def integrate_unit_square(family, degree):
power = 5
m = UnitIntervalMesh(2**power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# A kernel which describes how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
fs = FunctionSpace(mesh, family, degree, name="fs")
f = Function(fs)
area = op2.Kernel(
"""
void comp_area(double A[1], double *x[], double *y[])
{
double area = (x[1][1]-x[0][1])*(x[2][0]-x[0][0]);
if (area < 0)
area = area * (-1.0);
A[0] += area;
}""", "comp_area")
g = op2.Global(1, data=0.0, name='g')
coords = f.function_space().mesh().coordinates
op2.par_loop(area, f.cell_set, g(op2.INC),
coords.dat(op2.READ, coords.cell_node_map()),
f.dat(op2.READ, f.cell_node_map()))
return np.abs(g.data[0] - 1.0)
def integrate_rhs(family, degree):
power = 5
m = UnitSquareMesh(2 ** power, 2 ** power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# TODO: provide a kernel which will describe how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
horiz = ufl.FiniteElement(family, "triangle", degree)
vert = ufl.FiniteElement(family, "interval", degree)
prod = ufl.TensorProductElement(horiz, vert)
fs = FunctionSpace(mesh, prod, name="fs")
f = Function(fs)
populate_p0 = op2.Kernel("""
void populate_tracer(double *x[], double *c[])
{
x[0][0] = ((c[1][2] + c[0][2]) / 2);
}""", "populate_tracer")
coords = f.function_space().mesh().coordinates
op2.par_loop(populate_p0, f.cell_set,
f.dat(op2.INC, f.cell_node_map()),
coords.dat(op2.READ, coords.cell_node_map()))
g = assemble(f * dx)
return np.abs(g - 0.5)
def integrate_rhs(family, degree):
power = 5
m = UnitSquareMesh(2**power, 2**power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# TODO: provide a kernel which will describe how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
horiz = ufl.FiniteElement(family, "triangle", degree)
vert = ufl.FiniteElement(family, "interval", degree)
prod = ufl.TensorProductElement(horiz, vert)
fs = FunctionSpace(mesh, prod, name="fs")
f = Function(fs)
populate_p0 = op2.Kernel(
"""
void populate_tracer(double *x[], double *c[])
{
x[0][0] = ((c[1][2] + c[0][2]) / 2);
}""", "populate_tracer")
coords = f.function_space().mesh().coordinates
op2.par_loop(populate_p0, f.cell_set, f.dat(op2.INC, f.cell_node_map()),
coords.dat(op2.READ, coords.cell_node_map()))
g = assemble(f * dx)
return np.abs(g - 0.5)
def integrate_unit_square(family, degree):
power = 5
m = UnitIntervalMesh(2 ** power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# A kernel which describes how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
fs = FunctionSpace(mesh, family, degree, name="fs")
f = Function(fs)
area = op2.Kernel("""
void comp_area(double A[1], double *x[], double *y[])
{
double area = (x[1][1]-x[0][1])*(x[2][0]-x[0][0]);
if (area < 0)
area = area * (-1.0);
A[0] += area;
}""", "comp_area")
g = op2.Global(1, data=0.0, name='g')
coords = f.function_space().mesh().coordinates
op2.par_loop(area, f.cell_set,
g(op2.INC),
coords.dat(op2.READ, coords.cell_node_map()),
f.dat(op2.READ, f.cell_node_map())
)
return np.abs(g.data[0] - 1.0)
def integrate_var_p0(family, degree):
power = 5
m = UnitSquareMesh(2 ** power, 2 ** power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# TODO: provide a kernel which will describe how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
fs = FunctionSpace(mesh, family, degree, name="fs")
f = Function(fs)
populate_p0 = op2.Kernel("""
void populate_tracer(double *x[], double *c[])
{
x[0][0] = (c[1][2] + c[0][2]) / 2;
}""", "populate_tracer")
coords = f.function_space().mesh().coordinates
op2.par_loop(populate_p0, f.cell_set,
f.dat(op2.INC, f.cell_node_map()),
coords.dat(op2.READ, coords.cell_node_map()))
volume = op2.Kernel("""
void comp_vol(double A[1], double *x[], double *y[])
{
double area = x[0][0]*(x[2][1]-x[4][1]) + x[2][0]*(x[4][1]-x[0][1])
+ x[4][0]*(x[0][1]-x[2][1]);
if (area < 0)
area = area * (-1.0);
A[0] += 0.5 * area * (x[1][2] - x[0][2]) * y[0][0];
}""", "comp_vol")
g = op2.Global(1, data=0.0, name='g')
op2.par_loop(volume, f.cell_set,
g(op2.INC),
coords.dat(op2.READ, coords.cell_node_map()),
f.dat(op2.READ, f.cell_node_map())
)
return np.abs(g.data[0] - 0.5)
def integrate_var_p0(family, degree):
power = 5
m = UnitSquareMesh(2**power, 2**power)
