In an update to @Giles' answer, please consider that the order of the include and exclude commands must be changed with current versions (>=3.x.x) to have the include options before the exlude options in order to build the correct file list. It is also my personal best practice to put the "include all subdirectories" instruction generally first and then the file pattern:
rsync -avh --include='*/' --include='file-pattern' --exclude='*' /sourcedir/ /targetdir/
i.e. in your case:
rsync -avh --include='*/' -include='*.pdf' --exclude='*' ~/LaTeX/ ~/Output/
Further explanation can also be drawn from the manual at https://www.samba.org/ftp/rsync/rsync.html under the headline "FILTER RULES":
Note that, when using the --recursive (-r) option (which is implied by -a), every subdir component of every path is visited left to right, with each directory having a chance for exclusion before its content. In this way include/exclude patterns are applied recursively to the pathname of each node in the filesystem's tree (those inside the transfer). The exclude patterns short-circuit the directory traversal stage as rsync finds the files to send.
For instance, to include "/foo/bar/baz", the directories "/foo" and "/foo/bar" must not be excluded. Excluding one of those parent directories prevents the examination of its content, cutting off rsync's recursion into those paths and rendering the include for "/foo/bar/baz" ineffectual (since rsync can't match something it never sees in the cut-off section of the directory hierarchy).
The concept path exclusion is particularly important when using a trailing '*' rule. For instance, this won't work:
This fails because the parent directory "some" is excluded by the '*' rule, so rsync never visits any of the files in the "some" or "some/path" directories. One solution is to ask for all directories in the hierarchy to be included by using a single rule: "+ */" (put it somewhere before the "- *" rule), and perhaps use the --prune-empty-dirs option. Another solution is to add specific include rules for all the parent dirs that need to be visited. For instance, this set of rules works fine:
Here are some examples of exclude/include matching:
"- *.o" would exclude all names matching *.o
"- /foo" would exclude a file (or directory) named foo in the transfer-root directory
"- foo/" would exclude any directory named foo
"- /foo/*/bar" would exclude any file named bar which is at two levels below a directory named foo in the transfer-root directory
"- /foo/**/bar" would exclude any file named bar two or more levels below a directory named foo in the transfer-root directory
The combination of "+ */", "+ *.c", and "- *" would include all directories and C source files but nothing else (see also the --prune-empty-dirs option)
The combination of "+ foo/", "+ foo/bar.c", and "- *" would include only the foo directory and foo/bar.c (the foo directory must be explicitly included or it would be excluded by the "*")
The following modifiers are accepted after a "+" or "-":
A / specifies that the include/exclude rule should be matched against the absolute pathname of the current item. For example, "-/ /etc/passwd" would exclude the passwd file any time the transfer was sending files from the "/etc" directory, and "-/ subdir/foo" would always exclude "foo" when it is in a dir named "subdir", even if "foo" is at the root of the current transfer.
A ! specifies that the include/exclude should take effect if the pattern fails to match. For instance, "-! */" would exclude all non-directories.
A C is used to indicate that all the global CVS-exclude rules should be inserted as excludes in place of the "-C". No arg should follow.
An s is used to indicate that the rule applies to the sending side. When a rule affects the sending side, it prevents files from being transferred. The default is for a rule to affect both sides unless --delete-excluded was specified, in which case default rules become sender-side only. See also the hide (H) and show (S) rules, which are an alternate way to specify sending-side includes/excludes.
An r is used to indicate that the rule applies to the receiving side. When a rule affects the receiving side, it prevents files from being deleted. See the s modifier for more info. See also the protect (P) and risk (R) rules, which are an alternate way to specify receiver-side includes/excludes.
A p indicates that a rule is perishable, meaning that it is ignored in directories that are being deleted. For instance, the -C option's default rules that exclude things like "CVS" and "*.o" are marked as perishable, and will not prevent a directory that was removed on the source from being deleted on the destination.
An x indicates that a rule affects xattr names in xattr copy/delete operations (and is thus ignored when matching file/dir names). If no xattr-matching rules are specified, a default xattr filtering rule is used (see the --xattrs option).