Merge lp:~simon-funke/libadjoint/online_revolve_dolfin_adjoint into lp:libadjoint

[Simon Funke]

- Implementation of the read, write and delete callbacks
- checkpoint burgers example uses memory and disk checkpoints

[lp:~simon-funke/libadjoint/online_revolve_dolfin_adjoint]

86. By Simon Funke on 2012-01-18

Use str() instead of __str__()

Unmerged revisions

86. By Simon Funke on 2012-01-18

Use str() instead of __str__()

85. By Simon Funke on 2012-01-17

Merge from "trunk"

84. By Simon Funke on 2012-01-17

Some final tidy up

83. By Simon Funke on 2012-01-17

Fix the timestep prediction in the checkpoint burgers test. The test now tests a multistage revolve with memory and disk checkpoints.

82. By Simon Funke on 2012-01-17

After implementing the Vector.delete() the offline checkpointing works.

81. By Simon Funke on 2012-01-17

An implementation of the Vector's read and write functions. With these we can now use offline checkpointing that stores the checkpoints on disk. However, the delete function is not implemented yet, causing the simulation to crash at the very end.

80. By Patrick Farrell on 2012-01-13

Get checkpointing working for simulations which solve multiple equations per timestep.
That was surprisingly easy, once I realised how.

Add a checkpoint_stokes test. We do 11 timesteps, but only give 5 checkpoint slots, so it has
to replay several times during the adjoint run in order to acquire the solutions about
which it wants to linearise.

79. By Simon Funke on 2012-01-12

Remove the print statement.

78. By Simon Funke on 2012-01-12

Commit a checkpointing test.

77. By Patrick Farrell on 2012-01-12

Impose the homogenised boundary conditions on the R* term, too.

=== added file '__init__.py'
--- __init__.py	1970-01-01 00:00:00 +0000
+++ __init__.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,3 @@
+from solving import *
+from assembly import *
+from utils import *

=== added file 'assembly.py'
--- assembly.py	1970-01-01 00:00:00 +0000
+++ assembly.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,23 @@
+import dolfin
+import copy
+import collections
+
+assembly_cache = {}
+bc_cache = collections.defaultdict(list)
+
+dolfin_assemble = dolfin.assemble
+def assemble(*args, **kwargs):
+  form = args[0]
+  output = dolfin_assemble(*args, **kwargs)
+  assembly_cache[output] = form
+  return output
+
+bc_apply = dolfin.DirichletBC.apply
+def adjoint_bc_apply(self, *args, **kwargs):
+  for arg in args:
+    bc_data = copy.copy(bc_cache[arg])
+    bc_data.append(self)
+    bc_cache[arg] = bc_data
+  return bc_apply(self, *args, **kwargs)
+dolfin.DirichletBC.apply = adjoint_bc_apply
+

