Police yesterday released a sketch of a man believed to have raped and tortured a Columbia University journalism student inside her Harlem apartment before setting the home on fire and leaving her to die.

The 23-year-old woman, who wasn’t identified, left the hospital yesterday afternoon.

On Friday night the suspect entered an elevator with the victim at the building where she lives, Hamilton Terrace near West 141st Street, police said. When the elevator reached her floor, he forced his way into her apartment, where he raped her for hours, cut her eyelids, and burned her with chemicals. About 4:30 p.m. Saturday he bound her to a chair and lit a futon on fire before fleeing, police said.

The woman was able to use the fire to break free of the chair and escape the building, police said.

Outside Columbia’s journalism school, about 75 students held a candlelight vigil yesterday in response to the attack. The students and faculty members placed candles on the stairs of the building, as many cried and linked arms.

“I just want to remind everyone that the candles are a symbol of hope on this campus,” a professor, who declined to give her name, said. “A candle represents survival. She will get better. It will take time, but she will get better.”

The suspect is described as a 6-foot, 180-pound black male in his 30s. He is bald with a goatee and has a scar on his abdomen. Police asked anyone with information about the suspect to call 800-577-TIPS.