def dyad(d, *iota):
"TODO: Develop this concept, can e.g. write A[i,j]*dyad(j,i) for the transpose."
from ufl.constantvalue import Identity
from ufl.operators import outer # a bit of circular dependency issue here
I = Identity(d)
i = iota[0]
e = as_vector(I[i, :], i)
for i in iota[1:]:
e = outer(e, as_vector(I[i, :], i))
return e
def dyad(d, *iota):
"TODO: Develop this concept, can e.g. write A[i,j]*dyad(j,i) for the transpose."
from ufl.constantvalue import Identity
from ufl.operators import outer # a bit of circular dependency issue here
Id = Identity(d)
i = iota[0]
e = as_vector(Id[i, :], i)
for i in iota[1:]:
e = outer(e, as_vector(Id[i, :], i))
return e
def unit_indexed_tensor(shape, component):
from ufl.constantvalue import Identity
from ufl.operators import outer # a bit of circular dependency issue here
r = len(shape)
if r == 0:
return 0, ()
jj = indices(r)
es = []
for i in range(r):
s = shape[i]
c = component[i]
j = jj[i]
e = Identity(s)[c, j]
es.append(e)
E = es[0]
for e in es[1:]:
E = outer(E, e)
return E, jj
def unit_indexed_tensor(shape, component):
from ufl.constantvalue import Identity
from ufl.operators import outer # a bit of circular dependency issue here
r = len(shape)
if r == 0:
return 0, ()
jj = indices(r)
es = []
for i in range(r):
s = shape[i]
c = component[i]
j = jj[i]
e = Identity(s)[c, j]
es.append(e)
E = es[0]
for e in es[1:]:
E = outer(E, e)
return E, jj
def outer(self, o, a, b):
a, ap = a
b, bp = b
return (o, outer(ap, b) + outer(a, bp)) # FIXME: Not valid for derivatives w.r.t. nonscalar variables!
def outer(self, o, a, b):
a, ap = a
b, bp = b
return (
o, outer(ap, b) + outer(a, bp)
) # FIXME: Not valid for derivatives w.r.t. nonscalar variables!