=== added file 'solving.py'
--- solving.py	1970-01-01 00:00:00 +0000
+++ solving.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,859 @@
+import ufl
+import ufl.classes
+import ufl.algorithms
+import ufl.operators
+
+import dolfin.fem.solving
+import dolfin
+
+import libadjoint
+import libadjoint.exceptions
+
+import hashlib
+import time
+
+import assembly
+
+debugging={}
+
+class CoeffStore(object):
+  '''This object manages the mapping from Dolfin coefficients to libadjoint Variables.
+  In the process, it also manages the incrementing of the timestep associated with each
+  variable, so that the user does not have to manually manage the time information.'''
+  def __init__(self):
+    self.coeffs={}
+
+  def next(self, coeff):
+    '''Increment the timestep corresponding to the provided Dolfin
+    coefficient and then return the corresponding libadjoint variable.'''
+
+    try:
+      self.coeffs[coeff]+=1
+    except KeyError:
+      self.coeffs[coeff]=0
+
+    return libadjoint.Variable(str(coeff), self.coeffs[coeff], 0)
+
+  def __getitem__(self, coeff):
+    '''Return the libadjoint variable corresponding to coeff.'''
+
+    if not self.coeffs.has_key(coeff):
+      self.coeffs[coeff]=0
+
+    return libadjoint.Variable(str(coeff), self.coeffs[coeff], 0)
+
+adj_variables=CoeffStore()
+
+# Set record_all to true to enable recording all variables in the forward
+# run. This is primarily useful for debugging.
+debugging["record_all"] = False
+debugging["test_hermitian"] = None
+debugging["test_derivative"] = None
+debugging["fussy_replay"] = True
+
+# Create the adjointer, the central object that records the forward solve
+# as it happens.
+adjointer = libadjoint.Adjointer()
+
+# A dictionary that saves the functionspaces of all checkpoint variables that have been saved to disk
+checkpoint_fs = {}
+
+def annotate(*args, **kwargs):
+  '''This routine handles all of the annotation, recording the solves as they
+  happen so that libadjoint can rewind them later.'''
+
+  if isinstance(args[0], ufl.classes.Equation):
+    # annotate !
+
+    # Unpack the arguments, using the same routine as the real Dolfin solve call
+    unpacked_args = dolfin.fem.solving._extract_args(*args, **kwargs)
+    eq = unpacked_args[0]
+    u  = unpacked_args[1]
+    bcs = unpacked_args[2]
+    J = unpacked_args[3]
+
+    if isinstance(eq.lhs, ufl.Form) and isinstance(eq.rhs, ufl.Form):
+      eq_lhs = eq.lhs
+      eq_rhs = eq.rhs
+      eq_bcs = bcs
+      linear = True
+    else:
+      eq_lhs, eq_rhs = define_nonlinear_equation(eq.lhs, u)
+      F = eq.lhs
+      eq_bcs = []
+      linear = False
+
+    newargs = list(args)
+
+    try:
+      solver_params = kwargs["solver_parameters"]
+      ksp = solver_params["linear_solver"]
+    except KeyError:
+      ksp = None
+
+    try:
+      solver_params = kwargs["solver_parameters"]
+      pc = solver_params["preconditioner"]
+    except KeyError:
+      pc = None
+
+  elif isinstance(args[0], dolfin.cpp.Matrix):
+    linear = True
+    try:
+      eq_lhs = assembly.assembly_cache[args[0]]
+    except KeyError:
+      raise libadjoint.exceptions.LibadjointErrorInvalidInputs("dolfin_adjoint did not assemble your form, and so does not recognise your matrix. Did you from dolfin_adjoint import *?")
+
+    try:
+      eq_rhs = assembly.assembly_cache[args[2]]
+    except KeyError:
+      raise libadjoint.exceptions.LibadjointErrorInvalidInputs("dolfin_adjoint did not assemble your form, and so does not recognise your right-hand side. Did you from dolfin_adjoint import *?")
+
+    u = args[1]
+    if not isinstance(u, dolfin.Function):
+      raise libadjoint.exceptions.LibadjointErrorInvalidInputs("dolfin_adjoint needs the Function you are solving for, rather than its .vector().")
+    newargs = list(args)
+    newargs[1] = u.vector() # for the real solve later
+
+    try:
+      ksp = args[3]
+    except IndexError:
+      ksp = None
+
+    try:
+      pc = args[4]
+    except IndexError:
+      pc = None
+
+    eq_bcs = list(set(assembly.bc_cache[args[0]] + assembly.bc_cache[args[2]]))
+  else:
+    raise libadjoint.exceptions.LibadjointErrorNotImplemented("Don't know how to annotate your equation, sorry!")
+
+  # Suppose we are solving for a variable w, and that variable shows up in the
+  # coefficients of eq_lhs/eq_rhs.
+  # Does that mean:
+  #  a) the /previous value/ of that variable, and you want to timestep?
+  #  b) the /value to be solved for/ in this solve?
+  # i.e. is it timelevel n-1, or n?
+  # if Dolfin is doing a linear solve, we want case a);
+  # if Dolfin is doing a nonlinear solve, we want case b).
+  # so if we are doing a nonlinear solve, we bump the timestep number here
+  # /before/ we map the coefficients -> dependencies,
+  # so that libadjoint records the dependencies with the right timestep number.
+  if not linear:
+    var = adj_variables.next(u)
+
+  # Set up the data associated with the matrix on the left-hand side. This goes on the diagonal
+  # of the 'large' system that incorporates all of the timelevels, which is why it is prefixed
+  # with diag.
+  diag_name = hashlib.md5(str(eq_lhs) + str(eq_rhs) + str(u) + str(time.time())).hexdigest() # we don't have a useful human-readable name, so take the md5sum of the string representation of the forms
+  diag_deps = [adj_variables[coeff] for coeff in ufl.algorithms.extract_coefficients(eq_lhs) if hasattr(coeff, "function_space")]
+  diag_coeffs = [coeff for coeff in ufl.algorithms.extract_coefficients(eq_lhs) if hasattr(coeff, "function_space")]
+  diag_block = libadjoint.Block(diag_name, dependencies=diag_deps, test_hermitian=debugging["test_hermitian"], test_derivative=debugging["test_derivative"])
+
+  # Similarly, create the object associated with the right-hand side data.
+  if linear:
+    rhs = RHS(eq_rhs)
+  else:
+    rhs = NonlinearRHS(eq_rhs, F, u, bcs, mass=eq_lhs)
+
+  # We need to check if this is the first equation,
+  # so that we can register the appropriate initial conditions.
+  # These equations are necessary so that libadjoint can assemble the
+  # relevant adjoint equations for the adjoint variables associated with
+  # the initial conditions.
+  for coeff, dep in zip(rhs.coefficients(),rhs.dependencies()) + zip(diag_coeffs, diag_deps):
+    # If coeff is not known, it must be an initial condition.
+    if not adjointer.variable_known(dep):
+
+      if not linear: # don't register initial conditions for the first nonlinear solve.
+        if dep == var:
+          continue
+
+      fn_space = coeff.function_space()
+      block_name = "Identity: %s" % str(fn_space)
+      identity_block = libadjoint.Block(block_name)
+    
+      init_rhs=Vector(coeff).duplicate()
+      init_rhs.axpy(1.0,Vector(coeff))
+
+      def identity_assembly_cb(variables, dependencies, hermitian, coefficient, context):
+        assert coefficient == 1
+        return (Matrix(ufl.Identity(fn_space.dim())), Vector(dolfin.Function(fn_space)))
+
+      identity_block.assemble=identity_assembly_cb
+
+      if debugging["record_all"]:
+        adjointer.record_variable(dep, libadjoint.MemoryStorage(Vector(coeff)))
+
+      initial_eq = libadjoint.Equation(dep, blocks=[identity_block], targets=[dep], rhs=RHS(init_rhs))
+      adjointer.register_equation(initial_eq)
+      assert adjointer.variable_known(dep)
+
+
+  # c.f. the discussion above. In the linear case, we want to bump the
+  # timestep number /after/ all of the dependencies' timesteps have been
+  # computed for libadjoint.
+  if linear:
+    var = adj_variables.next(u)
+
+  # With the initial conditions out of the way, let us now define the callbacks that
+  # define the actions of the operator the user has passed in on the lhs of this equation.
+
+  def diag_assembly_cb(dependencies, values, hermitian, coefficient, context):
+    '''This callback must conform to the libadjoint Python block assembly
+    interface. It returns either the form or its transpose, depending on
+    the value of the logical hermitian.'''
+
+    assert coefficient == 1
+
+    value_coeffs=[v.data for v in values]
+    eq_l=dolfin.replace(eq_lhs, dict(zip(diag_coeffs, value_coeffs)))
+
+    if hermitian:
+      # Homogenise the adjoint boundary conditions. This creates the adjoint
+      # solution associated with the lifted discrete system that is actually solved.
+      adjoint_bcs = [dolfin.homogenize(bc) for bc in eq_bcs if isinstance(bc, dolfin.DirichletBC)]
+      if len(adjoint_bcs) == 0: adjoint_bcs = None
+      return (Matrix(dolfin.adjoint(eq_l), bcs=adjoint_bcs, pc=pc, ksp=ksp), Vector(None, fn_space=u.function_space()))
+    else:
+      return (Matrix(eq_l, bcs=eq_bcs, pc=pc, ksp=ksp), Vector(None, fn_space=u.function_space()))
+  diag_block.assemble = diag_assembly_cb
+
+  def diag_action_cb(dependencies, values, hermitian, coefficient, input, context):
+    value_coeffs = [v.data for v in values]
+    eq_l = dolfin.replace(eq_lhs, dict(zip(diag_coeffs, value_coeffs)))
+
+    if hermitian:
+      eq_l = dolfin.adjoint(eq_l)
+
+    output_vec = dolfin.assemble(coefficient * dolfin.action(eq_l, input.data))
+    output_fn = dolfin.Function(input.data.function_space())
+    vec = output_fn.vector()
+    for i in range(len(vec)):
+      vec[i] = output_vec[i]
+
+    return Vector(output_fn)
+  diag_block.action = diag_action_cb
+
+  if len(diag_deps) > 0:
+    # If this block is nonlinear (the entries of the matrix on the LHS
+    # depend on any variable previously computed), then that will induce
+    # derivative terms in the adjoint equations. Here, we define the
+    # callback libadjoint will need to compute such terms.
+    def derivative_action(dependencies, values, variable, contraction_vector, hermitian, input, coefficient, context):
+      dolfin_variable = values[dependencies.index(variable)].data
+      dolfin_values = [val.data for val in values]
+
+      current_form = dolfin.replace(eq_lhs, dict(zip(diag_coeffs, dolfin_values)))
+
+      deriv = dolfin.derivative(current_form, dolfin_variable)
+      args = ufl.algorithms.extract_arguments(deriv)
+      deriv = dolfin.replace(deriv, {args[1]: contraction_vector.data}) # contract over the middle index
+
+      if hermitian:
+        deriv = dolfin.adjoint(deriv)
+
+      action = coefficient * dolfin.action(deriv, input.data)
+
+      return Vector(action)
+    diag_block.derivative_action = derivative_action
+
+  eqn = libadjoint.Equation(var, blocks=[diag_block], targets=[var], rhs=rhs)
+
+  cs = adjointer.register_equation(eqn)
+  if cs == int(libadjoint.constants.adj_constants["ADJ_CHECKPOINT_STORAGE_MEMORY"]):
+    for coeff in adj_variables.coeffs.keys(): 
+      if adj_variables[coeff] == var: continue
+      adjointer.record_variable(adj_variables[coeff], libadjoint.MemoryStorage(Vector(coeff), cs=True))
+
+  elif cs == int(libadjoint.constants.adj_constants["ADJ_CHECKPOINT_STORAGE_DISK"]):
+    for coeff in adj_variables.coeffs.keys(): 
+      if adj_variables[coeff] == var: continue
+      adjointer.record_variable(adj_variables[coeff], libadjoint.DiskStorage(Vector(coeff), cs=True))
+  return linear, newargs
+
+def solve(*args, **kwargs):
+  '''This solve routine comes from the dolfin_adjoint package, and wraps the real Dolfin
+  solve call. Its purpose is to annotate the model, recording what solves occur and what
+  forms are involved, so that the adjoint model may be constructed automatically by libadjoint. 
+
+  To disable the annotation, just pass annotate=False to this routine, and it acts exactly
+  like the Dolfin solve call. This is useful in cases where the solve is known to be irrelevant
+  or diagnostic for the purposes of the adjoint computation (such as projecting fields to
+  other function spaces for the purposes of visualisation).'''
+
+  # First, decide if we should annotate or not.
+  to_annotate = True
+  if "annotate" in kwargs:
+    to_annotate = kwargs["annotate"]
+    del kwargs["annotate"] # so we don't pass it on to the real solver
+
+  if to_annotate:
+    linear, newargs = annotate(*args, **kwargs)
+  else:
+    newargs = args
+
+  ret = dolfin.fem.solving.solve(*newargs, **kwargs)
+
+  if to_annotate:
+    if not linear and debugging["fussy_replay"]:
+      # we have annotated M.u = M.u - F(u),
+      # but actually solved F(u) = 0.
+      # so we need to do the mass solve too, so that the
+      # replay is exact.
+      nonlinear_post_solve_projection(*args, **kwargs)
+
+    # Finally, if we want to record all of the solutions of the real forward model
+    # (for comparison with a libadjoint replay later),
+    # then we should record the value of the variable we just solved for.
+    if debugging["record_all"]:
+      if isinstance(args[0], ufl.classes.Equation):
+        unpacked_args = dolfin.fem.solving._extract_args(*args, **kwargs)
+        u  = unpacked_args[1]
+        adjointer.record_variable(adj_variables[u], libadjoint.MemoryStorage(Vector(u)))
+      elif isinstance(args[0], dolfin.cpp.Matrix):
+        u = args[1]
+        adjointer.record_variable(adj_variables[u], libadjoint.MemoryStorage(Vector(u)))
+      else:
+        raise libadjoint.exceptions.LibadjointErrorInvalidInputs("Don't know how to record, sorry")
+
+  return ret
+
+def adj_html(*args, **kwargs):
+  '''This routine dumps the current state of the adjointer to a HTML visualisation.
+  Use it like:
+    adj_html("forward.html", "forward") # for the equations recorded on the forward run
+    adj_html("adjoint.html", "adjoint") # for the equations to be assembled on the adjoint run
+  '''
+  return adjointer.to_html(*args, **kwargs)
+
+
+class Vector(libadjoint.Vector):
+  '''This class implements the libadjoint.Vector abstract base class for the Dolfin adjoint.
+  In particular, it must implement the data callbacks for tasks such as adding two vectors
+  together, duplicating vectors, taking norms, etc., that occur in the process of constructing
+  the adjoint equations.'''
+
+  def __init__(self, data, zero=False, fn_space=None):
+
+    self.data=data
+    # self.zero is true if we can prove that the vector is zero.
+    if data is None:
+      self.zero=True
+    else:
+      self.zero=zero
+
+    if fn_space is not None:
+      self.fn_space = fn_space
+
+  def duplicate(self):
+
+    if isinstance(self.data, ufl.form.Form):
+      # The data type will be determined by the first addto.
+      data = None
+    elif isinstance(self.data, dolfin.Function):
+      data = dolfin.Function(self.data.function_space())
+    else:
+      data = None
+
+    fn_space = None
+    if hasattr(self, "fn_space"):
+      fn_space = self.fn_space
+
+    return Vector(data, zero=True, fn_space=fn_space)
+
+  def axpy(self, alpha, x):
+
+    if x.zero:
+      return
+
+    if (self.data is None):
+      # self is an empty form.
+      assert(isinstance(x.data, ufl.form.Form))
+      self.data=alpha*x.data
+    elif isinstance(self.data, dolfin.Coefficient):
+      if isinstance(x.data, dolfin.Coefficient):
+        self.data.vector().axpy(alpha, x.data.vector())
+      else:
+        # This occurs when adding a RHS derivative to an adjoint equation
+        # corresponding to the initial conditions.
+        self.data.vector().axpy(alpha, dolfin.assemble(x.data))
+    else:
+      # self is a non-empty form.
+      assert(isinstance(x.data, ufl.form.Form))
+      assert(isinstance(self.data, ufl.form.Form))
+
+      # Let's do a bit of argument shuffling, shall we?
+      xargs = ufl.algorithms.extract_arguments(x.data)
+      sargs = ufl.algorithms.extract_arguments(self.data)
+
+      if xargs != sargs:
+        # OK, let's check that all of the function spaces are happy and so on.
+        for i in range(len(xargs)):
+          assert xargs[i].element() == sargs[i].element()
+          assert xargs[i].function_space() == sargs[i].function_space()
+
+        # Now that we are happy, let's replace the xargs with the sargs ones.
+        x_form = dolfin.replace(x.data, dict(zip(xargs, sargs)))
+      else:
+        x_form = x.data
+
+      self.data+=alpha*x_form
+
+    self.zero = False
+
+  def norm(self):
+
+    if isinstance(self.data, dolfin.Function):
+      return (abs(dolfin.assemble(dolfin.inner(self.data, self.data)*dolfin.dx)))**0.5
+    elif isinstance(self.data, ufl.form.Form):
+      import scipy.linalg
+      vec = dolfin.assemble(self.data)
+      n = scipy.linalg.norm(vec)
+      return n
+
+  def dot_product(self,y):
+
+    if isinstance(self.data, ufl.form.Form):
+      return dolfin.assemble(dolfin.inner(self.data, y.data)*dolfin.dx)
+    elif isinstance(self.data, dolfin.Function):
+      import numpy
+      if isinstance(y.data, ufl.form.Form):
+        other = dolfin.assemble(y.data)
+      else:
+        other = y.data.vector()
+      return numpy.dot(numpy.array(self.data.vector()), numpy.array(other))
+    else:
+      raise libadjoint.exceptions.LibadjointErrorNotImplemented("Don't know how to dot anything else.")
+
+  def set_random(self):
+    assert isinstance(self.data, dolfin.Function) or hasattr(self, "fn_space")
+    import random
+
+    if self.data is None:
+      self.data = dolfin.Function(self.fn_space)
+
+    vec = self.data.vector()
+    for i in range(len(vec)):
+      vec[i] = random.random()
+
+    self.zero = False
+
+  def size(self):
+    if hasattr(self, "fn_space"):
+      return self.fn_space.dim()
+
+    if isinstance(self.data, dolfin.Function):
+      return len(self.data.vector())
+
+    if isinstance(self.data, ufl.form.Form):
+      return len(dolfin.assemble(self.data))
+
+    raise libadjoint.exceptions.LibadjointErrorNotImplemented("Don't know how to get the size.")
+
+  def set_values(self, array):
+    if isinstance(self.data, dolfin.Function):
+      vec = self.data.vector()
+      for i in range(len(array)):
+        vec[i] = array[i]
+      self.zero = False
+    else:
+      raise libadjoint.exceptions.LibadjointErrorNotImplemented("Don't know how to set values.")
+  
+  def write(self, var):
+    import os.path
+
+    filename = var.__str__()
+    suffix = "xml"
+    if not os.path.isfile(filename+".%s" % suffix):
+      print "Warning: Overwritting checkpoint file "+filename+"."+suffix
+    file = dolfin.File(filename+".%s" % suffix)
+    file << self.data
+
+    # Save the function space into checkpoint_fs. It will be needed when reading the variable back in.
+    checkpoint_fs[filename] = self.data.function_space()
+
+  @staticmethod
+  def read(var):
+
+    filename = var.__str__()
+    suffix = "xml"
+
+    V = checkpoint_fs[filename]
+    v = dolfin.Function(V, filename+".%s" % suffix)
+    return Vector(v)
+
+  @staticmethod
+  def delete(var):
+    import os
+    import os.path
+
+    filename = var.__str__()
+    suffix = "xml"
+
+    assert(os.path.isfile(filename+".%s" % suffix))
+    os.remove(filename+".%s" % suffix)
+
+class Matrix(libadjoint.Matrix):
+  '''This class implements the libadjoint.Matrix abstract base class for the Dolfin adjoint.
+  In particular, it must implement the data callbacks for tasks such as adding two matrices
+  together, duplicating matrices, etc., that occur in the process of constructing
+  the adjoint equations.'''
+
+  def __init__(self, data, bcs=None, ksp=None, pc=None):
+
+    if bcs is None:
+      self.bcs = []
+    else:
+      self.bcs=bcs
+
+    self.data=data
+
+    self.ksp = ksp
+    self.pc = pc
+
+  def solve(self, var, b):
+      
+    if isinstance(self.data, ufl.Identity):
+      x=b.duplicate()
+      x.axpy(1.0, b)
+    else:
+      if var.type in ['ADJ_TLM', 'ADJ_ADJOINT']:
+        bcs = [dolfin.homogenize(bc) for bc in self.bcs if isinstance(bc, dolfin.DirichletBC)] + [bc for bc in self.bcs if not isinstance(bc, dolfin.DirichletBC)]
+      else:
+        bcs = self.bcs
+
+      solver_parameters = {}
+      if self.pc is not None:
+        solver_parameters["preconditioner"] = self.pc
+      if self.ksp is not None:
+        solver_parameters["linear_solver"] = self.ksp
+
+      x=Vector(dolfin.Function(self.test_function().function_space()))
+      dolfin.fem.solving.solve(self.data==b.data, x.data, bcs, solver_parameters=solver_parameters)
+
+    return x
+
+  def axpy(self, alpha, x):
+    assert isinstance(x.data, ufl.Form)
+    assert isinstance(self.data, ufl.Form)
+
+    # Let's do a bit of argument shuffling, shall we?
+    xargs = ufl.algorithms.extract_arguments(x.data)
+    sargs = ufl.algorithms.extract_arguments(self.data)
+
+    if xargs != sargs:
+      # OK, let's check that all of the function spaces are happy and so on.
+      for i in range(len(xargs)):
+        assert xargs[i].element() == sargs[i].element()
+        assert xargs[i].function_space() == sargs[i].function_space()
+
+      # Now that we are happy, let's replace the xargs with the sargs ones.
+      x_form = dolfin.replace(x.data, dict(zip(xargs, sargs)))
+    else:
+      x_form = x.data
+
+    self.data+=alpha*x_form
+    self.bcs += x.bcs # Err, I hope they are compatible ...
+
+  def test_function(self):
+    '''test_function(self)
+
+    Return the ufl.Argument corresponding to the trial space for the form'''
+
+    return ufl.algorithms.extract_arguments(self.data)[-1]
+
+class Functional(libadjoint.Functional):
+  '''This class implements the libadjoint.Functional abstract base class for the Dolfin adjoint.
+  It takes in a form, and implements the necessary routines such as calling the functional
+  and taking its derivative.'''
+
+  def __init__(self, form):
+
+    self.form = form
+    self.activated = False
+
+  def __call__(self, dependencies, values):
+
+    dolfin_dependencies=[dep for dep in ufl.algorithms.extract_coefficients(self.form) if hasattr(dep, "function_space")]
+
+    dolfin_values=[val.data for val in values]
+
+    return dolfin.assemble(dolfin.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values))))
+
+  def derivative(self, variable, dependencies, values):
+
+    # Find the dolfin Function corresponding to variable.
+    dolfin_variable = values[dependencies.index(variable)].data
+
+    dolfin_dependencies = [dep for dep in ufl.algorithms.extract_coefficients(self.form) if hasattr(dep, "function_space")]
+
+    dolfin_values = [val.data for val in values]
+
+    current_form = dolfin.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values)))
+    test = dolfin.TestFunction(dolfin_variable.function_space())
+
+    return Vector(dolfin.derivative(current_form, dolfin_variable, test))
+
+  def dependencies(self, adjointer, timestep):
+
+    if self.activated is False:
+      deps = [adj_variables[coeff] for coeff in ufl.algorithms.extract_coefficients(self.form) if hasattr(coeff, "function_space")]      
+      self.activated = True
+    else:
+      deps = []
+    
+    return deps
+
+  def __str__(self):
+    
+    return hashlib.md5(str(self.form)).hexdigest()
+
+class RHS(libadjoint.RHS):
+  '''This class implements the libadjoint.RHS abstract base class for the Dolfin adjoint.
+  It takes in a form, and implements the necessary routines such as calling the right-hand side
+  and taking its derivative.'''
+  def __init__(self, form):
+
+    self.form=form
+
+    if isinstance(self.form, ufl.form.Form):
+      self.deps = [adj_variables[coeff] for coeff in ufl.algorithms.extract_coefficients(self.form) if hasattr(coeff, "function_space")]      
+    else:
+      self.deps = []
+
+    if isinstance(self.form, ufl.form.Form):
+      self.coeffs = [coeff for coeff in ufl.algorithms.extract_coefficients(self.form) if hasattr(coeff, "function_space")]      
+    else:
+      self.coeffs = []
+
+  def __call__(self, dependencies, values):
+
+    if isinstance(self.form, ufl.form.Form):
+
+      dolfin_dependencies=[dep for dep in ufl.algorithms.extract_coefficients(self.form) if hasattr(dep, "function_space")]
+
+      dolfin_values=[val.data for val in values]
+
+      return Vector(dolfin.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values))))
+
+    else:
+      # RHS is a Vector.
+      assert isinstance(self.form, Vector)
+      return self.form
+    
+
+  def derivative_action(self, dependencies, values, variable, contraction_vector, hermitian):
+
+    if isinstance(self.form, ufl.form.Form):
+      # Find the dolfin Function corresponding to variable.
+      dolfin_variable = values[dependencies.index(variable)].data
+
+      dolfin_dependencies = [dep for dep in ufl.algorithms.extract_coefficients(self.form) if hasattr(dep, "function_space")]
+
+      dolfin_values = [val.data for val in values]
+
+      current_form = dolfin.replace(self.form, dict(zip(dolfin_dependencies, dolfin_values)))
+      trial = dolfin.TrialFunction(dolfin_variable.function_space())
+
+      d_rhs=dolfin.derivative(current_form, dolfin_variable, trial)
+
+      if hermitian:
+        action = dolfin.action(dolfin.adjoint(d_rhs),contraction_vector.data)
+      else:
+        action = dolfin.action(d_rhs,contraction_vector.data)
+
+      return Vector(action)
+    else:
+      # RHS is a Vector. Its derivative is therefore zero.
+      raise exceptions.LibadjointErrorNotImplemented("No derivative method for constant RHS.")
+
+
+  def dependencies(self):
+
+    return self.deps
+
+  def coefficients(self):
+
+    return self.coeffs
+
+  def __str__(self):
+    
+    return hashlib.md5(str(self.form)).hexdigest()
+
+class NonlinearRHS(RHS):
+  '''For nonlinear problems, the source term isn't assembled in the usual way.
+  If the nonlinear problem is given as
+  F(u) = 0,
+  we annotate it as
+  M.u = M.u - F(u) .
+  So in order to actually assemble the right-hand side term,
+  we first need to solve F(u) = 0 to find the specific u,
+  and then multiply that by the mass matrix.'''
+  def __init__(self, form, F, u, bcs, mass):
+    '''form is M.u - F(u). F is the nonlinear equation, F(u) := 0.'''
+    RHS.__init__(self, form)
+    self.F = F
+    self.u = u
+    self.bcs = bcs
+    self.mass = mass
+
+    # We want to mark that the RHS term /also/ depends on
+    # the previous value of u, as that's what we need to initialise
+    # the nonlinear solver.
+    var = adj_variables[self.u]
+    if var.timestep > 0 and debugging["fussy_replay"]:
+      var.c_object.timestep = var.c_object.timestep - 1
+      self.deps.append(var)
+      self.ic_var = var
+    else:
+      self.ic_var = None
+
+  def __call__(self, dependencies, values):
+    assert isinstance(self.form, ufl.form.Form)
+
+    ic = self.u.function_space() # by default, initialise with a blank function in the solution FunctionSpace
+    replace_map = {}
+
+    for i in range(len(self.deps)):
+      if self.deps[i] in dependencies:
+        j = dependencies.index(self.deps[i])
+        if self.deps[i] == self.ic_var:
+          ic = values[j].data # ahah, we have found an initial condition!
+        else:
+          replace_map[self.coeffs[i]] = values[j].data
+
+    current_F    = dolfin.replace(self.F, replace_map)
+    u = dolfin.Function(ic)
+    current_F    = dolfin.replace(current_F, {self.u: u})
+
+    # OK, here goes nothing:
+    dolfin.solve(current_F == 0, u, self.bcs)
+
+    return Vector(dolfin.action(self.mass, u))
+
+  def derivative_action(self, dependencies, values, variable, contraction_vector, hermitian):
+    '''If variable is the variable for the initial condition, we want to ignore it,
+    and set the derivative to zero. Assuming the solver converges, the sensitivity of
+    the solution to the initial condition should be extremely small, and computing it
+    is very difficult (one would have to do a little adjoint solve to compute it).
+    Even I'm not that fussy.'''
+
+    if variable == self.ic_var:
+      deriv_value = values[dependencies.index(variable)].data
+      return Vector(None, fn_space=deriv_value.function_space())
+    else:
+      return RHS.derivative_action(self, dependencies, values, variable, contraction_vector, hermitian)
+
+  def derivative_assembly(self, dependencies, values, variable, hermitian):
+    replace_map = {}
+
+    for i in range(len(self.deps)):
+      if self.deps[i] == self.ic_var: continue
+      j = dependencies.index(self.deps[i])
+      replace_map[self.coeffs[i]] = values[j].data
+
+    diff_var = values[dependencies.index(variable)].data
+
+    current_form = dolfin.replace(self.form, replace_map)
+    deriv = dolfin.derivative(current_form, diff_var)
+
+    if hermitian:
+      deriv = dolfin.adjoint(deriv)
+      bcs = [dolfin.homogenize(bc) for bc in self.bcs if isinstance(bc, dolfin.DirichletBC)]
+    else:
+      bcs = self.bcs
+
+    return Matrix(deriv, bcs=bcs)
+
+dolfin_assign = dolfin.Function.assign
+def dolfin_adjoint_assign(self, other, annotate=True):
+  '''We also need to monkeypatch the Function.assign method, as it is often used inside 
+  the main time loop, and not annotating it means you get the adjoint wrong for totally
+  nonobvious reasons. If anyone objects to me monkeypatching your objects, my apologies
+  in advance.'''
+
+  # ignore anything not a dolfin.Function
+  if not isinstance(other, dolfin.Function) or annotate is False:
+    return dolfin_assign(self, other)
+
+  # ignore anything that is an interpolation, rather than a straight assignment
+  if self.function_space() != other.function_space():
+    return dolfin_assign(self, other)
+
+  other_var = adj_variables[other]
+  # ignore any functions we haven't seen before -- we DON'T want to
+  # annotate the assignment of initial conditions here. That happens
+  # in the main solve wrapper.
+  if not adjointer.variable_known(other_var):
+    return dolfin_assign(self, other)
+
+  # OK, so we have a variable we've seen before. Beautiful.
+  fn_space = other.function_space()
+  u, v = dolfin.TestFunction(fn_space), dolfin.TrialFunction(fn_space)
+  M = dolfin.inner(u, v)*dolfin.dx
+  if debugging["fussy_replay"]:
+    return solve(M == dolfin.action(M, other), self) # this takes care of all the annotation etc
+  else:
+    annotate(M == dolfin.action(M, other), self)
+    return dolfin_assign(self, other)
+
+dolfin.Function.assign = dolfin_adjoint_assign
+
+def define_nonlinear_equation(F, u):
+  # Given an F := 0,
+  # we write the equation for libadjoint's annotation purposes as
+  # M.u = M.u + F(u)
+  # as we need to have something on the diagonal in our big time system
+
+  fn_space = u.function_space()
+  test = dolfin.TestFunction(fn_space)
+  trial = dolfin.TrialFunction(fn_space)
+
+  mass = dolfin.inner(test, trial)*dolfin.dx
+
+  return (mass, dolfin.action(mass, u) - F)
+
+def nonlinear_post_solve_projection(*args, **kwargs):
+  '''we have annotated M.u = M.u - F(u),
+  but actually solved F(u) = 0.
+  so we need to do the mass solve too, so that the
+  replay is exact.'''
+
+  # Unpack the arguments, using the same routine as the real Dolfin solve call
+  unpacked_args = dolfin.fem.solving._extract_args(*args, **kwargs)
+  u  = unpacked_args[1]
+
+  fn_space = u.function_space()
+  test = dolfin.TestFunction(fn_space)
+  trial = dolfin.TrialFunction(fn_space)
+
+  mass = dolfin.inner(test, trial)*dolfin.dx
+
+  dolfin.fem.solving.solve(mass == dolfin.action(mass, u), u)
+
+def adjoint_checkpointing(strategy, steps, snaps_on_disk, snaps_in_ram, verbose=False):
+  adjointer.set_checkpoint_strategy(strategy)
+  adjointer.set_revolve_options(steps, snaps_on_disk, snaps_in_ram, verbose)
+
+class InitialConditionParameter(libadjoint.Parameter):
+  '''This Parameter is used as input to the tangent linear model (TLM)
+  when one wishes to compute dJ/d(initial condition) in a particular direction (perturbation).'''
+  def __init__(self, coeff, perturbation):
+    '''coeff: the variable whose initial condition you wish to perturb.
+       perturbation: the perturbation direction in which you wish to compute the gradient. Must be a Function.'''
+    self.var = adj_variables[coeff]
+    self.var.c_object.timestep = 0 # we want to put in the source term only at the initial condition.
+    self.perturbation = Vector(perturbation).duplicate()
+    self.perturbation.axpy(1.0, Vector(perturbation))
+
+  def __call__(self, dependencies, values, variable):
+    # The TLM source term only kicks in at the start, for the initial condition:
+    if self.var == variable:
+      return self.perturbation
+    else:
+      return None
+
+  def __str__(self):
+    return self.var.name + ':InitialCondition'

