# Source code for ufl.geometry

# -*- coding: utf-8 -*-
"Types for representing symbolic expressions for geometric quantities."

# Copyright (C) 2008-2016 Martin Sandve Alnæs
#
# This file is part of UFL (https://www.fenicsproject.org)
#
#
# Modified by Anders Logg, 2009.
# Modified by Kristian B. Oelgaard, 2009
# Modified by Marie E. Rognes 2012
# Modified by Massimiliano Leoni, 2016

from ufl.log import error
from ufl.core.ufl_type import ufl_type
from ufl.core.terminal import Terminal
from ufl.domain import as_domain

"""

Possible coordinate bootstrapping:

Xf = Xf[q]
FacetCoordinate = quadrature point on facet (ds,dS)

X = X[q]
CellCoordinate = quadrature point on cell (dx)

x = x[q]
SpatialCoordinate = quadrature point from input array (dc)

Jacobians of mappings between coordinates:

Jcf = dX/dXf = grad_Xf X(Xf)
CellFacetJacobian

Jxc = dx/dX = grad_X x(X)
Jacobian

Jxf = dx/dXf = grad_Xf x(Xf)  =  Jxc Jcf = dx/dX dX/dXf = grad_X x(X) grad_Xf X(Xf)
FacetJacobian = Jacobian * CellFacetJacobian

Possible computation of X from Xf:

X = Jcf Xf + X0f
CellCoordinate = CellFacetJacobian * FacetCoordinate + CellFacetOrigin

Possible computation of x from X:

x = f(X)
SpatialCoordinate = sum_k xdofs_k * xphi_k(X)

x = Jxc X + x0
SpatialCoordinate = Jacobian * CellCoordinate + CellOrigin

Possible computation of x from Xf:

x = x(X(Xf))

x = Jxf Xf + x0f
SpatialCoordinate = FacetJacobian * FacetCoordinate + FacetOrigin

Inverse relations:

X = K * (x - x0)
CellCoordinate = JacobianInverse * (SpatialCoordinate - CellOrigin)

Xf = FK * (x - x0f)
FacetCoordinate = FacetJacobianInverse * (SpatialCoordinate - FacetOrigin)

Xf = CFK * (X - X0f)
FacetCoordinate = CellFacetJacobianInverse * (CellCoordinate - CellFacetOrigin)

"""

# --- Expression node types

[docs]@ufl_type(is_abstract=True)
class GeometricQuantity(Terminal):
__slots__ = ("_domain",)

def __init__(self, domain):
Terminal.__init__(self)
self._domain = as_domain(domain)

[docs]    def ufl_domains(self):
return (self._domain,)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell (or over each facet for facet quantities)."
# NB! Geometric quantities are piecewise constant by
# default. Override if needed.
return True

# NB! Geometric quantities are scalar by default. Override if
# needed.
ufl_shape = ()

def _ufl_signature_data_(self, renumbering):
"Signature data of geometric quantities depend on the domain numbering."
return (self._ufl_class_.__name__,) + self._domain._ufl_signature_data_(renumbering)

def __str__(self):
return self._ufl_class_.name

def __repr__(self):
r = "%s(%s)" % (self._ufl_class_.__name__, repr(self._domain))
return r

def _ufl_compute_hash_(self):
return hash((type(self).__name__,) + self._domain._ufl_hash_data_())

def __eq__(self, other):
return isinstance(other, self._ufl_class_) and other._domain == self._domain

[docs]@ufl_type(is_abstract=True)
class GeometricCellQuantity(GeometricQuantity):
__slots__ = ()

[docs]@ufl_type(is_abstract=True)
class GeometricFacetQuantity(GeometricQuantity):
__slots__ = ()

# --- Coordinate represented in different coordinate systems

[docs]@ufl_type()
class SpatialCoordinate(GeometricCellQuantity):
"""UFL geometry representation: The coordinate in a domain.

In the context of expression integration,
represents the domain coordinate of each quadrature point.

