In the present design, the device is configured in the automatic current control mode.
White LEDs specifically need a well dimensioned input, technically the current to these LEDs must be strictly controlled.
By connecting its ADJ pin with the output makes sure that the current at the output is constantly monitored by the ADJ pin and is never allowed to go beyond the predetermined level set by the 0.6 Ohm resistor.
The device can support at least 3 amps of current through it, therefore easily becomes compatible for driving 1 to 5 numbers of 1 watt LEDs, each having their own current limiting resistors.
The current limiting resistors can be experimented with, probably lesser values may be tried for increasing the brightness levels of the LEDs, however anything less than 50 Ohms should not be tried, because it might cause a permanent damage to the LEDs.
The input to the LM 338 IC can be from an regulated DC power supply, capable of supplying 12 volts at 3 amps or more.
The IC LM 338 should be mounted over an heatsink for better performance.
The input diode should be rated at 3 amps, so a 1N5408 becomes OK for the application.
If the circuit is intended for operating outdoors, the input may be taken from a 12 v battery, like from an automobile battery.
Thus the proposed 4 watt LED driver circuit becomes especially suitable for illuminating vehicle interiors, for example as a roof light etc.
The formula for selecting the resistor value if a single 4 watt LED is conected is R = 1.25/LED current.
Here, LED current = 4/3.3 = 1.21A
Therefore R = 1.25/1.21 = about 1 ohm (0.6 is not correct)
R watts = 1.25 x 1.21 = 1.5 or 2 watt
for 4 nos 1 watt LEDs, total current is 300mA
Therefore R = 1.25/0.3 = 4 ohms
You would also want to make a transformerless SMPS version of a 1 watt to 12 watt LED driver circuit