=== added directory 'tests'
=== added directory 'tests/burgers_newton'
=== added file 'tests/burgers_newton/burgers_newton.py'
--- tests/burgers_newton/burgers_newton.py	1970-01-01 00:00:00 +0000
+++ tests/burgers_newton/burgers_newton.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,63 @@
+"""
+Implementation of Burger's equation with nonlinear solve in each
+timestep
+"""
+
+import sys
+
+from dolfin import *
+from dolfin_adjoint import *
+
+debugging["record_all"] = True
+
+n = 30
+mesh = UnitInterval(n)
+V = FunctionSpace(mesh, "CG", 2)
+
+def Dt(u, u_, timestep):
+    return (u - u_)/timestep
+
+def main(ic, annotate=False):
+
+    u_ = Function(ic)
+    u = Function(V)
+    v = TestFunction(V)
+
+    nu = Constant(0.0001)
+
+    timestep = Constant(1.0/n)
+
+    F = (Dt(u, u_, timestep)*v
+         + u*grad(u)*v + nu*grad(u)*grad(v))*dx
+    bc = DirichletBC(V, 0.0, "on_boundary")
+
+    t = 0.0
+    end = 0.2
+    while (t <= end):
+        solve(F == 0, u, bc, annotate=annotate)
+        u_.assign(u, annotate=annotate)
+
+        t += float(timestep)
+
+    return u_
+
+if __name__ == "__main__":
+
+    ic = project(Expression("sin(2*pi*x[0])"),  V)
+    forward = main(ic, annotate=True)
+
+    adj_html("burgers_newton_forward.html", "forward")
+    adj_html("burgers_newton_adjoint.html", "adjoint")
+
+    print "Running forward replay .... "
+    replay_dolfin()
+    print "Running adjoint ... "
+
+    J = Functional(forward*forward*dx)
+    adjoint = adjoint_dolfin(J)
+
+    def Jfunc(ic):
+      forward = main(ic, annotate=False)
+      return assemble(forward*forward*dx)
+
+    minconv = test_initial_condition_adjoint(Jfunc, ic, adjoint, seed=1.0e-6)

