ufl.formatting package

Submodules

ufl.formatting.graph module

Algorithms for working with linearized computational graphs.

class ufl.formatting.graph.Graph(expression)

Bases: object

Graph class which computes connectivity on demand.

E()

Ein()

Eout()

V()

Vin()

Vout()

class ufl.formatting.graph.HeapItem(incoming, outgoing, i)

Bases: object

class ufl.formatting.graph.StringDependencyDefiner(argument_deps=None, coefficient_deps=None)

Bases: MultiFunction

Given an expr, returns a frozenset of its dependencies.

Possible dependency values are:

“c” - depends on runtime information like the cell, local<->global coordinate mappings, facet normals, or coefficients “x” - depends on local coordinates “v%d” % i - depends on argument i, for i in [0,rank)

argument(x)

coefficient(x)

expr(o)

Trigger error for types with missing handlers.

facet_normal(o)

geometric_quantity(x)

spatial_derivative(o)

ufl.formatting.graph.build_graph(expr)

Build a linearized graph from an UFL Expr.

Returns G = (V, E), with V being a list of graph nodes (Expr objects) in post traversal ordering and E being a list of edges. Each edge is represented as a (i, j) tuple where i and j are vertex indices into V.

ufl.formatting.graph.depth_first_ordering(G)

ufl.formatting.graph.extract_incoming_edges(G)

Build lists of incoming edges to each vertex in a linearized graph.

ufl.formatting.graph.extract_incoming_vertex_connections(G)

Build lists of vertices in incoming and outgoing edges to and from each vertex in a linearized graph.

Returns lists Vin and Vout.

ufl.formatting.graph.extract_outgoing_edges(G)

Build list of outgoing edges from each vertex in a linearized graph.

ufl.formatting.graph.extract_outgoing_vertex_connections(G)

Build lists of vertices in incoming and outgoing edges to and from each vertex in a linearized graph.

Returns lists Vin and Vout.

ufl.formatting.graph.len_items(sequence)

ufl.formatting.graph.lists(n)

ufl.formatting.graph.partition(G, criteria=<function string_set_criteria>)

ufl.formatting.graph.string_set_criteria(v, keys)

ufl.formatting.printing module

A collection of utility algorithms for printing of UFL objects, mostly intended for debugging purposes.

ufl.formatting.printing.form_info(form)

ufl.formatting.printing.integral_info(integral)

ufl.formatting.printing.tree_format(expression, indentation=0, parentheses=True)

ufl.formatting.ufl2dot module

A collection of utility algorithms for printing of UFL objects in the DOT graph visualization language, mostly intended for debugging purposers.

class ufl.formatting.ufl2dot.CompactLabeller(function_mapping=None)

Bases: ReprLabeller

cell_avg(e)

component_tensor(e)

conj(e)

curl(e)

determinant(e)

dev(e)

diff(e)

div(e)

division(e)

dot(e)

facet_avg(e)

form_argument(e)

geometric_quantity(e)

grad(e)

identity(e)

imag(e)

index_sum(e)

indexed(e)

inner(e)

math_function(e)

multi_index(e)

nabla_div(e)

nabla_grad(e)

negative_restricted(e)

outer(e)

positive_restricted(e)

power(e)

product(e)

real(e)

scalar_value(e)

skew(e)

sum(e)

trace(e)

transposed(e)

zero(e)

class ufl.formatting.ufl2dot.FancyLabeller(function_mapping=None)

Bases: CompactLabeller

class ufl.formatting.ufl2dot.ReprLabeller

Bases: MultiFunction

operator(e)

terminal(e)

ufl.formatting.ufl2dot.build_entities(e, nodes, edges, nodeoffset, prefix='', labeller=None)

ufl.formatting.ufl2dot.format_entities(nodes, edges)

ufl.formatting.ufl2dot.ufl2dot(expression, formname='a', nodeoffset=0, begin=True, end=True, labeling='repr', object_names=None)

ufl.formatting.ufl2unicode module

class ufl.formatting.ufl2unicode.Expression2UnicodeHandler(argument_names=None, coefficient_names=None, colorama_bold=False)

Bases: MultiFunction

abs(o, a)

and_condition(o, a, b)

argument(o)

atan2(o, f1, f2)

bessel_K(o, nu, f)

bessel_i(o, nu, f)

bessel_j(o, nu, f)

bessel_y(o, nu, f)

cell_avg(o, f)

coefficient(o)

coefficient_derivative(o, f, w, v, cd)

cofactor(o, A)

component_tensor(o, A, ii)

conditional(o, c, t, f)

conj(o, a)

constant(o)

cross(o, a, b)

curl(o, f)

determinant(o, A)

deviatoric(o, A)

div(o, f)

division(o, a, b)

dot(o, a, b)

eq(o, a, b)

exp(o, f)

expr(o)

Trigger error for types with missing handlers.

