It is written, The Lord your God is testing you in order to know if you love him (Dt 13:3). The phrase in order to know means in order to enable you to know, because how strong ones love is is hidden from oneself unless it becomes known even to one's own self by God's testing it. (QQ in Heptateuchum, 57; PL 34, 563)

Nam et alibi scriptum est, Tentat vos Dominus Deus vester, ut sciat si diligitis eum (Deut. XIII, 3): etiam hoc genere locutionis, ut sciat, dictum est, ac si diceretur, ut scire vos faciat; quoniam vires dilectionis suae hominem latent, nisi divino experimento etiam eidem innotescant.

[JAK: This explanation is found in many other places in Augustine, as also in Aquinas, and I think the idea goes back at least to Aristotle: that one's spontaneous reaction in a sudden and urgent situation is the test of one's character and virtue. "Experimentum" has its original meaning of "test" and not "experience."]