=== added directory 'tests/burgers_picard'
=== added file 'tests/burgers_picard/burgers_picard.py'
--- tests/burgers_picard/burgers_picard.py	1970-01-01 00:00:00 +0000
+++ tests/burgers_picard/burgers_picard.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,80 @@
+"""
+Naive implementation of Burgers' equation, goes oscillatory later
+"""
+
+import sys
+
+from dolfin import *
+from dolfin_adjoint import *
+
+n = 100
+mesh = UnitInterval(n)
+V = FunctionSpace(mesh, "CG", 2)
+
+parameters["num_threads"] = 2
+
+debugging["record_all"] = True
+#debugging["test_hermitian"] = (100, 1.0e-14)
+#debugging["test_derivative"] = 6
+
+def Dt(u, u_, timestep):
+    return (u - u_)/timestep
+
+def main(ic, annotate=False):
+
+    u_ = ic
+    u = TrialFunction(V)
+    v = TestFunction(V)
+
+    nu = Constant(0.0001)
+
+    timestep = Constant(1.0/n)
+
+    F = (Dt(u, u_, timestep)*v
+         + u_*grad(u)*v + nu*grad(u)*grad(v))*dx
+
+    (a, L) = system(F)
+
+    bc = DirichletBC(V, 0.0, "on_boundary")
+
+    t = 0.0
+    end = 0.025
+    u = Function(V)
+    while (t <= end):
+        solve(a == L, u, bc, annotate=annotate)
+
+        u_.assign(u, annotate=annotate)
+
+        t += float(timestep)
+        #plot(u)
+
+    #interactive()
+    return u_
+
+if __name__ == "__main__":
+
+    ic = project(Expression("sin(2*pi*x[0])"),  V)
+    ic_copy = Function(ic)
+    forward = main(ic, annotate=True)
+    forward_copy = Function(forward)
+    adj_html("burgers_picard_forward.html", "forward")
+    adj_html("burgers_picard_adjoint.html", "adjoint")
+    print "Running adjoint ... "
+
+    J = Functional(forward*forward*dx)
+    adjoint = adjoint_dolfin(J, forget=False)
+
+    def Jfunc(ic):
+      forward = main(ic, annotate=False)
+      return assemble(forward*forward*dx)
+
+    ic.vector()[:] = ic_copy.vector()
+    minconv = test_initial_condition_adjoint(Jfunc, ic, adjoint, seed=1.0e-3)
+    if minconv < 1.9:
+      sys.exit(1)
+
+    ic.vector()[:] = ic_copy.vector()
+    dJ = assemble(derivative(forward_copy*forward_copy*dx, forward_copy))
+    minconv = test_initial_condition_tlm(Jfunc, dJ, ic, seed=1.0e-5)
+    if minconv < 1.9:
+      sys.exit(1)

