Mercedes Marquez, the general manager of the department, said the training was designed to help "center" Housing Department managers and teach them to react nimbly to problems such as the city's housing shortage. Up to 30 people attended each session.
"She asks when you center yourself to hold yourself in," Marquez said of the instructor.
The breathing exercises and stick play, she said, were a small part of two-day sessions, which also included discussions of team building and improving department procedures.
Some staff members, however, have found aspects of the training objectionable.
Lynn Hansen, a former assistant general manager, said she was put off by the presumption that she and her colleagues "had to be taught how to breathe and how to stand."
"I'm not sure how that helps me face an irate constituent," she said.
Hansen, who left the department in late 2005, participated in the first session. She said most training took place in a conference room but "at one point we went out in the parking lot to wield our swords."
Another attendee described how executives were asked to encircle Marquez with their backs to her while holding their sticks. They were instructed to imagine that they were shielding their boss from opposing forces such as City Council members or other departments.
"We had to make sure she was protected," said the participant, who spoke on condition of anonymity for fear of retaliation.
Marquez and her deputy, Yolanda Chavez, flatly denied that that ever happened.
According to advertisements about an appearance at the University of Wisconsin, Wong is considered an expert on Sun-Tzu's "Art of War," an early treatise on military strategy that has gained popularity among business executives who seek to apply its principles to capitalism.
Marquez said many people had told her that they found the training helpful. Her department, with more than 500 employees and a budget of $45 million, helps build affordable housing, enforce rent control laws and ensure apartments are up to code.