layers = 10
# Populate the coordinates of the extruded mesh by providing the
# coordinates as a field.
# TODO: provide a kernel which will describe how coordinates are extruded.
mesh = ExtrudedMesh(m, layers, layer_height=0.1)
fs = FunctionSpace(mesh, family, degree, name="fs")
f = Function(fs)
populate_p0 = op2.Kernel(
"""
void populate_tracer(double *x[], double *c[])
{
x[0][0] = (c[1][2] + c[0][2]) / 2;
}""", "populate_tracer")
coords = f.function_space().mesh().coordinates
op2.par_loop(populate_p0, f.cell_set, f.dat(op2.INC, f.cell_node_map()),
coords.dat(op2.READ, coords.cell_node_map()))
volume = op2.Kernel(
"""
void comp_vol(double A[1], double *x[], double *y[])
{
double area = x[0][0]*(x[2][1]-x[4][1]) + x[2][0]*(x[4][1]-x[0][1])
+ x[4][0]*(x[0][1]-x[2][1]);
if (area < 0)
area = area * (-1.0);
A[0] += 0.5 * area * (x[1][2] - x[0][2]) * y[0][0];
}""", "comp_vol")
g = op2.Global(1, data=0.0, name='g')
op2.par_loop(volume, f.cell_set, g(op2.INC),
coords.dat(op2.READ, coords.cell_node_map()),
f.dat(op2.READ, f.cell_node_map()))
return np.abs(g.data[0] - 0.5)
def computeAvgHessian(meshd, sol, t, tIni, tEnd, nbrSpl, H, hessian, options) :
print "DEBUG hessian-metric assembly"; sys.stdout.flush()
chrono1 = clock()
mesh = meshd.mesh
detMax = Function(meshd.V).interpolate(abs(det(H))).dat.data.max()
lbdmax = sqrt(detMax)
lbdmin = 1.e-20 * lbdmax
lbdMin = op2.Global(1, lbdmin, dtype=float);
op2.par_loop(options.absValHessian_kernel, H.node_set().superset, H.dat(op2.RW), lbdMin(op2.READ))
# sum with previous hessians
# 3 cases: if t=tIni or tEnd or in between
cof = float(tEnd-tIni)/(nbrSpl-1)
if (t == tIni) or (t == tEnd) : cof *= 0.5
hessian.dat.data[...] += cof*H.dat.data
chrono2 = clock()
print "DEBUG end Hessian-metric assembly. Elapsed time: %1.2e" %(chrono2-chrono1); sys.stdout.flush()
def par_loop(kernel, measure, args, **kwargs):
"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: is a string containing the C code to be executed.
:arg measure: is a UFL :class:`~ufl.measure.Measure` which determines the
manner in which the iteration over the mesh is to occur.
Alternatively, you can pass :data:`direct` to designate a direct loop.
:arg args: is a dictionary mapping variable names in the kernel to
:class:`.Function`\s or components of mixed :class:`.Function`\s and
indicates how these :class:`.Function`\s are to be accessed.