=== added directory 'tests/checkpoint_burgers'
=== added file 'tests/checkpoint_burgers/checkpoint_burgers.py'
--- tests/checkpoint_burgers/checkpoint_burgers.py	1970-01-01 00:00:00 +0000
+++ tests/checkpoint_burgers/checkpoint_burgers.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,79 @@
+"""
+Naive implementation of Burgers' equation, goes oscillatory later
+"""
+
+import sys
+
+from dolfin import *
+from dolfin_adjoint import *
+from math import ceil
+
+n = 100
+mesh = UnitInterval(n)
+V = FunctionSpace(mesh, "CG", 2)
+
+#debugging["record_all"] = True
+#debugging["test_hermitian"] = (100, 1.0e-14)
+#debugging["test_derivative"] = 6
+
+def Dt(u, u_, timestep):
+    return (u - u_)/timestep
+
+def main(ic, annotate=False):
+
+    u_ = Function(ic)
+    u = TrialFunction(V)
+    v = TestFunction(V)
+
+    nu = Constant(0.0001)
+
+    timestep = Constant(1.0/n)
+
+    F = (Dt(u, u_, timestep)*v
+         + u_*grad(u)*v + nu*grad(u)*grad(v))*dx
+
+    (a, L) = system(F)
+
+    bc = DirichletBC(V, 0.0, "on_boundary")
+
+    t = 0.0
+    end = 0.5
+    if annotate: 
+      adjoint_checkpointing('multistage', int(ceil(end/float(timestep)))+1, 5, 10, verbose=True)
+
+    u = Function(V)
+    while (t <= end):
+        solve(a == L, u, bc, annotate=annotate)
+
+        u_.assign(u, annotate=annotate)
+
+        t += float(timestep)
+        #plot(u)
+
+    #interactive()
+    return u_
+
+if __name__ == "__main__":
+
+    
+    ic = project(Expression("sin(2*pi*x[0])"),  V)
+    forward = main(ic, annotate=True)
+    adj_html("burgers_picard_checkpointing_forward.html", "forward")
+    adj_html("burgers_picard_checkpointing_adjoint.html", "adjoint")
+    #print "Running forward replay .... "
+    #replay_dolfin()
+    print "Running adjoint ... "
+
+    J = Functional(forward*forward*dx)
+    adjoint = adjoint_dolfin(J)
+
+    def Jfunc(ic):
+      forward = main(ic, annotate=False)
+      return assemble(forward*forward*dx)
+
+    minconv = test_initial_condition_adjoint(Jfunc, ic, adjoint, seed=1.0e-3)
+    if minconv < 1.9:
+      exit_code = 1
+    else:
+      exit_code = 0
+    sys.exit(exit_code)

