Demo

NOTE!

Sort Ascending/Descending

Use 0 or "a" for ascending sorts, and 1 or "d" for descending sorts*

([[0,0]]) ([[0,"a"],[1,"d"]])
([[0,1]]) ([[0,"d"],[1,"a"]])
$("#table1").trigger("sortReset");
* "a" & "d" values added v2.17.0.
First NameLast NameAgeTotalDiscountDate
PeterParker28$9.9920%Jul 6, 2006 8:14 AM
JohnHood33$19.9925%Dec 10, 2002 5:14 AM
ClarkKent18$15.8944%Jan 12, 2003 11:14 AM
BruceAlmighty45$153.1944%Jan 18, 2001 9:12 AM
BruceEvans22$13.1911%Jan 18, 2007 9:12 AM

Toggle sort (Next)

Either trigger a "sort" on the desired column, or "sorton" on the table using the "n" value*.
Toggle the option (false), then try these sorts (click a third time).

Trigger "sort" event: (v2.9)
$("#table2").find("th:contains(Discount)").trigger("sort");

Trigger "sorton" event using the direct method: (v2.23)
$.tablesorter.sortOn( $("#table2")[0].config, [ [1,"n"] ], function() {
  console.log("done"); /* callback after sort */
});

([[0,"n"]])
([[0,"n"],[1,"n"]]; columns are independent)
$("#table2").trigger("sortReset");
* "n" value added v2.17.0.
First NameLast NameAgeTotalDiscountDate
PeterParker28$9.9920%Jul 6, 2006 8:14 AM
JohnHood33$19.9925%Dec 10, 2002 5:14 AM
ClarkKent18$15.8944%Jan 12, 2003 11:14 AM
BruceAlmighty45$153.1944%Jan 18, 2001 9:12 AM
BruceEvans22$13.1911%Jan 18, 2007 9:12 AM

Sort Same/Opposite

The same ("s") or opposite ("o") sort values always set the column sort based on the primary column*.
Toggle the option (false), then try these sorts (click a third time).

([[0,"s"]]; always defaults to Asc sort if set on primary column)
([[0,0],[1,"s"]])
([[0,1],[1,"s"]])
([[0,"n"],[1,"s"]])
([[0,"n"],[1,"o"]])
([[0,"n"],[1,"o"],[2,"n"]])
([[0,"n"],[1,"o"],[2,"s"]])
([[0,"n"],[1,"o"],[2,"s"],[3,"o"]])
$("#table3").trigger("sortReset");
* "s" & "o" values added v2.17.0.
First NameLast NameAgeTotalDiscountDate
PeterParker28$9.9920%Jul 6, 2006 8:14 AM
JohnHood33$19.9925%Dec 10, 2002 5:14 AM
ClarkKent18$15.8944%Jan 12, 2003 11:14 AM
BruceAlmighty45$153.1944%Jan 18, 2001 9:12 AM
BruceEvans22$13.1911%Jan 18, 2007 9:12 AM