Correct: He called me to repair the computer. I am here to repair the computer. He invited me to repair the computer. (NOT for repairing)
We don't use 'for' before a verb to talk about purpose. Instead, we use to + infinitive.
She went to Canada to attend the conference. He is studying everyday to improve his English. I am going to New York to visit my grandmother. I went there to buy a watch.
[[ We can use for before a noun to talk about a purpose.
I went to Paris for an interview. He went to the pub for a drink. He is studying hard for the exam.
We can use before a verb to talk about the purpose of a thing. (the reason why we use it)
We use an altimeter measur height above sea level. That stuff is (used) clean leather. The garden shears are used clip the hedge. He wears these old trousers paint.]]