=== added directory 'tests/checkpoint_stokes'
=== added file 'tests/checkpoint_stokes/checkpoint_stokes.py'
--- tests/checkpoint_stokes/checkpoint_stokes.py	1970-01-01 00:00:00 +0000
+++ tests/checkpoint_stokes/checkpoint_stokes.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,137 @@
+"""
+Very stupid scheme for decoupled stationary Stokes + heat equation:
+
+Given nu and f, find (u, p) such that
+
+  (nu grad(u), grad(v)) + (p, div(v)) = (f, v)
+                          (div(u), q) = 0
+
+for all (v, q).
+
+Given velocity u, find T such that
+
+  (Dt(T), s) + (s*div(v) + (grad(T), grad(s)) = (1, s)
+
+for all s
+
+"""
+
+import sys
+from math import ceil
+
+from dolfin import *
+
+def stokes(W, nu, f):
+    (u, p) = TrialFunctions(W)
+    (v, q) = TestFunctions(W)
+    a = (nu*inner(grad(u), grad(v)) +
+         p*div(v) + q*div(u))*dx
+    L = inner(f, v)*dx
+    return (a, L)
+
+def temperature(X, kappa, v, t_, k):
+    t = TrialFunction(X)
+    s = TestFunction(X)
+
+    F = ((t - t_)/k*s + inner(kappa*grad(t), grad(s))
+         + dot(v, grad(t))*s)*dx - s*dx
+    (a, L) = system(F)
+    return (a, L)
+
+def flow_boundary_conditions(W):
+    u0 = Constant((0.0,0.0))
+    bottom = DirichletBC(W.sub(0), (0.0, 0.0), "near(x[1], 0.0)")
+    top = DirichletBC(W.sub(0), (0.0, 0.0), "near(x[1], 1.0)")
+    left = DirichletBC(W.sub(0).sub(0), 0.0, "near(x[0], 0.0)")
+    right = DirichletBC(W.sub(0).sub(0), 0.0, "near(x[0], 1.0)")
+    bcs = [bottom, top, left, right]
+    return bcs
+
+def temperature_boundary_conditions(Q):
+    bc = DirichletBC(Q, 0.0, "near(x[1], 1.0)")
+    return [bc]
+
+n = 16
+mesh = UnitSquare(n, n)
+X = FunctionSpace(mesh, "CG", 1)
+
+def main(ic, annotate=False):
+
+    # Define meshes and function spaces
+    V = VectorFunctionSpace(mesh, "CG", 2)
+    Q = FunctionSpace(mesh, "CG", 1)
+    W = V * Q
+
+    # Define boundary conditions
+    flow_bcs = flow_boundary_conditions(W)
+    temp_bcs = temperature_boundary_conditions(X)
+
+    # Temperature variables
+    T_ = Function(ic)
+    T = Function(ic)
+
+    # Flow variable(s)
+    w = Function(W)
+    (u, p) = split(w)
+
+    # Some parameters
+    Ra = Constant(1.e4)
+    nu = Constant(1.0)
+    kappa = Constant(1.0)
+    timestep = 0.1
+
+    # Define flow equation
+    g = as_vector((Ra*T_, 0))
+    flow_eq = stokes(W, nu, g)
+
+    # Define temperature equation
+    temp_eq = temperature(X, kappa, u, T_, timestep)
+
+    # Time loop
+    t = 0.0
+    end = 1.0
+
+    if annotate:
+      adjoint_checkpointing('multistage', int(ceil(end/float(timestep)))+2, 0, 5, verbose=True)
+      print "Velocity: ", w
+      print "Temperature: ", T
+
+    while (t <= end):
+
+        solve(flow_eq[0] == flow_eq[1], w, flow_bcs, annotate=annotate)
+
+        solve(temp_eq[0] == temp_eq[1], T, temp_bcs, annotate=annotate)
+        T_.assign(T, annotate=annotate)
+        #plot(T)
+
+        t += timestep
+
+    return T_
+
+if __name__ == "__main__":
+
+    from dolfin_adjoint import *
+
+    # Run model
+    T0_expr = "0.5*(1.0 - x[1]*x[1]) + 0.01*cos(pi*x[0]/l)*sin(pi*x[1]/h)"
+    T0 = Expression(T0_expr, l=1.0, h=1.0)
+    ic = Function(interpolate(T0, X))
+    T = main(ic, annotate=True)
+
+    adj_html("stokes_forward.html", "forward")
+    adj_html("stokes_adjoint.html", "adjoint")
+
+    print "Running adjoint ... "
+    adjoint = adjoint_dolfin(Functional(T*T*dx))
+
+    def J(ic):
+      T = main(ic, annotate=False)
+      return assemble(T*T*dx)
+
+    minconv = test_initial_condition_adjoint(J, ic, adjoint)
+    if minconv < 1.9:
+      exit_code = 1
+    else:
+      exit_code = 0
+    sys.exit(exit_code)
+