In the context of expression evaluation in a point,
represents the value of that point.
"""
__slots__ = ()
name = "x"

@property
def ufl_shape(self):
"""Return the number of coordinates defined (i.e. the geometric dimension
of the domain)."""
g = self._domain.geometric_dimension()
return (g,)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only case this is true is if the domain is a vertex cell.
t = self._domain.topological_dimension()
return t == 0

[docs]    def evaluate(self, x, mapping, component, index_values):
"Return the value of the coordinate."
if component == ():
if isinstance(x, (tuple, list)):
return float(x[0])
else:
return float(x)
else:
return float(x[component[0]])

[docs]    def count(self):
# FIXME: Hack to make SpatialCoordinate behave like a coefficient.
# When calling derivative, the count is used to sort over.
return -1

[docs]@ufl_type()
class CellCoordinate(GeometricCellQuantity):
"""UFL geometry representation: The coordinate in a reference cell.

In the context of expression integration,
represents the reference cell coordinate of each quadrature point.

In the context of expression evaluation in a point in a cell,
represents that point in the reference coordinate system of the cell.
"""
__slots__ = ()
name = "X"

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t,)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only case this is true is if the domain is a vertex cell.
t = self._domain.topological_dimension()
return t == 0

[docs]@ufl_type()
class FacetCoordinate(GeometricFacetQuantity):
"""UFL geometry representation: The coordinate in a reference cell of a facet.

In the context of expression integration over a facet,
represents the reference facet coordinate of each quadrature point.

In the context of expression evaluation in a point on a facet,
represents that point in the reference coordinate system of the facet.
"""
__slots__ = ()
name = "Xf"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("FacetCoordinate is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t - 1,)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only case this is true is if the domain is an interval cell
# (with a vertex facet).
t = self._domain.topological_dimension()
return t <= 1

# --- Origin of coordinate systems in larger coordinate systems

[docs]@ufl_type()
class CellOrigin(GeometricCellQuantity):
"""UFL geometry representation: The spatial coordinate corresponding to origin of a reference cell."""
__slots__ = ()
name = "x0"

@property
def ufl_shape(self):
g = self._domain.geometric_dimension()
return (g,)

[docs]    def is_cellwise_constant(self):
return True

[docs]@ufl_type()
class FacetOrigin(GeometricFacetQuantity):
"""UFL geometry representation: The spatial coordinate corresponding to origin of a reference facet."""
__slots__ = ()
name = "x0f"

@property
def ufl_shape(self):
g = self._domain.geometric_dimension()
return (g,)

[docs]@ufl_type()
class CellFacetOrigin(GeometricFacetQuantity):
"""UFL geometry representation: The reference cell coordinate corresponding to origin of a reference facet."""
__slots__ = ()
name = "X0f"

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t,)

# --- Jacobians of mappings between coordinate systems

[docs]@ufl_type()
class Jacobian(GeometricCellQuantity):
"""UFL geometry representation: The Jacobian of the mapping from reference cell to spatial coordinates.

.. math:: J_{ij} = \\frac{dx_i}{dX_j}
"""
__slots__ = ()
name = "J"

@property
def ufl_shape(self):
"""Return the number of coordinates defined (i.e. the geometric dimension
of the domain)."""
g = self._domain.geometric_dimension()
t = self._domain.topological_dimension()
return (g, t)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class FacetJacobian(GeometricFacetQuantity):
"""UFL geometry representation: The Jacobian of the mapping from reference facet to spatial coordinates.

FJ_ij = dx_i/dXf_j

The FacetJacobian is the product of the Jacobian and CellFacetJacobian:

FJ = dx/dXf = dx/dX dX/dXf = J * CFJ

"""
__slots__ = ()
name = "FJ"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("FacetJacobian is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
g = self._domain.geometric_dimension()
t = self._domain.topological_dimension()
return (g, t - 1)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex
# cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class CellFacetJacobian(GeometricFacetQuantity):  # dX/dXf
"""UFL geometry representation: The Jacobian of the mapping from reference facet to reference cell coordinates.

