Question about grouping

I have an XSLT problem that I haven't been able to figure out.  The example 
below is essentially the simplest version of the problem I have encountered.

Say you have a document like this:

<doc>
  <book title="aaa" author="jones"/>
  <book title="bbb" author="smith"/>
  <book title="ccc" author="douglas"/>
  <book title="ddd" author="jones"/>
  <book title="eee" author="jones"/>
  <book title="fff" author="douglas"/>
  <book title="ggg" author="smith"/>
</doc>


How can you produce a document like this?:

<report>
  <author name="jones">
	<title>aaa</title>
	<title>ddd</title>
	<title>eee</title>
  </author>
  <author name="smith">
	<title>bbb</title>
	<title>ggg</title>
  </author>
  <author name="douglas">
	<title>bbb</title>
	<title>fff</title>
  </author>
</report>

Restrictions:
- Only XSLT 1.0
- You can't hard-code the names of the books or the authors in the XSLT.


Thanks,
Dave