images_dimension in (2,3)), "images_dimension must be 2 or 3. Aborting."
fe = dolfin.FiniteElement(
family="Quadrature",
cell=mesh.ufl_cell(),
degree=images_quadrature,
quad_scheme="default")
ve = dolfin.VectorElement(
family="Quadrature",
cell=mesh.ufl_cell(),
degree=images_quadrature,
quad_scheme="default")
te = dolfin.TensorElement(
family="Quadrature",
cell=mesh.ufl_cell(),
degree=images_quadrature,
quad_scheme="default")
te._quad_scheme = "default"
for k in xrange(images_dimension**2):
te.sub_elements()[k]._quad_scheme = "default"
if (images_dimension == 2):
Iref = myFEniCS.ExprIm2(
filename=ref_image_filename,
element=fe)
DIref = myFEniCS.ExprGradIm2(
filename=ref_image_filename,
element=ve)
elif (images_dimension == 3):
Iref = myFEniCS.ExprIm3(
filename=ref_image_filename,
element=fe)
DIref = myFEniCS.ExprGradIm3(
filename=ref_image_filename,
element=ve)
Iref_norm = (dolfin.assemble(Iref**2 * dX)/mesh_volume)**(1./2)
assert (Iref_norm > 0.), "Iref_norm = "+str(Iref_norm)+" <= 0. Aborting."
print_var(tab+1,"Iref_norm",Iref_norm)
print_str(tab,"Defining functions…")
vfs = dolfin.VectorFunctionSpace(
mesh=mesh,
family="Lagrange",
degree=mesh_degree)
U = dolfin.Function(
vfs,
name="displacement")
U_norm = 0.
Uold = dolfin.Function(
vfs,
name="previous displacement")
Uold_norm = 0.
dU = dolfin.Function(
vfs,
name="displacement correction")
dU_ = dolfin.TrialFunction(vfs)
dV_ = dolfin.TestFunction(vfs)
print_str(tab,"Printing initial solution…")
if not os.path.exists(working_folder):
os.mkdir(working_folder)
pvd_basename = working_folder+"/"+working_basename+"_"
file_pvd = dolfin.File(pvd_basename+".pvd")
for vtu_filename in glob.glob(pvd_basename+"*.vtu"):
os.remove(vtu_filename)
file_pvd << (U, float(images_k_ref))
print_str(tab,"Defining variational forms…")
penalty = dolfin.Constant(penalty)
if (images_dimension == 2):
Idef = myFEniCS.ExprDefIm2(
U=U,
#filename=ref_image_filename,
element=fe)
DIdef = myFEniCS.ExprGradDefIm2(
U=U,
#filename=ref_image_filename,
element=ve)
if ("-wHess" in tangent_type):
DDIdef = myFEniCS.ExprHessDefIm2(
U=U,
#filename=ref_image_filename,
element=te)
Iold = myFEniCS.ExprDefIm2(
U=Uold,
#filename=ref_image_filename,
element=fe)
DIold = myFEniCS.ExprGradDefIm2(
U=Uold,
#filename=ref_image_filename,
element=ve)
elif (images_dimension == 3):
Idef = myFEniCS.ExprDefIm3(
U=U,
#filename=ref_image_filename,
element=fe)
DIdef = myFEniCS.ExprGradDefIm3(
U=U,
#filename=ref_image_filename,
element=ve)
if ("-wHess" in tangent_type):
DDIdef = myFEniCS.ExprHessDefIm3(
U=U,
filename=ref_image_filename,
element=te)
Iold = myFEniCS.ExprDefIm3(
U=Uold,
#filename=ref_image_filename,
element=fe)
DIold = myFEniCS.ExprGradDefIm3(
U=Uold,
#filename=ref_image_filename,
element=ve)
if (tangent_type.startswith("Idef")):
a = penalty * dolfin.inner(dolfin.dot(DIdef, dU_),
dolfin.dot(DIdef, dV_)) * dX
if ("-wHess" in tangent_type):
a += penalty * (Iref-Idef) * dolfin.inner(dolfin.dot(DDIdef, dU_),
dV_) * dX
elif (tangent_type == "Iold"):
a = penalty * dolfin.inner(dolfin.dot(DIold, dU_),
dolfin.dot(DIold, dV_)) * dX
elif (tangent_type == "Iref"):
a = penalty * dolfin.inner(dolfin.dot(DIref, dU_),
dolfin.dot(DIref, dV_)) * dX
bdef = - penalty * (Idef-Iref) * dolfin.dot(DIdef, dV_) * dX
bold = - penalty * (Idef-Iold) * dolfin.dot(DIdef, dV_) * dX
a += (1.-penalty) * dolfin.inner(dolfin.grad(dU_),
dolfin.grad(dV_)) * dX
bdef += - (1.-penalty) * dolfin.inner(dolfin.grad( U ),
dolfin.grad(dV_)) * dX
bold += - (1.-penalty) * dolfin.inner(dolfin.grad( U ),
dolfin.grad(dV_)) * dX
b0 = dolfin.inner(Iref, dolfin.dot(DIref, dV_)) * dX
B0 = dolfin.assemble(b0)
res_norm0 = numpy.linalg.norm(B0)
assert (res_norm0 > 0.), "res_norm0 = "+str(res_norm0)+" <= 0. Aborting."