CFJ_ij = dX_i/dXf_j
"""
__slots__ = ()
name = "CFJ"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("CellFacetJacobian is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t, t - 1)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always a constant mapping between two reference
# coordinate systems.
return True

[docs]@ufl_type()
class ReferenceCellEdgeVectors(GeometricCellQuantity):
"""UFL geometry representation: The vectors between reference cell vertices for each edge in cell."""
__slots__ = ()
name = "RCEV"

def __init__(self, domain):
GeometricCellQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("CellEdgeVectors is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
cell = self.ufl_domain().ufl_cell()
ne = cell.num_edges()
t = cell.topological_dimension()
return (ne, t)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always constant for a given cell type
return True

[docs]@ufl_type()
class ReferenceFacetEdgeVectors(GeometricFacetQuantity):
"""UFL geometry representation: The vectors between reference cell vertices for each edge in current facet."""
__slots__ = ()
name = "RFEV"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 3:
error("FacetEdgeVectors is only defined for topological dimensions >= 3.")

@property
def ufl_shape(self):
cell = self.ufl_domain().ufl_cell()
facet_types = cell.facet_types()

# Raise exception for cells with more than one facet type e.g. prisms
if len(facet_types) > 1:
raise Exception(f"Cell type {cell} not supported.")

nfe = facet_types[0].num_edges()
t = cell.topological_dimension()
return (nfe, t)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always constant for a given cell type
return True

[docs]@ufl_type()
class CellVertices(GeometricCellQuantity):
"""UFL geometry representation: Physical cell vertices."""
__slots__ = ()
name = "CV"

def __init__(self, domain):
GeometricCellQuantity.__init__(self, domain)

@property
def ufl_shape(self):
cell = self.ufl_domain().ufl_cell()
nv = cell.num_vertices()
g = cell.geometric_dimension()
return (nv, g)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always constant for a given cell type
return True

[docs]@ufl_type()
class CellEdgeVectors(GeometricCellQuantity):
"""UFL geometry representation: The vectors between physical cell vertices for each edge in cell."""
__slots__ = ()
name = "CEV"

def __init__(self, domain):
GeometricCellQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("CellEdgeVectors is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
cell = self.ufl_domain().ufl_cell()
ne = cell.num_edges()
g = cell.geometric_dimension()
return (ne, g)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always constant for a given cell type
return True

[docs]@ufl_type()
class FacetEdgeVectors(GeometricFacetQuantity):
"""UFL geometry representation: The vectors between physical cell vertices for each edge in current facet."""
__slots__ = ()
name = "FEV"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 3:
error("FacetEdgeVectors is only defined for topological dimensions >= 3.")

@property
def ufl_shape(self):
cell = self.ufl_domain().ufl_cell()
facet_types = cell.facet_types()

# Raise exception for cells with more than one facet type e.g. prisms
if len(facet_types) > 1:
raise Exception(f"Cell type {cell} not supported.")

nfe = facet_types[0].num_edges()
g = cell.geometric_dimension()
return (nfe, g)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# This is always constant for a given cell type
return True

# --- Determinants (signed or pseudo) of geometry mapping Jacobians

[docs]@ufl_type()
class JacobianDeterminant(GeometricCellQuantity):
"""UFL geometry representation: The determinant of the Jacobian.

Represents the signed determinant of a square Jacobian or the pseudo-determinant of a non-square Jacobian.
"""
__slots__ = ()
name = "detJ"

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex
# cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class FacetJacobianDeterminant(GeometricFacetQuantity):
"""UFL geometry representation: The pseudo-determinant of the FacetJacobian."""
__slots__ = ()
name = "detFJ"

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class CellFacetJacobianDeterminant(GeometricFacetQuantity):
"""UFL geometry representation: The pseudo-determinant of the CellFacetJacobian."""
__slots__ = ()
name = "detCFJ"

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex
# cells
return self._domain.is_piecewise_linear_simplex_domain()

# --- Inverses (signed or pseudo) of geometry mapping Jacobians

[docs]@ufl_type()
class JacobianInverse(GeometricCellQuantity):
"""UFL geometry representation: The inverse of the Jacobian.

