Dual purpose visit- Tourism and personal visit with a friend.

I am planning a trip to China for three week duration. I will begin with a three day hotel stay in Beijiing. A hotel reservation is confirmed for the first three days. I will be traveling to cities beyond and have a general itinerary but reservations are not confirmed beyond the first three days as I am not certain how long I will stay at each additional location. A friend, a Chinese national, will accompany me for a portion of the trip. It is possible that I will stay at their residence for about a week, and travel to nearby locations. I will be applying for a Tourist L visa. Is it also necessary to have a letter of invitation from my friend? Thank you.