Alstroemeria
Peruvian lily

This plant of Alstroemeria ligtu is 2 1/2 feet tall, and produces large clusters of blooms on long stems, which grow directly from the tuberous root.
I have three different plants, each in different colors, all nursery grown. Mine don't receive direct sun until about 11 am. Two grow on the south side of our house in a small bed with well-amended soil. The third grows in the light shade of a nearby ash tree, getting full sun only a few hours a day.

Alstroemerias are native to South America and are members of the amaryllis family. Their name comes from their discoverer, the Swedish botanist Baron Alstroemer.

Cultivation:
Tuberous roots are fragile and should be planted 6 to 9 inches deep. The plants will multiply rapidly if left undisturbed. Sunset magazine calls them "beautiful weeds" as they have a tendency to become invasive when they feel at home. The easiest propagation is by root division.
Alstroemerias can also be grown from seed, although I have not experimented with this; maybe this year. Seeds can be sown as soon as they are ripe, and germinate at 55 degrees. They will flower the second year.

Cut flowers:
It's a peculiarity of alstroemerias that the flowers should be pulled from the base by the stem, rather than cut, the better to stimulate more growth. It makes me crazy to do this, as it seems so ... uncouth ...but if the plant likes it, who am I to disagree?