=== added directory 'tests/heat'
=== added file 'tests/heat/heat.py'
--- tests/heat/heat.py	1970-01-01 00:00:00 +0000
+++ tests/heat/heat.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,115 @@
+import sys
+
+from dolfin import *
+from dolfin_adjoint import *
+
+debugging["record_all"] = True
+
+f = Expression("x[0]*(x[0]-1)*x[1]*(x[1]-1)")
+mesh = UnitSquare(4, 4)
+V = FunctionSpace(mesh, "CG", 1)
+
+def run_forward(initial_condition=None, annotate=True, dump=True):
+  u = TrialFunction(V)
+  v = TestFunction(V)
+
+  u_0 = Function(V)
+  if initial_condition is not None:
+    u_0.assign(initial_condition)
+
+  u_1 = Function(V)
+
+  dt = Constant(0.1)
+
+  F = ( (u - u_0)/dt*v + inner(grad(u), grad(v)) + f*v)*dx
+
+  bc = DirichletBC(V, 1.0, "on_boundary")
+
+  a, L = lhs(F), rhs(F)
+
+  t = float(dt)
+  T = 1.0
+  n = 1
+
+  if dump:
+    u_out = File("u.pvd", "compressed")
+    u_out << u_0
+
+  while t <= T:
+
+      solve(a == L, u_0, bc, annotate=annotate)
+      #solve(a == L, u_0, annotate=annotate)
+
+      t += float(dt)
+      if dump:
+        u_out << u_0
+
+  return u_0
+
+def run_replay():
+  print "Replaying forward model (will error if differs from correct solution) ..."
+
+
+  u_out = File("u_replay.pvd", "compressed")
+
+  for i in range(adjointer.equation_count):
+      (fwd_var, output) = adjointer.get_forward_solution(i)
+
+      storage = libadjoint.MemoryStorage(output)
+      storage.set_compare(tol=0.0)
+      storage.set_overwrite(True)
+      adjointer.record_variable(fwd_var, storage)
+
+      u_out << output.data
+
+def run_adjoint():
+  z_out = File("adjoint.pvd", "compressed")
+
+  for i in range(adjointer.equation_count)[::-1]:
+
+      (adj_var, output) = adjointer.get_adjoint_solution(i, functional)
+      
+      storage = libadjoint.MemoryStorage(output)
+      adjointer.record_variable(adj_var, storage)
+
+      # if we cared about memory, here is where we would put the call to forget
+      # any variables we no longer need.
+
+      z_out << output.data
+
+  return output.data
+
+if __name__ == "__main__":
+
+  final_forward = run_forward()
+
+  adj_html("heat_forward.html", "forward")
+  adj_html("heat_adjoint.html", "adjoint")
+
+  # The functional is only a function of final state.
+  functional=Functional(final_forward*final_forward*dx)
+  f_direct = adjointer.evaluate_functional(functional, adjointer.equation_count-1)
+
+  print "Running adjoint model ..."
+
+  final_adjoint = run_adjoint()
+
+  def J(ic):
+    perturbed_u0 = run_forward(initial_condition=ic, annotate=False, dump=False)
+    return assemble(perturbed_u0*perturbed_u0*dx)
+
+  minconv = test_initial_condition_adjoint(J, Function(V), final_adjoint, seed=10.0)
+
+  if minconv < 1.9:
+    sys.exit(1)
+
+  dJ = assemble(derivative(final_forward*final_forward*dx, final_forward))
+
+  ic = final_forward
+  ic.vector()[:] = 0
+
+  minconv = test_initial_condition_tlm(J, dJ, ic, seed=1.0)
+
+  if minconv < 1.9:
+    sys.exit(1)
+

=== added directory 'tests/navier_stokes'
=== added file 'tests/navier_stokes/lshape.xml.gz'
Binary files tests/navier_stokes/lshape.xml.gz	1970-01-01 00:00:00 +0000 and tests/navier_stokes/lshape.xml.gz	2012-01-17 22:06:24 +0000 differ
=== added file 'tests/navier_stokes/navier_stokes.py'
--- tests/navier_stokes/navier_stokes.py	1970-01-01 00:00:00 +0000
+++ tests/navier_stokes/navier_stokes.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,151 @@
+"""This demo program solves the incompressible Navier-Stokes equations
+on an L-shaped domain using Chorin's splitting method."""
+
+# Copyright (C) 2010-2011 Anders Logg
+#
+# This file is part of DOLFIN.
+#
+# DOLFIN is free software: you can redistribute it and/or modify
+# it under the terms of the GNU Lesser General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# DOLFIN is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with DOLFIN. If not, see <http://www.gnu.org/licenses/>.
+#
+# Modified by Mikael Mortensen 2011
+#
+# First added:  2010-08-30
+# Last changed: 2011-06-30
+
+# Begin demo
+
+from dolfin import *
+from dolfin_adjoint import *
+
+# Record all variables solved for
+debugging["record_all"] = True
+
+# Print log messages only from the root process in parallel
+parameters["std_out_all_processes"] = False;
+
+#parameters["mesh_partitioner"] = "SCOTCH";
+
+# Load mesh from file
+mesh = Mesh("lshape.xml.gz")
+
+# Define function spaces (P2-P1)
+V = VectorFunctionSpace(mesh, "CG", 2)
+Q = FunctionSpace(mesh, "CG", 1)
+
+# Define trial and test functions
+u = TrialFunction(V)
+p = TrialFunction(Q)
+v = TestFunction(V)
+q = TestFunction(Q)
+
+def main(ic, annotate=False):
+  # Set parameter values
+  dt = 0.01
+  T = 0.05
+  nu = 0.01
+
+  # Define time-dependent pressure boundary condition
+  p_in = Expression("sin(3.0*t)", t=1.0)
+
+  # Define boundary conditions
+  noslip  = DirichletBC(V, (0, 0),
+                        "on_boundary && \
+                         (x[0] < DOLFIN_EPS | x[1] < DOLFIN_EPS | \
+                         (x[0] > 0.5 - DOLFIN_EPS && x[1] > 0.5 - DOLFIN_EPS))")
+  inflow  = DirichletBC(Q, p_in, "x[1] > 1.0 - DOLFIN_EPS")
+  outflow = DirichletBC(Q, 0, "x[0] > 1.0 - DOLFIN_EPS")
+  bcu = [noslip]
+  bcp = [inflow, outflow]
+
+  # Create functions
+  u0 = Function(ic)
+  u1 = Function(V)
+  p1 = Function(Q)
+
+  # Define coefficients
+  k = Constant(dt)
+  f = Constant((0, 0))
+
+  # Tentative velocity step
+  F1 = (1/k)*inner(u - u0, v)*dx + inner(grad(u0)*u0, v)*dx + \
+       nu*inner(grad(u), grad(v))*dx - inner(f, v)*dx
+  a1 = lhs(F1)
+  L1 = rhs(F1)
+
+  # Pressure update
+  a2 = inner(grad(p), grad(q))*dx
+  L2 = -(1/k)*div(u1)*q*dx
+
+  # Velocity update
+  a3 = inner(u, v)*dx
+  L3 = inner(u1, v)*dx - k*inner(grad(p1), v)*dx
+
+  # Assemble matrices
+  A1 = assemble(a1)
+  A2 = assemble(a2)
+  A3 = assemble(a3)
+
+  # Time-stepping
+  t = dt
+  while t < T + DOLFIN_EPS:
+
+      # Update pressure boundary condition
+      #p_in.t = t
+
+      # Compute tentative velocity step
+      begin("Computing tentative velocity")
+      b1 = assemble(L1)
+      [bc.apply(A1, b1) for bc in bcu]
+      solve(A1, u1, b1, "gmres", "default")
+      end()
+
+      # Pressure correction
+      begin("Computing pressure correction")
+      b2 = assemble(L2)
+      [bc.apply(A2, b2) for bc in bcp]
+      solve(A2, p1, b2, "gmres", "amg")
+      end()
+
+      # Velocity correction
+      begin("Computing velocity correction")
+      b3 = assemble(L3)
+      [bc.apply(A3, b3) for bc in bcu]
+      solve(A3, u1, b3, "gmres", "default")
+      end()
+
+      # Move to next time step
+      u0.assign(u1)
+      t += dt
+  return u0
+
+if __name__ == "__main__":
+
+  import sys
+
+  ic = Function(V)
+  final_soln = main(ic, annotate=True)
+  adj_html("navier_stokes_forward.html", "forward")
+  adj_html("navier_stokes_adjoint.html", "adjoint")
+  replay_dolfin(forget=False)
+
+  J = Functional(inner(final_soln, final_soln)*dx)
+  final_adj = adjoint_dolfin(J, forget=False)
+
+  def J(ic):
+    soln = main(ic)
+    return assemble(inner(soln, soln)*dx)
+
+  minconv = test_initial_condition_adjoint(J, ic, final_adj, seed=1.0e-3)
+  if minconv < 1.9:
+    sys.exit(1)