:arg kwargs: additional keyword arguments are passed to the
:class:`~pyop2.op2.Kernel` constructor
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
par_loop('for (int i=0; i<A.dofs; i++) A[i][0] = fmax(A[i][0], B[0][0]);', dx,
{'A' : (A, RW), 'B': (B, READ)})
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` or :class:`.Constant` and an
argument intent. The string is the c language variable name by
which this function will be accessed in the kernel. The argument
intent indicates how the kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
.. note::
Only `READ` intents are valid for :class:`.Constant`
coefficients, and an error will be raised in other cases.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FIAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FIAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
A direct loop over nodes without any indirections can be specified
by passing :data:`direct` as the measure. In this case, all of the
arguments must be :class:`.Function`\s in the same
:class:`.FunctionSpace`.
**The kernel code**
The kernel code is plain C in which the variables specified in the
`args` dictionary are available to be read or written in according
to the argument intent specified. Most basic C operations are
permitted. However there are some restrictions:
* Only functions from `math.h
<http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html>`_
may be called.
* Pointer operations other than dereferencing arrays are prohibited.
Indirect free variables referencing :class:`.Function`\s are all
of type `double**` in which the first index is the local node
number, while the second index is the vector (or tensor)
component. The latter only applies to :class:`.Function`\s over a
:class:`.FunctionSpace` with :attr:`.FunctionSpace.rank` greater
than zero (spaces with a VectorElement or TensorElement). In the
case of scalar :class:`FunctionSpace`\s, the second index is
always 0.
In a direct :func:`par_loop`, the variables will all be of type
`double*` with the single index being the vector component.
:class:`.Constant`\s are always of type `double*`, both for
indirect and direct :func:`par_loop` calls.
"""
_map = _maps[measure.integral_type()]
# Ensure that the dict args passed in are consistently ordered
# (sorted by the string key).
sorted_args = collections.OrderedDict()
for k in sorted(args.iterkeys()):
sorted_args[k] = args[k]
args = sorted_args
if measure is direct:
mesh = None
for (func, intent) in args.itervalues():
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
if mesh and c.node_set[idx] is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = c.node_set[idx]
else:
try:
if mesh and func.node_set is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = func.node_set
except AttributeError:
# Argument was a Global.
pass
if not mesh:
raise TypeError("No Functions passed to direct par_loop")
else:
domains = []
for func, _ in args.itervalues():
domains.extend(func.ufl_domains())
domains = join_domains(domains)
# Assume only one domain
domain, = domains
mesh = domain
op2args = [_form_kernel(kernel, measure, args, **kwargs)]
op2args.append(_map['itspace'](mesh, measure))
def mkarg(f, intent):
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
m = _map['nodes'](c)
return c.dat[idx](intent, m.split[idx] if m else None)
return f.dat(intent, _map['nodes'](f))
op2args += [mkarg(func, intent) for (func, intent) in args.itervalues()]
return pyop2.par_loop(*op2args)
def par_loop(kernel, measure, args, **kwargs):
"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: is a string containing the C code to be executed.
:arg measure: is a UFL :class:`~ufl.measure.Measure` which determines the
manner in which the iteration over the mesh is to occur.
Alternatively, you can pass :data:`direct` to designate a direct loop.
:arg args: is a dictionary mapping variable names in the kernel to
:class:`.Function`\s or components of mixed :class:`.Function`\s and
indicates how these :class:`.Function`\s are to be accessed.
:arg kwargs: additional keyword arguments are passed to the
:class:`~pyop2.op2.Kernel` constructor
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
par_loop('for (int i=0; i<A.dofs; i++) A[i][0] = fmax(A[i][0], B[0][0]);', dx,
{'A' : (A, RW), 'B': (B, READ)})
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` or :class:`.Constant` and an
argument intent. The string is the c language variable name by
which this function will be accessed in the kernel. The argument
intent indicates how the kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
.. note::
Only `READ` intents are valid for :class:`.Constant`
coefficients, and an error will be raised in other cases.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FInAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FInAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
A direct loop over nodes without any indirections can be specified
by passing :data:`direct` as the measure. In this case, all of the
arguments must be :class:`.Function`\s in the same
:class:`.FunctionSpace`.