expr_list(o, *ops)

expr_mapping(o, *ops)

facet_avg(o, f)

facet_normal(o)

ge(o, a, b)

grad(o, f)

gt(o, a, b)

identity(o)

imag(o, a)

index_sum(o, f, i)

indexed(o, A, ii)

inner(o, a, b)

inverse(o, A)

label(o)

le(o, a, b)

list_tensor(o, *ops)

lt(o, a, b)

math_function(o, f)

max_value(o, a, b)

min_value(o, a, b)

multi_index(o)

nabla_div(o, f)

nabla_grad(o, f)

ne(o, a, b)

negative_restricted(o, f)

not_condition(o, a)

or_condition(o, a, b)

outer(o, a, b)

permutation_symbol(o)

positive_restricted(o, f)

power(o, a, b)

product(o, a, b)

real(o, a)

scalar_value(o)

skew(o, A)

spatial_coordinate(o)

sqrt(o, f)

sum(o, a, b)

sym(o, A)

trace(o, A)

transposed(o, a)

variable(o, f, l)

variable_derivative(o, f, v)

zero(o)

class ufl.formatting.ufl2unicode.PrecedenceRules

Bases: MultiFunction

An enum-like class for C operator precedence levels.

add(o)

and_condition(o)

bessel_function(o)

call(o)

cell_avg(o)

cofactor(o)

component_tensor(o)

conditional(o)

cross(o)

derivative(o)

deviatoric(o)

division(o)

dot(o)

eq(o)

facet_avg(o)

ge(o)

gt(o)

highest(o)

index_sum(o)

indexed(o)

inner(o)

le(o)

list_tensor(o)

lowest(o)

lt(o)

math_function(o)

mathop(o)

max_value(o)

min_value(o)

ne(o)

not_condition(o)

operator(o)

or_condition(o)

outer(o)

power(o)

product(o)

restricted(o)

skew(o)

sym(o)

terminal(o)

trace(o)

class ufl.formatting.ufl2unicode.UC

Bases: object

An enum-like class for unicode characters.

Gamma = 'Γ'

Omega = 'Ω'

bold_math_A = '𝐀'

bold_math_a = '𝐚'

circled_times = '⊗'

combining_overline = '̅'

combining_right_arrow_above = '⃗'

cross_product = '⨯'

division_slash = '∕'

dot = '⋅'

element_of = '∈'

epsilon = 'ε'

for_all = '∀'

gamma = 'γ'

ge = '≥'

gt = '>'

integral = '∫'

integral_contour = '∮'

integral_double = '∬'

integral_surface = '∯'

integral_triple = '∭'

integral_volume = '∰'

le = '≤'

left_angled_bracket = '⟨'

left_double_angled_bracket = '⟪'

left_white_square_bracket = '⟦'

logical_and = '∧'

logical_not = '¬'

logical_or = '∨'

lt = '<'

nabla = '∇'

nary_product = '∏'

ne = '≠'

not_element_of = '∉'

omega = 'ω'

partial = '∂'

right_angled_bracket = '⟩'

right_double_angled_bracket = '⟫'

right_white_squared_bracket = '⟧'

sqrt = '√'

subscript_digits = ['₀', '₁', '₂', '₃', '₄', '₅', '₆', '₇', '₈', '₉']

subscript_equals = '₌'

subscript_left_paren = '₍'

subscript_minus = '₋'

subscript_plus = '₊'

subscript_right_paren = '₎'

sum = '∑'

superscript_digits = ['⁰', '¹', '²', '³', '⁴', '⁵', '⁶', '⁷', '⁸', '⁹']

superscript_equals = '⁼'

superscript_left_paren = '⁽'

superscript_minus = '⁻'

superscript_plus = '⁺'

superscript_right_paren = '⁾'

thin_space = '\u2009'

transpose = 'ᵀ'

ufl.formatting.ufl2unicode.binop(expr, a, b, op, sep=' ')

ufl.formatting.ufl2unicode.bolden_letter(c)

ufl.formatting.ufl2unicode.bolden_string(s)

ufl.formatting.ufl2unicode.expression2unicode(expression, argument_names=None, coefficient_names=None)

ufl.formatting.ufl2unicode.form2unicode(form, formdata)

ufl.formatting.ufl2unicode.format_index(ii)

ufl.formatting.ufl2unicode.get_integral_symbol(integral_type, domain, subdomain_id)

ufl.formatting.ufl2unicode.is_int(s)

ufl.formatting.ufl2unicode.mathop(expr, arg, opname)

ufl.formatting.ufl2unicode.measure_font(dx)

ufl.formatting.ufl2unicode.opfont(opname)

ufl.formatting.ufl2unicode.overline_string(f)

ufl.formatting.ufl2unicode.par(s)

ufl.formatting.ufl2unicode.prec(expr)

ufl.formatting.ufl2unicode.precedence(expr)

ufl.formatting.ufl2unicode.subscript_digit(digit)

ufl.formatting.ufl2unicode.subscript_number(number)

ufl.formatting.ufl2unicode.superscript_digit(digit)

ufl.formatting.ufl2unicode.superscript_number(number)

ufl.formatting.ufl2unicode.ufl2unicode(expression)

Generate Unicode string for a UFL expression or form.

Module contents