=== added directory 'tests/stokes'
=== added file 'tests/stokes/stokes.py'
--- tests/stokes/stokes.py	1970-01-01 00:00:00 +0000
+++ tests/stokes/stokes.py	2012-01-17 22:06:24 +0000
@@ -0,0 +1,146 @@
+"""
+Very stupid scheme for decoupled stationary Stokes + heat equation:
+
+Given nu and f, find (u, p) such that
+
+  (nu grad(u), grad(v)) + (p, div(v)) = (f, v)
+                          (div(u), q) = 0
+
+for all (v, q).
+
+Given velocity u, find T such that
+
+  (Dt(T), s) + (s*div(v) + (grad(T), grad(s)) = (1, s)
+
+for all s
+
+"""
+
+import sys
+
+from dolfin import *
+
+def stokes(W, nu, f):
+    (u, p) = TrialFunctions(W)
+    (v, q) = TestFunctions(W)
+    a = (nu*inner(grad(u), grad(v)) +
+         p*div(v) + q*div(u))*dx
+    L = inner(f, v)*dx
+    return (a, L)
+
+def temperature(X, kappa, v, t_, k):
+    t = TrialFunction(X)
+    s = TestFunction(X)
+
+    F = ((t - t_)/k*s + inner(kappa*grad(t), grad(s))
+         + dot(v, grad(t))*s)*dx - s*dx
+    (a, L) = system(F)
+    return (a, L)
+
+def flow_boundary_conditions(W):
+    u0 = Constant((0.0,0.0))
+    bottom = DirichletBC(W.sub(0), (0.0, 0.0), "near(x[1], 0.0)")
+    top = DirichletBC(W.sub(0), (0.0, 0.0), "near(x[1], 1.0)")
+    left = DirichletBC(W.sub(0).sub(0), 0.0, "near(x[0], 0.0)")
+    right = DirichletBC(W.sub(0).sub(0), 0.0, "near(x[0], 1.0)")
+    bcs = [bottom, top, left, right]
+    return bcs
+
+def temperature_boundary_conditions(Q):
+    bc = DirichletBC(Q, 0.0, "near(x[1], 1.0)")
+    return [bc]
+
+n = 16
+mesh = UnitSquare(n, n)
+X = FunctionSpace(mesh, "CG", 1)
+
+def main(ic, annotate=False):
+
+    # Define meshes and function spaces
+    V = VectorFunctionSpace(mesh, "CG", 2)
+    Q = FunctionSpace(mesh, "CG", 1)
+    W = V * Q
+
+    # Define boundary conditions
+    flow_bcs = flow_boundary_conditions(W)
+    temp_bcs = temperature_boundary_conditions(X)
+
+    # Temperature variables
+    T_ = Function(ic)
+    T = Function(ic)
+
+    # Flow variable(s)
+    w = Function(W)
+    (u, p) = split(w)
+
+    # Some parameters
+    Ra = Constant(1.e4)
+    nu = Constant(1.0)
+    kappa = Constant(1.0)
+    timestep = 0.1
+
+    # Define flow equation
+    g = as_vector((Ra*T_, 0))
+    flow_eq = stokes(W, nu, g)
+
+    # Define temperature equation
+    temp_eq = temperature(X, kappa, u, T_, timestep)
+
+    # Time loop
+    t = 0.0
+    end = 1.0
+    while (t <= end):
+
+        solve(flow_eq[0] == flow_eq[1], w, flow_bcs, annotate=annotate)
+
+        solve(temp_eq[0] == temp_eq[1], T, temp_bcs, annotate=annotate)
+        T_.assign(T, annotate=annotate)
+        #plot(T)
+
+        t += timestep
+
+    return T_
+
+def replay():
+    print "Replaying forward run"
+
+    for i in range(adjointer.equation_count):
+        (fwd_var, output) = adjointer.get_forward_solution(i)
+
+        s=libadjoint.MemoryStorage(output)
+        s.set_compare(0.0)
+        s.set_overwrite(True)
+
+        adjointer.record_variable(fwd_var, s)
+
+if __name__ == "__main__":
+
+    from dolfin_adjoint import *
+    debugging["record_all"] = True
+
+    # Run model
+    T0_expr = "0.5*(1.0 - x[1]*x[1]) + 0.01*cos(pi*x[0]/l)*sin(pi*x[1]/h)"
+    T0 = Expression(T0_expr, l=1.0, h=1.0)
+    ic = Function(interpolate(T0, X))
+    T = main(ic, annotate=True)
+
+    adj_html("stokes_forward.html", "forward")
+    adj_html("stokes_adjoint.html", "adjoint")
+
+    # Replay model
+    replay()
+
+    print "Running adjoint ... "
+    adjoint = adjoint_dolfin(Functional(T*T*dx))
+
+    def J(ic):
+      T = main(ic, annotate=False)
+      return assemble(T*T*dx)
+
+    minconv = test_initial_condition_adjoint(J, ic, adjoint)
+    if minconv < 1.9:
+      exit_code = 1
+    else:
+      exit_code = 0
+    sys.exit(exit_code)
+

=== added directory 'tests/sw'
=== added file 'tests/sw/basin.geo'
--- tests/sw/basin.geo	1970-01-01 00:00:00 +0000
+++ tests/sw/basin.geo	2012-01-17 22:06:24 +0000
@@ -0,0 +1,9 @@
+Point(1) = {250000.0,0,0,10000.0};
+Point(2) = {0,0,0,10000.0};
+Point(3) = {-250000.0,0,0,10000.0};
+Circle(1) = {1,2,3};
+Circle(2) = {3,2,1};
+Physical Line(3) = {1,2};
+Line Loop(4) = {1,2};
+Plane Surface(5) = {4};
+Physical Surface(6) = {5};

=== added file 'tests/sw/basin.msh'
--- tests/sw/basin.msh	1970-01-01 00:00:00 +0000
+++ tests/sw/basin.msh	2012-01-17 22:06:24 +0000
@@ -0,0 +1,7135 @@
+$MeshFormat
+2.2 0 8
+$EndMeshFormat
+$Nodes
+2376
[phone]
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