**The kernel code**
The kernel code is plain C in which the variables specified in the
`args` dictionary are available to be read or written in according
to the argument intent specified. Most basic C operations are
permitted. However there are some restrictions:
* Only functions from `math.h
<http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html>`_
may be called.
* Pointer operations other than dereferencing arrays are prohibited.
Indirect free variables referencing :class:`.Function`\s are all
of type `double**` in which the first index is the local node
number, while the second index is the vector (or tensor)
component. The latter only applies to :class:`.Function`\s over a
:class:`.FunctionSpace` with :attr:`.FunctionSpace.rank` greater
than zero (spaces with a VectorElement or TensorElement). In the
case of scalar :class:`FunctionSpace`\s, the second index is
always 0.
In a direct :func:`par_loop`, the variables will all be of type
`double*` with the single index being the vector component.
:class:`.Constant`\s are always of type `double*`, both for
indirect and direct :func:`par_loop` calls.
"""
_map = _maps[measure.integral_type()]
# Ensure that the dict args passed in are consistently ordered
# (sorted by the string key).
sorted_args = collections.OrderedDict()
for k in sorted(args.iterkeys()):
sorted_args[k] = args[k]
args = sorted_args
if measure is direct:
mesh = None
for (func, intent) in args.itervalues():
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
if mesh and c.node_set[idx] is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = c.node_set[idx]
else:
try:
if mesh and func.node_set is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = func.node_set
except AttributeError:
# Argument was a Global.
pass
if not mesh:
raise TypeError("No Functions passed to direct par_loop")
else:
domains = []
for func, _ in args.itervalues():
domains.extend(func.ufl_domains())
domains = join_domains(domains)
# Assume only one domain
domain, = domains
mesh = domain
op2args = [_form_kernel(kernel, measure, args, **kwargs)]
op2args.append(_map['itspace'](mesh, measure))
def mkarg(f, intent):
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
m = _map['nodes'](c)
return c.dat[idx](intent, m.split[idx] if m else None)
return f.dat(intent, _map['nodes'](f))
op2args += [mkarg(func, intent) for (func, intent) in args.itervalues()]
return pyop2.par_loop(*op2args)
def par_loop(kernel, measure, args, kernel_kwargs=None, is_loopy_kernel=False, **kwargs):
r"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: a string containing the C code to be executed. Or a
2-tuple of (domains, instructions) to create a loopy kernel
(must also set ``is_loopy_kernel=True``). If loopy syntax is
used, the domains and instructions should be specified in
loopy kernel syntax. See the `loopy tutorial
<https://documen.tician.de/loopy/tutorial.html>`_ for details.
:arg measure: is a UFL :class:`~ufl.measure.Measure` which determines the
manner in which the iteration over the mesh is to occur.
Alternatively, you can pass :data:`direct` to designate a direct loop.
:arg args: is a dictionary mapping variable names in the kernel to
:class:`.Function`\s or components of mixed :class:`.Function`\s and
indicates how these :class:`.Function`\s are to be accessed.
:arg kernel_kwargs: keyword arguments to be passed to the
:class:`~pyop2.op2.Kernel` constructor
:arg kwargs: additional keyword arguments are passed to the underlying
:class:`~pyop2.par_loop`
:kwarg iterate: Optionally specify which region of an
:class:`ExtrudedSet` to iterate over.
Valid values are the following objects from pyop2:
- ``ON_BOTTOM``: iterate over the bottom layer of cells.
- ``ON_TOP`` iterate over the top layer of cells.
- ``ALL`` iterate over all cells (the default if unspecified)
- ``ON_INTERIOR_FACETS`` iterate over all the layers
except the top layer, accessing data two adjacent (in
the extruded direction) cells at a time.