print_var(tab+1,"res_norm0",res_norm0)
# linear system
A = None
if (tangent_type == "Iref"):
A = dolfin.assemble(a, tensor=A)
B = None
print_str(tab,"Looping over frames…")
n_iter_tot = 0
global_success = True
for forward_or_backward in ["forward", "backward"]:
print_var(tab,"forward_or_backward",forward_or_backward)
if (forward_or_backward == "forward"):
k_frames_old = range(images_k_ref , n_frames-1, +1)
k_frames = range(images_k_ref+1, n_frames , +1)
elif (forward_or_backward == "backward"):
k_frames_old = range(images_k_ref , 0, -1)
k_frames = range(images_k_ref-1, -1, -1)
print_var(tab,"k_frames",k_frames)
if (forward_or_backward == "backward"):
U.vector()[:] = 0.
U_norm = 0.
Uold.vector()[:] = 0.
Uold_norm = 0.
tab += 1
success = True
for (k_frame,k_frame_old) in zip(k_frames,k_frames_old):
print_var(tab-1,"k_frame",k_frame)
if (print_iterations):
frame_basename = working_folder+"/"+working_basename+"-frame="+str(k_frame).zfill(images_zfill)
if (os.path.exists(frame_basename+".pdf")):
os.remove(frame_basename+".pdf")
file_dat_frame = open(frame_basename+".dat", "w")
file_dat_frame.write("#k_iter res_norm res_err relax dU_norm U_norm dU_err im_diff im_err im_err_rel\n")
file_pvd_frame = dolfin.File(frame_basename+"_.pvd")
for vtu_filename in glob.glob(frame_basename+"_*.vtu"):
os.remove(vtu_filename)
file_pvd_frame << (U, 0.)
print_str(tab,"Loading image, image gradient and image hessian…")
image_filename = images_folder+"/"+images_basename+"_"+str(k_frame).zfill(images_zfill)+".vti"
Idef.init_image( filename=image_filename)
DIdef.init_image(filename=image_filename)
if ("-wHess" in tangent_type):
DDIdef.init_image(filename=image_filename)
image_filename = images_folder+"/"+images_basename+"_"+str(k_frame_old).zfill(images_zfill)+".vti"
Iold.init_image( filename=image_filename)
DIold.init_image(filename=image_filename)
# linear system: matrix
if (tangent_type == "Iold"):
A = dolfin.assemble(a, tensor=A)
#print_var(tab,"A",A.array())
#A_norm = numpy.linalg.norm(A.array())
#print_var(tab,"A_norm",A_norm)
if (print_iterations):
U.vector()[:] = 0.
im_diff = (dolfin.assemble((Idef-Iref)**2 * dX)/mesh_volume)**(1./2)
im_err = im_diff/Iref_norm
file_dat_frame.write(" ".join([str(val) for val in [-2, None, None, None, None, None, None, im_diff, im_err, None]])+"\n")
U.vector()[:] = Uold.vector()[:]
im_diff = (dolfin.assemble((Idef-Iref)**2 * dX)/mesh_volume)**(1./2)
im_err = im_diff/Iref_norm
file_dat_frame.write(" ".join([str(val) for val in [-1, None, None, None, None, None, None, im_diff, im_err, None]])+"\n")
print_str(tab,"Running registration…")
tab += 1
k_iter = 0
if (residual_type.startswith("Iref")):
using_Iold_residual = False
elif (residual_type.startswith("Iold")):
using_Iold_residual = True
while (True):
print_var(tab-1,"k_iter",k_iter)
n_iter_tot += 1
# linear system: matrix
if (tangent_type.startswith("Idef")):
A = dolfin.assemble(a, tensor=A)
#print_var(tab,"A",A.array())
#A_norm = numpy.linalg.norm(A.array())
#print_sci(tab,"A_norm",A_norm)
# linear system: residual
if (relax_type == "aitken"):
if (k_iter == 1):
B_old = B.copy()
elif (k_iter > 1):
B_old[:] = B[:]
if (using_Iold_residual):
B = dolfin.assemble(bold, tensor=B)
else:
B = dolfin.assemble(bdef, tensor=B)
#print_var(tab,"B",B.array())
# residual error
res_norm = numpy.linalg.norm(B.array())
#print_sci(tab,"res_norm",res_norm)
res_err = res_norm/res_norm0
print_sci(tab,"res_err",res_err)
# linear system: solve
dolfin.solve(A, dU.vector(), B)
#print_var(tab,"dU",dU.vector().array())
# relaxation
if (relax_type == "constant"):
if (k_iter == 0):
relax = relax_init
elif (relax_type == "aitken"):
if (k_iter == 0):
relax = relax_init
else:
if (k_iter == 1):
