def test_latex_2d_5():
DIM = 2
domain = Domain('Omega', dim=DIM)
# ... abstract model
W1 = VectorFunctionSpace('W1', domain)
w1 = element_of(W1, name='w1')
F = element_of(W1, 'F')
int_0 = lambda expr: integral(domain, expr)
# ...
l1 = LinearForm(w1, int_0(dot(w1, F)))
print(latex(l1))
print('')
# ...
# ...
l2 = LinearForm(w1, int_0(rot(w1) * rot(F) + div(w1) * div(F)))
print(latex(l2))
print('')
def test_latex_2d_2():
DIM = 2
domain = Domain('Omega', dim=DIM)
V = VectorFunctionSpace('V', domain)
x, y = V.coordinates
v = element_of(V, name='v')
u = element_of(V, name='u')
# F = element_of(V, name='F')
int_0 = lambda expr: integral(domain, expr)
assert (latex(v) == r'\mathbf{v}')
assert (latex(inner(
grad(v), grad(u))) == r'\nabla{\mathbf{u}} : \nabla{\mathbf{v}}')
a = BilinearForm((v, u), int_0(inner(grad(v), grad(u))))
print(latex(a))
# assert(latex(a) == r'\int_{0}^{1}\int_{0}^{1} \nabla{\mathbf{v}} : \nabla{\mathbf{u}} dxdy')
b = LinearForm(v, int_0(sin(pi * x) * cos(pi * y) * div(v)))
print(latex(b))
def test_latex_2d_3():
DIM = 2
domain = Domain('Omega', dim=DIM)
B1 = Boundary(r'\Gamma_1', domain)
B2 = Boundary(r'\Gamma_2', domain)
B3 = Boundary(r'\Gamma_3', domain)
V = ScalarFunctionSpace('V', domain)
x = V.coordinates
v = element_of(V, name='v')
u = element_of(V, name='u')
int_0 = lambda expr: integral(domain, expr)
int_1 = lambda expr: integral(B1, expr)
# ...
expr = dot(grad(v), grad(u))
a_0 = BilinearForm((v, u), int_0(expr))
expr = v * u
a_bnd = BilinearForm((v, u), int_1(expr))
expr = a_0(v, u) + a_bnd(v, u)
a = BilinearForm((v, u), expr)
print(latex(a_0))
print(latex(a_bnd))
print(latex(a))
# print(a)
print('')
def test_latex_ec_3d_1():
n = 3
# ...
u_0 = DifferentialForm('u_0', index=0, dim=n)
v_0 = DifferentialForm('v_0', index=0, dim=n)
u_1 = DifferentialForm('u_1', index=1, dim=n)
v_1 = DifferentialForm('v_1', index=1, dim=n)
u_2 = DifferentialForm('u_2', index=2, dim=n)
v_2 = DifferentialForm('v_2', index=2, dim=n)
u_3 = DifferentialForm('u_3', index=3, dim=n)
v_3 = DifferentialForm('v_3', index=3, dim=n)
# ...
# ...
domain = Domain('Omega', dim=3)
V = VectorFunctionSpace('V', domain)
beta = element_of(V, 'beta')
# ...
print(latex(u_0))
print(latex(d(u_0)))
print(latex(d(delta(u_3))))
print(latex(d(delta(u_2)) + delta(d(u_2))))
print(latex(wedge(u_0, u_1)))
print(latex(ip(beta, u_1)))
print(latex(hodge(u_1)))
print(latex(jp(beta, u_1)))
def test_latex_2d_1():
DIM = 2
domain = Domain('Omega', dim=DIM)
V = ScalarFunctionSpace('V', domain)
x, y = V.coordinates
v = element_of(V, name='v')
u = element_of(V, name='u')
# F = element_of(V, name='F')
int_0 = lambda expr: integral(domain, expr)
assert (latex(grad(v)) == r'\nabla{v}')
assert (latex(dot(grad(v), grad(u))) == r'\nabla{u} \cdot \nabla{v}')
a = BilinearForm((v, u), int_0(dot(grad(v), grad(u))))
print(latex(a))
# assert(latex(a) == r'\int_{0}^{1}\int_{0}^{1} \nabla{v} \cdot \nabla{u} dxdy')
b = LinearForm(v, int_0(sin(pi * x) * cos(pi * y) * v))
print(latex(b))
def test_latex_2d_4():
DIM = 2
domain = Domain('Omega', dim=DIM)
# ... abstract model
V = VectorFunctionSpace('V', domain)
W = ScalarFunctionSpace('W', domain)
v = element_of(V, name='v')
u = element_of(V, name='u')
p = element_of(W, name='p')
q = element_of(W, name='q')
int_0 = lambda expr: integral(domain, expr)
a = BilinearForm((v, u), int_0(inner(grad(v), grad(u))))
b = BilinearForm((v, p), int_0(div(v) * p))
A = BilinearForm(((v, q), (u, p)), a(v, u) - b(v, p) + b(u, q))
# ...
print(latex(A))
# print(latex(tensorize(A)))
print('')
f = open('{}.dot'.format(name), 'w')
f.write(txt)
f.close()
cmd = 'dot {name}.dot -Tpng -o {name}.png'.format(name=name)
os.system(cmd)
# ...
from sympde import grad, dot
from sympde import FunctionSpace
from sympde import TestFunction
from sympde import BilinearForm
from sympde.core import tensorize
from sympde.printing.latex import latex
V = FunctionSpace('V', ldim=2)
U = FunctionSpace('U', ldim=2)
v = TestFunction(V, name='v')
u = TestFunction(U, name='u')
a = BilinearForm((v, u), dot(grad(v), grad(u)) + v * u)
print('> a = ', a)
print('> tensorize(a) = ', tensorize(a))
print(latex(tensorize(a)))
#dotexport(a, 'graph_laplace.png')
# ...