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
par_loop('for (int i=0; i<A.dofs; i++) A[i] = fmax(A[i], B[0]);', dx,
{'A' : (A, RW), 'B': (B, READ)})
The equivalent using loopy kernel syntax is::
domain = '{[i]: 0 <= i < A.dofs}'
instructions = '''
for i
A[i] = max(A[i], B[0])
end
'''
par_loop((domain, instructions), dx, {'A' : (A, RW), 'B': (B, READ)}, is_loopy_kernel=True)
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` or :class:`.Constant` and an
argument intent. The string is the c language variable name by
which this function will be accessed in the kernel. The argument
intent indicates how the kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
.. note::
Only `READ` intents are valid for :class:`.Constant`
coefficients, and an error will be raised in other cases.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FInAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FInAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
A direct loop over nodes without any indirections can be specified
by passing :data:`direct` as the measure. In this case, all of the
arguments must be :class:`.Function`\s in the same
:class:`.FunctionSpace`.
**The kernel code**
The kernel code is plain C in which the variables specified in the
`args` dictionary are available to be read or written in according
to the argument intent specified. Most basic C operations are
permitted. However there are some restrictions:
* Only functions from `math.h
<http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html>`_
may be called.
* Pointer operations other than dereferencing arrays are prohibited.
Indirect free variables referencing :class:`.Function`\s are all
of type `double*`. For spaces with rank greater than zero (Vector
or TensorElement), the data are laid out XYZ... XYZ... XYZ....
With the vector/tensor component moving fastest.
In loopy syntax, these may be addressed using 2D indexing::
A[i, j]
Where ``i`` runs over nodes, and ``j`` runs over components.
In a direct :func:`par_loop`, the variables will all be of type
`double*` with the single index being the vector component.
:class:`.Constant`\s are always of type `double*`, both for
indirect and direct :func:`par_loop` calls.
"""
if kernel_kwargs is None:
kernel_kwargs = {}
_map = _maps[measure.integral_type()]
# Ensure that the dict args passed in are consistently ordered
# (sorted by the string key).
sorted_args = collections.OrderedDict()
for k in sorted(args.keys()):
sorted_args[k] = args[k]
args = sorted_args
if measure is direct:
mesh = None
for (func, intent) in args.values():
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
if mesh and c.node_set[idx] is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = c.node_set[idx]
else:
try:
if mesh and func.node_set is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = func.node_set
except AttributeError:
# Argument was a Global.
pass
if not mesh:
raise TypeError("No Functions passed to direct par_loop")
else:
domains = []
for func, _ in args.values():
domains.extend(func.ufl_domains())
domains = join_domains(domains)
# Assume only one domain
domain, = domains
mesh = domain
if is_loopy_kernel:
kernel_domains, instructions = kernel
op2args = [_form_loopy_kernel(kernel_domains, instructions, measure, args, **kernel_kwargs)]
else:
op2args = [_form_string_kernel(kernel, measure, args, **kernel_kwargs)]
op2args.append(_map['itspace'](mesh, measure))
def mkarg(f, intent):
if isinstance(f, Indexed):
c, i = f.ufl_operands
idx = i._indices[0]._value
m = _map['nodes'](c)
return c.dat[idx](intent, m.split[idx] if m else None)
return f.dat(intent, _map['nodes'](f))
op2args += [mkarg(func, intent) for (func, intent) in args.values()]
return pyop2.par_loop(*op2args, **kwargs)
def par_loop(kernel, measure, args, kernel_kwargs=None, is_loopy_kernel=False, **kwargs):
r"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: a string containing the C code to be executed. Or a
2-tuple of (domains, instructions) to create a loopy kernel
(must also set ``is_loopy_kernel=True``). If loopy syntax is
used, the domains and instructions should be specified in
loopy kernel syntax. See the `loopy tutorial
<https://documen.tician.de/loopy/tutorial.html>`_ for details.
:arg measure: is a UFL :class:`~ufl.measure.Measure` which determines the
manner in which the iteration over the mesh is to occur.
Alternatively, you can pass :data:`direct` to designate a direct loop.
:arg args: is a dictionary mapping variable names in the kernel to
:class:`.Function`\s or components of mixed :class:`.Function`\s and
indicates how these :class:`.Function`\s are to be accessed.