dB = B - B_old
elif (k_iter > 1):
dB[:] = B[:] - B_old[:]
relax *= (-1.) * B_old.inner(dB) / dB.inner(dB)
print_sci(tab,"relax",relax)
elif (relax_type == "manual"):
res_norm_relax = numpy.empty(relax_n_iter)
tab += 1
for relax_k in xrange(relax_n_iter):
print_var(tab-1,"relax_k",relax_k)
U.vector()[:] += (1./relax_n_iter) * dU.vector()[:]
B = dolfin.assemble(b, tensor=B)
res_norm_relax[relax_k] = numpy.linalg.norm(B)
print_sci(tab,"res_norm_relax",res_norm_relax[relax_k])
U.vector()[:] -= dU.vector()[:]
#print_var(tab,"res_norm_relax",res_norm_relax)
if (print_iterations):
iter_basename = frame_basename+"-iter="+str(k_iter).zfill(3)
open(iter_basename+".dat", "w").write("\n".join([" ".join([str(val) for val in [float(relax_k+1)/relax_n_iter, res_norm_relax[relax_k]]]) for relax_k in xrange(relax_n_iter)]))
os.system("gnuplot -e \"set terminal pdf; set output '"+iter_basename+".pdf'; plot '"+iter_basename+".dat' u 1:2 w l notitle\"")
relax_k = numpy.argmin(res_norm_relax)
relax = float(relax_k+1)/relax_n_iter
print_sci(tab,"relax",relax)
else:
assert (0), "relax_type must be \"constant\", \"aitken\" or \"manual\". Aborting."
# solution update
U.vector()[:] += relax * dU.vector()[:]
U_norm = numpy.linalg.norm(U.vector().array())
if (print_iterations):
#print_var(tab,"U",U.vector().array())
file_pvd_frame << (U, float(k_iter+1))
# displacement error
dU_norm = numpy.linalg.norm(dU.vector().array())
dU_err = dU_norm/max(Uold_norm,U_norm)
print_sci(tab,"dU_err",dU_err)
# image error
if (k_iter > 0):
im_diff_old = im_diff
im_diff = (dolfin.assemble((Idef-Iref)**2 * dX)/mesh_volume)**(1./2)
#print_sci(tab,"im_diff",im_diff)
im_err = im_diff/Iref_norm
print_sci(tab,"im_err",im_err)
if (k_iter == 0):
im_err_rel = 1.
else:
im_err_rel = abs(im_diff-im_diff_old)/im_diff_old
print_sci(tab,"im_err_rel",im_err_rel)
if (print_iterations):
file_dat_frame.write(" ".join([str(val) for val in [k_iter, res_norm, res_err, relax, dU_norm, U_norm, dU_err, im_diff, im_err, im_err_rel]])+"\n")
# exit test
success = True
if (tol_res is not None) and (res_err > tol_res):
success = False
if (tol_dU is not None) and (dU_err > tol_dU):
success = False
if (tol_im is not None) and (im_err_rel > tol_im):
success = False
# exit
if (success):
print_str(tab,"Nonlinear solver converged…")
break
if (k_iter == n_iter_max-1):
if (residual_type=="Iref-then-Iold") and not (using_Iold_residual):
print_str(tab,"Warning! Nonlinear solver failed to converge…using Iold instead of Iref. (k_frame = "+str(k_frame)+")")
using_Iold_residual = True
U.vector()[:] = Uold.vector()[:]
U_norm = Uold_norm
k_iter = 0
continue
else:
print_str(tab,"Warning! Nonlinear solver failed to converge… (k_frame = "+str(k_frame)+")")
global_success = False
break
# increment counter
k_iter += 1
tab -= 1
if (print_iterations):
#os.remove(frame_basename+"_.pvd")
file_dat_frame.close()
os.system("gnuplot -e \"set terminal pdf; set output '"+frame_basename+".pdf'; set key box textcolor variable; set grid; set logscale y; set yrange [1e-4:1e1]; set ytics nomirror; set y2tics nomirror; plot '"+frame_basename+".dat' u 1:3 pt 1 lw 3 title 'res_err', '' u 1:7 pt 1 lw 3 title 'dU_err', '' using 1:9 pt 1 lw 3 title 'im_err', '' using 1:10 pt 1 lw 3 title 'im_err_rel', '' u 1:4 axis x1y2 pt 2 lw 3 title 'relax', "+str(tol_res or tol_dU or tol_im)+" lt -1 notitle\"")
if not (success) and not (continue_after_fail):
break
# solution update
Uold.vector()[:] = U.vector()[:]
Uold_norm = U_norm
print_str(tab,"Printing solution…")
file_pvd << (U, float(k_frame))
tab -= 1
if not (success) and not (continue_after_fail):
break
print_var(tab,"n_iter_tot",n_iter_tot)
#os.remove(pvd_basename+".pvd")
return global_success