Represents the inverse of a square Jacobian or the pseudo-inverse of a non-square Jacobian.
"""
__slots__ = ()
name = "K"

@property
def ufl_shape(self):
"""Return the number of coordinates defined (i.e. the geometric dimension
of the domain)."""
g = self._domain.geometric_dimension()
t = self._domain.topological_dimension()
return (t, g)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex
# cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class FacetJacobianInverse(GeometricFacetQuantity):
"""UFL geometry representation: The pseudo-inverse of the FacetJacobian."""
__slots__ = ()
name = "FK"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("FacetJacobianInverse is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
g = self._domain.geometric_dimension()
t = self._domain.topological_dimension()
return (t - 1, g)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex
# cells
return self._domain.is_piecewise_linear_simplex_domain()

[docs]@ufl_type()
class CellFacetJacobianInverse(GeometricFacetQuantity):
"""UFL geometry representation: The pseudo-inverse of the CellFacetJacobian."""
__slots__ = ()
name = "CFK"

def __init__(self, domain):
GeometricFacetQuantity.__init__(self, domain)
t = self._domain.topological_dimension()
if t < 2:
error("CellFacetJacobianInverse is only defined for topological dimensions >= 2.")

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t - 1, t)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# Only true for a piecewise linear coordinate field in simplex cells
return self._domain.is_piecewise_linear_simplex_domain()

# --- Types representing normal or tangent vectors

[docs]@ufl_type()
class FacetNormal(GeometricFacetQuantity):
"""UFL geometry representation: The outwards pointing normal vector of the current facet."""
__slots__ = ()
name = "n"

@property
def ufl_shape(self):
"""Return the number of coordinates defined (i.e. the geometric dimension
of the domain)."""
g = self._domain.geometric_dimension()
return (g,)

[docs]    def is_cellwise_constant(self):
"Return whether this expression is spatially constant over each cell."
# For product cells, this is only true for some but not all
# facets. Seems like too much work to fix right now.  Only
# true for a piecewise linear coordinate field with simplex
# _facets_.
is_piecewise_linear = self._domain.ufl_coordinate_element().degree() == 1
return is_piecewise_linear and self._domain.ufl_cell().has_simplex_facets()

[docs]@ufl_type()
class CellNormal(GeometricCellQuantity):
"""UFL geometry representation: The upwards pointing normal vector of the current manifold cell."""
__slots__ = ()
name = "cell_normal"

@property
def ufl_shape(self):
"""Return the number of coordinates defined (i.e. the geometric dimension
of the domain)."""
g = self._domain.geometric_dimension()
# t = self._domain.topological_dimension()
# return (g-t,g) # TODO: Should it be CellNormals? For interval in 3D we have two!
return (g,)

[docs]@ufl_type()
class ReferenceNormal(GeometricFacetQuantity):
"""UFL geometry representation: The outwards pointing normal vector of the current facet on the reference cell"""
__slots__ = ()
name = "reference_normal"

@property
def ufl_shape(self):
t = self._domain.topological_dimension()
return (t,)

# TODO: Implement in apply_geometry_lowering and enable
# @ufl_type()
# class FacetTangents(GeometricFacetQuantity):
#     """UFL geometry representation: The tangent vectors of the current facet."""
#     __slots__ = ()
#     name = "t"
#
#     def __init__(self, domain):
#         GeometricFacetQuantity.__init__(self, domain)
#         t = self._domain.topological_dimension()
#         if t < 2:
#             error("FacetTangents is only defined for topological dimensions >= 2.")
#
#    @property
#    def ufl_shape(self):
#        g = self._domain.geometric_dimension()
#        t = self._domain.topological_dimension()
#        return (t-1,g)
#
#    def is_cellwise_constant(self): # NB! Copied from FacetNormal
#        "Return whether this expression is spatially constant over each cell."
#        # For product cells, this is only true for some but not all facets. Seems like too much work to fix right now.
#        # Only true for a piecewise linear coordinate field with simplex _facets_.
#        is_piecewise_linear = self._domain.ufl_coordinate_element().degree() == 1
#        return is_piecewise_linear and self._domain.ufl_cell().has_simplex_facets()

# TODO: Implement in apply_geometry_lowering and enable
# @ufl_type()
# class CellTangents(GeometricCellQuantity):
#    """UFL geometry representation: The tangent vectors of the current manifold cell."""
#    __slots__ = ()
#    name = "cell_tangents"
#
#    @property
#    def ufl_shape(self):
#        g = self._domain.geometric_dimension()
#        t = self._domain.topological_dimension()
#        return (t,g)