:arg kernel_kwargs: keyword arguments to be passed to the
:class:`~pyop2.op2.Kernel` constructor
:arg kwargs: additional keyword arguments are passed to the underlying
:class:`~pyop2.par_loop`
:kwarg iterate: Optionally specify which region of an
:class:`ExtrudedSet` to iterate over.
Valid values are the following objects from pyop2:
- ``ON_BOTTOM``: iterate over the bottom layer of cells.
- ``ON_TOP`` iterate over the top layer of cells.
- ``ALL`` iterate over all cells (the default if unspecified)
- ``ON_INTERIOR_FACETS`` iterate over all the layers
except the top layer, accessing data two adjacent (in
the extruded direction) cells at a time.
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
par_loop('for (int i=0; i<A.dofs; i++) A[i] = fmax(A[i], B[0]);', dx,
{'A' : (A, RW), 'B': (B, READ)})
The equivalent using loopy kernel syntax is::
domain = '{[i]: 0 <= i < A.dofs}'
instructions = '''
for i
A[i] = max(A[i], B[0])
end
'''
par_loop((domain, instructions), dx, {'A' : (A, RW), 'B': (B, READ)}, is_loopy_kernel=True)
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` or :class:`.Constant` and an
argument intent. The string is the c language variable name by
which this function will be accessed in the kernel. The argument
intent indicates how the kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
.. note::
Only `READ` intents are valid for :class:`.Constant`
coefficients, and an error will be raised in other cases.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FInAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FInAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
A direct loop over nodes without any indirections can be specified
by passing :data:`direct` as the measure. In this case, all of the
arguments must be :class:`.Function`\s in the same
:class:`.FunctionSpace`.
**The kernel code**
The kernel code is plain C in which the variables specified in the
`args` dictionary are available to be read or written in according
to the argument intent specified. Most basic C operations are
permitted. However there are some restrictions:
* Only functions from `math.h
<http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html>`_
may be called.
* Pointer operations other than dereferencing arrays are prohibited.
Indirect free variables referencing :class:`.Function`\s are all
of type `double*`. For spaces with rank greater than zero (Vector
or TensorElement), the data are laid out XYZ... XYZ... XYZ....
With the vector/tensor component moving fastest.
In loopy syntax, these may be addressed using 2D indexing::
A[i, j]
Where ``i`` runs over nodes, and ``j`` runs over components.
In a direct :func:`par_loop`, the variables will all be of type
`double*` with the single index being the vector component.
:class:`.Constant`\s are always of type `double*`, both for
indirect and direct :func:`par_loop` calls.
"""
if kernel_kwargs is None:
kernel_kwargs = {}
_map = _maps[measure.integral_type()]
# Ensure that the dict args passed in are consistently ordered
# (sorted by the string key).
sorted_args = collections.OrderedDict()
for k in sorted(args.keys()):
sorted_args[k] = args[k]
args = sorted_args
if measure is direct:
mesh = None
for (func, intent) in args.values():
if isinstance(func, Indexed):
c, i = func.ufl_operands
idx = i._indices[0]._value
if mesh and c.node_set[idx] is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = c.node_set[idx]
else:
try:
if mesh and func.node_set is not mesh:
raise ValueError("Cannot mix sets in direct loop.")
mesh = func.node_set
except AttributeError:
# Argument was a Global.
pass
if not mesh:
raise TypeError("No Functions passed to direct par_loop")
else:
domains = []
for func, _ in args.values():
domains.extend(func.ufl_domains())
domains = join_domains(domains)
# Assume only one domain
domain, = domains
mesh = domain
if is_loopy_kernel:
kernel_domains, instructions = kernel
op2args = [_form_loopy_kernel(kernel_domains, instructions, measure, args, **kernel_kwargs)]
else:
op2args = [_form_string_kernel(kernel, measure, args, **kernel_kwargs)]
op2args.append(_map['itspace'](mesh, measure))
def mkarg(f, intent):
if isinstance(f, Indexed):
c, i = f.ufl_operands
idx = i._indices[0]._value
m = _map['nodes'](c)
return c.dat[idx](intent, m.split[idx] if m else None)
return f.dat(intent, _map['nodes'](f))
op2args += [mkarg(func, intent) for (func, intent) in args.values()]
return pyop2.par_loop(*op2args, **kwargs)
def par_loop(kernel, measure, args):
"""A :func:`par_loop` is a user-defined operation which reads and
writes :class:`.Function`\s by looping over the mesh cells or facets
and accessing the degrees of freedom on adjacent entities.
