The purification chamber is the main tool used to open the hearts of shadow Pokémon in Pokémon XD: Gale of Darkness.
At the beginning of the game, the Purification Chamber hasn't yet been completed, meaning the main protagonist must purify their snagged Pokémon via carrying them around in their party, battling with them and by using colognes to massage them. (Colognes can be bought at the Agate Village Poké-Mart after acquiring a Cologne Case)
However, after progressing through the game far enough, the Purifying Chamber is completed and able to use.
The Purifying Chamber works in a unique way. The Snagged Shadow Pokémon is placed in the center of a selected set. Then up to four other, non-shadow Pokémon can be placed around the said Shadow Pokémon.
The basic working of the Purification Chamber is based on the typing of Pokémon.
For example, say we wanted to purify a Shadow Flygon. Flygon is a Dual Ground and Dragon type. With Flygon in the middle, the first Pokémon we need to place around it needs to, preferably, be of a type weak to Ground or Dragon, the type of the Shadow Pokemon. Next, the second Pokémon on the outside, the Pokemon placed next to the previous addition, this Pokémon needs to be weak to that Pokémon's typing. So lets say the first Pokémon was a Manetric, an electric type meaning it's weak to the flygon in the middles Ground type. The second Pokémon could then be a blastoise, a water type, thats weak to electric types. Now this means that the next type must be weak to water, so lets say a torkoal, a fire type. But, the next and last Pokémon is the trickiest, as by know you might have guessed. This final pokémon must be weak to the third Pokémon, Fire type Torkoal, but it must also be strong against the first Pokémon, Manetric. This is where dual typing comes in helpful, as in a regular situation this wouldn't be possible but, with dual types it is. For example, Steelix is a Steel-Ground dual type Pokémon, this means that the steel side of it is weak to Torkoal's fire, but the Ground half also means Steelix is strong against Manetric! This completes the circle!
Now a completed circle stands at full tempo, the tempo being displayed in the bar marked tempo rising from small and dark blue to big and light blue. The faster the tempo of a Set, the quicker the pokemon gets purified.
Now, the more Sets that you have at full Tempo, the better. As when you begin to build more and more full tempo sets, the flow of these said sets builds slightly. This flow also contributes to the speed of purifying so it's a good thing!
Now when you have all 9 sets running at full tempo, a significant "un-purifiable" Pokémon can have it's heart opened, and via the Purifying chamber is the only way to do it so... Get set building!!!