caching subtotals: update vs sum -- aaugh!

to save a few cycles, i'm hoping to cache subtotals of
subsidiary records into the corresponding parent records -- but
i can't figure out how to update the parent table with the sums
of the child table fields:

create table invoice (
id serial,
bal numeric(8,2)
cost numeric(8,2),
charge numeric(8,2),
);
create table line_item (
id serial,
item_id integer references invoice ( id ),
bal numeric(8,2)
cost numeric(8,2),
charge numeric(8,2),
);

selecting the sums is easy:

select
item_id,
sum(bal) as bal,
sum(cost) as cost,
sum(charge) as charge
from
line_item
group by
item_id;

but i can't seem to get by cerebellum around how to flow all the
subtotals upstream -- these don't work:

-- all totals wind up in ONE invoice record
update invoice set
bal = sum(line_item.bal),
cost = sum(line_item.cost),
charge = sum(line_item.charge)
where line_item.item_id = set.id;

-- syntax error at 'group'
update invoice set
bal = sum(line_item.bal),
cost = sum(line_item.cost),
charge = sum(line_item.charge)
from line_item
where line_item.item_id = set.id GROUP BY line_item.item_id;

the next one works, but not even within earshot of 'elegant'.
there's GOTTA be a slicker way, right?

-- ridiculosity of redundancy but it limps into the right result
update invoice set
bal = (select sum(line_item.bal) where item_id = invoice.id),
cost = (select sum(line_item.cost) where item_id = invoice.id),
charge = (select sum(line_item.charge) where item_id = invoice.id)
from line_item
where line_item.item_id = set.id GROUP BY line_item.item_id;

or should i settle for something like

select
item_id,
sum(bal) as bal,
sum(cost) as cost,
sum(charge) as charge
into
fooey
from
line_item
group by
item_id
;
update invoice set
bal = fooey.bal,
cost = fooey.cost,
charge = fooey.charge
where fooey.item_id = id
;
drop table fooey
;

...? seems a bit of the old "long-way-around"... surely there's
a way--

--
DEBIAN NEWBIE TIP #110 from Dimitri Maziuk <dmaziuk(at)yola(dot)bmrb(dot)wisc(dot)edu>
:
Here's how to TUNNEL SECURE X11 CONNECTIONS THROUGH SSH: on the
client, do this:
client# export DISPLAY=client:0.0
client# ssh -X server
then once you're logged in at the server, do:
server# netscape &
The environment created at the server will include the DISPLAY
variable, so netscape (or whatever) will dialogue with the
client machine. (See "man ssh" for more.)

Also see http://newbieDoc.sourceForge.net/ ...