:arg kernel: is a string containing the C code to be executed.
:arg measure: is a :class:`ufl.Measure` which determines the manner in which the iteration over the mesh is to occur.
:arg args: is a dictionary mapping variable names in the kernel to :class:`.Functions` and indicates how these :class:`.Functions` are to be accessed.
**Example**
Assume that `A` is a :class:`.Function` in CG1 and `B` is a
:class:`.Function` in DG0. Then the following code sets each DoF in
`A` to the maximum value that `B` attains in the cells adjacent to
that DoF::
A.assign(numpy.finfo(0.).min)
parloop('for (int i=0; i<A.dofs; i++;) A[i] = fmax(A[i], B[0]);', dx,
{'A' : (A, RW), 'B', (B, READ)})
**Argument definitions**
Each item in the `args` dictionary maps a string to a tuple
containing a :class:`.Function` and an argument intent. The string
is the c language variable name by which this function will be
accessed in the kernel. The argument intent indicates how the
kernel will access this variable:
`READ`
The variable will be read but not written to.
`WRITE`
The variable will be written to but not read. If multiple kernel
invocations write to the same DoF, then the order of these writes
is undefined.
`RW`
The variable will be both read and written to. If multiple kernel
invocations access the same DoF, then the order of these accesses
is undefined, but it is guaranteed that no race will occur.
`INC`
The variable will be added into using +=. As before, the order in
which the kernel invocations increment the variable is undefined,
but there is a guarantee that no races will occur.
**The measure**
The measure determines the mesh entities over which the iteration
will occur, and the size of the kernel stencil. The iteration will
occur over the same mesh entities as if the measure had been used
to define an integral, and the stencil will likewise be the same
as the integral case. That is to say, if the measure is a volume
measure, the kernel will be called once per cell and the DoFs
accessible to the kernel will be those associated with the cell,
its facets, edges and vertices. If the measure is a facet measure
then the iteration will occur over the corresponding class of
facets and the accessible DoFs will be those on the cell(s)
adjacent to the facet, and on the facets, edges and vertices
adjacent to those facets.
For volume measures the DoFs are guaranteed to be in the FIAT
local DoFs order. For facet measures, the DoFs will be in sorted
first by the cell to which they are adjacent. Within each cell,
they will be in FIAT order. Note that if a continuous
:class:`.Function` is accessed via an internal facet measure, the
DoFs on the interface between the two facets will be accessible
twice: once via each cell. The orientation of the cell(s) relative
to the current facet is currently arbitrary.
**The kernel code**
The kernel code is plain C in which the variables specified in the
`args` dictionary are available to be read or written in according
to the argument intent specified. Most basic C operations are
permitted. However there are some restrictions:
* Only functions from `math.h
<http://pubs.opengroup.org/onlinepubs/9699919799/basedefs/math.h.html>`_
may be called.
* Pointer operations other than dereferencing arrays are prohibited.
The free variables are all of type `double**` in which the first
index is the local node number, while the second index is the
vector component. The latter only applies to :class:`.Function`\s
over a :class:`VectorFunctionSpace`, for :class:`.Function`\s over
a plain :class:`.FunctionSpace` the second index will always be 0.
"""
_map = _maps[measure.integral_type()]
mesh = measure.subdomain_data().function_space().mesh()
op2args = [_form_kernel(kernel, measure, args)]
op2args.append(_map['itspace'](mesh, measure))
op2args += [func.dat(intent, _map['nodes'](func))
for (func, intent) in args.itervalues()]
return pyop2.par_loop(*op2args)