# --- Types representing midpoint coordinates

# TODO: Implement in the rest of fenics
# @ufl_type()
# class CellMidpoint(GeometricCellQuantity):
#    """UFL geometry representation: The midpoint coordinate of the current cell."""
#    __slots__ = ()
#    name = "cell_midpoint"
#
#    @property
#    def ufl_shape(self):
#        g = self._domain.geometric_dimension()
#        return (g,)

# TODO: Implement in the rest of fenics
# @ufl_type()
# class FacetMidpoint(GeometricFacetQuantity):
#    """UFL geometry representation: The midpoint coordinate of the current facet."""
#    __slots__ = ()
#    name = "facet_midpoint"
#
#    @property
#    def ufl_shape(self):
#        g = self._domain.geometric_dimension()
#        return (g,)

# --- Types representing measures of the cell and entities of the cell, typically used for stabilisation terms

# TODO: Clean up this set of types? Document!

[docs]@ufl_type()
class ReferenceCellVolume(GeometricCellQuantity):
"""UFL geometry representation: The volume of the reference cell."""
__slots__ = ()
name = "reference_cell_volume"

[docs]@ufl_type()
class ReferenceFacetVolume(GeometricFacetQuantity):
"""UFL geometry representation: The volume of the reference cell of the current facet."""
__slots__ = ()
name = "reference_facet_volume"

[docs]@ufl_type()
class CellVolume(GeometricCellQuantity):
"""UFL geometry representation: The volume of the cell."""
__slots__ = ()
name = "volume"

[docs]@ufl_type()
"""UFL geometry representation: The circumradius of the cell."""
__slots__ = ()

[docs]@ufl_type()
class CellDiameter(GeometricCellQuantity):
"""UFL geometry representation: The diameter of the cell, i.e.,
maximal distance of two points in the cell."""
__slots__ = ()
name = "diameter"

# @ufl_type()
# class CellSurfaceArea(GeometricCellQuantity):
#    """UFL geometry representation: The total surface area of the cell."""
#    __slots__ = ()
#    name = "surfacearea"

[docs]@ufl_type()
class FacetArea(GeometricFacetQuantity):  # FIXME: Should this be allowed for interval domain?
"""UFL geometry representation: The area of the facet."""
__slots__ = ()
name = "facetarea"

[docs]@ufl_type()
class MinCellEdgeLength(GeometricCellQuantity):
"""UFL geometry representation: The minimum edge length of the cell."""
__slots__ = ()
name = "mincelledgelength"

[docs]@ufl_type()
class MaxCellEdgeLength(GeometricCellQuantity):
"""UFL geometry representation: The maximum edge length of the cell."""
__slots__ = ()
name = "maxcelledgelength"

[docs]@ufl_type()
class MinFacetEdgeLength(GeometricFacetQuantity):
"""UFL geometry representation: The minimum edge length of the facet."""
__slots__ = ()
name = "minfacetedgelength"

[docs]@ufl_type()
class MaxFacetEdgeLength(GeometricFacetQuantity):
"""UFL geometry representation: The maximum edge length of the facet."""
__slots__ = ()
name = "maxfacetedgelength"

# --- Types representing other stuff

[docs]@ufl_type()
class CellOrientation(GeometricCellQuantity):
"""UFL geometry representation: The orientation (+1/-1) of the current cell.

For non-manifold cells (tdim == gdim), this equals the sign
of the Jacobian determinant, i.e. +1 if the physical cell is
oriented the same way as the reference cell and -1 otherwise.

For manifold cells of tdim==gdim-1 this is input data belonging
to the mesh, used to distinguish between the sides of the manifold.
"""
__slots__ = ()
name = "cell_orientation"

[docs]@ufl_type()
class FacetOrientation(GeometricFacetQuantity):
"""UFL geometry representation: The orientation (+1/-1) of the current facet relative to the reference cell."""
__slots__ = ()
name = "facet_orientation"

# This doesn't quite fit anywhere. Make a special set of symbolic
[docs]@ufl_type()